Eye movements play an important role during social interaction, for instance, by indicating phases of mutual and joint attention. This type of gaze behavior has been researched extensively in pair collaboration but has been far less studied in the investigation of group activities. Further, the analysis of attention is often decoupled from speech, even though they are closely linked in social interactions. We introduce a visualization to facilitate joint analysis of gaze and speech among multiple participants during social activities. Our proposed social interaction graphs are two-layered arc diagrams that visualize pairwise relationships among participants. Our evaluation is based on two datasets of multiplayer tabletop gaming sessions recorded with five players. We present a traditional evaluation using eye-tracking metrics as a baseline and compare it with the additional findings possible with our approach.

How people interpret visualizations depends not only on bottom-up perceptual mechanisms but is also influenced by top-down mechanisms such as prior beliefs. Previous research studying the effect of prior beliefs found that belief strength of participants affected correlation estimation in scatterplots. We partially replicated this previous work at a smaller scale, and extended it with an eye tracking study to examine how prior belief affects gaze behavior. Participants (n = 12) estimated correlation coefficients in scatterplots that either have single-letter labels, nonsensical labels, or belief-triggering labels on the axis. Like the previous study, we too found that belief strength affected a participant’s ability to estimate correlations in scatterplots. An exploratory analysis of the gaze behavior showed that nonsensical and belief-triggering labels attracted more visual attention compared to single-letter labels. Additionally, participants seem to explore scatterplots with belief-triggering labels more fully compared to those with nonsensical labels. These initial results show that eye tracking offers a promising window into understanding the attentional mechanisms behind top-down perception. These results could inspire future research into bias in visualization perception and bias mitigation strategies.

We present a parallel k-Means clustering algorithm specifically designed to address large datasets and cluster counts. Our approach, BSP (binary space partitioning) k-Means, recursively partitions the input space optimally across the first principal component of the current subset of the data. From a single space partitioning, clusterings with arbitrary ?? can be found by a greedy tree search. Combining a reduction onto the first principal component and optimal binary clustering of 1D data is highly effective at reducing clustering costs. We attribute this to the close relationship between directional variance and the within-cluster sum of squares. We analyze our approach theoretically and, under an idealized population model, prove that the runtime is in O(n . max(d, lnn) · lnn) for a broad class of input distributions with high probability. We demonstrate that our algorithm consistently outperforms k-Means++ and performs similarly or better than other sophisticated algorithms in an evaluation with nine datasets and up to six cluster sizes. Our algorithm is parallelizable using common database operations such as Scan, Reduce, and Sort. We show that with our CUDA implementation, a significant speedup can be achieved. Additionally, our algorithm generates centers and datapoint assignments alike, removing the expensive cluster assignment step after initial seeding. Furthermore, our algorithm approximates k-Means accurately so that any additional use of Lloyd’s algorithm is optional and yields only incremental improvement.

Abstract Uncertainty in experimental measurements makes it challenging to determine which features are intrinsic to the phenomenon and which are most stable and reliable. Granular materials, such as sand, form a complex system in which the forces between individual particles influence the material's macroscopic behavior. However, these forces are also subject to uncertainty, as repeated measurements can yield different results. In this paper, we investigate how to model and visually analyze the uncertain structure of forces in granular materials. We adopt different perspectives on uncertainty by considering it as variance, probability, or additional variable. For a nuanced analysis of granular material data, we propose combining visualizations that represent these perspectives into a single visual analytics approach. We integrate uncertainty‐aware spatial visualizations that convey the probability of features, visualizations of derived measures and their variance over changes in the packing fraction, and overviews of varying probability thresholds. Finally, we evaluate our proposed approach in a case study conducted together with geotechnical engineers for the example of a 2D ensemble of photoelastic disks.

Abstract Case studies are central to evaluating visualization research as they provide evidence for how the developed approaches support real users, real analytical work, and real data. Conducting such studies can be challenging, since target users with relevant domain expertise are often scarce or even entirely unavailable, while the visualization researchers may lack the required expertise to perform the evaluation themselves. Current research on Large Language Models (LLMs) has shown their strong reasoning ability and usefulness in domain‐specific downstream tasks, provoking the question: to what degree and with what capacity can LLMs fill the role of the target users in visualization case studies? We investigate this question by evaluating how LLMs can participate across different phases of visualization case studies. We propose a conceptual framework that explores the different levels of LLM involvement and potential roles when simulating target users. To sketch where the LLM substitution is most plausible, we embed our suggested integration of LLMs within the nested model for visualization theory and design. For evaluation, we replicate case studies from published and unpublished visualization research using multiple state‐of‐the‐art LLMs and compare the model‐generated insights to those reported in the papers. Our results show that LLMs can often generate plausible and sometimes even novel interpretations of visual patterns when used for result analysis and validation, but can also struggle when highly contextual, domain‐specific knowledge is required.

Exploratory Data Analysis (EDA) is an essential yet tedious process for examining a new dataset. To facilitate it, Natural Language Interfaces (NLIs) can help people intuitively explore the dataset via data-oriented questions. However, existing NLIs primarily focus on providing accurate answers to questions, with few offering explanations or presentations of the data analysis pipeline used to uncover the answer. Such presentations are crucial for EDA as they enhance the interpretability and reliability of the answer, while also helping users understand the analysis process and derive insights. To fill this gap, we introduce Urania, a natural language interactive system that can visualize the data analysis pipelines used to resolve input questions. It integrates a NLI that allows users to explore data via questions, and a novel data-aware question decomposition algorithm that resolves each input question into a data analysis pipeline. This pipeline is visualized in the form of a datamation, with animated presentations of analysis operations and their corresponding data changes. Through two quantitative experiments and expert interviews, we demonstrated that our data-aware question decomposition algorithm shows competitive performance compared to existing techniques in terms of execution accuracy, and that Urania can help people explore datasets better. In the end, we discuss the observations from the studies and the potential future works.

An essential task in analyzing collaborative design processes, such as those that are part of workshops in design studies, is identifying design outcomes and understanding how the collaboration between participants formed the results and led to decision-making. However, findings are typically restricted to a consolidated textual form based on notes from interviews or observations. A challenge arises from integrating different sources of observations, leading to large amounts and heterogeneity of collected data. To address this challenge we propose a practical, modular, and adaptable framework of workshop setup, multimodal data acquisition, AI-based artifact extraction, and visual analysis. Our interactive visual analysis system, reCAPit, allows the flexible combination of different modalities, including video, audio, notes, or gaze, to analyze and communicate important workshop findings. A multimodal streamgraph displays activity and attention in the working area, temporally aligned topic cards summarize participants' discussions, and drill-down techniques allow inspecting raw data of included sources. As part of our research, we conducted six workshops across different themes ranging from social science research on urban planning to a design study on band-practice visualization. The latter two are examined in detail and described as case studies. Further, we present considerations for planning workshops and challenges that we derive from our own experience and the interviews we conducted with workshop experts. Our research extends existing methodology of collaborative design workshops by promoting data-rich acquisition of multimodal observations, combined AI-based extraction and interactive visual analysis, and transparent dissemination of results.

We propose Probabilistic Inclusion Depth (PID) for the ensemble visualization of scalar fields. By introducing a probabilistic inclusion operator $\subset_{p}$, our method is a general data depth model supporting ensembles of fuzzy contours, such as soft masks from modern segmentation methods, and conventional ensembles of binary contours. We also advocate for extending contour extraction in scalar field ensembles to become a fuzzy decision by considering the probabilistic distribution of an isovalue to encode the sensitivity information. To reduce the complexity of the data depth computation, an efficient approximation using the mean probabilistic contour is devised. Furthermore, an order-of-magnitude reduction in computational time is achieved with an efficient parallel algorithm on the GPU. Our new method enables the computation of contour boxplots for ensembles of probabilistic masks, ensembles defined on various types of grids, and large 3D ensembles not studied by existing methods. The effectiveness of our method is evaluated through numerical comparisons with existing techniques on synthetic datasets, examples of real-world ensemble datasets, and expert feedback.

Foveated rendering methods usually reduce spatial resolution in the periphery of the users' view. However, using foveated rendering to reduce temporal resolution, i.e., rendering frame rate, seems less explored. In this work, we present the results of a user study investigating the perceptual effects of foveated temporal resolution reduction, where only the temporal resolution (frame rate) is reduced in the periphery without affecting spatial quality (pixel density). In particular, we investigated the perception of temporal resolution artifacts caused by reducing the frame rate dependent on the eccentricity of the user's gaze. Our user study with 15 participants was conducted in a virtual reality setting using a head-mounted display. Our results indicate that it was possible to reduce average rendering costs, i.e., the number of rendered pixels, to a large degree before participants consistently reported perceiving temporal artifacts.

The eyes play an important role in human collaboration. Mutual and shared gaze help communicate visual attention to each other or to a specific object of interest. Shared gaze was typically investigated for pair collaborations in remote settings and with people in virtual and augmented reality. With our work, we expand this line of research by a new technique to communicate gaze between groups in tabletop workshop scenarios. To achieve this communication, we use an approach based on projection mapping to unify gaze data from multiple participants into a common visualization space on a tabletop. We showcase our approach with a collaborative puzzle-solving task that displays shared visual attention on individual pieces and provides hints to solve the problem at hand.

Multiple challenges emerge when analyzing eye-tracking data with areas of interest (AOIs) because recordings are subject to different sources of uncertainties. Previous work often presents gaze data without considering those inaccuracies in the data. To address this issue, we developed uncertainty-aware scarf plot visualizations that aim to make analysts aware of uncertainties with respect to the position-based mapping of gaze to AOIs and depth dependency in 3D scenes. Additionally, we also consider uncertainties in automatic AOI annotation. We showcase our approach in comparison to standard scarf plots in an augmented reality scenario.

The computation of a potentially visible set (PVS) can accelerate many computer graphics algorithms, such as framerate upsampling, streaming rendering, global illumination, and multi-fragment effects. Algorithms for from-region PVS have an inherently high complexity. Previous from-region PVS algorithms propagate occlusion through the scene in a front-to-back manner and are order-dependent, which places bounds on parallelism and restricts execution speed. We introduce the disocclusion buffer, which operates on a sparse, layered representation of the scene with quantized depth. In this representation, we invert the traditional PVS problem formulation and explicitly compute disocclusion rather than occlusion. Disocclusion can be computed in parallel in an order-independent manner, overcoming the main bottleneck in traditional PVS computation. Our PVS algorithm is over six times faster than the previous state of the art at the same level of accuracy in a direct comparison. It runs in shaders on the GPU without requiring any hardware extensions. We demonstrate how our work outperforms previous PVS algorithms in the range of supported camera motion without compromising quality.

Abstract Eye tracking provides a unique perspective on the inherently visual discourse between visualisation systems and their users, and has recently become sufficiently precise and affordable to be integrated as regular input into workstations and virtual or augmented reality headsets alike. As such, real‐time eye tracking can now contribute significantly towards the development of gaze‐aware visualisations that infer and monitor users' needs to actively support their activities. To facilitate such systems we make three contributions. First, we structure and discuss design considerations for gaze‐aware visualisations along four axes: measurable data; inferable data; opportunities for support; and limiting factors to beware. Second, we distill visualisation research challenges that preclude such systems. Finally, we show via three usage scenarios how to apply these design considerations to imagine how existing systems can benefit from real‐time eye tracking. We combined a structured literature analysis, a consideration of suitable places for eye‐tracking integration in the typical visualisation ecosystem, and design space modelling. Eye tracking has significant potential to improve the interactive visual analysis of data across many visualisation domains. Our paper attempts to provide a comprehensive, general survey and conceptual discussion in this promising field, outlining the state‐of‐the‐art and future research opportunities.

We introduce continuous indexed points for improved multivariate volume visualization. Indexed points represent linear structures in parallel coordinates and can be used to encode local correlation of multivariate (including multi-field, multifaceted, and multi-attribute) volume data. First, we perform local linear fitting in the spatial neighborhood of each volume sample using principal component analysis, accelerated by hierarchical spatial data structures. This local linear information is then visualized as continuous indexed points in parallel coordinates: a density representation of indexed points in a continuous domain. With our new method, multivariate volume data can be analyzed using eigenvector information from local spatial embeddings. We utilize both 1-flat and 2-flat indexed points, allowing us to identify correlations between two variables and even three variables, respectively. An interactive occlusion shading model facilitates good spatial perception of the volume rendering of volumetric correlation characteristics. Interactive exploration is supported by specifically designed multivariate transfer function widgets working in the image plane of parallel coordinates. We show that our generic technique works for multi-attribute datasets. The effectiveness and usefulness of our new method is demonstrated through a case study, an expert user study, and domain expert feedback.

One common task in time series analysis is the visual investigation of spectra such as Fourier spectra or wavelet spectra to identify dominating frequencies. In this article, we present the propagation of data uncertainty to the spectra and its visualization. We consider the Fourier and continuous wavelet transformations, which are two common spectral analysis methods. Deriving the propagation for time series that can be modeled as a Gaussian process leads to a combination of weighted non-central chi-squared distributions in the spectrum. Percentile-based visualizations explicitly encode the non-normal uncertainty in the 1D Fourier and 2D wavelet spectrum. We enrich the visualization by including correlations, sensitivity, and signal-to-noise analysis. For visual exploration, we combine the different visualizations into an interactive approach that allows for investigating the uncertain time series in the temporal and spectral domains. Finally, we show the usefulness of our approach by applying it to several real-world data sets and by a qualitative interview study with visualization experts.

We introduce a visual analysis method for multiple causal graphs with different outcome variables, namely, multi-outcome causal graphs. Multi-outcome causal graphs are important in healthcare for understanding multimorbidity and comorbidity. To support the visual analysis, we collaborated with medical experts to devise two comparative visualization techniques at different stages of the analysis process. First, a progressive visualization method is proposed for comparing multiple state-of-the-art causal discovery algorithms. The method can handle mixed-type datasets comprising both continuous and categorical variables and assist in the creation of a fine-tuned causal graph of a single o utcome. Second, a comparative graph layout technique and specialized visual encodings are devised for the quick comparison of multiple causal graphs. In our visual analysis approach, analysts start by building individual causal graphs for each outcome variable, and then, multi-outcome causal graphs are generated and visualized with our comparative technique for analyzing differences and commonalities of these causal graphs. Evaluation includes quantitative measurements on benchmark datasets, a case study with a medical expert, and expert user studies with real-world health research data.

Areas of interest (AOIs) are well-established means of providing semantic information for visualizing, analyzing, and classifying gaze data. However, the usual manual annotation of AOIs is time-consuming and further impaired by ambiguities in label assignments. To address these issues, we present an interactive labeling approach that combines visualization, machine learning, and user-centered explainable annotation. Our system provides uncertainty-aware visualization to build trust in classification with an increasing number of annotated examples. It combines specifically designed EyeFlower glyphs, dimensionality reduction, and selection and exploration techniques in an integrated workflow. The approach is versatile and hardware-agnostic, supporting video stimuli from stationary and unconstrained mobile eye tracking alike. We conducted an expert review to assess labeling strategies and trust building.

Seasonal-trend decomposition based on loess (STL) is a powerful tool to explore time series data visually. In this article, we present an extension of STL to uncertain data, named uncertainty-aware STL (UASTL). Our method propagates multivariate Gaussian distributions mathematically exactly through the entire analysis and visualization pipeline. Thereby, stochastic quantities shared between the components of the decomposition are preserved. Moreover, we present application scenarios with uncertainty modeling based on Gaussian processes, e.g., data with uncertain areas or missing values. Besides these mathematical results and modeling aspects, we introduce visualization techniques that address the challenges of uncertainty visualization and the problem of visualizing highly correlated components of a decomposition. The global uncertainty propagation enables the time series visualization with STL-consistent samples, the exploration of correlation between and within decomposition's components, and the analysis of the impact of varying uncertainty. Finally, we show the usefulness of UASTL and the importance of uncertainty visualization with several examples. Thereby, a comparison with conventional STL is performed.

Semi-Lagrangian texture advection (SLTA) enables efficient visualization of 2D and 3D unsteady flow. The major drawback of SLTA-based visualizations is numerical diffusion caused by iterative texture interpolation. We focus on reducing numerical diffusion in techniques that use textures sparsely populated by solid blobs, such as typically in dye advection. A ReLU-based model architecture is the foundation of our ML-based approach. Multiple model configurations are trained to learn a performant interpolation model that reduces numerical diffusion. Our evaluation investigates the models’ ability to generalize concerning the flow and length of the advection process. The model with the best tradeoff between the computational effort to compute, quality of the result, and generality of application is found to be single-layer ReLU-based. This model is further analyzed and explained in-depth and improved using symmetry constraints. Additionally, a metamodel is fitted to predict single-layer ReLU model parameters for advection processes of any length. The metamodel removes the need for any prior training when applying our technique to a new scenario. Additionally, we show that our model is compatible with Back and Forth Error Compensation and Correction to improve the quality of the advection result further. We demonstrate that our model shows excellent diffusion reduction properties in typical examples of 3D steady and unsteady flow visualization. Finally, we utilize the strong diffusion reduction capabilities of our model to compute dye advection with exponential decay, a novel method that we introduce to visualize the extent and evolution of unsteadiness in both 2D and 3D unsteady flow. • ML-based ReLU model for dye advection. • A thorough evaluation of the core ML part and the overall flow visualization technique. • A decay effect with dye streaklines to visualize unsteadiness in flow data. • Pretrained metamodels for direct deployment of our approach.

The interplay between text and visualization is gaining importance for media where traditional text is enriched by visual elements to improve readability and emphasize facts. In two controlled eye-tracking experiments (N = 12), we approach answers to the question: How do visualization techniques influence reading behavior? We compare plain text to that marked with highlights, icons, and word-sized data visualizations. We assess quantitative metrics (eye movement, completion time, error rate) and subjective feedback (personal preference and ratings). The results indicate that visualization techniques, especially in the first experiment, show promising trends for improved reading behavior. The results also show the need for further research to make reading more effective and inform suggestions for future studies.

The depiction of scanpaths from mobile eye-tracking recordings by thumbnails from the stimulus allows the application of visual computing to detect areas of interest in an unsupervised way. We suggest using nonnegative matrix factorization (NMF) to identify such areas in stimuli. For a user-defined integer k, NMF produces an explainable decomposition into k components, each consisting of a spatial representation associated with a temporal indicator. In the context of multiple eye-tracking recordings, this leads to k spatial representations, where the temporal indicator highlights the appearance within recordings. The choice of k provides an opportunity to control the refinement of the decomposition, i.e., the number of areas to detect. We combine our NMF-based approach with visualization techniques to enable an exploratory analysis of multiple recordings. Finally, we demonstrate the usefulness of our approach with mobile eye-tracking data of an art gallery.

Image thumbnails are a valuable data source for fixation filtering, scanpath classification, and visualization of eye tracking data. They are typically extracted with a constant size, approximating the foveated area. As a consequence, the focused area of interest in the scene becomes less prominent in the thumbnail with increasing distance, affecting image-based analysis techniques. In this work, we propose depth-adaptive thumbnails, a method for varying image size according to the eye-to-object distance. Adjusting the visual angle relative to the distance leads to a zoom effect on the focused area. We evaluate our approach on recordings in augmented reality, investigating the similarity of thumbnails and scanpaths. Our quantitative findings suggest that considering the eye-to-object distance improves the quality of data analysis and visualization. We demonstrate the utility of depth-adaptive thumbnails for applications in scanpath comparison and visualization.

We conducted an eye-tracking user study with 13 participants to investigate the influence of stimulus-question ordering and question modality on participants using visual question-answering (VQA) tasks. We examined cognitive load, task performance, and gaze allocations across five distinct experimental designs, aiming to identify setups that minimize the cognitive burden on participants. The collected performance and gaze data were analyzed using quantitative and qualitative methods. Our results indicate a significant impact of stimulus-question ordering on cognitive load and task performance, as well as a noteworthy effect of question modality on task performance. These findings offer insights for the experimental design of controlled user studies in visualization research.

Commercial videos are often used to familiarise potential buyers and users with new technologies and their possibilities. In addition, presenting visions of future applications is a way to configure users and define social worlds of technology use. We analyse 30 YouTube videos featuring augmented reality (AR) devices in industrial manufacturing and construction, to explore how these commercial videos situate AR technology and future users by showcasing techno-euphoric promises and imagined use cases. With a video analysis based on Grounded Theory and Situational Analysis, we untangle the promises of AR for manufacturing and construction work; second, we present two prevailing configurations of AR users: ‘experts in situ’ and ‘smart dummies’; and third, we discuss how YouTube videos put forward developmental expectations. In addition, we identify discrepancies between expectations and foreseeable requirements in construction work. Finally, our research could contribute to a more holistic understanding of workplaces and socially robust AR applications.

The datasets of most image quality assessment studies contain ratings on a categorical scale with five levels, from bad (1) to excellent (5). For each stimulus, the number of ratings from 1 to 5 is summarized and given in the form of the mean opinion score. In this study, we investigate families of multinomial probability distributions parameterized by mean and variance that are used to fit the empirical rating distributions. To this end, we consider quantized metric models based on continuous distributions that model perceived stimulus quality on a latent scale. The probabilities for the rating categories are determined by quantizing the corresponding random variables using threshold values. Furthermore, we introduce a novel discrete maximum entropy distribution for a given mean and variance. We compare the performance of these models and the state of the art given by the generalized score distribution for two large data sets, KonIQ-10k and VQEG HDTV. Given an input distribution of ratings, our fitted two-parameter models predict unseen ratings better than the empirical distribution. In contrast to empirical distributions of absolute category ratings and their discrete models, our continuous models can provide fine-grained estimates of quantiles of quality of experience that are relevant to service providers to satisfy a certain fraction of the user population.

We introduce a conceptual model for scalability designed for visualization research. With this model, we systematically analyze over 120 visualization publications from 1990 to 2020 to characterize the different notions of scalability in these works. While many article have addressed scalability issues, our survey identifies a lack of consistency in the use of the term in the visualization research community. We address this issue by introducing a consistent terminology meant to help visualization researchers better characterize the scalability aspects in their research. It also helps in providing multiple methods for supporting the claim that a work is "scalable." Our model is centered around an effort function with inputs and outputs. The inputs are the problem size and resources, whereas the outputs are the actual efforts, for instance, in terms of computational run time or visual clutter. We select representative examples to illustrate different approaches and facets of what scalability can mean in visualization literature. Finally, targeting the diverse crowd of visualization researchers without a scalability tradition, we provide a set of recommendations for how scalability can be presented in a clear and consistent way to improve fair comparison between visualization techniques and systems and foster reproducibility.

Scatter plots are popular for displaying 2D data, but in practice, many data sets have more than two dimensions. For the analysis of such multivariate data, it is often necessary to switch between scatter plots of different dimension pairs, e.g., in a scatter plot matrix (SPLOM). Alternative approaches include a "grand tour" for an overview of the entire data set or creating artificial axes from dimensionality reduction (DR). A cross-cutting concern in all techniques is the ability of viewers to find correspondence between data points in different views. Previous work proposed animations to preserve the mental map between view changes and to trace points as well as clusters between scatter plots of the same underlying data set. In this article, we evaluate a variety of spline- and rotation-based view transitions in a crowdsourced user study focusing on ecological validity. Using the study results, we assess each animation's suitability for tracing points and clusters across view changes. We evaluate whether the order of horizontal and vertical rotation is relevant for task accuracy. The results show that rotations with an orthographic camera or staged expansion of a depth axis significantly outperform all other animation techniques for the traceability of individual points. Further, we provide a ranking of the animated transition techniques for traceability of individual points. However, we could not find any significant differences for the traceability of clusters. Furthermore, we identified differences by animation direction that could guide further studies to determine potential confounds for these differences. We publish the study data for reuse and provide the animation framework as a D3.js plug-in.

Abstract In architectural design optimization, fitness landscapes are used to visualize design space parameters in relation to one or more objective functions for which they are being optimized. In our design study with domain experts, we developed a visual analytics framework for exploring and analyzing fitness landscapes spanning data, projection, and visualization layers. Within the data layer, we employ two surrogate models and three sampling strategies to efficiently generate a wide array of landscapes. On the projection layer, we use star coordinates and UMAP as two alternative methods for obtaining a 2D embedding of the design space. Our interactive user interface can visualize fitness landscapes as a continuous density map or a discrete glyph-based map. We investigate the influence of surrogate models and sampling strategies on the resulting fitness landscapes in a parameter study. Additionally, we present findings from a user study (N= 12), revealing how experts’ preferences regarding projection methods and visual representations may be influenced by their level of expertise, characteristics of the techniques, and the specific task at hand. Furthermore, we demonstrate the usability and usefulness of our framework by a case study from the architecture domain, involving one domain expert.

Dimensionality reduction is often used to project time series data from multidimensional to two-dimensional space to generate visual representations of the temporal evolution. In this context, we address the problem of multidimensional time series visualization by presenting a new method to show and handle projection errors introduced by dimensionality reduction techniques on multidimensional temporal data. For visualization, subsequent time instances are rendered as dots that are connected by lines or curves to indicate the temporal dependencies. However, inevitable projection artifacts may lead to poor visualization quality and misinterpretation of the temporal information. Wrongly projected data points, inaccurate variations in the distances between projected time instances, and intersections of connecting lines could lead to wrong assumptions about the original data. We adapt local and global quality metrics to measure the visual quality along the projected time series, and we introduce a model to assess the projection error at intersecting lines. These serve as a basis for our new uncertainty visualization techniques that use different visual encodings and interactions to indicate, communicate, and work with the visualization uncertainty from projection errors and artifacts along the timeline of data points, their connections, and intersections. Our approach is agnostic to the projection method and works for linear and non-linear dimensionality reduction methods alike.

We investigate reading strategies for node-link diagrams that wrap around the boundaries in a flattened torus topology by examining eye tracking data recorded in a previous controlled study. Prior work showed that torus drawing affords greater flexibility in clutter reduction than traditional node-link representations, but impedes link-and-path exploration tasks, while repeating tiles around boundaries aids comprehension. However, it remains unclear what strategies users apply in different wrapping settings. This is important for design implications for future work on more effective wrapped visualizations for network applications, and cyclic data that could benefit from wrapping. We perform visual-exploratory data analysis of gaze data, and conduct statistical tests derived from the patterns identified. Results show distinguishable gaze behaviors, with more visual glances and transitions between areas of interest in the non-replicated layout. Full-context has more successful visual searches than partial-context, but the gaze allocation indicates that the layout could be more space-efficient.

We present a novel, web-based visual eye-tracking analytics tool called Gazealytics. Our open-source toolkit features a unified combination of gaze analytics features that support flexible exploratory analysis, along with annotation of areas of interest (AOI) and filter options based on multiple criteria to visually analyse eye tracking data across time and space. Gazealytics features coordinated views unifying spatiotemporal exploration of fixations and scanpaths for various analytical tasks. A novel matrix representation allows analysis of relationships between such spatial or temporal features. Data can be grouped across samples, user-defined AOIs or time windows of interest (TWIs) to support aggregate or filtered analysis of gaze activity. This approach exceeds the capabilities of existing systems by supporting flexible comparison between and within subjects, hypothesis generation, data analysis and communication of insights. We demonstrate in a walkthrough that Gazealytics supports multiple types of eye tracking datasets and analytical tasks.

Scene-graph-based Visual Question Answering (VQA) has emerged as a burgeoning field in Deep Learning research, with a growing demand for robust and interpretable VQA systems. In this paper, we present a novel visual analysis approach that addresses two critical objectives in VQA: identifying and correcting prediction issues and providing insights into model decision-making processes through visualizing internal information. Our approach builds on the GraphVQA framework, which uses graph neural networks to process scene graphs representing images and which was trained on the widely-used GQA dataset. Our analysis tool aims at users familiar with the basics of graph-based VQA. By leveraging query-based scene analysis and visualization of crucial internal states, we are able to detect and pinpoint reasons for inaccurate predictions, facilitating model refinement and dataset curation. Identifying expressive internal states is a challenge. Through rigorous computer-based evaluations and presentation of a use case, we demonstrate the effectiveness of our analysis tool and model state visualization.

Abstract Augmented Reality (AR) provides new ways for situated visualization and human‐computer interaction in physical environments. Current evaluation procedures for AR applications rely primarily on questionnaires and interviews, providing qualitative means to assess usability and task solution strategies. Eye tracking extends these existing evaluation methodologies by providing indicators for visual attention to virtual and real elements in the environment. However, the analysis of viewing behavior, especially the comparison of multiple participants, is difficult to achieve in AR. Specifically, the definition of areas of interest (AOIs), which is often a prerequisite for such analysis, is cumbersome and tedious with existing approaches. To address this issue, we present a new visualization approach to define AOIs, label fixations, and investigate the resulting annotated scanpaths. Our approach utilizes automatic annotation of gaze on virtual objects and an image‐based approach that also considers spatial context for the manual annotation of objects in the real world. Our results show, that with our approach, eye tracking data from AR scenes can be annotated and analyzed flexibly with respect to data aspects and annotation strategies.

Abstract The distribution of visual attention can be evaluated using eye tracking, providing valuable insights into usability issues and interaction patterns. However, when used in real, augmented, and collaborative environments, new challenges arise that go beyond desktop scenarios and purely virtual environments. Toward addressing these challenges, we present a visualization technique that provides complementary views on the movement and eye tracking data recorded from multiple people in real‐world environments. Our method is based on a space‐time cube visualization and a linked 3D replay of recorded data. We showcase our approach with an experiment that examines how people investigate an artwork collection. The visualization provides insights into how people moved and inspected individual pictures in their spatial context over time. In contrast to existing methods, this analysis is possible for multiple participants without extensive annotation of areas of interest. Our technique was evaluated with a think‐aloud experiment to investigate analysis strategies and an interview with domain experts to examine the applicability in other research fields.

We present angle-uniform parallel coordinates, a data-independent technique that deforms the image plane of parallel coordinates so that the angles of linear relationships between two variables are linearly mapped along the horizontal axis of the parallel coordinates plot. Despite being a common method for visualizing multidimensional data, parallel coordinates are ineffective for revealing positive correlations since the associated parallel coordinates points of such structures may be located at infinity in the image plane and the asymmetric encoding of negative and positive correlations may lead to unreliable estimations. To address this issue, we introduce a transformation that bounds all points horizontally using an angle-uniform mapping and shrinks them vertically in a structure-preserving fashion; polygonal lines become smooth curves and a symmetric representation of data correlations is achieved. We further propose a combined subsampling and density visualization approach to reduce visual clutter caused by overdrawing. Our method enables accurate visual pattern interpretation of data correlations, and its data-independent nature makes it applicable to all multidimensional datasets. The usefulness of our method is demonstrated using examples of synthetic and real-world datasets.

This work investigates and compares the performance of node-link diagrams, adjacency matrices, and bipartite layouts for visualizing networks. In a crowd-sourced user study ( n=150), we measure the task accuracy and completion time of the three representations for different network classes and properties. In contrast to the literature, which covers mostly topology-based tasks (e.g., path finding) in small datasets, we mainly focus on overview tasks for large and directed networks. We consider three overview tasks on networks with 500 nodes: (T1) network class identification, (T2) cluster detection, and (T3) network density estimation, and two detailed tasks: (T4) node in-degree vs. out-degree and (T5) representation mapping, on networks with 50 and 20 nodes, respectively. Our results show that bipartite layouts are beneficial for revealing the overall network structure, while adjacency matrices are most reliable across the different tasks.

We present an extension of multidimensional scaling (MDS) to uncertain data, facilitating uncertainty visualization of multidimensional data. Our approach uses local projection operators that map high-dimensional random vectors to low-dimensional space to formulate a generalized stress. In this way, our generic model supports arbitrary distributions and various stress types. We use our uncertainty-aware multidimensional scaling (UAMDS) concept to derive a formulation for the case of normally distributed random vectors and a squared stress. The resulting minimization problem is numerically solved via gradient descent. We complement UAMDS by additional visualization techniques that address the sensitivity and trustworthiness of dimensionality reduction under uncertainty. With several examples, we demonstrate the usefulness of our approach and the importance of uncertainty-aware techniques.

Frequency-based decomposition of time series data is used in many visualization applications. Most of these decomposition methods (such as Fourier transform or singular spectrum analysis) only provide interaction via pre- and post-processing, but no means to influence the core algorithm. A method that also belongs to this class is Dynamic Mode Decomposition (DMD), a spectral decomposition method that extracts spatio-temporal patterns from data. In this paper, we incorporate frequency-based constraints into DMD for an adaptive decomposition that leads to user-controllable visualizations, allowing analysts to include their knowledge into the process. To accomplish this, we derive an equivalent reformulation of DMD that implicitly provides access to the eigenvalues (and therefore to the frequencies) identified by DMD. By utilizing a constrained minimization problem customized to DMD, we can guarantee the existence of desired frequencies by minimal changes to DMD. We complement this core approach by additional techniques for constrained DMD to facilitate explorative visualization and investigation of time series data. With several examples, we demonstrate the usefulness of constrained DMD and compare it to conventional frequency-based decomposition methods.

We introduce relaxed dot plots as an improvement of nonlinear dot plots for unit visualization. Our plots produce more faithful data representations and reduce moiré effects. Their contour is based on a customized kernel frequency estimation to match the shape of the distribution of underlying data values. Previous nonlinear layouts introduce column-centric nonlinear scaling of dot diameters for visualization of high-dynamic-range data with high peaks. We provide a mathematical approach to convert that column-centric scaling to our smooth envelope shape. This formalism allows us to use linear, root, and logarithmic scaling to find ideal dot sizes. Our method iteratively relaxes the dot layout for more correct and aesthetically pleasing results. To achieve this, we modified Lloyd's algorithm with additional constraints and heuristics. We evaluate the layouts of relaxed dot plots against a previously existing nonlinear variant and show that our algorithm produces less error regarding the underlying data while establishing the blue noise property that works against moiré effects. Further, we analyze the readability of our relaxed plots in three crowd-sourced experiments. The results indicate that our proposed technique surpasses traditional dot plots.

We present an exploratory study on the accessibility of images in publications when viewed with color vision deficiencies (CVDs). The study is based on 1,710 images sampled from a visualization dataset (VIS30K) over five years. We simulated four CVDs on each image. First, four researchers (one with a CVD) identified existing issues and helpful aspects in a subset of the images. Based on the resulting labels, 200 crowdworkers provided 30,000 ratings on present CVD issues in the simulated images. We analyzed this data for correlations, clusters, trends, and free text comments to gain a first overview of paper figure accessibility. Overall, about 60 % of the images were rated accessible. Furthermore, our study indicates that accessibility issues are subjective and hard to detect. On a meta-level, we reflect on our study experience to point out challenges and opportunities of large-scale accessibility studies for future research directions.

Test methods that can keep up with the ongoing increase in complexity of semiconductor products and their underlying technologies are an essential prerequisite for maintaining quality and safety of our daily lives and for continued success of our economies and societies. There is a huge potential how test methods can benefit from recent breakthroughs in domains such as artificial intelligence, data analytics, virtual/augmented reality, and security. The Graduate School on “Intelligent Methods for Semiconductor Test and Reliability” (GS-IMTR) at the University of Stuttgart is a large-scale, radically interdisciplinary effort to address the scientific-technological challenges in this domain. It is funded by Advantest, one of the world leaders in automatic test equipment. In this paper, we describe the overall philosophy of the Graduate School and the specific scientific questions targeted by its ten projects.

We propose a three-step concept and visual design for supporting the visual exploration of high-dimensional data in scatterplots through eye-tracking. First, we extract subsets in the underlying data using existing classifications, automated clustering algorithms, or eye-tracking. For the latter, we map gaze to the underlying data dimensions in the scatterplot. Clusters of data points that have been the focus of the viewers’ gaze are marked as clusters of interest (eye-mind hypothesis). In a second step, our concept extracts various properties from statistics and scagnostics from the clusters. The third step uses these measures to compare the current data clusters from the main scatterplot to the same data in other dimensions. The results enable analysts to retrieve similar or dissimilar views as guidance to explore the entire data set. We provide a proof-of-concept implementation as a test bench and describe a use case to show a practical application and initial results.

Gaze-based analysis of areas of interest (AOIs) is widely used in information visualisation research to understand how people explore visualisations or assess the quality of visualisations concerning key characteristics such as memorability. However, nearby AOIs in visualisations amplify the uncertainty caused by the gaze estimation error, which strongly influences the mapping between gaze samples or fixations and different AOIs. We contribute a novel investigation into gaze uncertainty and quantify its impact on AOI-based analysis on visualisations using two novel metrics: the Flipping Candidate Rate (FCR) and Hit Any AOI Rate (HAAR). Our analysis of 40 real-world visualisations, including human gaze and AOI annotations, shows that gaze uncertainty frequently and significantly impacts the analysis conducted in AOI-based studies. Moreover, we analysed four visualisation types and found that bar and scatter plots are usually designed in a way that causes more uncertainty than line and pie plots in gaze-based analysis.

Data visualization relies on efficient rendering to allow users to interactively explore and understand their data. However, achieving interactive frame rates is often challenging, especially for high-resolution displays or large datasets. In computer graphics, several methods temporally reconstruct full-resolution images from multiple consecutive lower-resolution frames. Besides providing temporal image stability, they amortize the rendering costs over multiple frames and thus improve the minimum frame rate. We present a method that adopts this idea to accelerate 2D information visualization, without requiring any changes to the rendering itself. By exploiting properties of orthographic projection, our method significantly improves rendering performance while minimizing the loss of image quality during camera manipulation. For static scenes, it quickly converges to the full-resolution image. We discuss the characteristics of our method concerning rendering performance and image quality and the corresponding trade-offs. Finally, we present extensive rendering benchmarks to examine real-world performance for examples of parallel coordinates and scatterplot matrix visualizations, and discuss appropriate application scenarios and contraindications for usage.

Authoring situated visualizations in-situ is challenging due to the need of writing code in a mobile and highly dynamic fashion. To provide better support for that, we define requirements for text input methods that target situated visualization authoring. We identify wearable chorded keyboards as a potentially suitable method that fulfills some of these requirements. To further investigate this approach, we tailored a chorded keyboard device to visualization authoring, developed a learning application, and conducted a pilot user study. Our results confirm that learning a high number of chords is the main barrier for adoption, as in other application areas. Based on that, we discuss ideas on how chorded keyboards with a strongly reduced alphabet, hand gestures, and voice recognition might be used as a viable, multi-modal support for authoring situated visualizations in-situ.

We instrument Group Diagrams (GDs) to reduce clutter in sets of eye-tracking scanpaths. Group Diagrams consist of trajectory subsets that cover, or represent, the whole set of trajectories with respect to some distance measure and an adjustable distance threshold. The original GDs allow for an application of various distance measures. We implement the GD framework and evaluate it on scanpaths that were collected by a former user study on public transit maps. We find that the Fréchet distance is the most appropriate measure to get meaningful results, yet it is flexible enough to cover outliers. We discuss several implementation-specific challenges and improve the scalability of the algorithm.

Abstract We present an approach for visual analysis of high‐dimensional measurement data with varying sampling rates as routinely recorded in intensive care units. In intensive care, most assessments not only depend on one single measurement but a plethora of mixed measurements over time. Even for trained experts, efficient and accurate analysis of such multivariate data remains a challenging task. We present a linked‐view post hoc visual analytics application that reduces data complexity by combining projection‐based time curves for overview with small multiples for details on demand. Our approach supports not only the analysis of individual patients but also of ensembles by adapting existing techniques using non‐parametric statistics. We evaluated the effectiveness and acceptance of our approach through expert feedback with domain scientists from the surgical department using real‐world data: a post‐surgery study performed on a porcine surrogate model to identify parameters suitable for diagnosing and prognosticating the volume state, and clinical data from a public database. The results show that our approach allows for detailed analysis of changes in patient state while also summarizing the temporal development of the overall condition.

We are delighted to present a first issue of the Proceedings of the ACM on Human-Computer Interaction to focus on contributions from the Eye Tracking Research and Applications (ETRA) community.

Abstract We propose a novel method for the computation of Jacobi sets in 2D domains. The Jacobi set is a topological descriptor based on Morse theory that captures gradient alignments among multiple scalar fields, which is useful for multi-field visualization. Previous Jacobi set computations use piecewise linear approximations on triangulations that result in discretization artifacts like zig-zag patterns. In this paper, we utilize a local bilinear method to obtain a more precise approximation of Jacobi sets by preserving the topology and improving the geometry. Consequently, zig-zag patterns on edges are avoided, resulting in a smoother Jacobi set representation. Our experiments show a better convergence with increasing resolution compared to the piecewise linear method. We utilize this advantage with an efficient local subdivision scheme. Finally, our approach is evaluated qualitatively and quantitatively in comparison with previous methods for different mesh resolutions and across a number of synthetic and real-world examples.

We introduce a novel visual analytics approach for analyzing, understanding, and correcting neural machine translation. Our system supports users in automatically translating documents using neural machine translation and identifying and correcting possible erroneous translations. User corrections can then be used to fine-tune the neural machine translation model and automatically improve the whole document. While translation results of neural machine translation can be impressive, there are still many challenges such as overand under-translation, domain-specific terminology, and handling long sentences, making it necessary for users to verify translation results; our system aims at supporting users in this task. Our visual analytics approach combines several visualization techniques in an interactive system. A parallel coordinates plot with multiple metrics related to translation quality can be used to find, filter, and select translations that might contain errors. An interactive beam search visualization and graph visualization for attention weights can be used for post-editing and understanding machine-generated translations. The machine translation model is updated from user corrections to improve the translation quality of the whole document. We designed our approach for an LSTM-based translation model and extended it to also include the Transformer architecture. We show for representative examples possible mistranslations and how to use our system to deal with them. A user study revealed that many participants favor such a system over manual text-based translation, especially for translating large documents.

A common enhancement of scatterplots represents points as small multiples, glyphs, or thumbnail images. As this encoding often results in overlaps, a general strategy is to alter the position of the data points, for instance, to a grid-like structure. Previous approaches rely on solving expensive optimization problems or on dividing the space that alter the global structure of the scatterplot. To find a good balance between efficiency and neighborhood and layout preservation, we propose Hagrid, a technique that uses space-filling curves (SFCs) to “gridify” a scatterplot without employing expensive collision detection and handling mechanisms. Using SFCs ensures that the points are plotted close to their original position, retaining approximately the same global structure. The resulting scatterplot is mapped onto a rectangular or hexagonal grid, using Hilbert and Gosper curves. We discuss and evaluate the theoretic runtime of our approach and quantitatively compare our approach to three state-of-the-art gridifying approaches, DGrid, Small multiples with gaps SMWG, and CorrelatedMultiples CMDS, in an evaluation comprising 339 scatterplots. Here, we compute several quality measures for neighborhood preservation together with an analysis of the actual runtimes. The main results show that, compared to the best other technique, Hagrid is faster by a factor of four, while achieving similar or even better quality of the gridified layout. Due to its computational efficiency, our approach also allows novel applications of gridifying approaches in interactive settings, such as removing local overlap upon hovering over a scatterplot.

The concept of biological age (BA) - although important in clinical practice - is hard to grasp mainly due to the lack of a clearly defined reference standard. For specific applications, especially in pediatrics, medical image data are used for BA estimation in a routine clinical context. Beyond this young age group, BA estimation is mostly restricted to whole-body assessment using non-imaging indicators such as blood biomarkers, genetic and cellular data. However, various organ systems may exhibit different aging characteristics due to lifestyle and genetic factors. Thus, a whole-body assessment of the BA does not reflect the deviations of aging behavior between organs. To this end, we propose a new imaging-based framework for organ-specific BA estimation. In this initial study we focus mainly on brain MRI. As a first step, we introduce a chronological age (CA) estimation framework using deep convolutional neural networks (Age-Net). We quantitatively assess the performance of this framework in comparison to existing state-of-the-art CA estimation approaches. Furthermore, we expand upon Age-Net with a novel iterative data-cleaning algorithm to segregate atypical-aging patients (BA [Formula: see text] CA) from the given population. We hypothesize that the remaining population should approximate the true BA behavior. We apply the proposed methodology on a brain magnetic resonance image (MRI) dataset containing healthy individuals as well as Alzheimer's patients with different dementia ratings. We demonstrate the correlation between the predicted BAs and the expected cognitive deterioration in Alzheimer's patients. A statistical and visualization-based analysis has provided evidence regarding the potential and current challenges of the proposed methodology.

We introduce inverted stippling , a method to mimic an inversion technique used by artists when performing stippling. To this end, we extend Linde-Buzo-Gray (LBG) stippling to multi-class LBG (MLBG) stippling with multiple layers. MLBG stippling couples the layers stochastically to optimize for per-layer and overall blue-noise properties. We propose a stipple-based filling method to generate solid color backgrounds for inverting areas. Our experiments demonstrate the effectiveness of MLBG in terms of reducing overlapping and intensity accuracy. In addition, we showcase MLBG with color stippling and dynamic multi-class blue-noise sampling, which is possible due to its support for temporal coherence.

We propose a visualization method to understand the effect of multidimensional projection on local subspaces, using implicit function differentiation. Here, we understand the local subspace as the multidimensional local neighborhood of data points. Existing methods focus on the projection of multidimensional data points, and the neighborhood information is ignored. Our method is able to analyze the shape and directional information of the local subspace to gain more insights into the global structure of the data through the perception of local structures. Local subspaces are fitted by multidimensional ellipses that are spanned by basis vectors. An accurate and efficient vector transformation method is proposed based on analytical differentiation of multidimensional projections formulated as implicit functions. The results are visualized as glyphs and analyzed using a full set of specifically-designed interactions supported in our efficient web-based visualization tool. The usefulness of our method is demonstrated using various multi- and high-dimensional benchmark datasets. Our implicit differentiation vector transformation is evaluated through numerical comparisons; the overall method is evaluated through exploration examples and use cases.

Causality is crucial to understanding the mechanisms behind complex systems and making decisions that lead to intended outcomes. Event sequence data is widely collected from many real-world processes, such as electronic health records, web clickstreams, and financial transactions, which transmit a great deal of information reflecting the causal relations among event types. Unfortunately, recovering causalities from observational event sequences is challenging, as the heterogeneous and high-dimensional event variables are often connected to rather complex underlying event excitation mechanisms that are hard to infer from limited observations. Many existing automated causal analysis techniques suffer from poor explainability and fail to include an adequate amount of human knowledge. In this paper, we introduce a visual analytics method for recovering causalities in event sequence data. We extend the Granger causality analysis algorithm on Hawkes processes to incorporate user feedback into causal model refinement. The visualization system includes an interactive causal analysis framework that supports bottom-up causal exploration, iterative causal verification and refinement, and causal comparison through a set of novel visualizations and interactions. We report two forms of evaluation: a quantitative evaluation of the model improvements resulting from the user-feedback mechanism, and a qualitative evaluation through case studies in different application domains to demonstrate the usefulness of the system.

Abstract-We propose a data-driven space-filling curve method for 2D and 3D visualization. Our flexible curve traverses the data elements in the spatial domain in a way that the resulting linearization better preserves features in space compared to existing methods. We achieve such data coherency by calculating a Hamiltonian path that approximately minimizes an objective function that describes the similarity of data values and location coherency in a neighborhood. Our extended variant even supports multiscale data via quadtrees and octrees. Our method is useful in many areas of visualization including multivariate or comparative visualization ensemble visualization of 2D and 3D data on regular grids or multiscale visual analysis of particle simulations. The effectiveness of our method is evaluated with numerical comparisons to existing techniques and through examples of ensemble and multivariate datasets.

Dynamic Mode Decomposition (DMD) is a data-driven and model-free decomposition technique. It is suitable for revealing spatio-temporal features of both numerically and experimentally acquired data. Conceptually, DMD performs a low-dimensional spectral decomposition of the data into the following components: the modes, called DMD modes, encode the spatial contribution of the decomposition, whereas the DMD amplitudes specify their impact. Each associated eigenvalue, referred to as DMD eigenvalue, characterizes the frequency and growth rate of the DMD mode. In this paper, we demonstrate how the components of DMD can be utilized to obtain temporal and spatial information from time-dependent flow fields. We begin with the theoretical background of DMD and its application to unsteady flow. Next, we examine the conventional process with DMD mathematically and put it in relationship to the discrete Fourier transform. Our analysis shows that the current use of DMD components has several drawbacks. To resolve these problems we adjust the components and provide new and meaningful insights into the decomposition: we show that our improved components capture the spatio-temporal patterns of the flow better. Moreover, we remove redundancies in the decomposition and clarify the interplay between components, allowing users to understand the impact of components. These new representations, which respect the spatio-temporal character of DMD, enable two clustering methods that segment the flow into physically relevant sections and can therefore be used for the selection of DMD components. With a number of typical examples, we demonstrate that the combination of these techniques allows new insights with DMD for unsteady flow.

Rectangular treemaps visualize hierarchical numerical data by recursively partitioning an input rectangle into smaller rectangles whose areas match the data. Numerical data often has uncertainty associated with it. To visualize uncertainty in a rectangular treemap, we identify two conflicting key requirements: (i) to assess the data value of a node in the hierarchy, the area of its rectangle should directly match its data value, and (ii) to facilitate comparison between data and uncertainty, uncertainty should be encoded using the same visual variable as the data, that is, area. We present Uncertainty Treemaps, which meet both requirements simultaneously by introducing the concept of hierarchical uncertainty masks. First, we define a new cost function that measures the quality of Uncertainty Treemaps. Then, we show how to adapt existing treemapping algorithms to support uncertainty masks. Finally, we demonstrate the usefulness and quality of our technique through an expert review and a computational experiment on real-world datasets.

We propose ClaVis, a visual analytics system for comparative analysis of classification models. ClaVis allows users to visually compare the performance and behavior of tens to hundreds of classifiers trained with different hyperparameter configurations. Our approach is plugin-based and classifier-agnostic and allows users to add their own datasets and classifier implementations. It provides multiple visualizations, including a multivariate ranking, a similarity map, a scatterplot that reveals correlations between parameters and scores, and a training history chart. We demonstrate the effectivity of our approach in multiple case studies for training classification models in the domain of natural language processing.

We propose a new technique for visual analytics and annotation of long-term pervasive eye tracking data for which a combined analysis of gaze and egocentric video is necessary. Our approach enables two important tasks for such data for hour-long videos from individual participants: (1) efficient annotation and (2) direct interpretation of the results. Exemplary time spans can be selected by the user and are then used as a query that initiates a fuzzy search of similar time spans based on gaze and video features. In an iterative refinement loop, the query interface then provides suggestions for the importance of individual features to improve the search results. A multi-layered timeline visualization shows an overview of annotated time spans. We demonstrate the efficiency of our approach for analyzing activities in about seven hours of video in a case study and discuss feedback on our approach from novices and experts performing the annotation task.

We present a novel variant of parallel coordinates plots (PCPs) in which we show clusters in 2D subspaces of multivariate data and emphasize flow between them. We achieve this by duplicating and stacking individual axes vertically. On a high level, our clusterflow layout shows how data points move from one cluster to another in different subspaces. We achieve cluster-based bundling and limit plot growth through the reduction of available vertical space for each duplicated axis. Although we introduce space between clusters, we preserve the readability of intra-cluster correlations by starting and ending with the original slopes from regular PCPs and drawing Hermite spline segments in between. Moreover, our rendering technique enables the visualization of small and large data sets alike. Cluster-flow PCPs can even propagate the uncertainty inherent to fuzzy clustering through the layout and rendering stages of our pipeline. Our layout algorithm is based on A*. It achieves an optimal result with regard to a novel set of cost functions that allow us to arrange axes horizontally (dimension ordering) and vertically (cluster ordering).

We present a systematic review of 45S papers that report on evaluations in mixed and augmented reality (MR/AR) published in ISMAR, CHI, IEEE VR, and UIST over a span of 11 years (2009-2019). Our goal is to provide guidance for future evaluations of MR/AR approaches. To this end, we characterize publications by paper type (e.g., technique, design study), research topic (e.g., tracking, rendering), evaluation scenario (e.g., algorithm performance, user performance), cognitive aspects (e.g., perception, emotion), and the context in which evaluations were conducted (e.g., lab vs. in-thewild). We found a strong coupling of types, topics, and scenarios. We observe two groups: (a) technology-centric performance evaluations of algorithms that focus on improving tracking, displays, reconstruction, rendering, and calibration, and (b) human-centric studies that analyze implications of applications and design, human factors on perception, usability, decision making, emotion, and attention. Amongst the 458 papers, we identified 248 user studies that involved 5,761 participants in total, of whom only 1,619 were identified as female. We identified 43 data collection methods used to analyze 10 cognitive aspects. We found nine objective methods, and eight methods that support qualitative analysis. A majority (216/248) of user studies are conducted in a laboratory setting. Often (138/248), such studies involve participants in a static way. However, we also found a fair number (30/248) of in-the-wild studies that involve participants in a mobile fashion. We consider this paper to be relevant to academia and industry alike in presenting the state-of-the-art and guiding the steps to designing, conducting, and analyzing results of evaluations in MR/AR.

We present time-aligned edge plots: time- and edge-scalable representations of dynamic graphs. Vertices are mapped to two vertical parallel axes. The left axis depicts the source vertices, whereas the right one depicts the destination vertices. The time axis is horizontally embedded in-between the two axes, resulting in a two-dimensional graph layout. Edges are added by drawing straight lines connecting the corresponding source and destination vertices through time, while the pixels along the lines are used to encode the time-varying information. In this way, the depiction of edges at the individual timepoints is reduced to only a few pixels, resulting in a less cluttered representation of dynamic graphs, while the alignment of edges over time reveals the temporal patterns in the data and preserves the users' mental map. We evaluate our approach by comparing it theoretically and empirically against the state-of-the-art using dynamic graphs of varying complexities.

In this paper, we introduce a visualization technique aimed to help machine learning experts to analyze the hidden states of layers in recurrent neural networks (RNNs). Our technique allows the user to visually inspect how hidden states store and process information throughout the feeding of an input sequence into the network. It can answer questions such as which parts of the input data had a higher impact on the prediction and how the model correlates each hidden state configuration with a certain output. Our visualization comprises several components: our input visualization shows the input sequence and how it relates to the output (using color coding); hidden states are visualized by nonlinear projection to 2-D visualization space via t-SNE in order to understand the shape of the space of hidden states; time curves are employed to show the details of the evolution of hidden state configurations; and a time-multi-class heatmap matrix visualizes the evolution of expected predictions for multi-class classifiers. To demonstrate the capability of our approach, we discuss two typical use cases for long short-term memory (LSTM) models applied to two widely used natural language processing (NLP) datasets.

Nonlinear programming targets nonlinear optimization with constraints, which is a generic yet complex methodology involving humans for problem modeling and algorithms for problem solving. We address the particularly hard challenge of supporting domain experts in handling, understanding, and trouble-shooting high-dimensional optimization with a large number of constraints. Leveraging visual analytics, users are supported in exploring the computation process of nonlinear constraint optimization. Our system was designed for robot motion planning problems and developed in tight collaboration with domain experts in nonlinear programming and robotics. We report on the experiences from this design study, illustrate the usefulness for relevant example cases, and discuss the extension to visual analytics for nonlinear programming in general.

We introduce an approach for the visual analysis of eye movement data from two people playing competitive virtual board games. Our approach provides methods to temporally synchronize and spatially register gaze and mouse recordings from two eye tracking devices. Analysts can examine such fused data visually with a combination of techniques: attention maps and gaze plots as well as a temporal summary of the distance between gaze positions and mouse events of the two players. We show different game scenarios from the competitive game Go, which is especially complex for analyzing strategies of individual players, to demonstrate our methods. In general, our visual analysis approach can provide analysts with insights into strategies, learning processes, and means of communication between people.

Abstract We present a method to simulate fluid flow on evolving surfaces, e.g., an oil film on a water surface. Given an animated surface (e.g., extracted from a particle‐based fluid simulation) in three‐dimensional space, we add a second simulation on this base animation. In general, we solve a partial differential equation (PDE) on a level set surface obtained from the animated input surface. The properties of the input surface are transferred to a sparse volume data structure that is then used for the simulation. We introduce one‐way coupling strategies from input properties to our simulation and we add conservation of mass and momentum to existing methods that solve a PDE in a narrow‐band using the Closest Point Method. In this way, we efficiently compute high‐resolution 2D simulations on coarse input surfaces. Our approach helps visual effects creators easily integrate a workflow to simulate material flow on evolving surfaces into their existing production pipeline.

We present a technique to perform dimensionality reduction on data that is subject to uncertainty. Our method is a generalization of traditional principal component analysis (PCA) to multivariate probability distributions. In comparison to non-linear methods, linear dimensionality reduction techniques have the advantage that the characteristics of such probability distributions remain intact after projection. We derive a representation of the PCA sample covariance matrix that respects potential uncertainty in each of the inputs, building the mathematical foundation of our new method: uncertainty-aware PCA. In addition to the accuracy and performance gained by our approach over sampling-based strategies, our formulation allows us to perform sensitivity analysis with regard to the uncertainty in the data. For this, we propose factor traces as a novel visualization that enables to better understand the influence of uncertainty on the chosen principal components. We provide multiple examples of our technique using real-world datasets. As a special case, we show how to propagate multivariate normal distributions through PCA in closed form. Furthermore, we discuss extensions and limitations of our approach.

Good code quality is a prerequisite for efficiently developing maintainable software. In this paper, we present a novel approach to generate exploranative (explanatory and exploratory) data-driven documents that report code quality in an interactive, exploratory environment. We employ a template-based natural language generation method to create textual explanations about the code quality, dependent on data from software metrics. The interactive document is enriched by different kinds of visualization, including parallel coordinates plots and scatterplots for data exploration and graphics embedded into text. We devise an interaction model that allows users to explore code quality with consistent linking between text and visualizations; through integrated explanatory text, users are taught background knowledge about code quality aspects. Our approach to interactive documents was developed in a design study process that included software engineering and visual analytics experts. Although the solution is specific to the software engineering scenario, we discuss how the concept could generalize to multivariate data and report lessons learned in a broader scope.

We propose a photographic method to show scalar values of high dynamic range (HDR) by color mapping for 2D visualization. We combine (1) tone-mapping operators that transform the data to the display range of the monitor while preserving perceptually important features, based on a systematic evaluation, and (2) simulated glares that highlight high-value regions. Simulated glares are effective for highlighting small areas (of a few pixels) that may not be visible with conventional visualizations; through a controlled perception study, we confirm that glare is preattentive. The usefulness of our overall photographic HDR visualization is validated through the feedback of expert users.

In this paper, we propose a perceptually-guided visualization sharpening technique. We analyze the spectral behavior of an established comprehensive perceptual model to arrive at our approximated model based on an adapted weighting of the bandpass images from a Gaussian pyramid. The main benefit of this approximated model is its controllability and predictability for sharpening color-mapped visualizations. Our method can be integrated into any visualization tool as it adopts generic image-based post-processing, and it is intuitive and easy to use as viewing distance is the only parameter. Using highly diverse datasets, we show the usefulness of our method across a wide range of typical visualizations.

Yarbus' claim to decode the observer's task from eye movements has received mixed reactions. In this paper, we have supported the hypothesis that it is possible to decode the task. We conducted an exploratory analysis on the dataset by projecting features and data points into a scatter plot to visualize the nuance properties for each task. Following this analysis, we eliminated highly correlated features before training an SVM and Ada Boosting classifier to predict the tasks from this filtered eye movements data. We achieve an accuracy of 95.4% on this task classification problem and hence, support the hypothesis that task classification is possible from a user's eye movement data.

We present a method for the spatio-temporal analysis of gaze data from multiple participants in the context of a video stimulus. For such data, an overview of the recorded patterns is important to identify common viewing behavior (such as attentional synchrony) and outliers. We adopt the approach of space-time cube visualization, which extends the spatial dimensions of the stimulus by time as the third dimension. Previous work mainly handled eye tracking data in the space-time cube as point cloud, providing no information about the stimulus context. This paper presents a novel visualization technique that combines gaze data, a dynamic stimulus, and optical flow with volume rendering to derive an overview of the data with contextual information. With specifically designed transfer functions, we emphasize different data aspects, making the visualization suitable for explorative analysis and for illustrative support of statistical findings alike.

Visual analytics (VA) research provides helpful solutions for interactive visual data analysis when exploring large and complex datasets. Due to recent advances in eye tracking technology, promising opportunities arise to extend these traditional VA approaches. Therefore, we discuss foundations for eye tracking support in VA systems. We first review and discuss the structure and range of typical VA systems. Based on a widely used VA model, we present five comprehensive examples that cover a wide range of usage scenarios. Then, we demonstrate that the VA model can be used to systematically explore how concrete VA systems could be extended with eye tracking, to create supportive and adaptive analytics systems. This allows us to identify general research and application opportunities, and classify them into research themes. In a call for action, we map the road for future research to broaden the use of eye tracking and advance visual analytics.

In immersive display environments, such as virtual or augmented reality, we can make explicit the connections between data points in visualisations and their context in the world, or in other visualisations. This paper considers the requirements and design space for drawing such links in order to minimise occlusion and clutter. A novel possibility in immersive environments is to optimise the link layout with respect to a particular point of view. In collaborative scenarios there is the need to do this for multiple points of view. We present an algorithm to achieve such link layouts and demonstrate its applicability in a variety of practical use cases.

The following topics are dealt with: software maintenance; program visualisation; data visualisation; graph theory; program diagnostics; software metrics; source code (software); software tools; program debugging; configuration management.

We present a framework for rapid prototyping of pervasive visual deficiency simulation in the context of graphical interfaces, virtual reality, and augmented reality. Our framework facilitates the emulation of various visual deficiencies for a wide range of applications, which allows users with normal vision to experience combinations of conditions such as myopia, hyperopia, presbyopia, cataract, nyctalopia, protanopia, deuteranopia, tritanopia, and achromatopsia. Our framework provides an infrastructure to encourage researchers to evaluate visualization and other display techniques regarding visual deficiencies, and opens up the field of visual disease simulation to a broader audience. The benefits of our framework are easy integration, configuration, fast prototyping, and portability to new emerging hardware. To demonstrate the applicability of our framework, we showcase a desktop application and an Android application that transform commodity hardware into glasses for visual deficiency simulation. We expect that this work promotes a greater understanding of visual impairments, leads to better product design for the visually impaired, and forms a basis for research to compensate for these impairments as everyday help.

We present a novel technique to correct errors introduced by the discretization of a fluid body when animating it with smoothed particle hydrodynamics (SPH). Our approach is based on the Shepard correction, which reduces the interpolation errors from irregularly spaced data. With Shepard correction, the smoothing kernel function is normalized using the weighted sum of the kernel function values in the neighborhood. To compute the correction factor, densities of neighboring particles are needed, which themselves are computed with the uncorrected kernel. This results in an inconsistent formulation and an error-prone correction of the kernel. As a consequence, the density computation may be inaccurate, thus the pressure forces are erroneous and may cause instabilities in the simulation process. We present a consistent formulation by using the corrected densities to compute the exact kernel correction factor and, thereby, increase the accuracy of the simulation. Employing our method, a smooth density distribution is achieved, i.e., the noise in the density field is reduced by orders of magnitude. To show that our method is independent of the SPH variant, we evaluate our technique on weakly compressible SPH and on divergence-free SPH. Incorporating the corrected density into the correction process, the problem cannot be stated explicitly anymore. We propose an efficient and easy-to-implement algorithm to solve the implicit problem by applying the power method. Additionally, we demonstrate how our model can be applied to improve the density distribution on rigid bodies when using a well-known rigid-fluid coupling approach.

This January 2019 issue of theIEEE Transactions on Visualization and Computer Graphics (TVCG)contains the proceedings of IEEE VIS 2018, held during 21-26 October 2018 at the Estrel Hotel & Congress Center in Berlin. With IEEE VIS 2018, the conference series is in its 29th year.IEEE VIS consists of three conferences, held concurrently: the IEEE Visual Analytics Science and Technology Conference (IEEE VAST), the IEEE Information Visualization Conference (IEEE InfoVis), and the IEEE Scientific Visualization Conference (IEEE SciVis). These three conferences are the premier venues for the visualization community to exchange the latest ideas and developments, attracting researchers and practitioners alike.

We propose a technique to represent two-dimensional data using stipples. While stippling is often regarded as an illustrative method, we argue that it is worth investigating its suitability for the visualization domain. For this purpose, we generalize the Linde-Buzo-Gray stippling algorithm for information visualization purposes to encode continuous and discrete 2D data. Our proposed modifications provide more control over the resulting distribution of stipples for encoding additional information into the representation, such as contours. We show different approaches to depict contours in stipple drawings based on locally adjusting the stipple distribution. Combining stipple-based gradients and contours allows for simultaneous assessment of the overall structure of the data while preserving important local details. We discuss the applicability of our technique using datasets from different domains and conduct observation-validating studies to assess the perception of stippled representations.

Selecting a good aspect ratio is crucial for effective 2D diagrams. There are several aspect ratio selection methods for function plots and line charts, but only few can handle general, discrete diagrams such as 2D scatter plots. However, these methods either lack a perceptual foundation or heavily rely on intermediate isoline representations, which depend on choosing the right isovalues and are time-consuming to compute. This paper introduces a general image-based approach for selecting aspect ratios for a wide variety of 2D diagrams, ranging from scatter plots and density function plots to line charts. Our approach is derived from Federer's co-area formula and a line integral representation that enable us to directly construct image-based versions of existing selection methods using density fields. In contrast to previous methods, our approach bypasses isoline computation, so it is faster to compute, while following the perceptual foundation to select aspect ratios. Furthermore, this approach is complemented by an anisotropic kernel density estimation to construct density fields, allowing us to more faithfully characterize data patterns, such as the subgroups in scatterplots or dense regions in time series. We demonstrate the effectiveness of our approach by quantitatively comparing to previous methods and revisiting a prior user study. Finally, we present extensions for ROI banking, multi-scale banking, and the application to image data.

We present a technique that conveys the uncertainty in the secondary structure of proteins-an abstraction model based on atomic coordinates. While protein data inherently contains uncertainty due to the acquisition method or the simulation algorithm, we argue that it is also worth investigating uncertainty induced by analysis algorithms that precede visualization. Our technique helps researchers investigate differences between multiple secondary structure assignment methods. We modify established algorithms for fuzzy classification and introduce a discrepancy-based approach to project an ensemble of sequences to a single importance-weighted sequence. In 2D, we depict the aggregated secondary structure assignments based on the per-residue deviation in a collapsible sequence diagram. In 3D, we extend the ribbon diagram using visual variables such as transparency, wave form, frequency, or amplitude to facilitate qualitative analysis of uncertainty. We evaluated the effectiveness and acceptance of our technique through expert reviews using two example applications: the combined assignment against established algorithms and time-dependent structural changes originating from simulated protein dynamics.

Eye movement data can be regarded as a set of scan paths, each corresponding to one of the visual scanning strategies of a certain study participant. Finding common subsequences in those scan paths is a challenging task since they are typically not equally temporally long, do not consist of the same number of fixations, or do not lead along similar stimulus regions. In this paper we describe a technique based on pairwise and multiple sequence alignment to support a data analyst to see the most important patterns in the data. To reach this goal the scan paths are first transformed into a sequence of characters based on metrics as well as spatial and temporal aggregations. The result of the algorithmic data transformation is used as input for an interactive consensus matrix visualization. We illustrate the usefulness of the concepts by applying it to formerly recorded eye movement data investigating route finding tasks in public transport maps.

The comparison of scanpaths between multiple participants is an important analysis task in eye tracking research. Established methods typically inspect recorded gaze sequences based on geometrical trajectory properties or strings derived from annotated areas of interest (AOIs). We propose a new approach based on image similarities of gaze-guided slit-scans: For each time step, a vertical slice is extracted from the stimulus at the gaze position. Placing the slices next to each other over time creates a compact representation of a scanpath in the context of the stimulus. These visual representations can be compared based on their image similarity, providing a new measure for scanpath comparison without the need for annotation. We demonstrate how comparative slit-scan visualization can be integrated into a visual analytics approach to support the interpretation of scanpath similarities in general.

We present an approach for interactively analyzing large dynamic graphs consisting of several thousand time steps with a particular focus on temporal aspects. we employ a static representation of the time-varying graph based on the concept of space-time cubes, i.e., we create a volumetric representation of the graph by stacking the adjacency matrices of each of its time steps. To achieve an efficient analysis of complex data, we discuss three classes of analytics methods of particular importance in this context: data views, aggregation and filtering, and comparison. For these classes, we present a GPU-based implementation of respective analysis methods that enable the interactive analysis of large graphs. We demonstrate the utility as well as the scalability of our approach by presenting application examples for analyzing different time-varying data sets.

In this paper, we propose an image-space contrast enhancement method for color-encoded visualization. The contrast of an image is enhanced through a perceptually-guided approach that interfaces with the user with a single and intuitive parameter of the virtual viewing distance. To this end, we analyze a multiscale contrast model of the input image and test the visibility of bandpass images of all scales at a virtual viewing distance. By adapting weights of bandpass images with a threshold model of spatial vision, this image-based method enhances contrast to compensate for contrast loss caused by viewing the image at a certain distance. Relevant features in the color image can be further emphasized by the user using overcompensation. The method is efficient and can be integrated into any visualization tool as it is a generic image-based post-processing technique. Using highly diverse datasets, we show the usefulness of perception compensation across a wide range of typical visualizations.

Parallel coordinates plots and RadViz are two visualization techniques that deal with multivariate data. They complement each other in identifying data patterns, clusters, and outliers. In this paper, we analyze multivariate software metrics linking the two approaches for detecting outliers, which could be the indicators for bad smells in software systems. Parallel coordinates plots provide an overview, whereas the RadViz representation allows for comparing a smaller subset of metrics in detail. We develop an interactive visual analytics system supporting automatic detection of bad smell patterns. In addition, we investigate the distinctive properties of outliers that are not considered harmful, but noteworthy for other reasons. We demonstrate our approach with open source Java systems and describe detected bad smells and other outlier patterns.

We propose a tree visualization technique for comparison of structures and attributes across multiple hierarchies. Many software systems are structured hierarchically by design. For example, developers subdivide source code into libraries, modules, and functions. This design propagates to software configuration and business processes, rendering software hierarchies even more important. Often these structural elements are attributed with reference counts, code quality metrics, and the like. Throughout the entire software life cycle, these hierarchies are reviewed, integrated, debugged, and changed many times by different people so that the identity of a structural element and its attributes is not clearly traceable. We argue that pairwise comparison of similar trees is a tedious task due to the lack of overview, especially when applied to a large number of hierarchies. Therefore, we strive to visualize multiple similar trees as a whole by merging them into one supertree. To merge structures and combine attributes from different trees, we leverage the Jaccard similarity and solve a matching problem while keeping track of the origin of a structure element and its attributes. Our visualization approach allows users to inspect these supertrees using node-link diagrams and indented tree plots. The nodes in these plots depict aggregated attributes and, using word-sized line plots, detailed data. We demonstrate the usefulness of our method by exploring the evolution of software repositories and debugging data processing pipelines using provenance data.

Abstract The visualization community has developed to date many intuitions and understandings of how to judge thequalityof views in visualizing data. The computation of a visualization's quality and usefulness ranges from measuring clutter and overlap, up to the existence and perception of specific (visual) patterns. This survey attempts to report, categorize and unify the diverse understandings and aims to establish a common vocabulary that will enable a wide audience to understand their differences and subtleties. For this purpose, we present a commonly applicable quality metric formalization that should detail and relate all constituting parts of a quality metric. We organize our corpus of reviewed research papers along the data types established in the information visualization community: multi‐ and high‐dimensional, relational, sequential, geospatial and text data. For each data type, we select the visualization subdomains in which quality metrics are an active research field and report their findings, reason on the underlying concepts, describe goals and outline the constraints and requirements. One central goal of this survey is to provide guidance on future research opportunities for the field and outline how different visualization communities could benefit from each other by applying or transferring knowledge to their respective subdomain. Additionally, we aim to motivate the visualization community to compare computed measures to the perception of humans.

Abstract There is an ongoing discussion in the visualization community about the relevant factors that render a visualization effective, expressive, memorable, aesthetically pleasing, etc. These factors lead to a large design space for visualizations. To explore this design space, qualitative research methods based on observations and interviews are often necessary. We describe an interview method that allows us to systematically acquire and assess important factors from subjective answers by interviewees. To this end, we adopt the repertory grid methodology in the context of visualization. It is based on the personal construct theory: each personality interprets a topic based on a set of personal, basic constructs expressed as contrasts. For the individual interpretation of visualizations, this means that these personal terms can be very different, depending on numerous influences, such as the prior experiences of the interviewed person. We present an interviewing process, visual interface, and qualitative and quantitative analysis procedures that are specifically devised to fit the needs of visualization applications. A showcase interview with 15 typical static information visualizations and 10 participants demonstrates that our approach is effective in identifying common constructs as well as individual differences. In particular, we investigate differences between expert and nonexpert interviewees. Finally, we discuss the differences to other qualitative methods and how the repertory grid can be embedded in existing theoretical frameworks of visualization research for the design process.

We address the problem of visualizing multivariate correlations in parallel coordinates. We focus on multivariate correlation in the form of linear relationships between multiple variables. Traditional parallel coordinates are well prepared to show negative correlations between two attributes by distinct visual patterns. However, it is difficult to recognize positive correlations in parallel coordinates. Furthermore, there is no support to highlight multivariate correlations in parallel coordinates. In this paper, we exploit the indexed point representation of p -flats (planes in multidimensional data) to visualize local multivariate correlations in parallel coordinates. Our method yields clear visual signatures for negative and positive correlations alike, and it supports large datasets. All information is shown in a unified parallel coordinates framework, which leads to easy and familiar user interactions for analysts who have experience with traditional parallel coordinates. The usefulness of our method is demonstrated through examples of typical multidimensional datasets.

We present a novel type of circular treemap, where we intentionally allocate extra space for additional visual variables. With this extended visual design space, we encode hierarchically structured data along with their uncertainties in a combined diagram. We introduce a hierarchical and force-based circle-packing algorithm to compute Bubble Treemaps, where each node is visualized using nested contour arcs. Bubble Treemaps do not require any color or shading, which offers additional design choices. We explore uncertainty visualization as an application of our treemaps using standard error and Monte Carlo-based statistical models. To this end, we discuss how uncertainty propagates within hierarchies. Furthermore, we show the effectiveness of our visualization using three different examples: the package structure of Flare, the S&P 500 index, and the US consumer expenditure survey.

Conventional dot plots use a constant dot size and are typically applied to show the frequency distribution of small data sets. Unfortunately, they are not designed for a high dynamic range of frequencies. We address this problem by introducing nonlinear dot plots. Adopting the idea of nonlinear scaling from logarithmic bar charts, our plots allow for dots of varying size so that columns with a large number of samples are reduced in height. For the construction of these diagrams, we introduce an efficient two-way sweep algorithm that leads to a dense and symmetrical layout. We compensate aliasing artifacts at high dot densities by a specifically designed low-pass filtering method. Examples of nonlinear dot plots are compared to conventional dot plots as well as linear and logarithmic histograms. Finally, we include feedback from an expert review.

Welcome to the proceedings of the IEEE Pacific Visualization Symposium 2017 (IEEE PacificVis 2017), tenth in a series of successful events that have been sponsored by the IEEE Computer Society Visualization and Graphics Technical Committee (VGTC). Past IEEE PacificVis symposia were held in Kyoto (2008), Beijing (2009), Taipei (2010), Hong Kong (2011), Songdo (2012), Sydney (2013), Yokohama (2014), Hangzhou (2015), and Taipei (2016). This year, PacificVis is held at Seoul, Korea from April 18 to 21, 2017, hosted by Seoul National University.

The incorporation of subtitles in multimedia content plays an important role in communicating spoken content. For example, subtitles in the respective language are often preferred to expensive audio translation of foreign movies. The traditional representation of subtitles displays text centered at the bottom of the screen. This layout can lead to large distances between text and relevant image content, causing eye strain and even that we miss visual content. As a recent alternative, the technique of speaker-following subtitles places subtitle text in speech bubbles close to the current speaker. We conducted a controlled eye-tracking laboratory study (n = 40) to compare the regular approach (center-bottom subtitles) with content-sensitive, speaker-following subtitles. We compared different dialog-heavy video clips with the two layouts. Our results show that speaker-following subtitles lead to higher fixation counts on relevant image regions and reduce saccade length, which is an important factor for eye strain.

Smoothed particle hydrodynamics (SPH) is a popular mesh-free, particle-based fluid simulation approach for a wide range of applications. There are several numerical variants of SPH along with a variety of models for aspects such as boundary conditions, compressibility or incompressibility, and surface tension. Different combinations of these models lead to varying effects that occur during simulation, and their analysis is a critical challenge for fluid mechanics. In this paper, we address this challenge by presenting a visual debugging application for simulations, which allows users to evaluate the properties of the models and to detect possible computational errors. Our multi-view application uses a combination of interactive 3D visualization of the particles and non-spatial visualizations from the field of information visualization, namely scatter plots and parallel coordinates plots. Our visual debugging environment thus enables a quantitative analysis of the multidimensional simulation attributes, including internal and physical properties contributing to the simulation process. All views support brushing and linking, that is, selections of interesting value ranges in the plots are directly visible in the 3D view and, conversely, the selection of particles in the 3D view highlights the corresponding data points in the plots. Since typical SPH simulations come with large numbers of data points, we employ stochastic subsampling to reduce visual clutter in the non-spatial views and accelerate the rendering speed. We discuss four real-world use cases for visual debugging of fluid simulations that showcase how our visual debugging environment is instrumental for identify code errors and increases the understanding of the simulation models. We also show how the combination of coupled views can reveal internal details, thus serving to improve simulation results.

We investigate the problem of analyzing word frequencies in multiple text sources with the aim to give an overview of word-based similarities in several texts as a starting point for further analysis. To reach this goal, we designed a visual analytics approach composed of typical stages and processes, combining algorithmic analysis, visualization techniques, the human users with their perceptual abilities, as well as interaction methods for both the data analysis and the visualization component. By our algorithmic analysis, we first generate a multivariate dataset where words build the cases and the individual text sources the attributes. Real-valued relevances express the significances of each word in each of the text sources. From the visualization perspective, we describe how this multivariate dataset can be visualized to generate, confirm, rebuild, refine, or reject hypotheses with the goal to derive meaning, knowledge, and insights from several text sources. We discuss benefits and drawbacks of the visualization approaches when analyzing word relevances in multiple texts.

Visualizing time series data with a spatial context is a problem that appears more and more often, since small and lightweight GPS devices allow us to enrich the time series data with position information. One example is the visualization of the energy output of power plants. We present a web-based application that aims to provide information about the energy production of a specified region, along with location information about the power plants. The application is intended to be used as a solid data basis for political discussions, nudging, and story telling about the German energy transition to renewables, called "Energiewende". It was therefore designed to be intuitive, easy to use, and provide information for a broad spectrum of users that do not need any domain-specific knowledge. Users are able to select different categories of power plants and look up their positions on an overview map. Glyphs indicate their exact positions and a selection mechanism allows users to compare the power output on different time scales using stacked area charts or ThemeRivers. As an evaluation of the application, we have collected web access statistics and conducted an online survey with respect to the intuitiveness, usability, and informativeness.

To obtain an accurate understanding of program behavior, developers use a set of tools and techniques such as logging outputs, debuggers, profilers, and visualizations. These support an in-depth analysis of the program behavior, each approach focusing on a different aspect. What is missing, however, is an approach to get an overview of a program execution. As a first step to fill this gap, this paper presents an approach to generate Method Execution Reports. Each report summarizes the execution of a selected method for a specific execution of the program using natural-language text and embedded visualizations. A report provides an overview of the dynamic calls and time consumption related to the selected method. We present a framework to generate these reports and discuss the specific instantiation and phrasing we have chosen. Our results comprise feedback from developers discussing the understandability and usefulness of our approach and a task-based comparison to state-of-the-art solutions.

Software systems can grow large, consisting of thousands of hierarchically organized elements like directories, subdirectories, files, and functions. Moreover, those hierarchy elements can carry additional information worth investigating for a software developer. Getting an overview of both the hierarchy and the attached static or dynamic data can become a tedious task if it is not supported by a visually scalable visualization technique. In this paper, we use a hierarchy visualization based on the visual metaphor of indentation to generate an overview of the software system hierarchy and easily attach additional attributes. The extra information is aligned with the hierarchy elements and, hence, supports visual comparisons of the attachments on different levels of hierarchical granularity. Through interaction, we provide additional views on the data, e.g., by filtering, hierarchy transformations, or details-on-demand. We illustrate the usefulness of our hierarchy visualization technique by means of an application example exploring data from the open-source software project jEdit. We investigated the readability of the hierarchy visualization with a user experiment, comparing indentation to node-link diagrams for varying sizes of a hierarchy.

Analysis of software performance typically takes into account clock cycles and memory consumption at each sampling point in time. Although this is a valid strategy, we argue that it is also worth investigating data and control flow structures, as observed using memory traces and call stacks, because of their importance for performance engineering. In this work, we present a visual approach to memory profiling that supports analysis of memory layout, access patterns, and aliasing in correlation to program execution. Our method leverages language-agnostic dynamic code instrumentation to minimize the impact of tracing on performance, i.e., the application remains usable on commodity hardware. The profiled data is then clustered and visualized using a density-based scatter plot. If debug symbols are available, the scatter plot is augmented by a flame graph to ease linking to the high-level source code. Our visualization helps software engineers to identify runtime behavior by relating memory addresses to instruction execution. We demonstrate our approach using a set of examples revealing different memory access patterns and discuss their influence on software performance.

Abstract Dynamic graph visualization focuses on the challenge of representing the evolution of relationships between entities in readable, scalable and effective diagrams. This work surveys the growing number of approaches in this discipline. We derive a hierarchical taxonomy of techniques by systematically categorizing and tagging publications. While static graph visualizations are often divided into node‐link and matrix representations, we identify the representation of time as the major distinguishing feature for dynamic graph visualizations: either graphs are represented as animated diagrams or as static charts based on a timeline. Evaluations of animated approaches focus on dynamic stability for preserving the viewer's mental map or, in general, compare animated diagrams to timeline‐based ones. A bibliographic analysis provides insights into the organization and development of the field and its community. Finally, we identify and discuss challenges for future research. We also provide feedback from experts, collected with a questionnaire, which gives a broad perspective of these challenges and the current state of the field.

Abstract This survey provides an introduction into eye tracking visualization with an overview of existing techniques. Eye tracking is important for evaluating user behaviour. Analysing eye tracking data is typically done quantitatively, applying statistical methods. However, in recent years, researchers have been increasingly using qualitative and exploratory analysis methods based on visualization techniques. For this state‐of‐the‐art report, we investigated about 110 research papers presenting visualization techniques for eye tracking data. We classified these visualization techniques and identified two main categories: point‐based methods and methods based on areas of interest. Additionally, we conducted an expert review asking leading eye tracking experts how they apply visualization techniques in their analysis of eye tracking data. Based on the experts' feedback, we identified challenges that have to be tackled in the future so that visualizations will become even more widely applied in eye tracking research.

Abstract The visualization of dynamic graphs demands visually encoding at least three major data dimensions: vertices, edges, and time steps. Many of the state‐of‐the‐art techniques can show an overview of vertices and edges but lack a data‐scalable visual representation of the time aspect. In this paper, we address the problem of displaying dynamic graphs with a thousand or more time steps. Our proposed interleaved parallel edge splatting technique uses a time‐to‐space mapping and shows the complete dynamic graph in a static visualization. It provides an overview of all data dimensions, allowing for visually detecting time‐varying data patterns; hence, it serves as a starting point for further data exploration. By applying clustering and ordering techniques on the vertices, edge splatting on the links, and a dense time‐to‐space mapping, our approach becomes visually scalable in all three dynamic graph data dimensions. We illustrate the usefulness of our technique by applying it to call graphs and US domestic flight data with several hundred vertices, several thousand edges, and more than a thousand time steps.

Abstract Graph visualizations encode relationships between objects. Abstracting the objects into group structures provides an overview of the data. Groups can be disjoint or overlapping, and might be organized hierarchically. However, the underlying graph still needs to be represented for analyzing the data in more depth. This work surveys research in visualizing group structures as part of graph diagrams. A particular focus is the explicit visual encoding of groups, rather than only using graph layout to indicate groups implicitly. We introduce a taxonomy of visualization techniques structuring the field into four main categories: visual node attributes vary properties of the node representation to encode the grouping, juxtaposed approaches use two separate visualizations, superimposed techniques work with two aligned visual layers, and embedded visualizations tightly integrate group and graph representation. The derived taxonomies for group structure and visualization types are also applied to group visualizations of edges. We survey group‐only, group–node, group–edge and group–network tasks that are described in the literature as use cases of group visualizations. We discuss results from evaluations of existing visualization techniques as well as main areas of application. Finally, we report future challenges based on interviews we conducted with leading researchers of the field.

Generating visualizations at the size of a word creates dense information representations often called sparklines. The integration of word-sized graphics into text could avoid additional cognitive load caused by splitting the readers' attention between figures and text. In scientific publications, these graphics make statements easier to understand and verify because additional quantitative information is available where needed. In this work, we perform a literature review to find out how researchers have already applied such word-sized representations. Illustrating the versatility of the approach, we leverage these representations for reporting empirical and bibliographic data in three application examples. For interactive Web-based publications, we explore levels of interactivity and discuss interaction patterns to link visualization and text. We finally call the visualization community to be a pioneer in exploring new visualization-enriched and interactive publication formats.

The analysis of eye tracking data often requires the annotation of areas of interest (AOIs) to derive semantic interpretations of human viewing behavior during experiments. This annotation is typically the most time-consuming step of the analysis process. Especially for data from wearable eye tracking glasses, every independently recorded video has to be annotated individually and corresponding AOIs between videos have to be identified. We provide a novel visual analytics approach to ease this annotation process by image-based, automatic clustering of eye tracking data integrated in an interactive labeling and analysis system. The annotation and analysis are tightly coupled by multiple linked views that allow for a direct interpretation of the labeled data in the context of the recorded video stimuli. The components of our analytics environment were developed with a user-centered design approach in close cooperation with an eye tracking expert. We demonstrate our approach with eye tracking data from a real experiment and compare it to an analysis of the data by manual annotation of dynamic AOIs. Furthermore, we conducted an expert user study with 6 external eye tracking researchers to collect feedback and identify analysis strategies they used while working with our application.

Visual search can be time-consuming, especially if the scene contains a large number of possibly relevant objects. An instance of this problem is present when using geographic or schematic maps with many different elements representing cities, streets, sights, and the like. Unless the map is well-known to the reader, the full map or at least large parts of it must be scanned to find the elements of interest. In this paper, we present a controlled eye-tracking study (30 participants) to compare four variants of map annotation with labels: within-image annotations, grid reference annotation, directional annotation, and miniature annotation. Within-image annotation places labels directly within the map without any further search support. Grid reference annotation corresponds to the traditional approach known from atlases. Directional annotation utilizes a label in combination with an arrow pointing in the direction of the label within the map. Miniature annotation shows a miniature grid to guide the reader to the area of the map in which the label is located. The study results show that within-image annotation is outperformed by all other annotation approaches. Best task completion times are achieved with miniature annotation. The analysis of eye-movement data reveals that participants applied significantly different visual task solution strategies for the different visual annotations.

Dimensionality Reduction (DR) is a core building block in visualizing multidimensional data. For DR techniques to be useful in exploratory data analysis, they need to be adapted to human needs and domain-specific problems, ideally, interactively, and on-the-fly. Many visual analytics systems have already demonstrated the benefits of tightly integrating DR with interactive visualizations. Nevertheless, a general, structured understanding of this integration is missing. To address this, we systematically studied the visual analytics and visualization literature to investigate how analysts interact with automatic DR techniques. The results reveal seven common interaction scenarios that are amenable to interactive control such as specifying algorithmic constraints, selecting relevant features, or choosing among several DR algorithms. We investigate specific implementations of visual analysis systems integrating DR, and analyze ways that other machine learning methods have been combined with DR. Summarizing the results in a "human in the loop" process model provides a general lens for the evaluation of visual interactive DR systems. We apply the proposed model to study and classify several systems previously described in the literature, and to derive future research opportunities.

We present a novel uncertain network visualization technique based on node-link diagrams. Nodes expand spatially in our probabilistic graph layout, depending on the underlying probability distributions of edges. The visualization is created by computing a two-dimensional graph embedding that combines samples from the probabilistic graph. A Monte Carlo process is used to decompose a probabilistic graph into its possible instances and to continue with our graph layout technique. Splatting and edge bundling are used to visualize point clouds and network topology. The results provide insights into probability distributions for the entire network-not only for individual nodes and edges. We validate our approach using three data sets that represent a wide range of network types: synthetic data, protein-protein interactions from the STRING database, and travel times extracted from Google Maps. Our approach reveals general limitations of the force-directed layout and allows the user to recognize that some nodes of the graph are at a specific position just by chance.

We investigate task performance and reading characteristics for scatterplots (Cartesian coordinates) and parallel coordinates. In a controlled eye-tracking study, we asked 24 participants to assess the relative distance of points in multidimensional space, depending on the diagram type (parallel coordinates or a horizontal collection of scatterplots), the number of data dimensions (2, 4, 6, or 8), and the relative distance between points (15%, 20%, or 25%). For a given reference point and two target points, we instructed participants to choose the target point that was closer to the reference point in multidimensional space. We present a visual scanning model that describes different strategies to solve this retrieval task for both diagram types, and propose corresponding hypotheses that we test using task completion time, accuracy, and gaze positions as dependent variables. Our results show that scatterplots outperform parallel coordinates significantly in 2 dimensions, however, the task was solved more quickly and more accurately with parallel coordinates in 8 dimensions. The eye-tracking data further shows significant differences between Cartesian and parallel coordinates, as well as between different numbers of dimensions. For parallel coordinates, there is a clear trend toward shorter fixations and longer saccades with increasing number of dimensions. Using an area-of-interest (AOI) based approach, we identify different reading strategies for each diagram type: For parallel coordinates, the participants’ gaze frequently jumped back and forth between pairs of axes, while axes were rarely focused on when viewing Cartesian coordinates. We further found that participants’ attention is biased: toward the center of the whole plotfor parallel coordinates and skewed to the center/left side for Cartesian coordinates. We anticipate that these results may support the design of more effective visualizations for multidimensional data.

In eye tracking studies a complex visual stimulus requires the definition of many areas of interest (AOIs). Often these AOIs have an inherent, nested hierarchical structure that can be utilized to facilitate analysis tasks. We discuss how this hierarchical AOI structure in combination with appropriate visualization techniques can be applied to analyze fixation sequences on differently aggregated levels. An AOI View, AOI Tree, AOI Matrix, and AOI Graph enable a bottom-up and top-down evaluation of fixation sequences. We conducted an expert review and compared our techniques to current state-of-the-art visualization techniques in eye movement research to further improve and extend our approach. To show how our approach is used in practice, we evaluate fixation sequences collected during a study where 101 AOIs are organized hierarchically.

We facilitate the comparative visual analysis of eye tracking data from multiple participants with a visualization that represents the temporal changes of viewing behavior. Common approaches to visually analyze eye tracking data either occlude or ignore the underlying visual stimulus, impairing the interpretation of displayed measures. We introduce fixation-image charts: a new technique to display the temporal changes of fixations in the context of the stimulus without visual overlap between participants. Fixation durations, the distance and direction of saccades between consecutive fixations, as well as the stimulus context can be interpreted in one visual representation. Our technique is not limited to static stimuli, but can be applied to dynamic stimuli as well. Using fixation metrics and the visual similarity of stimulus regions, we complement our visualization technique with an interactive filter concept that allows for the identification of interesting fixation sequences without the time-consuming annotation of areas of interest. We demonstrate how our technique can be applied to different types of stimuli to perform a range of analysis tasks. Furthermore, we discuss advantages and shortcomings derived from a preliminary user study.

In this short paper, we present a lightweight application for the interactive annotation of eye tracking data for both static and dynamic stimuli. The main functionality is the annotation of fixations that takes into account the scanpath and stimulus. Our visual interface allows the annotator to work through a sequence of fixations, while it shows the context of the scanpath in the form of previous and subsequent fixations. The context of the stimulus is included as visual overlay. Our application supports the automatic initial labeling according to areas of interest (AOIs), but is not dependent on AOIs. The software is easily configurable, supports user-defined annotation schemes, and fits in existing workflows of eye tracking experiments and the evaluation thereof by providing import and export functionalities for data files.

Plenty of songs are composed, written, and releasedevery year being recorded in a variety of databases. Thosedo not only store the audio, but also additional data like theartists' names, the years of release, the lengths of the songs, or number of visits, comments, and remarks of visitors andthe like. However, another important data is the lyrics, i.e., thetextual content which can give insights about the topic, genre, or intention of the musicians. Getting an overview about thetextual content of a song, i.e., the lyrics can become a tediouschallenge since listening to the songs or reading the texts is a timeconsuming task. To support users of song databases we propose a visualization tool that is able to generate word clouds from lyrics. Interaction techniques are incorporated in the tool to give more detailed information about the occurrence of words in a song that finally help to find insights about the genre or to just compare the content very rapidly, for example. Our visualization tool is implemented as a web-based interface, that stores requests, updates the local tool database based on those requests, and finally, provides an interactive visualization for the user.

Software is modularized to make its high complexity manageable. However, a multitude of modularization criteria exists and is applied. Hence, to extend, reuse, or restructure a system, it is important for developers to understand which criteria have been used. To this end, we provide an interactive visualization approach that compares the current modularization of a system to several software clustering results. The visualization is based on juxtaposed icicle plot representations of the hierarchical modularizations, encoding similarity by color. A detailed comparison is facilitated by an advanced selection concept. Coupling graphs, which form the basis for software clustering, can be explored on demand in matrix representations. We discuss typical modularization patterns that indicate criteria used for structuring the software or suggest opportunities for partial remodularization of the system. We apply the approach to analyze 16 open source Java projects. The results show that identifying those modularization patterns provides valuable insights and can be done efficiently.

The analysis of inherent structures of movies plays an important role in studying stylistic devices and specific, content-related questions. Examples are the analysis of personal constellations in movie scenes, dialogue-based content analysis, or the investigation of image-based features. We provide a visual analytics approach that supports the analytical reasoning process to derive higher level insights about the content on a semantic level. Combining automatic methods for semantic scene analysis based on script and subtitle text, we perform a low-level analysis of the data automatically. Our approach features an interactive visualization that allows a multilayer interpretation of descriptive features to characterize movie content. For semantic analysis, we extract scene information from movie scripts and match them with the corresponding subtitles. With text- and image-based query techniques, we facilitate an interactive comparison of different movie scenes on an image and on a semantic level. We demonstrate how our approach can be applied for content analysis on a popular Hollywood movie.

Bibliographic data such as collections of scientific articles and citation networks have been studied extensively in information visualization and visual analytics research. Powerful systems have been built to support various types of bibliographic analysis, but they require some training and cannot be used to disseminate the insights gained. In contrast, we focused on developing a more accessible visual analytics system, called SurVis, that is ready to disseminate a carefully surveyed literature collection. The authors of a survey may use our Web-based system to structure and analyze their literature database. Later, readers of the survey can obtain an overview, quickly retrieve specific publications, and reproduce or extend the original bibliographic analysis. Our system employs a set of selectors that enable users to filter and browse the literature collection as well as to control interactive visualizations. The versatile selector concept includes selectors for textual search, filtering by keywords and meta-information, selection and clustering of similar publications, and following citation links. Agreement to the selector is represented by word-sized sparkline visualizations seamlessly integrated into the user interface. Based on an analysis of the analytical reasoning process, we derived requirements for the system. We developed the system in a formative way involving other researchers writing literature surveys. A questionnaire study with 14 visual analytics experts confirms that SurVis meets the initially formulated requirements.

We present a new visualization approach for displaying eye tracking data from multiple participants. We aim to show the spatio-temporal data of the gaze points in the context of the underlying image or video stimulus without occlusion. Our technique, denoted as gaze stripes, does not require the explicit definition of areas of interest but directly uses the image data around the gaze points, similar to thumbnails for images. A gaze stripe consists of a sequence of such gaze point images, oriented along a horizontal timeline. By displaying multiple aligned gaze stripes, it is possible to analyze and compare the viewing behavior of the participants over time. Since the analysis is carried out directly on the image data, expensive post-processing or manual annotation are not required. Therefore, not only patterns and outliers in the participants' scanpaths can be detected, but the context of the stimulus is available as well. Furthermore, our approach is especially well suited for dynamic stimuli due to the non-aggregated temporal mapping. Complementary views, i.e., markers, notes, screenshots, histograms, and results from automatic clustering, can be added to the visualization to display analysis results. We illustrate the usefulness of our technique on static and dynamic stimuli. Furthermore, we discuss the limitations and scalability of our approach in comparison to established visualization techniques.

Graphs are used to model relations between objects, where these objects can be grouped hierarchically based on their connectivity. In many applications, the relations change over time and so does the hierarchical group structure. We developed a visualization technique that supports the analysis of the topology and the hierarchical group structure of a dynamic graph and the tracking of changes over time. Each graph of a sequence is visualized by an adjacency matrix, where the hierarchical group structure is encoded within the matrix using indentation and nested contours, complemented by icicle plots attached to the matrices. The density within and between subgroups of the hierarchy is represented within the matrices using a gray scale. To visualize changes, transitions and dissimilarities between the hierarchically structured graphs are shown using a flow metaphor and color coding. The design of our visualization technique allows us to show more than one hierarchical group structure of the same graph by stacking the sequences, where hierarchy comparison is supported not only within but also between sequences. To improve the readability, we minimize the number of crossing curves within and between sequences based on a sorting algorithm that sweeps through the sequences of hierarchies.

The Digital Bibliography and Library Project (DBLP) is a popular computer science bibliography website hosted at the University of Trier in Germany. It currently contains 2,722,212 computer science publications with additional information about the authors and conferences, journals, or books in which these are published. Although the database covers the majority of papers published in this field of research, it is still hard to browse the vast amount of textual data manually to find insights and correlations in it, in particular time-varying ones. This is also problematic if someone is merely interested in all papers of a specific topic and possible correlated scientific words which may hint at related papers. To close this gap, we propose an interactive tool which consists of two separate components, namely data analysis and data visualization. We show the benefits of our tool and explain how it might be used in a scenario where someone is confronted with the task of writing a state-of-the art report on a specific topic. We illustrate how data analysis, data visualization, and the human user supported by interaction features can work together to find insights which makes typical literature search tasks faster.

Software systems typically consist of many lines of source code organized in several files hierarchically structured into directories and packages. Since the code is the key data in software development, in many scenarios an overview of it is required, in particular for similar code passages. In this paper, we investigate the visual analysis of source code similarities for local as well as global code passages. To this end, we first compute all subsequence occurrence frequencies (support metric) and relative occurrence frequencies (confidence metric) in local as well as global code regions. The resulting textual data attached by its occurrence values is displayed in a triangular matrix. Several interaction techniques are integrated in our visualization tool which are illustrated in the corresponding case study illustrating similarities in source code written in Assembler consisting of 10,641 characters.

Module workflows are used to generate custom applications with modular software frameworks. They describe data flow between the modular components and their execution under certain parameter configurations. In many cases, module workflows are modeled in a graphical way by the user. To come up with the final result or to explore multiple solutions, they often undergo many iterations of adaptation. Furthermore, existing workflows may be reused for new applications. We visualize the evolution of module workflows with a focus-and-context approach and visualization techniques for time-dependent data. Our approach provides insight into user behavior and the characteristics of the underlying systems. As our examples show, this can help identify usability issues and indicate options to improve the effectiveness of the system. We demonstrate our approach for module workflows in Vis Trails, a modular visualization system that allows building custom visualizations by combining different modules for processing and visualizing data.

The visual exploration of spatio-temporal eye movement data is challenging, especially if we are interested in the movement patterns of a large number of study participants. For example, if popular visualization techniques like heat maps or gaze plots are used, we may lose the temporal information or get lost in visual clutter. To address these issues, we propose an approach for filtering saccadic eye movement data called hierarchical filter wheels, which employs a radial representation of saccade information. It supports the analysis of sequences of saccades by filtering them with respect to direction and length. The focus of our approach is a fast initial analysis of data from eye tracking studies without the need of defining areas of interest (AOIs) or other preprocessing of the data. The hierarchical filters are interactively generated on users' demand by creating a hierarchy of multiple filter wheels each filtering one element of the sequence. We use a bubble tree layout to represent the generated filter hierarchy. The node positions in our layout directly represent the spatial properties of the filter criteria allowing an intuitive incremental generation and understanding of filter hierarchies. We illustrate the approach by applying it to eye movement data formerly recorded in an eye tracking study investigating the readability of different node-link tree diagrams. We further demonstrate how the hierarchical filter wheels can be used in combination with gaze plots.

Locating features in large software systems is a fundamental maintenance task for developers when fixing bugs and extending software. We introduce In Situ Impact Insight (I3), a novel user interface to support feature location. In addition to a list of search results, I3 provides support for developers during browsing and inspecting the retrieved code entities. In situ visualizations augment results and source code with additional information relevant for further exploration. Developers are able to retrieve details on the textual similarity of a source code entity to the search query and to other entities, as well as the information on co-changed entities from a project's history. Execution traces recorded during program runs can be used as filters to further refine the search results. We implemented I3 as an Eclipse plug-in and tested it in a user study involving 18 students and professional developers that were asked to perform three feature location tasks chosen from the issue tracking system of jEdit. The results of our study suggest that I3's user interface is intuitive and unobtrusively supports developers with the required information when and where they need it.

Work processes involving dozens or hundreds of collaborators are complex and difficult to manage. Problems within the process may have severe organizational and financial consequences. Visualization helps monitor and analyze those processes. In this paper, we study the development of large software systems as an example of a complex work process. We introduce Developer Rivers, a timeline-based visualization technique that shows how developers work on software modules. The flow of developers' activity is visualized by a river metaphor: activities are transferred between modules represented as rivers. Interactively switching between hierarchically organized modules and workload metrics allows for exploring multiple facets of the work process. We study typical development patterns by applying our visualization to Python and the Linux kernel.

High-throughput and high-resolution experimental methods in biology pose enormous challenges for current biological data visualization approaches. To address these challenges, researchers in the visualization and bioinformatics communities need to engage in the design, implementation, application, and evaluation of novel visualization techniques and tools that provide insight into large and highly complex data sets. BioVis 2015 - the fifth Symposium on Biological Data Visualization - brought together researchers from the visualization, bioinformatics, and biology communities to establish an interdisciplinary dialogue and promote the sharing of expertise between both meeting participants and the communities at large. The meeting educated, inspired, and engaged visualization researchers in problems in biological data visualization as well as bioinformatics and biology researchers in state-of-the-art visualization research. The symposium serves as a platform for researchers from these fields to increase the impact of data visualization approaches in biology. The BioVis 2015 symposium is affiliated with ISMB, the Intelligent Systems for Molecular Biology conference, as a Special Interest Group (SIG) and was colocated with ISMB in Dublin, Ireland, July 10-11 2015. Each paper was reviewed by researchers from both the bioinformatics and visualization fields and was evaluated for improvements over state-of-the-art and for scientific soundness. The review process was organized in two review cycles. In the first review cycle, each paper was reviewed by three to four reviewers. In the second review cycle, the primary reviewers checked whether the required revisions for conditionally accepted papers were successfully included. Based on the reviewers' scores, reviews, and recommendations, the BioVis 2015 Paper and Publication Chairs and the BMC Bioinformatics Section Editor together selected those that would be published as a BMC Bioinformatics supplement. The papers from BioVis 2015 appear in two different proceedings: As of the 5th Symposium on Biological Data Visualization: Part 1 in this BMC Bioinformatics supplement and as of the 5th Symposium on Biological Data Visualization: Part 2 in BMC Proceedings (http://www.biomedcentral.com/bmcproc/supplements/9/S6). From the 21 papers submitted to BioVis 2015, 9 papers are published in this BMC Bioinformatics supplement and 5 papers are published in BMC Proceedings. The articles in this supplement cover a wide spectrum of challenging problems in biological data visualization and their solutions. Overall, three main themes arise from the BioVis 2015 articles: omics, proteins, and imaging. In the omics field, Younesy et al. [1] describe VisRseq: a user-friendly interface for biologists to use libraries in R that provides a method for linking R-apps with interactive components. Chelaru et al. [2] expand on the design behind Epiviz, another tool for bringing genome visualization and computational environments together. Hennig et al. [3] describe Pan-Tetris and Aurisano et al. [4] describe BactoGeNIE: both systems are designed for comparing different genomes. The XCluSim tool by L'Yi et al. [5] has a more general application field and aims to provide insight into how different clustering results relate to each other. In the protein field, Stolte et al. [6] give an overview of the design decisions that underlie Aquaria, a visual analytics tool for exploring protein-related data. Finally, three papers are included from the imaging field. Topics range from image generation, as discussed by Abdellah et al. [7], to a method for parameter optimization in image processing by Pretorius et al. [9] (e.g. for cell nuclei detection and colour deconvolution for histology), and all the way to graph-based exploration of histology images in the GRAPHIE system proposed by Ding et al. [8]. The diversity of topics covered in this issue highlights the wide range of challenges in applying existing visualization techniques to biological data. With this analysis and formalization of our collective experiences, we hope to motivate visualization researchers to think about new problems and new approaches to pressing problems in biology.

BACKGROUND: The interpretation of the results from genome-scale experiments is a challenging and important problem in contemporary biomedical research. Biological networks that integrate experimental results with existing knowledge from biomedical databases and published literature can provide a rich resource and powerful basis for hypothesizing about mechanistic explanations for observed gene-phenotype relationships. However, the size and density of such networks often impede their efficient exploration and understanding. RESULTS: We introduce a visual analytics approach that integrates interactive filtering of dense networks based on degree-of-interest functions with attribute-based layouts of the resulting subnetworks. The comparison of multiple subnetworks representing different analysis facets is facilitated through an interactive super-network that integrates brushing-and-linking techniques for highlighting components across networks. An implementation is freely available as a Cytoscape app. CONCLUSIONS: We demonstrate the utility of our approach through two case studies using a dataset that combines clinical data with high-throughput data for studying the effect of β-blocker treatment on heart failure patients. Furthermore, we discuss our team-based iterative design and development process as well as the limitations and generalizability of our approach.

Abstract We present a robust and efficient method for the two‐way coupling between particle‐based fluid simulations and infinitesimally thin solids represented by triangular meshes. Our approach is based on a hybrid method that combines a repulsion force approach with a continuous intersection handling to guarantee that no penetration occurs. Moreover, boundary conditions for the tangential component of the fluid's velocity are implemented to model the different slip conditions. The proposed method is particularly useful for dynamic surfaces, like cloth and thin shells. In addition, we demonstrate how standard fluid surface reconstruction algorithms can be modified to prevent the calculated surface from intersecting close objects. For both the two‐way coupling and the surface reconstruction, we take into account that the fluid can wet the cloth. We have implemented our approach for the bidirectional interaction between liquid simulations based on Smoothed Particle Hydrodynamics (SPH) and standard mesh‐based cloth simulation systems.

Abstract The community structure of graphs is an important feature that gives insight into the high‐level organization of objects within the graph. In real‐world systems, the graph topology is oftentimes not static but changes over time and hence, also the community structure changes. Previous timeline‐based approaches either visualize the dynamic graph or the dynamic community structure. In contrast, our approach combines both in a single image and therefore allows users to investigate the community structure together with the underlying dynamic graph. Our optimized ordering of vertices and selection of colours in combination with interactive highlighting techniques increases the traceability of communities along the time axis. Users can identify visual signatures, estimate the reliability of the derived community structure and investigate whether community evolution interacts with changes in the graph topology. The utility of our approach is demonstrated in two application examples.

During eye tracking studies, vast amounts of spatio-temporal data in the form of eye gaze trajectories are recorded. Finding insights into these time-varying data sets is a challenging task. Visualization techniques such as heat maps or gaze plots help find patterns in the data but highly aggregate the data (heat maps) or are difficult to read due to overplotting (gaze plots). In this paper, we propose transforming eye movement data into a dynamic graph data structure to explore the visualization problem from a new perspective. By aggregating gaze trajectories of participants over time periods or Areas of Interest (AOIs), a fair trade-off between aggregation and details is achieved. We show that existing dynamic graph visualizations can be used to display the transformed data and illustrate the approach by applying it to eye tracking data recorded for investigating the readability of tree diagrams.

Visualization by heat maps is a powerful technique for showing frequently visited areas in displayed stimuli. However, by aggregating the spatio-temporal data, heat maps lose the information about the transitions between fixations, i.e., the saccades. In gaze plots, instead, trajectories are shown as overplotted polylines, leading to much visual clutter, which makes those diagrams difficult to read. In this paper, we introduce Saccade Plots as a novel technique that combines the benefits of both approaches: it shows the gaze frequencies as a heat map and the saccades in the form of color-coded triangular matrices that surround the heat map. We illustrate the usefulness of our technique by applying it to a representative example from a previously conducted eye tracking study.

We introduce a new design for the visual analysis of eye tracking data recorded from dynamic stimuli such as video. ISeeCube includes multiple coordinated views to support different aspects of various analysis tasks. It combines methods for the spatiotemporal analysis of gaze data recorded from unlabeled videos as well as the possibility to annotate and investigate dynamic Areas of Interest (AOIs). A static overview of the complete data set is provided by a space-time cube visualization that shows gaze points with density-based color mapping and spatiotemporal clustering of the data. A timeline visualization supports the analysis of dynamic AOIs and the viewers' attention on them. AOI-based scanpaths of different viewers can be clustered by their Levenshtein distance, an attention map, or the transitions between AOIs. With the provided visual analytics techniques, the exploration of eye tracking data recorded from several viewers is supported for a wide range of analysis tasks.

We introduce a new design for the visual analysis of eye tracking data recorded from dynamic stimuli such as video. ISeeCube includes multiple coordinated views to support different aspects of various analysis tasks. It combines methods for the spatiotemporal analysis of gaze data recorded from unlabeled videos as well as the possibility to annotate and investigate dynamic Areas of Interest (AOIs). A static overview of the complete data set is provided by a space-time cube visualization that shows gaze points with density-based color mapping and spatiotemporal clustering of the data. A timeline visualization supports the analysis of dynamic AOIs and the viewers' attention on them. AOI-based scanpaths of different viewers can be clustered by their Levenshtein distance, an attention map, or the transitions between AOIs. With the provided visual analytics techniques, the exploration of eye tracking data recorded from several viewers is supported for a wide range of analysis tasks.

Word clouds are a popular means for summarizing text documents. They usually visualize the word frequencies from single text sources, sometimes along with other attributes. However, the visualization of several text documents in one word cloud has rarely been addressed so far. This paper presents Rad Cloud, a technique for text visualization based on multiple word clouds merged into a single view. Inspired by the Rad Viz approach, the words are radially arranged in an overlap-free layout. The text sources are indicated by the spatial word arrangement and stacked bar charts. The approach has been implemented in an interactive text visualization tool and its usefulness is illustrated by an example.

Partially drawn links in graph visualizations have been introduced as a concept for further reducing visual clutter caused by many link crossings in combination to a formerly applied layout algorithm focusing on aesthetic graph drawing criteria. Although this visualization strategy has been shown to be useful for a faster and more accurate visual exploration of node-link diagrams in some scenarios, it has not been integrated into a graph visualization tool as an interaction feature to this end. Apart from representing the entire displayed graph in the partially drawn link style we allow the viewer to apply this feature to several nodes, links, or regions of interest. To avoid possible ambiguities introduced by the disconnectedness of start and target nodes further interaction techniques can be applied to mitigate this situation by showing the complete link information for single selected vertices or edges again.

The visualization of relational data by node-link diagrams quickly leads to a degradation of performance at some exploration tasks when the diagrams show visual clutter and overdraw. To address this challenge of large-data graph visualization, we introduce Graph Metric Views, a technique that enriches the visualization of traditional layout strategies for node-link diagrams by additionally allowing an analyst to interactively explore graph-specific metrics such as number of nodes, number of link crossings, link coverage, or degree of orthogonality. To this end, we support an analyst with additional histogram-like representations at the axes of the display space for graph-specific metrics. In this way, a cluttered and densely packed node-link diagram becomes more explorable even for dense graph regions: The user can use the distribution of metric values as an overview and then select regions of interest for further investigation and filtering.

Dynamic graph visualization techniques can be based on animated or static diagrams showing the evolution over time. In this paper, we apply the concept of small multiples representations to visually illustrate the dynamics of a graph. Node-link diagrams are used as the basic visual metaphor for displaying individual graphs of the sequence. To improve the readability of the diagram and reduce visual clutter we apply an edge splatting technique. Here, we discuss the benefits of splatted radial graph layouts on a modifiable 2D grid. Moreover, to obtain a more scalable dynamic graph visualization we interactively support a graph analyst by a Rapid Serial Visual Presentation (RSVP) feature to rapidly flip between the sequences of displayed graphs. The usefulness of the technique is illustrated in two case studies investigating a dynamic call graph and an evolving social network that consists of more than 1,000 graphs.

Abstract Multi‐dimensional data originate from many different sources and are relevant for many applications. One specific sub‐type of such data is continuous trajectory data in multi‐dimensional state spaces of complex systems. We adapt the concept of spatially continuous scatterplots and spatially continuous parallel coordinate plots to such trajectory data, leading to continuous‐time scatterplots and continuous‐time parallel coordinates. Together with a temporal heat map representation, we design coordinated views for visual analysis and interactive exploration. We demonstrate the usefulness of our visualization approach for three case studies that cover examples of complex dynamic systems: cyber‐physical systems consisting of heterogeneous sensors and actuators networks (the collection of time‐dependent sensor network data of an exemplary smart home environment), the dynamics of robot arm movement and motion characteristics of humanoids.

Abstract Visualization of pathlines is common and highly relevant for the analysis of unsteady flow. However, pathlines can intersect, leading to visual clutter and perceptual issues. This makes it intrinsically difficult to provide expressive visualizations of the entire domain by an arrangement of multiple pathlines, in contrast to well‐established streamline placement techniques. We present an approach to reduce these problems. It is inspired by glyph‐based visualization and small multiples: we partition the domain into cells, each corresponding to a downscaled version of the entire domain. Inside these cells, a single downscaled pathline is drawn. On the overview scale, our pathline glyphs lead to emergent visual patterns that provide insight into time‐dependent flow behavior. Zooming‐in allows us to analyze individual pathlines in detail and compare neighboring lines. The overall approach is complemented with a context‐preserving zoom lens and interactive pathline‐based exploration. While we primarily target the visualization of 2D flow, we also address the extension to 3D. Our evaluation includes several examples, comparison to other flow visualization techniques, and a user study with domain experts.

We introduce a refractive radiative transfer equation to the graphics community for the physically based rendering of participating media that have a spatially varying index of refraction. We review principles of geometric nonlinear optics that are crucial to discuss a more generic light transport equation. In particular, we present an optical model that has an integral form suitable for rendering. We show rigorously that the continuous bending of light rays leads to a nonlinear scaling of radiance. To obtain physically correct results, we build on the concept of basic radiance—known from discontinuous refraction—to conserve energy in such complex media. Furthermore, the generic model accounts for the reduction in the speed of light due to the index of refraction to render transient effects like the propagation of light echoes. We solve the refractive volume rendering equation by extending photon mapping with transient light transport in a refractive, participating medium. We demonstrate the impact of our approach on the correctness of rendered images of media that are dominated by spatially continuous refraction and multiple scattering. Furthermore, our model enables us to render visual effects like the propagation of light echoes or time-of-flight imagery that cannot be produced with previous approaches.

We present a novel and efficient method to compute volumetric soft shadows for interactive direct volume visualization to improve the perception of spatial depth. By direct control of the softness of volumetric shadows, disturbing visual patterns due to hard shadows can be avoided and users can adapt the illumination to their personal and application-specific requirements. We compute the shadowing of a point in the data set by employing spatial filtering of the optical depth over a finite area patch pointing toward each light source. Conceptually, the area patch spans a volumetric region that is sampled with shadow rays; afterward, the resulting optical depth values are convolved with a low-pass filter on the patch. In the numerical computation, however, to avoid expensive shadow ray marching, we show how to align and set up summed area tables for both directional and point light sources. Once computed, the summed area tables enable efficient evaluation of soft shadows for each point in constant time without shadow ray marching and the softness of the shadows can be controlled interactively. We integrated our method in a GPU-based volume renderer with ray casting from the camera, which offers interactive control of the transfer function, light source positions, and viewpoint, for both static and time-dependent data sets. Our results demonstrate the benefit of soft shadows for visualization to achieve user-controlled illumination with many-point lighting setups for improved perception combined with high rendering speed.

We present a visual representation for dynamic, weighted graphs based on the concept of adjacency lists. Two orthogonal axes are used: one for all nodes of the displayed graph, the other for the corresponding links. Colors and labels are employed to identify the nodes. The usage of color allows us to scale the visualization to single pixel level for large graphs. In contrast to other techniques, we employ an asymmetric mapping that results in an aligned and compact representation of links. Our approach is independent of the specific properties of the graph to be visualized, but certain graphs and tasks benefit from the asymmetry. As we show in our results, the strength of our technique is the visualization of dynamic graphs. In particular, sparse graphs benefit from the compact representation. Furthermore, our approach uses visual encoding by size to represent weights and therefore allows easy quantification and comparison. We evaluate our approach in a quantitative user study that confirms the suitability for dynamic and weighted graphs. Finally, we demonstrate our approach for two examples of dynamic graphs.

We present the results of an eye tracking study that compares different visualization methods for long, dense, complex, and piecewise linear spatial trajectories. Typical sources of such data are from temporally discrete measurements of the positions of moving objects, for example, recorded GPS tracks of animals in movement ecology. In the repeated-measures within-subjects user study, four variants of node-link visualization techniques are compared, with the following representations of directed links: standard arrow, tapered, equidistant arrows, and equidistant comets. In addition, we investigate the effect of rendering order for the halo visualization of those links as well as the usefulness of node splatting. All combinations of link visualization techniques are tested for different trajectory density levels. We used three types of tasks: tracing of paths, identification of longest links, and estimation of the density of trajectory clusters. Results are presented in the form of the statistical evaluation of task completion time, task solution accuracy, and two eye tracking metrics. These objective results are complemented by a summary of subjective feedback from the participants. The main result of our study is that tapered links perform very well. However, we discuss that equidistant comets and equidistant arrows are a good option to perceive direction information independent of zoom-level of the display.

We investigate visual task solution strategies when exploring traditional, orthogonal, and radial node-link tree layouts, four orientations of the non-radial layouts, as well as varying difficulty of the task. The strategies are identified by examining eye movement data recorded in a controlled user study previously conducted by Burch et al. For detailed analysis of the spatio-temporal structures and patterns in the eye tracking data, we employ visual analytics techniques adopted from related methodology for geographic movement data by Andrienko et al. In this way, we complement the statistical analysis of task completion times and error rates reported by Burch et al. with spatio-temporal strategies that explain the variation in completion times. We identify differences between task solution strategies dependent on layout type, orientation, and task difficulty. Furthermore, we examine differences between groups of participants split according to completion time. Our analysis identifies that for all layouts it took nearly the same time to find the task solution node, but in the radial layout the solution was not confirmed directly. Instead, a more frequent cross-checking occurs afterwards, which is the main reason for the impaired performance of radial layouts.

Graphs are used to model relations between sets of objects. Objects are represented by vertices and relations by edges of the graph. Besides vertex-vertex relations, in some application domains also relations between edges exist. Our new visualization approach supports the investigation of both relation types in one diagram. Edge-edge relations are visualized as curves that are directly integrated into the node-link diagram that represents the object-relation structure. In contrast, vertex-vertex relations are illustrated distinguishably from edge-edge relations using straight links as representations. While the shape of links is used to differentiate between the relation types, the weights of the edge-edge relations are mapped to the width and color of the curves. To facilitate an extensive analysis of interrelations, our approach incorporates several interaction techniques that can be used for filtering and highlighting. The usability of our visualization is demonstrated with two case studies in the application domains of bioinformatics and financial services.

Tag clouds are a popular way to visually represent word frequencies. However, one major limitation is that they do not relate different word forms but treat every form as an individual tag. This results not only in a non-efficient use of screen space but, in particular, leaves the viewer with no indication whether there are other forms of a word or not. To overcome this limitation, we introduce prefix tag clouds: a visualization technique that uses a prefix tree to group different word forms and visualizes the sub trees as tag cloud. The grouping is emphasized by color, while the relative frequencies of the word forms are indicated by font size. A circular tag cloud layout supports the quick identification of the most frequent words and word forms. We show the usefulness of the approach for a large dataset of paper titles from the computer science bibliography DBLP.

We introduce a technique for bundling edges in graphs where a hierarchical organization of the vertices is not available. Instead of applying time-complex force-directed edge bundling, we adopt the concept of Rapidly-Exploring Random Trees (RRTs). We use RRTs for fast computation of a hierarchical space organization that is independent of the spatial structure of the graph layout. Due to this independency, edge bundling can be applied to any graph layout and even allows us to define spatial obstacles through which no bundles may lead. Furthermore, when adding or removing graph nodes and edges on-the-fly, the bundling structure remains stable, which cannot be guaranteed for force-directed bundling. The main benefit of RRT bundling is its high efficiency, supporting interactive exploration. We rely on the low runtime complexity for a new interaction technique for visual clutter reduction in node-link diagrams that we refer to as the RRT edge bundling lens.

We introduce a matrix-based visualization technique for exploring time-varying directed and weighted graphs. Two overview representations are shown: one for the time-aggregated relations with attached quantitative weighted attributes and one for the results of an automatic dynamic pattern identification algorithm, i.e., relations accompanied by categorical attributes. Apart from a dynamic edge pattern categorization, our tool can also compute graph-specific properties---such as shortest paths or the existence of cliques---and highlight their evolution over time. The visualization method is complemented by interaction techniques that allow the user to navigate, explore, and browse the data, based on the Visual Information Seeking Mantra---overview first, zoom and filter, then details-on-demand. If an additional hierarchical organization of the vertices is available, this is attached to the matrix by vertical and horizontal layered icicle plots allowing one to explore the data on different levels of hierarchical granularity. The usefulness of the tool is demonstrated by applying it to time-varying migration data in the hierarchically structured world.

We propose a novel radial layered matrix visualization for dynamic directed weighted graphs in which the vertices can also be hierarchically organized. Edges are represented as color-coded arcs within the radial diagram. Their positions are defined by polar coordinates instead of Cartesian coordinates as in traditional adjacency matrix representations: the angular position of an edge within an annulus is given by the angle bisector of the two related vertices, the radial position depends linearly on the angular distance between these vertices. The exploration of time-varying relational data is facilitated by aligning graph patterns radially. Furthermore, our approach incorporates several interaction techniques to explore dynamic patterns such as trends and countertrends. The usefulness is illustrated by two case studies analyzing large dynamic call graphs acquired from open source software projects.

Numeric variables are one of the most frequently used data types. During the execution of a program, their values might change often. Tracing these changes can be necessary for understanding specific behavior of the program or for locating bugs. However, using a breakpoint debugger requires tedious stepping, and logging changes implies analyzing large text files. To make the monitoring of numeric variables easier, this work introduces a visualization approach that augments the source code view of an IDE by small, word-sized graphics: the visualizations accompanying the declarations of monitored variables plot read and write accesses on a timeline; detail views can be retrieved on demand. As suggested by a case study, this approach might support program comprehension and debugging.

BACKGROUND: Mathematical models are nowadays widely used to describe biochemical reaction networks. One of the main reasons for this is that models facilitate the integration of a multitude of different data and data types using parameter estimation. Thereby, models allow for a holistic understanding of biological processes. However, due to measurement noise and the limited amount of data, uncertainties in the model parameters should be considered when conclusions are drawn from estimated model attributes, such as reaction fluxes or transient dynamics of biological species. METHODS AND RESULTS: We developed the visual analytics system iVUN that supports uncertainty-aware analysis of static and dynamic attributes of biochemical reaction networks modeled by ordinary differential equations. The multivariate graph of the network is visualized as a node-link diagram, and statistics of the attributes are mapped to the color of nodes and links of the graph. In addition, the graph view is linked with several views, such as line plots, scatter plots, and correlation matrices, to support locating uncertainties and the analysis of their time dependencies. As demonstration, we use iVUN to quantitatively analyze the dynamics of a model for Epo-induced JAK2/STAT5 signaling. CONCLUSION: Our case study showed that iVUN can be used to perform an in-depth study of biochemical reaction networks, including attribute uncertainties, correlations between these attributes and their uncertainties as well as the attribute dynamics. In particular, the linking of different visualization options turned out to be highly beneficial for the complex analysis tasks that come with the biological systems as presented here.

Abstract It is difficult to explore and analyze eye gaze trajectories for commonly applied visual task solution strategies because such data shows complex spatio‐temporal structure. In particular, the traditional eye gaze plots of scan paths fail for a large number of study participants since these plots lead to much visual clutter. To address this problem we introduce the AOI Rivers technique as a novel interactive visualization method for investigating time‐varying fixation frequencies, transitions between areas of interest (AOIs), and the sequential order of gaze visits to AOIs in a visual stimulus of an eye tracking experiment. To this end, we extend the ThemeRiver technique by influents, effluents, and transitions similar to the concept of Sankey diagrams. The AOI Rivers visualization is complemented by linked spatial views of the data in the form of heatmaps, gaze plots, or display of the visual stimulus. The usefulness of our technique is demonstrated for gaze trajectory data recorded in a previously conducted eye tracking experiment.

Abstract It is difficult to create appropriate bar charts for data that cover large value ranges. The usual approach for these cases employs a logarithmic scale, which, however, suffers from issues inherent to its non‐linear mapping: for example, a quantitative comparison of different values is difficult. We present a new approach for bar charts that combines the advantages of linear and logarithmic scales, while avoiding their drawbacks. Our scale‐stack bar charts use multiple scales to cover a large value range, while the linear mapping within each scale preserves the ability to visually compare quantitative ratios. Scale‐stack bar charts can be used for the same applications as classic bar charts; in particular, they can readily handle stacked bar representations and negative values. Our visualization technique is demonstrated with results for three different application areas and is assessed by an expert review and a quantitative user study confirming advantages of our technique for quantitative comparisons.

Abstract We investigate four different variants of attention‐guiding video visualization techniques that aim to help users distribute their attention equally among potential objects of interest: bounding box visualization, force‐directed visualization, top‐down visualization, grid visualization. Objects of interest are highlighted by rectangular shapes and then we concentrate on the manipulation of color, motion, and size. We conducted a controlled laboratory user study (n=25) to compare the four visualization techniques and the unmodified video material as baseline. We evaluated task performance and distribution of attention in a search task. These two properties become especially important when video material with numerous objects has to be observed. The distribution of attention was measured by eye tracking. Our results show that a more even distribution of attention between the objects can be achieved by attention‐guiding visualization, compared to unmodified video. Many participants feel more comfortable when they look at bounding boxes and the grid, but improvements in search task performance could not be confirmed.

We present a scalable technique to explore surveillance videos by scatter/gather browsing of trajectories of moving objects. Trajectories are clustered according to a variety of properties, such as location, orientation, and velocity that can be selected by the users. These properties allow for faceted video exploration and refinement of previous browsing steps. The proposed approach facilitates interactive clustering of trajectories by an effective way of cluster visualization that we term schematic summaries. This novel visualization illustrates cluster summaries in a schematic, nonphotorealistic style. To reduce visual clutter, we introduce the trajectory bundling technique. Further, schematic summaries include a timeline view and a showcase view to represent the facets present in a cluster. The fusion of schematic summaries, a variety of facets, and user interaction lead to efficient hierarchical exploration of video data. Examples of different browsing scenarios and initial user feedback demonstrate the potentials of our method.

We present ambient scattering as a preintegration method for scattering on mesoscopic scales in direct volume rendering. Far-range scattering effects usually provide negligible contributions to a given location due to the exponential attenuation with increasing distance. This motivates our approach to preintegrating multiple scattering within a finite spherical region around any given sample point. To this end, we solve the full light transport with a Monte-Carlo simulation within a set of spherical regions, where each region may have different material parameters regarding anisotropy and extinction. This precomputation is independent of the data set and the transfer function, and results in a small preintegration table. During rendering, the look-up table is accessed for each ray sample point with respect to the viewing direction, phase function, and material properties in the spherical neighborhood of the sample. Our rendering technique is efficient and versatile because it readily fits in existing ray marching algorithms and can be combined with local illumination and volumetric ambient occlusion. It provides interactive volumetric scattering and soft shadows, with interactive control of the transfer function, anisotropy parameter of the phase function, lighting conditions, and viewpoint. A GPU implementation demonstrates the benefits of ambient scattering for the visualization of different types of data sets, with respect to spatial perception, high-quality illumination, translucency, and rendering speed.

We introduce a visual analytics method to analyze eye movement data recorded for dynamic stimuli such as video or animated graphics. The focus lies on the analysis of data of several viewers to identify trends in the general viewing behavior, including time sequences of attentional synchrony and objects with strong attentional focus. By using a space-time cube visualization in combination with clustering, the dynamic stimuli and associated eye gazes can be analyzed in a static 3D representation. Shotbased, spatiotemporal clustering of the data generates potential areas of interest that can be filtered interactively. We also facilitate data drill-down: the gaze points are shown with density-based color mapping and individual scan paths as lines in the space-time cube. The analytical process is supported by multiple coordinated views that allow the user to focus on different aspects of spatial and temporal information in eye gaze data. Common eye-tracking visualization techniques are extended to incorporate the spatiotemporal characteristics of the data. For example, heat maps are extended to motion-compensated heat maps and trajectories of scan paths are included in the space-time visualization. Our visual analytics approach is assessed in a qualitative users study with expert users, which showed the usefulness of the approach and uncovered that the experts applied different analysis strategies supported by the system.

An important feature of networks for many application domains is their community structure. This is because objects within the same community usually have at least one property in common. The investigation of community structure can therefore support the understanding of object attributes from the network topology alone. In real-world systems, objects may belong to several communities at the same time, i.e., communities can overlap. Analyzing fuzzy community memberships is essential to understand to what extent objects contribute to different communities and whether some communities are highly interconnected. We developed a visualization approach that is based on node-link diagrams and supports the investigation of fuzzy communities in weighted undirected graphs at different levels of detail. Starting with the network of communities, the user can continuously drill down to the network of individual nodes and finally analyze the membership distribution of nodes of interest. Our approach uses layout strategies and further visual mappings to graphically encode the fuzzy community memberships. The usefulness of our approach is illustrated by two case studies analyzing networks of different domains: social networking and biological interactions. The case studies showed that our layout and visualization approach helps investigate fuzzy overlapping communities. Fuzzy vertices as well as the different communities to which they belong can be easily identified based on node color and position.

The vast amount of contents posted to microblogging services each day offers a rich source of information for analytical tasks. The aggregated posts provide a broad sense of the informal conversations complementing other media. However, analyzing the textual content is challenging due to its large volume, heterogeneity, and time-dependence. In this paper, we exploit the idea of tag clouds to visually analyze microblog content. As a major contribution, tag clouds are extended by an interactive visualization technique that we refer to as time-varying co-occurrence highlighting. It combines colored histograms with visual highlighting of co-occurrences, thus allowing for a time-dependent analysis of term relations. An example dataset of Twitter posts illustrates the applicability and usefulness of the approach.

Rapid Serial Visual Presentation is an effective approach for browsing and searching large amounts of data. By presenting subsequent images at high frequency, we utilize the perceptual abilities of the human visual system to rapidly process certain visual features. While this concept is successfully used in video and image browsing, we demonstrate how it can be applied to dynamic graph visualization. In this paper, we introduce a visualization technique for time-varying graphs that is scalable with respect to the number of time steps. The graph visualization is based on the Parallel Edge Splatting technique, which employs a space-efficient display of a sequence of dynamically changing graphs. To illustrate the usefulness of our approach we analyzed method call graphs recorded during the execution of the open source software system JHotDraw. Furthermore, we studied a time-varying social network representing researchers and their dynamic communication structure while attending the ACM Hypertext 2009 conference.

In the search for single-nucleotide polymorphisms which influence the observable phenotype, genome wide association studies have become an important technique for the identification of associations between genotype and phenotype of a diverse set of sequence-based data. We present a methodology for the visual assessment of single-nucleotide polymorphisms using interactive hierarchical aggregation techniques combined with methods known from traditional sequence browsers and cluster heatmaps. Our tool, the interactive Hierarchical Aggregation Table (iHAT), facilitates the visualization of multiple sequence alignments, associated metadata, and hierarchical clusterings. Different color maps and aggregation strategies as well as filtering options support the user in finding correlations between sequences and metadata. Similar to other visualizations such as parallel coordinates or heatmaps, iHAT relies on the human pattern-recognition ability for spotting patterns that might indicate correlation or anticorrelation. We demonstrate iHAT using artificial and real-world datasets for DNA and protein association studies as well as expression Quantitative Trait Locus data.

Abstract Magnetic fields exhibit higher‐order, nonlinear singularities in the form of point‐dipole singularities. In addition, due to absence of divergence, they feature only a subset of invariant structures from traditional vector field topology. For magnetic fields of sets of point dipoles—widely present in physics and often used as an approximation—we present a technique revealing the topology of magnetic flux. The flux topology is identified with areas covered by field lines that directly connect pairs of dipoles. We introduce the dipole connectrix as a reduced one‐manifold representation of those areas. The set of connectrices serves as our concise visualization of the global structure of magnetic flux. In addition, the quantitative values of flux are displayed by the thickness of the connectrices. We evaluate our technique for simulations of ferroparticle monolayers and magnetic gels.

Abstract In recent years, a collection of new techniques which deal with video as input data, emerged in computer graphics and visualization. In this survey, we report the state of the art in video‐based graphics and video visualization. We provide a review of techniques for making photo‐realistic or artistic computer‐generated imagery from videos, as well as methods for creating summary and/or abstract visual representations to reveal important features and events in videos. We provide a new taxonomy to categorize the concepts and techniques in this newly emerged body of knowledge. To support this review, we also give a concise overview of the major advances in automated video analysis, as some techniques in this field (e.g. feature extraction, detection, tracking and so on) have been featured in video‐based modelling and rendering pipelines for graphics and visualization.

Abstract Advection has been the standard transport mechanism in flow visualization. Diffusion, in contrast, has not been considered important in visual flow field analysis so far, although it is inherent to many physical processes. We present a novel technique that allows for interactive 3D visualization of both advection and diffusion in unsteady fluid flow. We extend texture‐based flow visualization, which is advection‐oriented, by diffusion. Our finite volume approach based on WENO (weighted essentially non‐oscillatory) reconstruction is well parallelizable and features low numerical diffusion at interactive rates. Our scheme contributes to three different applications: (a) high‐quality dye advection at low numerical diffusion, (b) physically‐based dye advection accounting for diffusivity of virtual media, and (c) visualization of advection‐diffusion fluxes in physical media where the velocity field is accompanied by a concentration field. Interactive rendering of the virtual dye is accomplished by ray casting. We apply our GPU implementation to CFD examples of thermal convection and evaporation phenomena.

Eye movement analysis is gaining popularity as a tool for evaluation of visual displays and interfaces. However, the existing methods and tools for analyzing eye movements and scanpaths are limited in terms of the tasks they can support and effectiveness for large data and data with high variation. We have performed an extensive empirical evaluation of a broad range of visual analytics methods used in analysis of geographic movement data. The methods have been tested for the applicability to eye tracking data and the capability to extract useful knowledge about users' viewing behaviors. This allowed us to select the suitable methods and match them to possible analysis tasks they can support. The paper describes how the methods work in application to eye tracking data and provides guidelines for method selection depending on the analysis tasks.

We evaluate and compare video visualization techniques based on fast-forward. A controlled laboratory user study (n = 24) was conducted to determine the trade-off between support of object identification and motion perception, two properties that have to be considered when choosing a particular fast-forward visualization. We compare four different visualizations: two representing the state-of-the-art and two new variants of visualization introduced in this paper. The two state-of-the-art methods we consider are frame-skipping and temporal blending of successive frames. Our object trail visualization leverages a combination of frame-skipping and temporal blending, whereas predictive trajectory visualization supports motion perception by augmenting the video frames with an arrow that indicates the future object trajectory. Our hypothesis was that each of the state-of-the-art methods satisfies just one of the goals: support of object identification or motion perception. Thus, they represent both ends of the visualization design. The key findings of the evaluation are that object trail visualization supports object identification, whereas predictive trajectory visualization is most useful for motion perception. However, frame-skipping surprisingly exhibits reasonable performance for both tasks. Furthermore, we evaluate the subjective performance of three different playback speed visualizations for adaptive fast-forward, a subdomain of video fast-forward.

For 3D scatterplots, we present an interpolation and projection technique that supports the smooth exchange of one or two data dimensions at a time. Even though this exchange can be considered as a rotation in 4D or 5D data domains, we guarantee that the projection to image space is perceived as a 3D rigid body rotation--with a consistent motion of the data points. We conducted a controlled user study showing that 3D rigid body rotations outperform direct transition between scatterplots. We further extend our technique to support navigation between 3D scatterplots by introducing 3D scatterplot matrices. The usefulness of our approach is demonstrated by application examples, including a case study with a natural language processing expert.

The 3D visualization of astronomical nebulae is a challenging problem since only a single 2D projection is observable from our fixed vantage point on Earth. We attempt to generate plausible and realistic looking volumetric visualizations via a tomographic approach that exploits the spherical or axial symmetry prevalent in some relevant types of nebulae. Different types of symmetry can be implemented by using different randomized distributions of virtual cameras. Our approach is based on an iterative compressed sensing reconstruction algorithm that we extend with support for position-dependent volumetric regularization and linear equality constraints. We present a distributed multi-GPU implementation that is capable of reconstructing high-resolution datasets from arbitrary projections. Its robustness and scalability are demonstrated for astronomical imagery from the Hubble Space Telescope. The resulting volumetric data is visualized using direct volume rendering. Compared to previous approaches, our method preserves a much higher amount of detail and visual variety in the 3D visualization, especially for objects with only approximate symmetry.

We introduce a novel technique for visualizing dense time-varying directed and weighted multi-graphs with an additional hierarchical organization of the graph nodes. Combining Indented Tree Plots and TimeRadarTrees, we show the temporal evolution of relations in a static view. The graph edges are layered around thumbnail wheels consisting of color-coded sectors that are representatives of the graph nodes. These sectors generate implicit representations of graph edges. Start and target vertices are perceived by inspecting the color coding of sectors in the context of other sectors and their orientations. The technique puts emphasis on newer relations and hence, these are mapped to a larger display space in the radial diagram. The benefit of our technique is reduction of visual clutter from which node-link diagrams typically suffer. The visualization focuses on an easy exploration of trends, countertrends, periodicity, temporal shifts, and anomalies in time-varying relational data. We demonstrate the usefulness of the approach by applying it to dense dynamic graph data acquired from a soccer match of the 2D Soccer Simulation League.

We present a new and scalable technique to explore surveillance videos by scatter/gather browsing of trajectories of moving objects. The proposed approach facilitates interactive clustering of trajectories by an effective way of cluster visualization that we term schematic summaries. This novel visualization illustrates cluster summaries in a schematic, non-photorealistic style. To reduce visual clutter, we introduce the trajectory bundling technique. The fusion of schematic summaries and user interaction leads to efficient hierarchical exploration of video data. Examples of different browsing scenarios demonstrate the effectiveness of the proposed method.

Abstract Continuous scatterplots and parallel coordinates are used to visualize multivariate data defined on a continuous domain. With the existing techniques, rendering such plots becomes prohibitively slow, especially for large scientific datasets. This paper presents a scalable and progressive rendering algorithm for continuous data plots that allows exploratory analysis of large datasets at interactive framerates. The algorithm employs splatting to produce a series of plots that are combined using alpha blending to achieve a progressively improving image. For each individual frame, splats are obtained by transforming Gaussian density kernels from the 3‐D domain of the input dataset to the respective data domain. A closed‐form analytic description of the resulting splat footprints is derived to allow pre‐computation of splat textures for efficient GPU rendering. The plotting method is versatile because it supports arbitrary reconstruction or interpolation schemes for the input data and the splatting technique is scalable because it chooses splat samples independently from the size of the input dataset. Finally, the effectiveness of the method is compared to existing techniques regarding rendering performance and quality.

Abstract The parallel vectors (PV) operator is a feature extraction approach for defining line‐type features such as creases (ridges and valleys) in scalar fields, as well as separation, attachment, and vortex core lines in vector fields. In this work, we extend PV feature extraction to higher‐order data represented by piecewise analytical functions defined over grid cells. The extraction uses PV in two distinct stages. First, seed points on the feature lines are placed by evaluating the inclusion form of the PV criterion with reduced affine arithmetic. Second, a feature flow field is derived from the higher‐order PV expression where the features can be extracted as streamlines starting at the seeds. Our approach allows for guaranteed bounds regarding accuracy with respect to existence, position, and topology of the features obtained. The method is suitable for parallel implementation and we present results obtained with our GPU‐based prototype. We apply our method to higher‐order data obtained from discontinuous Galerkin fluid simulations.

Abstract Anaglyph stereo provides a low‐budget solution to viewing stereoscopic images. However, it may suffer from ghosting and bad color reproduction. Here we address the first issue. We present a novel technique to perceptually calibrate an anaglyph stereoscopic system and to use the calibration to eliminate ghosting from the anaglyph image. We build a model based on luminance perception by the left and right eyes through the anaglyph glasses. We do not rely on power spectra of a monitor or on transmission spectra of anaglyph glasses, but show how the five parameters of our model can be captured with just a few measurements within a minute. We present how full color, half color, and gray anaglyphs can be rendered with our technique and compare them to the traditional method.

Node-link diagrams are an effective and popular visualization approach for depicting hierarchical structures and for showing parent-child relationships. In this paper, we present the results of an eye tracking experiment investigating traditional, orthogonal, and radial node-link tree layouts as a piece of empirical basis for choosing between those layouts. Eye tracking was used to identify visual exploration behaviors of participants that were asked to solve a typical hierarchy exploration task by inspecting a static tree diagram: finding the least common ancestor of a given set of marked leaf nodes. To uncover exploration strategies, we examined fixation points, duration, and saccades of participants' gaze trajectories. For the non-radial diagrams, we additionally investigated the effect of diagram orientation by switching the position of the root node to each of the four main orientations. We also recorded and analyzed correctness of answers as well as completion times in addition to the eye movement data. We found out that traditional and orthogonal tree layouts significantly outperform radial tree layouts for the given task. Furthermore, by applying trajectory analysis techniques we uncovered that participants cross-checked their task solution more often in the radial than in the non-radial layouts.

We present a novel dynamic graph visualization technique based on node-link diagrams. The graphs are drawn side-byside from left to right as a sequence of narrow stripes that are placed perpendicular to the horizontal time line. The hierarchically organized vertices of the graphs are arranged on vertical, parallel lines that bound the stripes; directed edges connect these vertices from left to right. To address massive overplotting of edges in huge graphs, we employ a splatting approach that transforms the edges to a pixel-based scalar field. This field represents the edge densities in a scalable way and is depicted by non-linear color mapping. The visualization method is complemented by interaction techniques that support data exploration by aggregation, filtering, brushing, and selective data zooming. Furthermore, we formalize graph patterns so that they can be interactively highlighted on demand. A case study on software releases explores the evolution of call graphs extracted from the JUnit open source software project. In a second application, we demonstrate the scalability of our approach by applying it to a bibliography dataset containing more than 1.5 million paper titles from 60 years of research history producing a vast amount of relations between title words.

THIS special section on Parallel Graphics and Visualization features extended versions of three selected papers from the Eurographics Symposium on Parallel Graphics and Visualization (EGPGV) in 2009. EGPGV 2009 was held in Munich, Germany, from 29-30 March 2009. It was the ninth event of this successful series of symposia, and was colocated with the Eurographics Annual Conference, which took place from 30 March to 3 April 2009. More information on EGPGV and its supporting Eurographics Working Group on Parallel Graphics can be found at http:// www.egpgv.org. EGPGV 2009 received 27 full paper submissions, which were reviewed by an International Program Committee with 23 members and by the three editors of the symposium proceedings (the symposium chair and the two paper cochairs). Each submission received three or more reviews, culminating with a final program that contained 14 papers, for an acceptance rate just short of 52 percent. Accepted papers for EGPGV 2009 covered a healthy range of topics from the fields of both computer graphics and visualization. The topics included simulation, global illumination, rendering, visualization, and general purpose computing on graphics processing units (GPUs), covering a wide variety of parallel computing platforms ranging from multicore to grid computing. Based on the reviewers’ comments and scoring as well as the quality of the oral presentations at EGPGV 2009, a committee that consisted of the proceedings editors and additional members selected three papers to be invited for submission to this special section of the IEEE Transactions on Visualization and Computer Graphics (TVCG). The authors extended their papers to include new additional material. The extended paper then underwent a full journal review process, including multiple cycles of editing and reviewing. The paper “GPU-Based Multilevel Clustering” by Iurie Chiosa and Andreas Kolb addresses the problem of mesh and data clustering. They present an efficient parallel algorithm for multilevel clustering, specifically designed for fast execution on GPUs. They demonstrate that their clustering method is useful for mesh clustering and general data clustering alike. “Parallel Iteration to the Radiative Transport in Inhomogeneous Media with Bootstrapping” by Laszlo SzirmayKalos, Gabor Liktor, Tamas Umenhoffer, Balazs Toth, Shree Kumar, and Glenn Lupton presents a method to solve the radiative transport equation in inhomogeneous participating media. The proposed solution involves running a multiple-scattering solver in parallel on the GPU or across different nodes in a cluster. “Efficient Rasterization for Outdoor Radio Wave Propagation” by Arne Schmitz, Tobias Rick, Thomas Karolski, Torsten Kuhlen, and Leif Kobbelt considers the problem of simulating and propagating radio waves, which is more complex than the analogous light transport problem due to the fact that waves bend around corners because of diffraction. In this work, the authors present a parallel beam tracing solution to this problem. We would like to thank all members of the International Program Committee of EGPGV 2009, the external reviewers for EGPGV 2009, and the reviewers for the extended papers for TVCG for their help. We would also like to take this opportunity to thank Kurt Debattista for his great work as symposium chair and his support and help during the reviewing process of EGPGV 2009, as well as all of the people from the University of Warwick who designed and hosted the symposium Web pages. Finally, we thank the local organizers of the Eurographics Conference, Rudiger Westermann and Joachim Georgii, who were very supportive of local arrangements for EGPGV 2009.

A new type of glyph is introduced to visualize unsteady flow with static images, allowing easier analysis of time-dependent phenomena compared to animated visualization. Adopting the visual metaphor of radar displays, this glyph represents flow directions by angles and time by radius in spherical coordinates. Dense seeding of flow radar glyphs on the flow domain naturally lends itself to multi-scale visualization: zoomed-out views show aggregated overviews, zooming-in enables detailed analysis of spatial and temporal characteristics. Uncertainty visualization is supported by extending the glyph to display possible ranges of flow directions. The paper focuses on 2D flow, but includes a discussion of 3D flow as well. Examples from CFD and the field of stochastic hydrogeology show that it is easy to discriminate regions of different spatiotemporal flow behavior and regions of different uncertainty variations in space and time. The examples also demonstrate that parameter studies can be analyzed because the glyph design facilitates comparative visualization. Finally, different variants of interactive GPU-accelerated implementations are discussed.

This paper presents an acceleration scheme for the numerical computation of sets of trajectories in vector fields or iterated solutions in maps, possibly with simultaneous evaluation of quantities along the curves such as integrals or extrema. It addresses cases with a dense evaluation on the domain, where straightforward approaches are subject to redundant calculations. These are avoided by first calculating short solutions for the whole domain. From these, longer solutions are then constructed in a hierarchical manner until the designated length is achieved. While the computational complexity of the straightforward approach depends linearly on the length of the solutions, the computational cost with the proposed scheme grows only logarithmically with increasing length. Due to independence of subtasks and memory locality, our algorithm is suitable for parallel execution on many-core architectures like GPUs. The trade-offs of the method--lower accuracy and increased memory consumption--are analyzed, including error order as well as numerical error for discrete computation grids. The usefulness and flexibility of the scheme are demonstrated with two example applications: line integral convolution and the computation of the finite-time Lyapunov exponent. Finally, results and performance measurements of our GPU implementation are presented for both synthetic and simulated vector fields from computational fluid dynamics.

This paper generalizes the concept of Lagrangian coherent structures, which is known for its potential to visualize coherent regions in vector fields and to distinguish them from each other. In particular, we extend the concept of the flow map to generic mappings of coordinates. As the major application of this generalization, we present a semiglobal method for visualizing coherent structures in symmetric second order tensor fields. We demonstrate the usefulness by examples from DT-MRI, uncovering anatomical structures in linearly anisotropic regions not amenable to local feature criteria. To further exemplify the suitability of our concept, we also present its application to stress tensor fields. Last, an accelerated implementation utilizing GPUs is presented.

The Body-Centered Cubic (BCC) and Face-Centered Cubic (FCC) lattices have been analytically shown to be more efficient sampling lattices than the traditional Cartesian Cubic (CC) lattice, but there has been no estimate of their visual comparability. Two perceptual studies (each with N = 12 participants) compared the visual quality of images rendered from BCC and FCC lattices to images rendered from the CC lattice. Images were generated from two signals: the commonly used Marschner-Lobb synthetic function and a computed tomography scan of a fish tail. Observers found that BCC and FCC could produce images of comparable visual quality to CC, using 30-35 percent fewer samples. For the images used in our studies, the L(2) error metric shows high correlation with the judgement of human observers. Using the L(2) metric as a proxy, the results of the experiments appear to extend across a wide range of images and parameter choices.

Sort-first distributions have been studied and used far less than sort-last distributions for parallel volume rendering, especially when the data are too large to be replicated fully. We demonstrate that sort-first distributions are not only a viable method of performing data-scalable parallel volume rendering, but more importantly they allow for a range of rendering algorithms and techniques that are not efficient with sort-last distributions. Several of these algorithms are discussed and two of them are implemented in a parallel environment: a new improved variant of early ray termination to speed up rendering when volumetric occlusion occurs and a volumetric shadowing technique that produces more realistic and informative images based on half angle slicing. Improved methods of distributing the computation of the load balancing and loading portions of a subdivided data set are also presented. Our detailed test results for a typical GPU cluster with distributed memory show that our sort-first rendering algorithm outperforms sort-last rendering in many scenarios.

In this paper, we present a visualization and tracking system for coherent structures. For this purpose, we propose to consider shear stress-the stretching and shear of particles inside a flow-in vortex dynamics. Based on a discussion and comparison of recent methods for computing shear stress, we introduce visualization techniques in order to provide a representation of shear layers according to their physical interpretation. This paper contributes a combination of theory in fluid mechanics and the corresponding visualization: 1) shear layer criteria are assessed according to how well they can be combined with common vortex identification criteria; 2) sheets of maximal shear are introduced as an appropriate visual representation of shear layers; 3) a visualization method is described for simultaneous tracking of vortices and shear layers as well as their interaction; and 4) the relevance of shear layers in vortex dynamics is demonstrated by means of several examples. We have implemented these new techniques in an interactive visualization system for time-dependent 3D flow. The system is used by fluid mechanics experts in their research of shear-vortex interaction.

We present a parallel conjugate gradient solver for the Poisson problem optimized for multi-GPU platforms. Our approach includes a novel heuristic Poisson preconditioner well suited for massively-parallel SIMD processing. Furthermore, we address the problem of limited transfer rates over typical data channels such as the PCI-express bus relative to the bandwidth requirements of powerful GPUs. Specifically, naive communication schemes can severely reduce the achievable speedup in such communication-intense algorithms. For this reason, we employ overlapping memory transfers to establish a high level of concurrency and to improve scalability. We have implemented our model on a high-performance workstation with multiple hardware accelerators. We discuss the mathematical principles, give implementation details, and present the performance and the scalability of the system.

Abstract We present a feasibility study on using video visualization to aid snooker skill training. By involving the coaches and players in the loop of intelligent reasoning, our approach addresses the difficulties of automated semantic reasoning, while benefiting from mature video processing techniques. This work was conducted in conjunction with a snooker club and a sports scientist. In particular, we utilized the principal design of the VideoPerpetuoGram (VPG) to convey spatiotemporal information to the viewers through static visualization, removing the burden of repeated video viewing. We extended the VPG design to accommodate the need for depicting multiple video streams and respective temporal attribute fields, including silhouette extrusion, spatial attributes, and non‐spatial attributes. Our results and evaluation have shown that video visualization can provide snooker coaching with visually quantifiable and comparable summary records, and is thus a cost‐effective means for assessing skill levels and monitoring progress objectively and consistently.

Abstract This paper presents an approach to a time‐dependent variant of the concept of vector field topology for 2‐D vector fields. Vector field topology is defined for steady vector fields and aims at discriminating the domain of a vector field into regions of qualitatively different behaviour. The presented approach represents a generalization for saddle‐type critical points and their separatrices to unsteady vector fields based on generalized streak lines, with the classical vector field topology as its special case for steady vector fields. The concept is closely related to that of Lagrangian coherent structures obtained as ridges in the finite‐time Lyapunov exponent field. The proposed approach is evaluated on both 2‐D time‐dependent synthetic and vector fields from computational fluid dynamics.

We extend direct volume rendering with a unified model for generalized isosurfaces, also called interval volumes, allowing a wider spectrum of visual classification. We generalize the concept of scale-invariant opacity—typical for isosurface rendering—to semi-transparent interval volumes. Scale-invariant rendering is independent of physical space dimensions and therefore directly facilitates the analysis of data characteristics. Our model represents sharp isosurfaces as limits of interval volumes and combines them with features of direct volume rendering. Our objective is accurate rendering, guaranteeing that all isosurfaces and interval volumes are visualized in a crack-free way with correct spatial ordering. We achieve simultaneous direct and interval volume rendering by extending preintegration and explicit peak finding with data-driven splitting of ray integration and hybrid computation in physical and data domains. Our algorithm is suitable for efficient parallel processing for interactive applications as demonstrated by our CUDA implementation.

Special relativistic visualization offers the possibility of experiencing the optical effects of traveling near the speed of light, including apparent geometric distortions as well as Doppler and searchlight effects. Early high-quality computer graphics images of relativistic scenes were created using offline, computationally expensive CPU-side 4D ray tracing. Alternate approaches such as image-based rendering and polygon-distortion methods are able to achieve interactivity, but exhibit inferior visual quality due to sampling artifacts. In this paper, we introduce a hybrid rendering technique based on polygon distortion and local ray tracing that facilitates interactive high-quality visualization of multiple objects moving at relativistic speeds in arbitrary directions. The method starts by calculating tight image-space footprints for the apparent triangles of the 3D scene objects. The final image is generated using a single image-space ray tracing step incorporating Doppler and searchlight effects. Our implementation uses GPU shader programming and hardware texture filtering to achieve high rendering speed.

Abstract We extend the rendering technique for continuous scatterplots to allow for a broad class of interpolation methods within the spatial grid instead of only linear interpolation. To do this, we propose an approach that projects the image of a cell from the spatial domain to the scatterplot domain. We approximate this image using either the convex hull or an axis‐aligned rectangle that forms a tight fit of the projected points. In both cases, the approach relies on subdivision in the spatial domain to control the approximation error introduced in the scatterplot domain. Acceleration of this algorithm in homogeneous regions of the spatial domain is achieved using an octree hierarchy. The algorithm is scalable and adaptive since it allows us to balance computation time and scatterplot quality. We evaluate and discuss the results with respect to accuracy and computational speed. Our methods are applied to examples of 2‐D transfer function design.

Abstract We present a design technique for colors with the purpose of lowering the energy consumption of the display device. Our approach is based on a screen space variant energy model. The result of our design is a set of distinguishable iso‐lightness colors guided by perceptual principles. We present two variations of our approach. One is based on a set of discrete user‐named (categorical) colors, which are analyzed according to their energy consumption. The second is based on the constrained continuous optimization of color energy in the perceptually uniform CIELAB color space. We quantitatively compare our two approaches with a traditional choice of colors, demonstrating that we typically save approximately 40 percent of the energy. The color sets are applied to examples from the 2D visualization of nominal data and volume rendering of 3D scalar fields.

In this paper, we propose an experimental study of an inexpensive off-the-shelf sort-last volume visualization architecture based upon multiple GPUs and a single CPU.We show how to efficiently make use of this architecture to achieve high performance sort-last volume visualization of large datasets.We analyze the bottlenecks of this architecture.We compare this architecture to a classical sort-last visualization system using a cluster of commodity machines interconnected by a gigabit Ethernet network.Based on extensive experiments, we show that this solution competes very well with a mid-sized PC cluster, while it significantly improves performance compared to a single standard PC.

Abstract In contrast to 2D scatterplots, the existing 3D variants have the advantage of showing one additional data dimension, but suffer from inadequate spatial and shape perception and therefore are not well suited to display structures of the underlying data. We improve shape perception by applying a new illumination technique to the pointcloud representation of 3D scatterplots. Points are classified as locally linear, planar, and volumetric structures—according to the eigenvalues of the inverse distance‐weighted covariance matrix at each data element. Based on this classification, different lighting models are applied: codimension‐2 illumination, surface illumination, and emissive volumetric illumination. Our technique lends itself to efficient GPU point rendering and can be combined with existing methods like semi‐transparent rendering, halos, and depth or attribute based color coding. The user can interactively navigate in the dataset and manipulate the classification and other visualization parameters. We demonstrate our visualization technique by showing examples of multi‐dimensional data and of generic pointcloud data.

We propose a new perception-guided compositing operator for color blending. The operator maintains the same rules for achromatic compositing as standard operators (such as the over operator), but it modifies the computation of the chromatic channels. Chromatic compositing aims at preserving the hue of the input colors; color continuity is achieved by reducing the saturation of colors that are to change their hue value. The main benefit of hue preservation is that color can be used for proper visual labeling, even under the constraint of transparency rendering or image overlays. Therefore, the visualization of nominal data is improved. Hue-preserving blending can be used in any existing compositing algorithm, and it is particularly useful for volume rendering. The usefulness of hue-preserving blending and its visual characteristics are shown for several examples of volume visualization.

Typical scientific data is represented on a grid with appropriate interpolation or approximation schemes,defined on a continuous domain. The visualization of such data in parallel coordinates may reveal patterns latently contained in the data and thus can improve the understanding of multidimensional relations. In this paper, we adopt the concept of continuous scatterplots for the visualization of spatially continuous input data to derive a density model for parallel coordinates. Based on the point-line duality between scatterplots and parallel coordinates, we propose a mathematical model that maps density from a continuous scatterplot to parallel coordinates and present different algorithms for both numerical and analytical computation of the resulting density field. In addition, we show how the 2-D model can be used to successively construct continuous parallel coordinates with an arbitrary number of dimensions. Since continuous parallel coordinates interpolate data values within grid cells, a scalable and dense visualization is achieved, which will be demonstrated for typical multi-variate scientific data.

Abstract Typically, flow volumes are visualized by defining their boundary as iso‐surface of a level set function. Grid‐based level sets offer a good global representation but suffer from numerical diffusion of surface detail, whereas particle‐based methods preserve details more accurately but introduce the problem of unequal global representation. The particle level set (PLS) method combines the advantages of both approaches by interchanging the information between the grid and the particles. Our work demonstrates that the PLS technique can be adapted to volumetric dye advection via streak volumes, and to the visualization by time surfaces and path volumes. We achieve this with a modified and extended PLS, including a model for dye injection. A new algorithmic interpretation of PLS is introduced to exploit the efficiency of the GPU, leading to interactive visualization. Finally, we demonstrate the high quality and usefulness of PLS flow visualization by providing quantitative results on volume preservation and by discussing typical applications of 3D flow visualization.

Abstract We propose a novel vortex core line extraction method based on the λ2vortex region criterion in order to improve the detection of vortex features for 3D flow visualization. The core line is defined as a curve that connects λ2minima restricted to planes that are perpendicular to the core line. The basic algorithm consists of the following stages: (1) λ2field construction and isosurface extraction; (2) computation of the curve skeleton of the λ2isosurface to build an initial prediction for the core line; (3) correction of the locations of the prediction by searching for λ2minima on planes perpendicular to the core line. In particular, we consider the topology of the vortex core lines, guaranteeing the same topology as the initial curve skeleton. Furthermore, we propose a geometry‐guided definition of vortex bifurcation, which represents the split of one core line into two parts. Finally, we introduce a user‐guided approach in order to narrow down vortical regions taking into account the graph of λ2along the computed vortex core line. We demonstrate the effectiveness of our method by comparing our results to previous core line detection methods with both simulated and experimental data; in particular, we show robustness of our method for noise‐affected data.

Itisoftendesirableornecessarytoperformscientificvisualizationingeographicallyremotelocations,awayfrom thecentralizeddatastoragesystemsthatholdmassiveamountsofscientificresults.Thelargersuchscientific datasetsare,thelesspracticalitistomovethesedatasetstoremotelocationsforcollaborators.Insuchscenarios,efficientremotevisualizationsolutionscanbecrucial.Yettheuseofdistributedorheterogeneouscomputing resourcesraisesseveralchallengesforlarge-scaledatavisualization.Algorithmsmustberobustandincorporate advancedloadbalancingandschedulingtechniques.Inthispaper,weproposeatime-criticalremotevisualization systemthatcanbedeployedoverdistributedandheterogeneouscomputingresources.Weintroducean“importance”metrictomeasuretheneedforprocessingeachdatapartitionbasedonitsdegreeofcontributiontothe finalvisualimage.Factorscontributingtothismetricincludespecificapplicationrequirements,valuedistributionsinsidethedatapartition,andviewingparameters.Weincorporate“visibility”inourmeasurementaswell sothatemptyorinvisibleblockswillnotbeprocessed.Guidedbythedatablocks’importancevalues,ourdynamic schedulingschemedeterminestherenderingpriorityforeachvisibleblock.Thatis,moreimportantblockswillbe renderedfirst.Intime-criticalscenarios,ourschedulingalgorithmalsodynamicallyreducesthelevel-of-detailfor thelessimportantregionssothatvisualizationcanbefinishedinauser-specifiedtimelimitwithhighestpossible imagequality.Thissystemenablesinteractivesharingofvisualizationresults.Toevaluatetheperformanceofthis system,wepresentacasestudyusinga250Gigabytedataseton170distributedprocessors.

This paper introduces orthogonal vector field visualization on 2D manifolds: a representation by lines that are perpendicular to the input vector field. Line patterns are generated by line integral convolution (LIC). This visualization is combined with animation based on motion along the vector field. This decoupling of the line direction from the direction of animation allows us to choose the spatial frequencies along the direction of motion independently from the length scales along the LIC line patterns. Vision research indicates that local motion detectors are tuned to certain spatial frequencies of textures, and the above decoupling enables us to generate spatial frequencies optimized for motion perception. Furthermore, we introduce a combined visualization that employs orthogonal LIC patterns together with conventional, tangential streamline LIC patterns in order to benefit from the advantages of these two visualization approaches. In addition, a filtering process is described to achieve a consistent and temporally coherent animation of orthogonal vector field visualization. Different filter kernels and filter methods are compared and discussed in terms of visualization quality and speed. We present respective visualization algorithms for 2D planar vector fields and tangential vector fields on curved surfaces, and demonstrate that those algorithms lend themselves to efficient and interactive GPU implementations.

Scatterplots are well established means of visualizing discrete data values with two data variables as a collection of discrete points. We aim at generalizing the concept of scatterplots to the visualization of spatially continuous input data by a continuous and dense plot. An example of a continuous input field is data defined on an n-D spatial grid with respective interpolation or reconstruction of in-between values. We propose a rigorous, accurate, and generic mathematical model of continuous scatterplots that considers an arbitrary density defined on an input field on an n-D domain and that maps this density to m-D scatterplots. Special cases are derived from this generic model and discussed in detail: scatterplots where the n-D spatial domain and the m-D data attribute domain have identical dimension, 1-D scatterplots as a way to define continuous histograms, and 2-D scatterplots of data on 3-D spatial grids. We show how continuous histograms are related to traditional discrete histograms and to the histograms of isosurface statistics. Based on the mathematical model of continuous scatterplots, respective visualization algorithms are derived, in particular for 2-D scatterplots of data from 3-D tetrahedral grids. For several visualization tasks, we show the applicability of continuous scatterplots. Since continuous scatterplots do not only sample data at grid points but interpolate data values within cells, a dense and complete visualization of the data set is achieved that scales well with increasing data set size. Especially for irregular grids with varying cell size, improved results are obtained when compared to conventional scatterplots. Therefore, continuous scatterplots are a suitable extension of a statistics visualization technique to be applied to typical data from scientific computation.

One challenge in video processing is to detect actions and events, known or unknown, in video streams dynamically. This paper proposes a visualization solution, where a video stream is depicted as a series of snapshots at a relatively sparse interval, and detected actions are highlighted with continuous abstract illustrations. The combined imagery and illustrative visualization conveys multi-field information in a manner similar to electrocardiograms (ECG) and seismographs. We thus name this type of video visualization as VideoPerpetuoGram (VPG). In this paper, we describe a system that handles the aw and processed information of the video stream in a multi-field visualization pipeline. As examples, we consider the needs for highlighting several types of processed information, including detected actions in video streams, and estimated relationship between recognized objects. We examine the effective means for depicting multi-field information in VPG, and support our choice of visual mappings through a survey. Our GPU implementation facilitates the VPG-specific viewing specification through a sheared object space, as well as volume bricking and combinational rendering of volume data and glyphs.

We propose an output-sensitive visualization method for 3D line integral convolution (LIC) whose rendering speed is largely independent of the data set size and mostly governed by the complexity of the output on the image plane. Our approach of view-dependent visualization tightly links the LIC generation with the volume rendering of the LIC result in order to avoid the computation of unnecessary LIC points: early-ray termination and empty-space leaping techniques are used to skip the computation of the LIC integral in a lazy-evaluation approach; both ray casting and texture slicing can be used as volume-rendering techniques. The input noise is modeled in object space to allow for temporal coherence under object and camera motion. Different noise models are discussed, covering dense representations based on filtered white noise all the way to sparse representations similar to oriented LIC. Aliasing artifacts are avoided by frequency control over the 3D noise and by employing a 3D variant of MIPmapping. A range of illumination models is applied to the LIC streamlines: different codimension-2 lighting models and a novel gradient-based illumination model that relies on precomputed gradients and does not require any direct calculation of gradients after the LIC integral is evaluated. We discuss the issue of proper sampling of the LIC and volume-rendering integrals by employing a frequency-space analysis of the noise model and the precomputed gradients. Finally, we demonstrate that our visualization approach lends itself to a fast graphics processing unit (GPU) implementation that supports both steady and unsteady flow. Therefore, this 3D LIC method allows users to interactively explore 3D flow by means of high-quality, view-dependent, and adaptive LIC volume visualization. Applications to flow visualization in combination with feature extraction and focus-and-context visualization are described, a comparison to previous methods is provided, and a detailed performance analysis is included.

We introduce a novel flow visualization method called Flow Charts, which uses a texture atlas approach for the visualization of flows defined over curved surfaces. In this scheme the surface and its associated flow are segmented into overlapping patches which are then parameterized and packed in the texture domain. This scheme allows accurate particle advection across multiple charts in the texture domain, providing a flexible framework that supports various flow visualization techniques. The use of surface parameterization enables flow visualization techniques requiring the global view of the surface over long time spans, such as Unsteady Flow LIC (UFLIC), particle-based Unsteady Flow Advection-Convolution (UFAC), or dye advection. It also prevents visual artifacts normally associated with view-dependent methods. Represented as textures, Flow Charts can be naturally integrated into GPU flow visualization techniques for interactive performance.

We use a haptically enhanced mixing board with a video projector as an interface to various data visualization tasks. We report results of an expert review with four participants, qualitatively evaluating task), parallel coordinates interface (multi-dimensional combinato-rial search), and ExoVis (3D spatial navigation). Our investigation sought to determine the strengths of this physical input given its ca-pability to facilitate bimanual interaction, constraint maintenance, tight coupling of input and output, and other features. Participants generally had little difficulty with the mappings of parameters to sliders. The graspable sliders apparently reduced the mental exer-tion needed to acquire control, allowing participants to attend more directly to understanding the visualization. Participants often des-ignated specific roles for each hand, but only rarely moved both hands simultaneously.

This paper presents a user study of the visual quality of an imaging pipeline employing the optimal body-centered cubic (BCC) sampling lattice. We provide perceptual evidence supporting the theoretical expectation that sampling and reconstruction on the BCC lattice offer superior imaging quality over the traditionally popular Cartesian cubic (CC) sampling lattice. We asked 12 participants to choose the better of two images: one image rendered from data sampled on the CC lattice and one image that is rendered from data sampled on the BCC lattice. We used both synthetic and CT volumetric data, and confirm that the theoretical advantages of BCC sampling carry over to the perceived quality of rendered images. Using 25% to 35% fewer samples, BCC sampled data result in images that exhibit comparable visual quality to their CC counterparts.

We introduce a point-based algorithm for computing and rendering stream surfaces and path surfaces of a 3D flow. The points are generated by particle tracing, and an even distribution of those particles on the surfaces is achieved by selective particle removal and creation. Texture-based surface flow visualization is added to show inner flow structure on those surfaces. We demonstrate that our visualization method is designed for steady and unsteady flow alike: both the path surface component and the texture-based flow representation are capable of processing time-dependent data. Finally, we show that our algorithms lend themselves to an efficient GPU implementation that allows the user to interactively visualize and explore stream surfaces and path surfaces, even when seed curves are modified and even for time-dependent vector fields.

This paper presents an interactive technique for the dense texture-based visualization of unsteady 3D flow, taking into account issues of computational efficiency and visual perception. High efficiency is achieved by a 3D graphics processing unit (GPU)-based texture advection mechanism that implements logical 3D grid structures by physical memory in the form of 2D textures. This approach results in fast read and write access to physical memory, independent of GPU architecture. Slice-based direct volume rendering is used for the final display. We investigate two alternative methods for the volumetric illumination of the result of texture advection: First, gradient-based illumination that employs a real-time computation of gradients, and, second, line-based lighting based on illumination in codimension 2. In addition to the Phong model, perception-guided rendering methods are considered, such as cool/warm shading, halo rendering, or color-based depth cueing. The problems of clutter and occlusion are addressed by supporting a volumetric importance function that enhances features of the flow and reduces visual complexity in less interesting regions. GPU implementation aspects, performance measurements, and a discussion of results are included to demonstrate our visualization approach.

In this paper we investigate the effects of function composition in the form g(f(x)) = h(x) by means of a spectral analysis of h. We decompose the spectral description of h(x) into a scalar product of the spectral description of g(x) and a term that solely depends on f(x) and that is independent of g(x). We then use the method of stationary phase to derive the essential maximum frequency of g(f(x)) bounding the main portion of the energy of its spectrum. This limit is the product of the maximum frequency of g(x) and the maximum derivative of f(x). This leads to a proper sampling of the composition h of the two functions g and f. We apply our theoretical results to a fundamental open problem in volume rendering-the proper sampling of the rendering integral after the application of a transfer function. In particular, we demonstrate how the sampling criterion can be incorporated in adaptive ray integration, visualization with multi-dimensional transfer functions, and pre-integrated volume rendering.

Video visualization is a computation process that extracts meaningful information from original video data sets and conveys the extracted information to users in appropriate visual representations. This paper presents a broad treatment of the subject, following a typical research pipeline involving concept formulation, system development, a path-finding user study, and a field trial with real application data. In particular, we have conducted a fundamental study on the visualization of motion events in videos. We have, for the first time, deployed flow visualization techniques in video visualization. We have compared the effectiveness of different abstract visual representations of videos. We have conducted a user study to examine whether users are able to learn to recognize visual signatures of motions, and to assist in the evaluation of different visualization techniques. We have applied our understanding and the developed techniques to a set of application video clips. Our study has demonstrated that video visualization is both technically feasible and cost-effective. It has provided the first set of evidence confirming that ordinary users can be accustomed to the visual features depicted in video visualizations, and can learn to recognize visual signatures of a variety of motion events.

This paper describes methods for explanatory and illustrative visualizations used to communicate aspects of Einstein's theories of special and general relativity, their geometric structure, and of the related fields of cosmology and astrophysics. Our illustrations target a general audience of laypersons interested in relativity. We discuss visualization strategies, motivated by physics education and the didactics of mathematics, and describe what kind of visualization methods have proven to be useful for different types of media, such as still images in popular science magazines, film contributions to TV shows, oral presentations, or interactive museum installations. Our primary approach is to adopt an egocentric point of view: The recipients of a visualization participate in a visually enriched thought experiment that allows them to experience or explore a relativistic scenario. In addition, we often combine egocentric visualizations with more abstract illustrations based on an outside view in order to provide several presentations of the same phenomenon. Although our visualization tools often build upon existing methods and implementations, the underlying techniques have been improved by several novel technical contributions like image-based special relativistic rendering on GPUs, special relativistic 4D ray tracing for accelerating scene objects, an extension of general relativistic ray tracing to manifolds described by multiple charts, GPU-based interactive visualization of gravitational light deflection, as well as planetary terrain rendering. The usefulness and effectiveness of our visualizations are demonstrated by reporting on experiences with, and feedback from, recipients of visualizations and collaborators.

This paper presents an interactive technique for the dense texture-based visualization of unsteady 3D flow, taking into account issues of computational efficiency and visual perception. High efficiency is achieved by a novel 3D GPU-based texture advection mechanism that implements logical 3D grid structures by physical memory in the form of 2D textures. This approach results in fast read and write access to physical memory, independent of GPU architecture. Slice-based direct volume rendering is used for the final display. A real-time computation of gradients is employed to achieve volume illumination. Perception-guided volume shading methods are included, such as halos, cool/warm shading, or color-based depth cueing. The problems of clutter and occlusion are addressed by supporting a volumetric importance function that enhances features of the flow and reduces visual complexity in less interesting regions.

In this paper, we present two novel texture-based techniques to visualize uncertainty in time-dependent 2D flow fields. Both methods use semi-Lagrangian texture advection to show flow direction by streaklines and convey uncertainty by blurring these streaklines. The first approach applies a cross advection perpendicular to the flow direction. The second method employs isotropic diffusion that can be implemented by Gaussian filtering. Both methods are derived from a generic filtering process that is incorporated into the traditional texture advection pipeline. Our visualization methods allow for a continuous change of the density of flow representation by adapting the density of particle injection. All methods can be mapped to efficient GPU implementations. Therefore, the user can interactively control all important characteristics of the system like particle density, error influence, or dye injection to create meaningful illustrations of the underlying uncertainty. Even though there are many sources of uncertainties, we focus on uncertainty that occurs during data acquisition. We demonstrate the usefulness of our methods for the example of real-world fluid flow data measured with the particle image velocimetry (PIV) technique. Furthermore, we compare these techniques with an adapted multi-frequency noise approach.

In this application paper, we report on over fifteen years of experience with relativistic and astrophysical visualization, which has been culminating in a substantial engagement for visualization in the Einstein Year 2005 - the 100/sup th/ anniversary of Einstein's publications on special relativity, the photoelectric effect, and Brownian motion. This paper focuses on explanatory and illustrative visualizations used to communicate aspects of the difficult theories of special and general relativity, their geometric structure, and of the related fields of cosmology and astrophysics. We discuss visualization strategies, motivated by physics education and didactics of mathematics, and describe what kind of visualization methods have proven to be useful for different types of media, such as still images in popular-science magazines, film contributions to TV shows, oral presentations, or interactive museum installations. Although our visualization tools build upon existing methods and implementations, these techniques have been improved by several novel technical contributions like image-based special relativistic rendering on GPUs, an extension of general relativistic ray tracing to manifolds described by multiple charts, GPU-based interactive visualization of gravitational light deflection, as well as planetary terrain rendering. The usefulness and effectiveness of our visualizations are demonstrated by reporting on experiences with, and feedback from, recipients of visualizations and collaborators.

We propose a hybrid particle and texture based approach for the visualization of time-dependent vector fields. The underlying space-time framework builds a dense vector field representation in a two-step process: 1) particle-based forward integration of trajectories in spacetime for temporal coherence, and 2) texture-based convolution along another set of paths through the spacetime for spatially correlated patterns. Particle density is controlled by stochastically injecting and removing particles, taking into account the divergence of the vector field. Alternatively, a uniform density can be maintained by placing exactly one particle in each cell of a uniform grid, which leads to particle-in-cell forward advection. Moreover, we discuss strategies of previous visualization methods for unsteady flow and show how they address issues of spatiotemporal coherence and dense visual representations. We demonstrate how our framework is capable of realizing several of these strategies. Finally, we present an efficient GPU implementation that facilitates an interactive visualization of unsteady 2D flow on Shader Model 3 compliant graphics hardware.

3D texture-based volume rendering is a popular way of realizing direct volume visualization on graphics hardware. However, the slice-oriented texture memory layout of many current CPUs may lead to a strongly view-dependent performance, which reduces the fields of application of volume rendering. In this short technical note, we propose a slight modification of texture-based volume rendering that maintains roughly constant frame rates on any GPU architecture. The idea is to split the volume into smaller sub-volumes. These bricks can be oriented in different directions; thus the varying performance for different viewing directions is averaged out

We investigate two important, common fluid flow patterns from computational fluid dynamics (CFD) simulations, namely, swirl and tumble motion typical of automotive engines. We study and visualize swirl and tumble flow using three different flow visualization techniques: direct, geometric, and texture-based. When illustrating these methods side-by-side, we describe the relative strengths and weaknesses of each approach within a specific spatial dimension and across multiple spatial dimensions typical of an engineer's analysis. Our study is focused on steady-state flow. Based on this investigation we offer perspectives on where and when these techniques are best applied in order to visualize the behavior of swirl and tumble motion.

Although luminance contrast plays a predominant role in motion perception, significant additional effects are introduced by chromatic contrasts. In this paper, relevant results from psychophysical and physiological research are described to clarify the role of color in motion detection. Interpreting these psychophysical experiments, we propose guidelines for the design of animated visualizations, and a calibration procedure that improves the reliability of visual motion representation. The guidelines are applied to examples from texture-based flow visualization, as well as graph and tree visualisation.

Abstract Flow visualization has been a very attractive component of scientific visualization research for a long time. Usually very large multivariate datasets require processing. These datasets often consist of a large number of sample locations and several time steps. The steadily increasing performance of computers has recently become a driving factor for a reemergence in flow visualization research, especially in texture‐based techniques. In this paper, dense, texture‐based flow visualization techniques are discussed. This class of techniques attempts to provide a complete, dense representation of the flow field with high spatio‐temporal coherency. An attempt of categorizing closely related solutions is incorporated and presented. Fundamentals are shortly addressed as well as advantages and disadvantages of the methods.

Abstract Dye advection is an intuitive and versatile technique to visualize both steady and unsteady flow. Dye can be easily combined with noise‐based dense vector field representations and is an important element in user‐centric visual exploration processes. However, fast texture‐based implementations of dye advection rely on linear interpolation operations that lead to severe diffusion artifacts. In this paper, a novel approach for dye advection is proposed to avoid this blurring and to achieve long and clearly defined streaklines or extended streak‐like patterns. The interface between dye and background is modeled as a level‐set within a signed distance field. The level‐set evolution is governed by the underlying flow field and is computed by a semi‐Lagrangian method. A reinitialization technique is used to counteract the distortions introduced by the level‐set evolution and to maintain a level‐set function that represents a local distance field. This approach works for 2D and 3D flow fields alike. It is demonstrated how the texture‐based level‐set representation lends itself to an efficient GPU implementation and therefore facilitates interactive visualization. Categories and Subject Descriptors (according to ACM CCS): I.3.3 [Computer Graphics]: Picture/Image Generation I.3.7 [Computer Graphics]: Three‐Dimensional Graphics and Realism

Abstract In this paper, we present a mapping of nonlinear ray tracing to the GPU which avoids any data transfer back to main memory. The rendering process consists of the following parts: ray setup according to the camera parameters, ray integration, ray‐object intersection, and local illumination. Bent rays are approximated by polygonal lines that are represented by textures. Ray integration is based on an iterative numerical solution of ordinary differential equations whose initial values are determined during ray setup. To improve the rendering performance, we propose acceleration techniques such as early ray termination and adaptive ray integration. Finally, we discuss a variety of applications that range from the visualization of dynamical systems to the general relativistic visualization in astrophysics and the rendering of the continuous refraction in media with varying density. Categories and Subject Descriptors (according to ACM CCS): I.3.3 [Computer Graphics]: Picture/Image Generation I.3.7 [Computer Graphics]: Three‐Dimensional Graphics and Realism

We propose unsteady flow advection-convolution (UFAC) as a novel visualization approach for unsteady flows. It performs time evolution governed by pathlines, but builds spatial correlation according to instantaneous streamlines whose spatial extent is controlled by the flow unsteadiness. UFAC is derived from a generic framework that provides spacetime-coherent dense representations of time dependent-vector fields by a two-step process: 1) construction of continuous trajectories in spacetime for temporal coherence; and 2) convolution along another set of paths through the above spacetime for spatially correlated patterns. Within the framework, known visualization techniques-such as Lagrangian-Eulerian advection, image-based flow visualization, unsteady flow LIC, and dynamic LIC-can be reproduced, often with better image quality, higher performance, or increased flexibility of the visualization style. Finally, we present a texture-based discretization of the framework and its interactive implementation on graphics hardware, which allows the user to gradually balance visualization speed against quality.

Abstract In this paper we discuss different approaches to generate cutaway illustrations. The purpose of such a drawingis to allow the viewer to have a look into an otherwise solid opaque object. Traditional methods to draw thesekinds of illustrations are evaluated to extract a small and effective set of rules for a computer‐based renderingof cutaway illustrations. We show that our approaches are not limited to a specific rendering style but can besuccessfully combined with a great variety of well‐known artistic or technical illustration techniques. All methodsof this paper make use of modern graphics hardware functionality to achieve interactive frame rates.

We propose clipping methods that are capable of using complex geometries for volume clipping. The clipping tests exploit per-fragment operations on the graphics hardware to achieve high frame rates. In combination with texture-based volume rendering, these techniques enable the user to interactively select and explore regions of the data set. We present depth-based clipping techniques that analyze the depth structure of the boundary representation of the clip geometry to decide which parts of the volume have to be clipped. In another approach, a voxelized clip object is used to identify the clipped regions. Furthermore, the combination of volume clipping and volume shading is considered. An optical model is introduced to merge aspects of surface-based and volume-based illumination in order to achieve a consistent shading of the clipping surface. It is demonstrated how this model can be efficiently incorporated in the aforementioned clipping techniques.

We propose new clipping methods that are capable of using complex geometries for volume clipping. The clipping tests exploit per-fragment operations on the graphics hardware to achieve high frame rates. In combination with texture-based volume rendering, these techniques enable the user to interactively select and explore regions of the data set. We present depth-based clipping techniques that analyze the depth structure of the boundary representation of the clip geometry to decide which parts of the volume have to be clipped. In another approach, a voxelized clip object is used to identify the clipped regions.

This paper describes how technical illustrations containing opaque and non-opaque objects can be automatically generated. Traditional methods to show transparency in manual drawings are evaluated to extract a small and effective set of rules for computer-based rendering of technical illustrations, leading to a novel view-dependent transparency model. We propose a hardware-accelerated depth sorting algorithm in image-space which specifically meets the requirements of our transparency model. In this way, real-time rendering of semi-transparent technical illustrations is achieved. Finally, it is described how our approach can be combined with other methods in the field of non-photorealistic rendering in order to enhance the visual perception of technical illustrations. Categories and Subject Descriptors (according to ACM CCS): I.3.7 [Computer Graphics]: Color, shading, shadowing and texture

General relativistic ray tracing is presented as a tool for gravitational physics. It is shown how standard three-dimensional ray tracing can be extended to allow for general relativistic visualization. This visualization technique provides images as seen by an observer under the influence of a gravitational field and allows to probe space-time by null geodesics. Moreover, a technique is proposed for visualizing the caustic surfaces generated by a gravitational lens. The suitability of general relativistic ray tracing is demonstrated by means of two examples, namely the visualization of the rigidly rotating disk of dust and the warp drive metric.

This paper describes a novel rendering technique for special relativistic visualization. It is an image-based method which allows to render high speed flights through real-world scenes filmed by a standard camera. The relativistic effects on image generation are determined by the relativistic aberration of light, the Doppler effect, and the searchlight effect. These account for changes of apparent geometry, color and brightness of the objects. It is shown how the relativistic effects can be taken into account by a modification of the plenoptic function. Therefore, all known image-based nonrelativistic rendering methods can easily be extended to incorporate relativistic rendering. Our implementation allows interactive viewing of relativistic panoramas and the production of movies which show super-fast travel. Examples in the form of snapshots and film sequences are included.

We address the issue of illumination and acceleration in special relativistic visualization. Betts (J. Visual. Comput. Animat. 1998; 9: 17–31) presents an incorrect derivation of the transformation of the Rayleigh–Jeans radiation, which we compare to the correct transformation of radiance in the framework of special relativity. His rendering algorithm can be modified to correctly account for the relativistic effects on illumination. Furthermore, we show how acceleration can be included in special relativistic visualization by calculating the trajectory of accelerating objects, which is a prerequisite for a physically based camera model. Therefore interaction and animation in special relativistic visualization are possible. Copyright © 2000 John Wiley & Sons, Ltd.

We demonstrate that a photo-realistic image of a rapidly moving object is dominated by the searchlight and Doppler effects. Using a photon-counting technique, we derive expressions for the relativistic transformation of radiance. We show how to incorportate the Doppler and searchlight effects in the two common techniques of special relativistic visualization, namely ray tracing and polygon rendering. Most authors consider geometrical appearance only and neglect relativistic effects on the lighting model. Chang et al. [1996] present an incorrect derivation of the searchlight effect, which we compare to our results. Some examples are given to show the results of image synthesis with relativistic effects taken into account.