Time series in domains such as climate, traffic, and energy often contain multiple, overlapping periodic patterns. Spiral visualizations can support the exploration of such data, but their effectiveness is limited in practice. Outliers and global trends skew the color mapping, dominant periodic components can hide weaker patterns, selecting a meaningful period length is challenging, and comparing subsequences within large datasets remains cumbersome. To address these challenges, we present a guided analytical workflow centered on an enhanced time series spiral visualization. A regression model tailored to periodic data helps identify suitable period lengths and exposes secondary patterns through its residuals. Visual guidance mitigates issues caused by skewed color mappings and highlights relevant spiral sectors even when global trends or outliers are present. Users can interactively select and compare sectors based on measures of average, trend, and similarity, and examine them in linked views or a provenance dashboard, which maintains a record of all user interactions and allows comparing multiple spirals with each other. Application examples demonstrate use cases where the visual sector selection guidance together with the exploration of model residuals leads to insights. In traffic data, for instance, removing the dominant day–night rhythm reveals rush-hour effects that become visible through exploration of the residuals.

Abstract We introduce HamCat, a novel visualization method for exploring and analyzing multidimensional categorical survey data. Typical visualization approaches for multidimensional categorical data do not support simultaneous analysis of attributes and items, nor do they allow for in‐depth similarity analysis of an entire dataset from the perspective of a specific reference point. HamCat, in contrast, aims to facilitate detailed analysis of multidimensional categorical data across both attributes and items. Our approach builds on the concept of a Hammingball combined with a force‐directed layout to support ego‐centric, user‐steered analysis of inter‐item and inter‐attribute relationships in multidimensional categorical survey data. In addition, our method supports the inclusion and nuanced visualization of missingness. We illustrate the value of HamCat through two case studies. The first case focuses on a survey on wellbeing collected by the European Social Survey, while the second is an expert‐driven study for a survey on sense of belonging in computer science higher education. These case studies show how HamCat complements existing analysis workflows to reveal relationships and item groupings across attributes that are not easily discoverable through conventional means. Supplementary materials for our method are available at https://osf.io/uz2jv/ .

The interactive visual analysis of set-typed data, i.e., data with attributes that are of type set, is a rewarding area of research and applications. Valuable prior work has contributed solutions that enable the study of such data with individual set-typed dimensions. In this paper, we present CrossSet, a novel method for the joint study of two set-typed dimensions and their interplay. Based on a task analysis, we describe a new, multi-scale approach to the interactive visual exploration and analysis of such data. Two set-typed data dimensions are jointly visualized using a hierarchical matrix layout, enabling the analysis of the interactions between two set-typed attributes at several levels, in addition to the analysis of individual such dimensions. CrossSet is anchored at a compact, large-scale overview that is complemented by drill-down opportunities to study the relations between and within the set-typed dimensions, enabling an interactive visual multi-scale exploration and analysis of bivariate set-typed data. Such an interactive approach makes it possible to study single set-typed dimensions in detail, to gain an overview of the interaction and association between two such dimensions, to refine one of the dimensions to gain additional details at several levels, and to drill down to the specific interactions of individual set-elements from the set-typed dimensions. To demonstrate the effectiveness and efficiency of CrossSet, we have evaluated the new method in the context of several application scenarios.

The optimization of cooling systems is important in many cases, for example for cabin and battery cooling in electric cars. Such an optimization is governed by multiple, conflicting objectives and it is performed across a multi-dimensional parameter space. The extent of the parameter space, the complexity of the non-linear model of the system, as well as the time needed per simulation run and factors that are not modeled in the simulation necessitate an iterative, semi-automatic approach. We present an interactive visual optimization approach, where the user works with a p-h diagram to steer an iterative, guided optimization process. A deep learning (DL) model provides estimates for parameters, given a target characterization of the system, while numerical simulation is used to compute system characteristics for an ensemble of parameter sets. Since the DL model only serves as an approximation of the inverse of the cooling system and since target characteristics can be chosen according to different, competing objectives, an iterative optimization process is realized, developing multiple sets of intermediate solutions, which are visually related to each other. The standard p-h diagram, integrated interactively in this approach, is complemented by a dual, also interactive visual representation of additional expressive measures representing the system characteristics. We show how the known four-points semantic of the p-h diagram meaningfully transfers to the dual data representation. When evaluating this approach in the automotive domain, we found that our solution helped with the overall comprehension of the cooling system and that it lead to a faster convergence during optimization.

This issue marks the start of a new volume of Computer Graphics Forum (CGF,

Numerical simulation has become omnipresent in the automotive domain, posing new challenges such as high-dimensional parameter spaces and large as well as incomplete and multi-faceted data. In this design study, we show how interactive visual exploration and analysis of high-dimensional, spectral data from noise simulation can facilitate design improvements in the context of conflicting criteria. Here, we focus on structure-borne noise, i.e., noise from vibrating mechanical parts. Detecting problematic noise sources early in the design and production process is essential for reducing a product's development costs and its time to market. In a close collaboration of visualization and automotive engineering, we designed a new, interactive approach to quickly identify and analyze critical noise sources, also contributing to an improved understanding of the analyzed system. Several carefully designed, interactive linked views enable the exploration of noises, vibrations, and harshness at multiple levels of detail, both in the frequency and spatial domain. This enables swift and smooth changes of perspective; selections in the frequency domain are immediately reflected in the spatial domain, and vice versa. Noise sources are quickly identified and shown in the context of their neighborhood, both in the frequency and spatial domain. We propose a novel drill-down view, especially tailored to noise data analysis. Split boxplots and synchronized 3D geometry views support comparison tasks. With this solution, engineers iterate over design optimizations much faster, while maintaining a good overview at each iteration. We evaluated the new approach in the automotive industry, studying noise simulation data for an internal combustion engine.

Abstract Combining elements of biology, chemistry, physics, and medicine, the science of human physiology is complex and multifaceted. In this report, we offer a broad and multiscale perspective on key developments and challenges in visualization for physiology. Our literature search process combined standard methods with a state‐of‐the‐art visual analysis search tool to identify surveys and representative individual approaches for physiology. Our resulting taxonomy sorts literature on two levels. The first level categorizes literature according to organizational complexity and ranges from molecule to organ. A second level identifies any of three high‐level visualization tasks within a given work: exploration, analysis, and communication. The findings of this report may be used by visualization researchers to understand the overarching trends, challenges, and opportunities in visualization for physiology and to provide a foundation for discussion and future research directions in this area.

Sketching is one common approach to query time series data for patterns of interest. Most existing solutions for matching the data with the interaction are based on an empirically modeled similarity function between the user's sketch and the time series data with limited efficiency and accuracy. In this article, we introduce a machine learning based solution for fast and accurate querying of time series data based on a swift sketching interaction. We build on existing LSTM technology (long short-term memory) to encode both the sketch and the time series data in a network with shared parameters. We use data from a user study to let the network learn a proper similarity function. We focus our approach on perceived similarities and achieve that the learned model also includes a user-side aspect. To the best of our knowledge, this is the first data-driven solution for querying time series data in visual analytics. Besides evaluating the accuracy and efficiency directly in a quantitative way, we also compare our solution to the recently published Qetch algorithm as well as the commonly used dynamic time warping (DTW) algorithm.

The identification of interesting patterns and relationships is essential to exploratory data analysis. This becomes increasingly difficult in high dimensional datasets. While dimensionality reduction techniques can be utilized to reduce the analysis space, these may unintentionally bury key dimensions within a larger grouping and obfuscate meaningful patterns. With this work we introduce DimLift, a novel visual analysis method for creating and interacting with dimensional bundles. Generated through an iterative dimensionality reduction or user-driven approach, dimensional bundles are expressive groups of dimensions that contribute similarly to the variance of a dataset. Interactive exploration and reconstruction methods via a layered parallel coordinates plot allow users to lift interesting and subtle relationships to the surface, even in complex scenarios of missing and mixed data types. We exemplify the power of this technique in an expert case study on clinical cohort data alongside two additional case examples from nutrition and ecology.

The Dual Analysis framework is a powerful enabling technology for the exploration of high dimensional quantitative data by treating data dimensions as first-class objects that can be explored in tandem with data values. In this article, we extend the Dual Analysis framework through the joint treatment of quantitative (numerical) and qualitative (categorical) dimensions. Computing common measures for all dimensions allows us to visualize both quantitative and qualitative dimensions in the same view. This enables a natural joint treatment of mixed data during interactive visual exploration and analysis. Several measures of variation for nominal qualitative data can also be applied to ordinal qualitative and quantitative data. For example, instead of measuring variability from a mean or median, other measures assess inter-data variation or average variation from a mode. In this work, we demonstrate how these measures can be integrated into the Dual Analysis framework to explore and generate hypotheses about high-dimensional mixed data. A medical case study using clinical routine data of patients suffering from Cerebral Small Vessel Disease (CSVD), conducted with a senior neurologist and a medical student, shows that a joint Dual Analysis approach for quantitative and qualitative data can rapidly lead to new insights based on which new hypotheses may be generated.

Empirical models, fitted to data from observations, are often used in natural sciences to describe physical behaviour and support discoveries. However, with more complex models, the regression of parameters quickly becomes insufficient, requiring a visual parameter space analysis to understand and optimize the models. In this work, we present a design study for building a model describing atmospheric convection. We present a mixed-initiative approach to visually guided modelling, integrating an interactive visual parameter space analysis with partial automatic parameter optimization. Our approach includes a new, semi-automatic technique called IsoTrotting, where we optimize the procedure by navigating along isocontours of the model. We evaluate the model with unique observational data of atmospheric convection based on flight trajectories of paragliders.

When studying multi-body protein complexes, biochemists use computational tools that can suggest hundreds or thousands of their possible spatial configurations. However, it is not feasible to experimentally verify more than only a very small subset of them. In this paper, we propose a novel multiscale visual drilldown approach that was designed in tight collaboration with proteomic experts, enabling a systematic exploration of the configuration space. Our approach takes advantage of the hierarchical structure of the data - from the whole ensemble of protein complex configurations to the individual configurations, their contact interfaces, and the interacting amino acids. Our new solution is based on interactively linked 2D and 3D views for individual hierarchy levels. At each level, we offer a set of selection and filtering operations that enable the user to narrow down the number of configurations that need to be manually scrutinized. Furthermore, we offer a dedicated filter interface, which provides the users with an overview of the applied filtering operations and enables them to examine their impact on the explored ensemble. This way, we maintain the history of the exploration process and thus enable the user to return to an earlier point of the exploration. We demonstrate the effectiveness of our approach on two case studies conducted by collaborating proteomic experts.

Understanding large amounts of spatiotemporal data from particle-based simulations, such as molecular dynamics, often relies on the computation and analysis of aggregate measures. These, however, by virtue of aggregation, hide structural information about the space/time localization of the studied phenomena. This leads to degenerate cases where the measures fail to capture distinct behaviour. In order to drill into these aggregate values, we propose a multi-scale visual exploration technique. Our novel representation, based on partial domain aggregation, enables the construction of a continuous scale-space for discrete datasets and the simultaneous exploration of scales in both space and time. We link these two scale-spaces in a scale-space space-time cube and model linked views as orthogonal slices through this cube, thus enabling the rapid identification of spatio-temporal patterns at multiple scales. To demonstrate the effectiveness of our approach, we showcase an advanced exploration of a protein-ligand simulation.

In many cases, protein reactions with other small molecules (ligands) occur in a deeply buried active site. When studying these types of reactions, it is crucial for biochemists to examine trajectories of ligand motion. These trajectories are predicted with in-silico methods that produce large ensembles of possible trajectories. In this paper, we propose a novel approach to the interactive visual exploration and analysis of large sets of ligand trajectories, enabling the domain experts to understand protein function based on the trajectory properties. The proposed solution is composed of multiple linked 2D and 3D views, enabling the interactive exploration and filtering of trajectories in an informed way. In the workflow, we focus on the practical aspects of the interactive visual analysis specific to ligand trajectories. We adapt the small multiples principle to resolve an overly large number of trajectories into smaller chunks that are easier to analyze. We describe how drill-down techniques can be used to create and store selections of the trajectories with desired properties, enabling the comparison of multiple datasets. In appropriately designed 2D and 3D views, biochemists can either observe individual trajectories or choose to aggregate the information into a functional boxplot or density visualization. Our solution is based on a tight collaboration with the domain experts, aiming to address their needs as much as possible. The usefulness of our novel approach is demonstrated by two case studies, conducted by the collaborating protein engineers.

Abstract Hierarchical embeddings, such as HSNE, address critical visual and computational scalability issues of traditional techniques for dimensionality reduction. The improved scalability comes at the cost of the need for increased user interaction for exploration. In this paper, we provide a solution for the interactive visual Focus+Context exploration of such embeddings. We explain how to integrate embedding parts from different levels of detail, corresponding to focus and context groups, in a joint visualization. We devise an according interaction model that relates typical semantic operations on a Focus+Context visualization with the according changes in the level‐of‐detail‐hierarchy of the embedding, including also a mode for comparative Focus+Context exploration and extend HSNE to incorporate the presented interaction model. In order to demonstrate the effectiveness of our approach, we present a use case based on the visual exploration of multi‐dimensional images.

Abstract Brushing plays a central role in most modern visual analytics solutions and effective and efficient techniques for data selection are key to establishing a successful human‐computer dialogue. With this paper, we address the need for brushing techniques that are bothfast, enabling a fluid interaction in visual data exploration and analysis, and alsoaccurate, i.e., enabling the user to effectively select specific data subsets, even when their geometric delimination is non‐trivial. We present a new solution for a near‐perfect sketch‐based brushing technique, where we exploit a convolutional neural network (CNN) for estimating the intended data selection from a fast and simple click‐and‐drag interaction and from the data distribution in the visualization. Our key contributions include a drastically reduced error rate—now below 3%, i.e., less than half of the so far best accuracy—and an extension to a larger variety of selected data subsets, going beyond previous limitations due to linear estimation models.

BACKGROUND: Protein structures and their interaction with ligands have been in the focus of biochemistry and structural biology research for decades. The transportation of ligand into the protein active site is often complex process, driven by geometric and physico-chemical properties, which renders the ligand path full of jitter and impasses. This prevents understanding of the ligand transportation and reasoning behind its behavior along the path. RESULTS: To address the needs of the domain experts we design an explorative visualization solution based on a multi-scale simplification model. It helps to navigate the user to the most interesting parts of the ligand trajectory by exploring different attributes of the ligand and its movement, such as its distance to the active site, changes of amino acids lining the ligand, or ligand "stuckness". The process is supported by three linked views - 3D representation of the simplified trajectory, scatterplot matrix, and bar charts with line representation of ligand-lining amino acids. CONCLUSIONS: The usage of our tool is demonstrated on molecular dynamics simulations provided by the domain experts. The tool was tested by the domain experts from protein engineering and the results confirm that it helps to navigate the user to the most interesting parts of the ligand trajectory and to understand the ligand behavior.

BACKGROUND: Protein function is determined by many factors, namely by its constitution, spatial arrangement, and dynamic behavior. Studying these factors helps the biochemists and biologists to better understand the protein behavior and to design proteins with modified properties. One of the most common approaches to these studies is to compare the protein structure with other molecules and to reveal similarities and differences in their polypeptide chains. RESULTS: We support the comparison process by proposing a new visualization technique that bridges the gap between traditionally used 1D and 3D representations. By introducing the information about mutual positions of protein chains into the 1D sequential representation the users are able to observe the spatial differences between the proteins without any occlusion commonly present in 3D view. Our representation is designed to serve namely for comparison of multiple proteins or a set of time steps of molecular dynamics simulation. CONCLUSIONS: The novel representation is demonstrated on two usage scenarios. The first scenario aims to compare a set of proteins from the family of cytochromes P450 where the position of the secondary structures has a significant impact on the substrate channeling. The second scenario focuses on the protein flexibility when by comparing a set of time steps our representation helps to reveal the most dynamically changing parts of the protein chain.

The study of spatial data ensembles leads to substantial visualization challenges in a variety of applications. In this paper, we present a model for comparative visualization that supports the design of according ensemble visualization solutions by partial automation. We focus on applications, where the user is interested in preserving selected spatial data characteristics of the data as much as possible-even when many ensemble members should be jointly studied using comparative visualization. In our model, we separate the design challenge into a minimal set of user-specified parameters and an optimization component for the automatic configuration of the remaining design variables. We provide an illustrated formal description of our model and exemplify our approach in the context of several application examples from different domains in order to demonstrate its generality within the class of comparative visualization problems for spatial data ensembles.

In interactive data analysis processes, the dialogue between the human and the computer is the enabling mechanism that can lead to actionable observations about the phenomena being investigated. It is of paramount importance that this dialogue is not interrupted by slow computational mechanisms that do not consider any known temporal human-computer interaction characteristics that prioritize the perceptual and cognitive capabilities of the users. In cases where the analysis involves an integrated computational method, for instance to reduce the dimensionality of the data or to perform clustering, such non-optimal processes are often likely. To remedy this, progressive computations, where results are iteratively improved, are getting increasing interest in visual analytics. In this paper, we present techniques and design considerations to incorporate progressive methods within interactive analysis processes that involve high-dimensional data. We define methodologies to facilitate processes that adhere to the perceptual characteristics of users and describe how online algorithms can be incorporated within these. A set of design recommendations and according methods to support analysts in accomplishing high-dimensional data analysis tasks are then presented. Our arguments and decisions here are informed by observations gathered over a series of analysis sessions with analysts from finance. We document observations and recommendations from this study and present evidence on how our approach contribute to the efficiency and productivity of interactive visual analysis sessions involving high-dimensional data.

Comparing time surfaces at different integration time points, or from different seeding areas, can provide valuable insight into transport phenomena of fluid flows. Such a comparative study is challenging due to the often convoluted shapes of these surfaces. We propose a new approach for comparative flow visualization based on time surfaces, which exploits the idea of embedding the surfaces in a carefully designed, reformed 2D visualization space. Such an embedding enables new opportunities for comparative flow visualization. We present three different strategies for comparative flow visualization that take advantage of the reformation. By reforming the time surfaces, we not only mitigate occlusion issues, but we can devote also the third dimension of the visualization space to the comparative aspects of the visualization. Our approach is effective in a variety of flow study cases. The direct comparison of individual time surfaces reveals small scale differences and fine details about the fluid's motion. The concurrent study of multiple surface families enables the identification and the comparison of the most prominent motion patterns. This work was developed in close collaboration with an expert in fluid dynamics, who assessed the potential usefulness of this approach in his field.

Abstract Sets comprise a generic data model that has been used in a variety of data analysis problems. Such problems involve analysing and visualizing set relations between multiple sets defined over the same collection of elements. However, visualizing sets is a non‐trivial problem due to the large number of possible relations between them. We provide a systematic overview of state‐of‐the‐art techniques for visualizing different kinds of set relations. We classify these techniques into six main categories according to the visual representations they use and the tasks they support. We compare the categories to provide guidance for choosing an appropriate technique for a given problem. Finally, we identify challenges in this area that need further research and propose possible directions to address these challenges. Further resources on set visualization are available at http://www.setviz.net .

Abstract Until now a lot of visual analytics predominantly delivers qualitative results—based, for example, on a continuous color map or a detailed spatial encoding. Important target applications, however, such as medical diagnosis and decision making, clearly benefit from quantitative analysis results. In this paper we propose several specific extensions to the well‐established concept of linking&brushing in order to make the analysis results more quantitative. We structure the brushing space in order to improve the reproducibility of the brushing operation, e.g., by introducing the percentile grid. We also enhance the linked visualization with overlaid descriptive statistics to enable a more quantitative reading of the resulting focus+context visualization. Additionally, we introduce two novel brushing techniques: the percentile brush and the Mahalanobis brush. Both use the underlying data to support statistically meaningful interactions with the data. We illustrate the use of the new techniques in the context of two case studies, one based on meteorological data and the other one focused on data from the automotive industry where we evaluate a shaft design in the context of mechanical power transmission in cars.

BACKGROUND: Research in cell biology is steadily contributing new knowledge about many aspects of physiological processes, both with respect to the involved molecular structures as well as their related function. Illustrations of the spatio-temporal development of such processes are not only used in biomedical education, but also can serve scientists as an additional platform for in-silico experiments. RESULTS: In this paper, we contribute a new, three-level modeling approach to illustrate physiological processes from the class of polymerization at different time scales. We integrate physical and empirical modeling, according to which approach best suits the different involved levels of detail, and we additionally enable a form of interactive steering, while the process is illustrated. We demonstrate the suitability of our approach in the context of several polymerization processes and report from a first evaluation with domain experts. CONCLUSION: We conclude that our approach provides a new, hybrid modeling approach for illustrating the process of emergence in physiology, embedded in a densely filled environment. Our approach of a complementary fusion of three systems combines the strong points from the different modeling approaches and is capable to bridge different spatial and temporal scales.

Multi-class classifiers often compute scores for the classification samples describing probabilities to belong to different classes. In order to improve the performance of such classifiers, machine learning experts need to analyze classification results for a large number of labeled samples to find possible reasons for incorrect classification. Confusion matrices are widely used for this purpose. However, they provide no information about classification scores and features computed for the samples. We propose a set of integrated visual methods for analyzing the performance of probabilistic classifiers. Our methods provide insight into different aspects of the classification results for a large number of samples. One visualization emphasizes at which probabilities these samples were classified and how these probabilities correlate with classification error in terms of false positives and false negatives. Another view emphasizes the features of these samples and ranks them by their separation power between selected true and false classifications. We demonstrate the insight gained using our technique in a benchmarking classification dataset, and show how it enables improving classification performance by interactively defining and evaluating post-classification rules.

In this paper we propose a novel approach to hybrid visual steering of simulation ensembles. A simulation ensemble is a collection of simulation runs of the same simulation model using different sets of control parameters. Complex engineering systems have very large parameter spaces so a naïve sampling can result in prohibitively large simulation ensembles. Interactive steering of simulation ensembles provides the means to select relevant points in a multi-dimensional parameter space (design of experiment). Interactive steering efficiently reduces the number of simulation runs needed by coupling simulation and visualization and allowing a user to request new simulations on the fly. As system complexity grows, a pure interactive solution is not always sufficient. The new approach of hybrid steering combines interactive visual steering with automatic optimization. Hybrid steering allows a domain expert to interactively (in a visualization) select data points in an iterative manner, approximate the values in a continuous region of the simulation space (by regression) and automatically find the "best" points in this continuous region based on the specified constraints and objectives (by optimization). We argue that with the full spectrum of optimization options, the steering process can be improved substantially. We describe an integrated system consisting of a simulation, a visualization, and an optimization component. We also describe typical tasks and propose an interactive analysis workflow for complex engineering systems. We demonstrate our approach on a case study from automotive industry, the optimization of a hydraulic circuit in a high pressure common rail Diesel injection system.

The visual analysis of geographically referenced datasets with a large number of attributes is challenging due to the fact that the characteristics of the attributes are highly dependent upon the locations at which they are focussed, and the scale and time at which they are measured. Specialized interactive visual methods are required to help analysts in understanding the characteristics of the attributes when these multiple aspects are considered concurrently. Here, we develop attribute signatures-interactively crafted graphics that show the geographic variability of statistics of attributes through which the extent of dependency between the attributes and geography can be visually explored. We compute a number of statistical measures, which can also account for variations in time and scale, and use them as a basis for our visualizations. We then employ different graphical configurations to show and compare both continuous and discrete variation of location and scale. Our methods allow variation in multiple statistical summaries of multiple attributes to be considered concurrently and geographically, as evidenced by examples in which the census geography of London and the wider UK are explored.

In many applications, data tables contain multi-valued attributes that often store the memberships of the table entities to multiple sets such as which languages a person masters, which skills an applicant documents, or which features a product comes with. With a growing number of entities, the resulting element-set membership matrix becomes very rich of information about how these sets overlap. Many analysis tasks targeted at set-typed data are concerned with these overlaps as salient features of such data. This paper presents Radial Sets, a novel visual technique to analyze set memberships for a large number of elements. Our technique uses frequency-based representations to enable quickly finding and analyzing different kinds of overlaps between the sets, and relating these overlaps to other attributes of the table entities. Furthermore, it enables various interactions to select elements of interest, find out if they are over-represented in specific sets or overlaps, and if they exhibit a different distribution for a specific attribute compared to the rest of the elements. These interactions allow formulating highly-expressive visual queries on the elements in terms of their set memberships and attribute values. As we demonstrate via two usage scenarios, Radial Sets enable revealing and analyzing a multitude of overlapping patterns between large sets, beyond the limits of state-of-the-art techniques.

The papers in this special section are extended versions of three selected papers from the IEEE Pacific Visualization Symposium 2012 (PacificVis) which took place in Songdo, Korea from 28 February to 2 March 2012.

Visualization and visual analysis play important roles in exploring, analyzing, and presenting scientific data. In many disciplines, data and model scenarios are becoming multifaceted: data are often spatiotemporal and multivariate; they stem from different data sources (multimodal data), from multiple simulation runs (multirun/ensemble data), or from multiphysics simulations of interacting phenomena (multimodel data resulting from coupled simulation models). Also, data can be of different dimensionality or structured on various types of grids that need to be related or fused in the visualization. This heterogeneity of data characteristics presents new opportunities as well as technical challenges for visualization research. Visualization and interaction techniques are thus often combined with computational analysis. In this survey, we study existing methods for visualization and interactive visual analysis of multifaceted scientific data. Based on a thorough literature review, a categorization of approaches is proposed. We cover a wide range of fields and discuss to which degree the different challenges are matched with existing solutions for visualization and visual analysis. This leads to conclusions with respect to promising research directions, for instance, to pursue new solutions for multirun and multimodel data as well as techniques that support a multitude of facets.

Recent work has shown the great potential of interactive flow analysis by the analysis of path lines. The choice of suitable attributes, describing the path lines, is, however, still an open question. This paper addresses this question performing a statistical analysis of the path line attribute space. In this way we are able to balance the usage of computing power and storage with the necessity to not loose relevant information. We demonstrate how a carefully chosen attribute set can improve the benefits of state-of-the art interactive flow analysis. The results obtained are compared to previously published work.

Datasets with a large number of dimensions per data item (hundreds or more) are challenging both for computational and visual analysis. Moreover, these dimensions have different characteristics and relations that result in sub-groups and/or hierarchies over the set of dimensions. Such structures lead to heterogeneity within the dimensions. Although the consideration of these structures is crucial for the analysis, most of the available analysis methods discard the heterogeneous relations among the dimensions. In this paper, we introduce the construction and utilization of representative factors for the interactive visual analysis of structures in high-dimensional datasets. First, we present a selection of methods to investigate the sub-groups in the dimension set and associate representative factors with those groups of dimensions. Second, we introduce how these factors are included in the interactive visual analysis cycle together with the original dimensions. We then provide the steps of an analytical procedure that iteratively analyzes the datasets through the use of representative factors. We discuss how our methods improve the reliability and interpretability of the analysis process by enabling more informed selections of computational tools. Finally, we demonstrate our techniques on the analysis of brain imaging study results that are performed over a large group of subjects.

In this paper, we discuss the extension and integration of the statistical concept of Kernel Density Estimation (KDE) in a scatterplot-like visualization for dynamic data at interactive rates. We present a line kernel for representing streaming data, we discuss how the concept of KDE can be adapted to enable a continuous representation of the distribution of a dependent variable of a 2D domain. We propose to automatically adapt the kernel bandwith of KDE to the viewport settings, in an interactive visualization environment that allows zooming and panning. We also present a GPU-based realization of KDE that leads to interactive frame rates, even for comparably large datasets. Finally, we demonstrate the usefulness of our approach in the context of three application scenarios - one studying streaming ship traffic data, another one from the oil & gas domain, where process data from the operation of an oil rig is streaming in to an on-shore operational center, and a third one studying commercial air traffic in the US spanning 1987 to 2008.

Abstract In this work, we present a technique based on kernel density estimation for rendering smooth curves. With this approach, we produce uncluttered and expressive pictures, revealing frequency information about one, or, multiple curves, independent of the level of detail in the data, the zoom level, and the screen resolution. With this technique the visual representation scales seamlessly from an exact line drawing, (for low‐frequency/low‐complexity curves) to a probability density estimate for more intricate situations. This scale‐independence facilitates displays based on non‐linear time, enabling high‐resolution accuracy of recent values, accompanied by long historical series for context. We demonstrate the functionality of this approach in the context of prediction scenarios and in the context of streaming data.

Abstract Vector fields are a common concept for the representation of many different kinds of flow phenomena in science and engineering. Methods based on vector field topology are known for their convenience for visualizing and analysing steady flows, but a counterpart for unsteady flows is still missing. However, a lot of good and relevant work aiming at such a solution is available. We give an overview of previous research leading towards topology‐based and topology‐inspired visualization of unsteady flow, pointing out the different approaches and methodologies involved as well as their relation to each other, taking classical (i.e. steady) vector field topology as our starting point. Particularly, we focus on Lagrangian methods, space–time domain approaches, local methods and stochastic and multifield approaches. Furthermore, we illustrate our review with practical examples for the different approaches.

Abstract In the visualization of flow simulation data, feature detectors often tend to result in overly rich response, making some sort of filtering or simplification necessary to convey meaningful images. In this paper we present an approach that builds upon a decomposition of the flow field according to dynamical importance of different scales of motion energy. Focusing on the high‐energy scales leads to a reduction of the flow field while retaining the underlying physical process. The presented method acknowledges the intrinsic structures of the flow according to its energy and therefore allows to focus on the energetically most interesting aspects of the flow. Our analysis shows that this approach can be used for methods based on both local feature extraction and particle integration and we provide a discussion of the error caused by the approximation. Finally, we illustrate the use of the proposed approach for both a local and a global feature detector and in the context of numerical flow simulations.

Abstract Cluster analysis is a useful method which reveals underlying structures and relations of items after grouping them into clusters. In the case of temporal data, clusters are defined over time intervals where they usually exhibit structural changes. Conventional cluster analysis does not provide sufficient methods to analyze these structural changes, which are, however, crucial in the interpretation and evaluation of temporal clusters. In this paper, we present two novel and interactive visualization techniques that enable users to explore and interpret the structural changes of temporal clusters. We introduce the temporal cluster view, which visualizes the structural quality of a number of temporal clusters, and temporal signatures, which represents the structure of clusters over time. We discuss how these views are utilized to understand the temporal evolution of clusters. We evaluate the proposed techniques in the cluster analysis of mixed lipid bilayers.

Flows through tubular structures are common in many fields, including blood flow in medicine and tubular fluid flows in engineering. The analysis of such flows is often done with a strong reference to the main flow direction along the tubular boundary. In this paper we present an approach for straightening the visualization of tubular flow. By aligning the main reference direction of the flow, i.e., the center line of the bounding tubular structure, with one axis of the screen, we are able to natively juxtapose (1.) different visualizations of the same flow, either utilizing different flow visualization techniques, or by varying parameters of a chosen approach such as the choice of seeding locations for integration-based flow visualization, (2.) the different time steps of a time-dependent flow, (3.) different projections around the center line , and (4.) quantitative flow visualizations in immediate spatial relation to the more qualitative classical flow visualization. We describe how to utilize this approach for an informative interactive visual analysis. We demonstrate the potential of our approach by visualizing two datasets from two different fields: an arterial blood flow measurement and a tubular gas flow simulation from the automotive industry.

We present a systematic approach to the interactive visual analysis of heterogeneous scientific data. The data consist of two interrelated parts given on spatial grids over time (e.g., atmosphere and ocean part from a coupled climate model). By integrating both data parts in a framework of coordinated multiple views (with linking and brushing), the joint investigation of features across the data parts is enabled. An interface is constructed between the data parts that specifies 1) which grid cells in one part are related to grid cells in the other part, and vice versa, 2) how selections (in terms of feature extraction via brushing) are transferred between the two parts, and 3) how an update mechanism keeps the feature specification in both data parts consistent during the analysis. We also propose strategies for visual analysis that result in an iterative refinement of features specified across both data parts. Our approach is demonstrated in the context of a complex simulation of fluid-structure interaction and a multirun climate simulation.

In many application fields, data analysts have to deal with datasets that contain many expressions per item. The effective analysis of such multivariate datasets is dependent on the user's ability to understand both the intrinsic dimensionality of the dataset as well as the distribution of the dependent values with respect to the dimensions. In this paper, we propose a visualization model that enables the joint interactive visual analysis of multivariate datasets with respect to their dimensions as well as with respect to the actual data values. We describe a dual setting of visualization and interaction in items space and in dimensions space. The visualization of items is linked to the visualization of dimensions with brushing and focus+context visualization. With this approach, the user is able to jointly study the structure of the dimensions space as well as the distribution of data items with respect to the dimensions. Even though the proposed visualization model is general, we demonstrate its application in the context of a DNA microarray data analysis.

Abstract In this paper we present an extended critical point concept which allows us to apply vector field topology in the case of unsteady flow. We propose a measure forunsteadinesswhich describes the rate of change of the velocities in a fluid element over time. This measure allows us to select particles for which topological properties remain intact inside a finite spatio‐temporal neighborhood. One benefit of this approach is that the classification of critical points based on the eigenvalues of the Jacobian remains meaningful. In the steady case the proposed criterion reduces to the classical definition of critical points. As a first step we show that finding an optimal Galilean frame of reference can be obtained implicitly by analyzing the acceleration field. In a second step we show that this can be extended by switching to the Lagrangian frame of reference. This way the criterion can detect critical points moving along intricate trajectories. We analyze the behavior of the proposed criterion based on two analytical vector fields for which a correct solution is defined by their inherent symmetries and present results for numerical vector fields.

Abstract We present a systematic study of opportunities for the interactive visual analysis of multi‐dimensional scientific data that is based on the integration of statistical aggregations along selected independent data dimensions in a framework of coordinated multiple views (with linking and brushing). Traditional and robust estimates of the four statistical moments (mean, variance, skewness, and kurtosis) as well as measures ofoutlyingnessare integrated in an iterative visual analysis process. Brushing particular statistics, the analyst can investigate data characteristics such as trends and outliers. We present a categorization of beneficial combinations of attributes in 2D scatterplots: (a) kthvs. (k + 1)thstatistical moment of a traditional or robust estimate, (b) traditional vs. robust version of the same moment, (c) two different robust estimates of the same moment. We propose selected view transformations to iteratively construct this multitude of informative views as well as to enhance the depiction of the statistical properties in scatterplots and quantile plots. In the framework, we interrelate the original distributional data and the aggregated statistics, which allows the analyst to work with both data representations simultaneously. We demonstrate our approach in the context of two visual analysis scenarios of multi‐run climate simulations.

Multiple simulation runs using the same simulation model with different values of control parameters generate a large data set that captures the behavior of the modeled phenomenon. However, there is a conceptual and visual gap between the simulation model behavior and the data set that makes data analysis more difficult. We propose a simulation model view that helps to bridge that gap by visually combining the simulation model description and the generated data. The simulation model view provides a visual outline of the simulation process and the corresponding simulation model. The view is integrated in a Coordinated Multiple Views ;(CMV) system. As the simulation model view provides a limited display space, we use three levels of details. We explored the use of the simulation model view, in close collaboration with a domain expert, to understand and tune an electronic unit injector (EUI). We also developed analysis procedures based on the view. The EUI is mostly used in heavy duty Diesel engines. We were mainly interested in understanding the model and how to tune it for three different operation modes: low emission, low consumption, and high power. Very positive feedback from the domain expert shows that the use of the simulation model view and the corresponding ;analysis procedures within a CMV system represents an effective technique for interactive visual analysis of multiple simulation runs. We also developed new analysis procedures based on these results.

Abstract In this state‐of‐the‐art report we discuss relevant research works related to the visualization of complex, multi‐variate data. We discuss how different techniques take effect at specific stages of the visualization pipeline and how they apply to multi‐variate data sets being composed of scalars, vectors and tensors. We also provide a categorization of these techniques with the aim for a better overview of related approaches. Based on this classification we highlight combinable and hybrid approaches and focus on techniques that potentially lead towards new directions in visualization research. In the second part of this paper we take a look at recent techniques that are useful for the visualization of complex data sets either because they are general purpose or because they can be adapted to specific problems.

We present two visualization techniques for curve-centric volume reformation with the aim to create compelling comparative visualizations. A curve-centric volume reformation deforms a volume, with regards to a curve in space, to create a new space in which the curve evaluates to zero in two dimensions and spans its arc-length in the third. The volume surrounding the curve is deformed such that spatial neighborhood to the curve is preserved. The result of the curve-centric reformation produces images where one axis is aligned to arc-length, and thus allows researchers and practitioners to apply their arc-length parameterized data visualizations in parallel for comparison. Furthermore we show that when visualizing dense data, our technique provides an inside out projection, from the curve and out into the volume, which allows for inspection what is around the curve. Finally we demonstrate the usefulness of our techniques in the context of two application cases. We show that existing data visualizations of arc-length parameterized data can be enhanced by using our techniques, in addition to creating a new view and perspective on volumetric data around curves. Additionally we show how volumetric data can be brought into plotting environments that allow precise readouts. In the first case we inspect streamlines in a flow field around a car, and in the second we inspect seismic volumes and well logs from drilling.

The widespread use of computational simulation in science and engineering provides challenging research opportunities. Multiple independent variables are considered and large and complex data are computed, especially in the case of multi-run simulation. Classical visualization techniques deal well with 2D or 3D data and also with time-dependent data. Additional independent dimensions, however, provide interesting new challenges. We present an advanced visual analysis approach that enables a thorough investigation of families of data surfaces, i.e., datasets, with respect to pairs of independent dimensions. While it is almost trivial to visualize one such data surface, the visual exploration and analysis of many such data surfaces is a grand challenge, stressing the users' perception and cognition. We propose an approach that integrates projections and aggregations of the data surfaces at different levels (one scalar aggregate per surface, a 1D profile per surface, or the surface as such). We demonstrate the necessity for a flexible visual analysis system that integrates many different (linked) views for making sense of this highly complex data. To demonstrate its usefulness, we exemplify our approach in the context of a meteorological multi-run simulation data case and in the context of the engineering domain, where our collaborators are working with the simulation of elastohydrodynamic (EHD) lubrication bearing in the automotive industry.

There is a large number of interactive visualization tools, however no universal tool exists that covers all relevant aspects for all possible application domains. We have developed a tool, ComVis, which was intended to be used as are search prototype for new visualization techniques. We have identified some interesting aspects from developers' and users' points of view during tool development. In this paper we describe lessons learned during the process, and share our findings with visualization research community. In the end, some examples prove the usefulness of the developed tool. One particular example, the concept of families of function graphs and application to analysis of fuel injection concludes the paper.

Linking and brushing is a proven approach to analyzing multi-dimensional datasets in the context of multiple coordinated views. Nevertheless, most of the respective visualization techniques only offer qualitative visual results. Many user tasks, however, also require precise quantitative results as, for example, offered by statistical analysis. In succession of the useful Rank-by-Feature Framework, this paper describes a joint visual and statistical approach for guiding the user through a high-dimensional dataset by ranking dimensions (1D case) and pairs of dimensions (2D case) according to statistical summaries. While the original Rank-by-Feature Framework is limited to global features, the most important novelty here is the concept to consider local features, i.e., data subsets defined by brushing in linked views. The ability to compare subsets to other subsets and subsets to the whole dataset in the context of a large number of dimensions significantly extends the benefits of the approach especially in later stages of an exploratory data analysis. A case study illustrates the workflow by analyzing counts of keywords for classifying e-mails as spam or no-spam.

Abstract In this paper we present a new approach to the interactive visual analysis of time‐dependent scientific data – both from measurements as well as from computational simulation – by visualizing a scalar function over time for each of tenthousands or even millions of sample points. In order to cope with overdrawing and cluttering, we introduce a new four‐level method of focus+context visualization. Based on a setting of coordinated, multiple views (with linking and brushing), we integrate three different kinds of focus and also the context in every single view. Per data item we use three values (from the unit interval each) to represent to which degree the data item is part of the respective focus level. We present a color compositing scheme which is capable of expressing all three values in a meaningful way, taking semantics and their relations amongst each other (in the context of our multiple linked view setup) into account. Furthermore, we present additional image‐based postprocessing methods to enhance the visualization of large sets of function graphs, including a texture‐based technique based on line integral convolution (LIC). We also propose advanced brushing techniques which are specific to the time‐dependent nature of the data (in order to brush patterns over time more efficiently). We demonstrate the usefulness of the new approach in the context of medical perfusion data.

While it is quite typical to deal with attributes of different data types in the visualization of heterogeneous and multivariate datasets, most existing techniques still focus on the most usual data types such as numerical attributes or strings. In this paper we present a new approach to the interactive visual exploration and analysis of data that contains attributes which are of set type. A set-typed attribute of a data item--like one cell in a table--has a list of n > or = 0 elements as its value. We present the set'o'gram as a new visualization approach to represent data of set type and to enable interactive visual exploration and analysis. We also demonstrate how this approach is capable to help in dealing with datasets that have a larger number of dimensions (more than a dozen or more), especially also in the context of categorical data. To illustrate the effectiveness of our approach, we present the interactive visual analysis of a CRM dataset with data from a questionnaire on the education and shopping habits of about 90000 people.

Feature-based flow visualization is naturally dependent on feature extraction. To extract flow features, often higher-order properties of the flow data are used such as the Jacobian or curvature properties, implicitly describing the flow features in terms of their inherent flow characteristics (e.g., collinear flow and vorticity vectors). In this paper we present recent research which leads to the (not really surprising) conclusion that feature extraction algorithms need to be extended to a time-dependent analysis framework (in terms of time derivatives) when dealing with unsteady flow data. Accordingly, we present two extensions of the parallel vectors based vortex extraction criteria to the time-dependent domain and show the improvements of feature-based flow visualization in comparison to the steady versions of this extraction algorithm both in the context of a high-resolution dataset, i.e., a simulation specifically designed to evaluate our new approach, as well as for a real-world dataset from a concrete application.

One of the most prominent topics in climate research is the investigation, detection, and allocation of climate change. In this paper, we aim at identifying regions in the atmosphere (e.g., certain height layers) which can act as sensitive and robust indicators for climate change. We demonstrate how interactive visual data exploration of large amounts of multi-variate and time-dependent climate data enables the steered generation of promising hypotheses for subsequent statistical evaluation. The use of new visualization and interaction technology--in the context of a coordinated multiple views framework--allows not only to identify these promising hypotheses, but also to efficiently narrow down parameters that are required in the process of computational data analysis. Two datasets, namely an ECHAM5 climate model run and the ERA-40 reanalysis incorporating observational data, are investigated. Higher-order information such as linear trends or signal-to-noise ratio is derived and interactively explored in order to detect and explore those regions which react most sensitively to climate change. As one conclusion from this study, we identify an excellent potential for usefully generalizing our approach to other, similar application cases, as well.

Interactive steering with visualization has been a common goal of the visualization research community for twenty years, but it is rarely ever realized in practice. In this paper we describe a successful realization of a tightly coupled steering loop, integrating new simulation technology and interactive visual analysis in a prototyping environment for automotive industry system design. Due to increasing pressure on car manufacturers to meet new emission regulations, to improve efficiency, and to reduce noise, both simulation and visualization are pushed to their limits. Automotive system components, such as the powertrain system or the injection system have an increasing number of parameters, and new design approaches are required. It is no longer possible to optimize such a system solely based on experience or forward optimization. By coupling interactive visualization with the simulation back-end (computational steering), it is now possible to quickly prototype a new system, starting from a non-optimized initial prototype and the corresponding simulation model. The prototyping continues through the refinement of the simulation model, of the simulation parameters and through trial-and-error attempts to an optimized solution. The ability to early see the first results from a multidimensional simulation space--thousands of simulations are run for a multidimensional variety of input parameters--and to quickly go back into the simulation and request more runs in particular parameter regions of interest significantly improves the prototyping process and provides a deeper understanding of the system behavior. The excellent results which we achieved for the common rail injection system strongly suggest that our approach has a great potential of being generalized to other, similar scenarios.

Data sets often include information that can be represented as a mapping that describes how a dependent variable depends on an independent variable. Such a mapping, usually represented as a function graph, can be parameterized to provide a family of function graphs. The challenge is how to efficiently aggregate individual function graph views to represent the whole family and allow visual analysis and search for patterns. We propose a novel view, called the color lines view, which provides a two dimensional, rectangular view where each line represents a single function graph. The points on the line correspond to values of the independent variable. The point colors represent the value of the dependent variable. The lines, placed next to each other in parallel, show a family of function graphs. The color lines view offers sorting and brushing features which support visual analysis procedures that are difficult to perform with previously existing views.

We present smooth formulations of common vortex detectors that allow a seamless integration into the concept of interactive visual analysis of flow simulation data. We express the originally binary feature detectors as fuzzy-sets that can be combined using the linking and brushing concepts of interactive visual analysis. Both interaction and visualization gain from having multiple detectors concurrently available and from the ability to combine them. An application study on automotive data reveals how these vortex detectors combine and perform in praxis.

In this paper we present a novel approach to volume visualization for presentation purposes that improves both the comprehensibility and credibility of the intended visualization message. Therefore, we combine selected aspects from storytelling as well as from interactive volume visualization to create a guided but at the same time interactive visualization presentation approach. To ease the observer's access to a presented visualization result we not only communicate the result itself, but also deliver its creational process in the form of an annotated visualization animation, which we call a visualization story. Additionally, we enable variable means of interactivity during story playback. The story observers may just watch the presentation passively, but they are also allowed to reinvestigate the visualization independently from story guidance, offering the ability to verify, confirm, or even disapprove the presented visualization message. For demonstration purposes, we developed a prototype application that provides tools to author, edit, and watch visualization stories. We demonstrate the potential of our approach on the basis of medical visualization examples.

Proteins are highly flexible and large amplitude deformations of their structure, also called slow dynamics, are often decisive to their function. We present a two-level rendering approach that enables visualization of slow dynamics of large protein assemblies. Our approach is aligned with a hierarchical model of large scale molecules. Instead of constantly updating positions of large amounts of atoms, we update the position and rotation of residues, i.e., higher level building blocks of a protein. Residues are represented by one vertex only indicating its position and additional information defining the rotation. The atoms in the residues are generated on-the-fly on the GPU, exploiting the new graphics hardware geometry shader capabilities. Moreover, we represent the atoms by billboards instead of tessellated spheres. Our representation is then significantly faster and pixel precise. We demonstrate the usefulness of our new approach in the context of our collaborative bioinformatics project.

This paper presents a scalable framework for real-time raycasting of large unstructured volumes that employs a hybrid bricking approach. It adaptively combines original unstructured bricks in important (focus) regions, with structured bricks that are resampled on demand in less important (context) regions. The basis of this focus+context approach is interactive specification of a scalar degree of interest (DOI) function. Thus, rendering always considers two volumes simultaneously: a scalar data volume, and the current DOI volume. The crucial problem of visibility sorting is solved by raycasting individual bricks and compositing in visibility order from front to back. In order to minimize visual errors at the grid boundary, it is always rendered accurately, even for resampled bricks. A variety of different rendering modes can be combined, including contour enhancement. A very important property of our approach is that it supports a variety of cell types natively, i.e., it is not constrained to tetrahedral grids, even when interpolation within cells is used. Moreover, our framework can handle multi-variate data, e.g., multiple scalar channels such as temperature or pressure, as well as time-dependent data. The combination of unstructured and structured bricks with different quality characteristics such as the type of interpolation or resampling resolution in conjunction with custom texture memory management yields a very scalable system.

Perfusion data are dynamic medical image data which characterize the regional blood flow in human tissue. These data bear a great potential in medical diagnosis, since diseases can be better distinguished and detected at an earlier stage compared to static image data. The wide-spread use of perfusion data is hampered by the lack of efficient evaluation methods. For each voxel, a time-intensity curve characterizes the enhancement of a contrast agent. Parameters derived from these curves characterize the perfusion and have to be integrated for diagnosis. The diagnostic evaluation of this multi-field data is challenging and time-consuming due to its complexity. For the visual analysis of such datasets, feature-based approaches allow to reduce the amount of data and direct the user to suspicious areas. We present an interactive visual analysis approach for the evaluation of perfusion data. For this purpose, we integrate statistical methods and interactive feature specification. Correlation analysis and Principal Component Analysis (PCA) are applied for dimensionreduction and to achieve a better understanding of the inter-parameter relations. Multiple, linked views facilitate the definition of features by brushing multiple dimensions. The specification result is linked to all views establishing a focus+context style of visualization in 3D. We discuss our approach with respect to clinical datasets from the three major application areas: ischemic stroke diagnosis, breast tumor diagnosis, as well as the diagnosis of the coronary heart disease (CHD). It turns out that the significance of perfusion parameters strongly depends on the individual patient, scanning parameters, and data pre-processing.

Stream surfaces are a classic flow visualization technique used to portray the characteristics of vector fields, and texture advection research has made rapid advances in recent years. We present a novel hybrid visualization of texture advection on stream surfaces. This approach conveys properties of the vector field that stream surfaces alone cannot. We apply the visualization technique to various patterns of flow from CFD data important to automotive engine simulation including two patterns of in-cylinder flow (swirl and tumble motion) as well as flow through a cooling jacket. In addition, we explore multiple vector fields defined at the stream surface such as velocity, vorticity, and pressure gradient. The results of our investigation highlight both the strengths and limitations of the hybrid stream surface-texture advection visualization technique and offer new insight to engineers exploring and analyzing their simulations.

This paper presents an approach to extracting a path line oriented topological segmentation for periodic 2D timedependent vector fields. Topological methods aiming in capturing the asymptotic behavior of path lines rarely exist because path lines are usually only defined over a fixed time-interval, making statements about their asymptotic behavior impossible. For the data class of periodic vector fields, this restriction does not apply any more. Our approach detects critical path lines as well as basins from which the path lines converge to the critical ones. We demonstrate our approach on a number of test data sets.

The analysis and exploration of multidimensional and multivariate data is still one of the most challenging areas in the field of visualization. In this paper, we describe an approach to visual analysis of an especially challenging set of problems that exhibit a complex internal data structure. We describe the interactive visual exploration and analysis of data that includes several (usually large) families of function graphs fi (x, t). We describe analysis procedures and practical aspects of the interactive visual analysis specific to this type of data (with emphasis on the function graph characteristic of the data). We adopted the well-proven approach of multiple, linked views with advanced interactive brushing to assess the data. Standard views such as histograms, scatterplots, and parallel coordinates are used to jointly visualize data. We support iterative visual analysis by providing means to create complex, composite brushes that span multiple views and that are constructed using different combination schemes. We demonstrate that engineering applications represent a challenging but very applicable area for visual analytics. As a case study, we describe the optimization of a fuel injection system in diesel engines of passenger cars.

Categorical data dimensions appear in many real-world data sets, but few visualization methods exist that properly deal with them. Parallel Sets are a new method for the visualization and interactive exploration of categorical data that shows data frequencies instead of the individual data points. The method is based on the axis layout of parallel coordinates, with boxes representing the categories and parallelograms between the axes showing the relations between categories. In addition to the visual representation, we designed a rich set of interactions. Parallel Sets allow the user to interactively remap the data to new categorizations and, thus, to consider more data dimensions during exploration and analysis than usually possible. At the same time, a metalevel, semantic representation of the data is built. Common procedures, like building the cross product of two or more dimensions, can be performed automatically, thus complementing the interactive visualization. We demonstrate Parallel Sets by analyzing a large CRM data set, as well as investigating housing data from two US states.

Focus+context visualization integrates a visually accentuated representation of selected data items in focus (more details, more opacity, etc.) with a visually deemphasized representation of the rest of the data, i.e., the context. The role of context visualization is to provide an overview of the data for improved user orientation and improved navigation. A good overview comprises the representation of both outliers and trends. Up to now, however, context visualization not really treated outliers sufficiently. In this paper we present a new approach to focus+context visualization in parallel coordinates which is truthful to outliers in the sense that small-scale features are detected before visualization and then treated specially during context visualization. Generally, we present a solution which enables context visualization at several levels of abstraction, both for the representation of outliers and trends. We introduce outlier detection and context generation to parallel coordinates on the basis of a binned data representation. This leads to an output-oriented visualization approach which means that only those parts of the visualization process are executed which actually affect the final rendering. Accordingly, the performance of this solution is much more dependent on the visualization size than on the data size which makes it especially interesting for large datasets. Previous approaches are outperformed, the new solution was successfully applied to datasets with up to 3 million data records and up to 50 dimensions.

We present a visual analysis and exploration of fluid flow through a cooling jacket. Engineers invest a large amount of time and serious effort to optimize the flow through this engine component because of its important role in transferring heat away from the engine block. In this study we examine the design goals that engineers apply in order to construct an ideal-as-possible cooling jacket geometry and use a broad range of visualization tools in order to analyze, explore, and present the results. We systematically employ direct, geometric, and texture-based flow visualization techniques as well as automatic feature extraction and interactive feature-based methodology. And we discuss the relative advantages and disadvantages of these approaches as well as the challenges, both technical and perceptual with this application. The result is a feature-rich state-of-the-art flow visualization analysis applied to an important and complex data set from real-world computational fluid dynamics simulations.

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.

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.

We present a side-by-side analysis of two recent image space approaches for the visualization of vector fields on surfaces. The two methods, Image Space Advection (ISA) and Image-Based Flow Visualization for Curved Surfaces (IBFVS) generate dense representations of time-dependent vector fields with high spatio-temporal correlation. While the 3D vector fields are associated with arbitrary surfaces represented by triangular meshes, the generation and advection of texture properties is confined to image space. Fast frame rates are achieved by exploiting frame-to-frame coherency and graphics hardware. In our comparison of ISA and IBFVS, we point out the strengths and weaknesses of each approach and give recommendations as to when and where they are best applied.

One of the most important goals in volume rendering is to be able to visually separate and selectively enable specific objects of interest contained in a single volumetric data set, which can be approached by using explicit segmentation information. We show how segmented data sets can be rendered interactively on current consumer graphics hardware with high image quality and pixel-resolution filtering of object boundaries. In order to enhance object perception, we employ different levels of object distinction. First, each object can be assigned an individual transfer function, multiple of which can be applied in a single rendering pass. Second, different rendering modes such as direct volume rendering, iso-surfacing, and non-photorealistic techniques can be selected for each object. A minimal number of rendering passes is achieved by processing sets of objects that share the same rendering mode in a single pass. Third, local compositing modes such as alpha blending and MIP can be selected for each object in addition to a single global mode, thus enabling high-quality two-level volume rendering on GPUs.

Simulation of rigid body dynamics has been a field of active research for quite some time. However, the presentation of simulation results has received far less attention so far. We present an interactive and intuitive 3D visualization framework for rigid body simulation data. We introduce various glyphs representing vector attributes such as force and velocity as well as angular attributes including angular velocity and torque. We have integrated our visualization method into an application developed at one of the leading companies in automotive engine design and simulation. We apply our principles to visualization of chain and belt driven timing drives in engines.

We present a technique for direct visualization of unsteady flow on surfaces from computational fluid dynamics. The method generates dense representations of time-dependent vector fields with high spatio-temporal correlation using both Lagrangian-Eulerian advection and image based flow visualization as its foundation. While the 3D vector fields are associated with arbitrary triangular surface meshes, the generation and advection of texture properties is confined to image space. Frame rates of up to 20 frames per second are realized by exploiting graphics card hardware. We apply this algorithm to unsteady flow on boundary surfaces of, large, complex meshes from computational fluid dynamics composed of more than 250,000 polygons, dynamic meshes with time-dependent geometry and topology, as well as medical data.

Abstract Flow visualisation is an attractive topic in data visualisation, offering great challenges for research. Very large data sets must be processed, consisting of multivariate data at large numbers of grid points, often arranged in many time steps. Recently, the steadily increasing performance of computers again has become a driving force for new advances in flow visualisation, especially in techniques based on texturing, feature extraction, vector field clustering, and topology extraction. In this article we present the state of the art in feature‐based flow visualisation techniques. We will present numerous feature extraction techniques, categorised according to the type of feature. Next, feature tracking and event detection algorithms are discussed, for studying the evolution of features in time‐dependent data sets. Finally, various visualisation techniques are demonstrated. ACM CSS: I.3.8 Computer Graphics— applications

This paper presents several distinguishing design features of RTVR-a Java-based library for real-time volume rendering. We describe, how the careful design of data structures, which in our case are based on voxel enumeration, and an intelligent use of lookup tables enable interactive volume rendering even on low-end PC hardware. By assigning voxels to distinct objects within the volume and by using an individual setup and combination of look-up tables for each object, object-aware rendering is performed: different transfer functions, shading models, and also compositing modes can be mixed within a single scene to depict each object in the most appropriate way, while still providing rendering results in real-time. While providing frame rates similar to volume visualization using 3D consumer hardware, the approach utilized by RTVR offers much more flexibility and extensibility due to its pure software nature. Furthermore, due to the memory-efficiency of the data representation and the implementation in Java, RTVR can be used to provide volume viewing facilities over low-bandwidth networks, with almost full control over rendering and visualization mapping parameters (clipping, shading, compositing, transfer function) for the user. This paper also addresses specific problems which arise by the use of Java for interactive visualization.

In this paper we present a fast visualization technique for volumetric data, which is based on a recent non-photorealistic rendering technique. Our new approach enables alternative insights into 3D data sets (compared to traditional approaches such as direct volume rendering or iso-surface rendering). Object contours, which usually are characterized by locally high gradient values, are visualized regardless of their density values. Cumbersome tuning of transfer functions, as usually needed for setting up DVR views is avoided. Instead, a small number of parameters is available to adjust the non-photorealistic display. Based on the magnitude of local gradient information as well as on the angle between viewing direction and gradient vector, data values are mapped to visual properties (color, opacity), which then are combined to form the rendered image (MIP is proposed as the default compositing stragtegy here). Due to the fast implementation of this alternative rendering approach, it is possible to interactively investigate the 3D data, and quickly learn about internal structures. Several further extensions of our new approach, such as level lines are also presented in this paper.

Presents a two-level approach for volume rendering, which allows for selectively using different rendering techniques for different subsets of a 3D data set. Different structures within the data set are rendered locally on an object-by-object basis by either direct volume rendering (DVR), maximum-intensity projection (MIP), surface rendering, value integration (X-ray-like images) or non-photorealistic rendering (NPR). All the results of subsequent object renderings are combined globally in a merging step (usually compositing in our case). This allows us to selectively choose the most suitable technique for depicting each object within the data while keeping the amount of information contained in the image at a reasonable level. This is especially useful when inner structures should be visualized together with semi-transparent outer parts, similar to the focus+context approach known from information visualization. We also present an implementation of our approach which allows us to explore volumetric data using two-level rendering at interactive frame rates.

Presents a two-level approach for fusing direct volume rendering (DVR) and maximum-intensity projection (MIP) within a joint rendering method. Different structures within the data set are rendered locally by either MIP or DVR on an object-by-object basis. Globally, all the results of subsequent object renderings are combined in a merging step (usually compositing in our case). This allows us to selectively choose the most suitable technique for depicting each object within the data, while keeping the amount of information contained in the image at a reasonable level. This is especially useful when inner structures should be visualized together with semi-transparent outer parts, similar to the focus-and-context approach known from information visualization. We also present an implementation of our approach which allows us to explore volumetric data using two-level rendering at interactive frame rates.

Maximum Intensity Projection (MIP) is a volume rendering technique which is used to visualize high‐intensity structures within volumetric data. At each pixel the highest data value, which is encountered along a corresponding viewing ray is depicted. MIP is, for example, commonly used to extract vascular structures from medical data sets (angiography). Due to lack of depth information in MIP images, animation or interactive variation of viewing parameters is frequently used for investigation. Up to now no MIP algorithms exist which are of both interactive speed and high quality. In this paper we present a high‐quality MIP algorithm (trilinear interpolation within cells), which is up to 50 times faster than brute‐force MIP and at least 20 times faster than comparable optimized techniques. This speed‐up is accomplished by using an alternative storage scheme for volume cells (sorted by value) and by removing cells which do not contribute to any MIP projection (regardless of the viewing direction) in a preprocessing step. Also, a fast maximum estimation within cells is used to further speed up the algorithm.