This manuscript proposes two novel interaction techniques for visualization-assisted exploration of urban data, namely, Layer Toggling and Visibility-Preserving Lenses. The former mitigates visual overload by organizing information into distinct layers while enabling multi-layer comparisons through controlled overlays. The technique supports focused analyses without sacrificing spatial context and enables users to quickly switch between layers through a dedicated physical button interface. Visibility-Preserving Lenses, on the other hand, dynamically adapt their size and transparency so that users can effectively examine dense spatial regions and temporal attributes in detail. Both techniques support urban data exploration and improve prediction. Exploring urban data is essential for understanding complex phenomena related to crime, mobility, and residents’ behavior and equally important is the ability to predict and explain how they evolve over time, supporting informed urban planning and policymaking. However, navigating urban data in all their complexity is challenging, often resulting in cognitive overload, loss of spatial context, and excessive visual clutter due to the many layers that must be examined simultaneously. Although layered visualizations aim to mitigate those challenges, they face limitations with occlusion and effortless comparisons across data layers. Additionally, interaction methods are typically confined to mouse-based controls, limiting the fluidity of dynamic exploration. The visualization tool was validated through a comprehensive user study that measured user performance, cognitive load, and interaction efficiency across multiple devices. Using real-world data from São Paulo, including mobility patterns, climate conditions, and crime statistics, the way the approach enhances both exploratory and analytical tasks is demonstrated. The results also show how users perform when playing with different interactive devices, providing guidelines for future developments and improvements. • Introduces a novel approach to toggle data layers for spatial crime analysis. • Proposes visibility-preserving lenses for comparisons of urban attributes with less occlusion. • Supports multi-attribute exploration in dense urban visualizations. • User study shows improved accuracy and interaction efficiency with proposed tools. • Enables better decision-making by enhancing insight into urban spatial patterns.

Visualizing multiple time series presents fundamental tradeoffs between scalability and visual clarity. Time series capture the behavior of many large-scale real-world processes, from stock market trends to urban activities. Users often gain insights by visualizing them as line charts, juxtaposing or superposing multiple time series to compare them and identify trends and patterns. However, existing representations struggle with scalability: when covering long time spans, leading to visual clutter from too many small multiples or overlapping lines. We propose TiVy, a new algorithm that summarizes time series using sequential patterns. It transforms the series into a set of symbolic sequences based on subsequence visual similarity using Dynamic Time Warping (DTW), then constructs a disjoint grouping of similar subsequences based on the frequent sequential patterns. The grouping result, a visual summary of time series, provides uncluttered superposition with fewer small multiples. Unlike common clustering techniques, TiVy extracts similar subsequences (of varying lengths) aligned in time. We also present an interactive time series visualization that renders large-scale time series in real-time. Our experimental evaluation shows that our algorithm (1) extracts clear and accurate patterns when visualizing time series data, (2) achieves a significant speed-up (1000×) compared to a straightforward DTW clustering. We also demonstrate the efficiency of our approach to explore hidden structures in massive time series data in two usage scenarios.

High-dimensional data, characterized by many features, can be difficult to visualize effectively. Dimensionality reduction techniques, such as PCA, UMAP, and t-SNE, address this challenge by projecting the data into a lower-dimensional space while preserving important relationships. TopoMap is another technique that excels at preserving the underlying structure of the data, leading to interpretable visualizations. In particular, TopoMap maps the high-dimensional data into a visual space, guaranteeing that the 0-dimensional persistence diagram of the Rips filtration of the visual space matches the one from the high-dimensional data. However, the original TopoMap algorithm can be slow and its layout can be too sparse for large and complex datasets. In this paper, we propose three improvements to TopoMap: 1) a more space-efficient layout, 2) a significantly faster implementation, and 3) a novel TreeMap-based representation that makes use of the topological hierarchy to aid the exploration of the projections. These advancements make TopoMap, now referred to as TopoMap++, a more powerful tool for visualizing high-dimensional data which we demonstrate through different use case scenarios.

Analyzing the impact of socioeconomic and urban variables on crime is a complex data analysis problem. Exploring synthetic, correlation-based scenarios using changes in a set of variables could alter a region's definition from unsafe to safe (known counterfactual explanation), which can aid decision-makers in interpreting crime in that region and define public policies to mitigate criminal activity. We propose CounterCrime, a visual analytics tool for crime analysis that uses counterfactual explanations to add insights for this problem. This tool employs various interactive visual metaphors to explore the counterfactual explorations generated in each region. To facilitate exploration, we organize our analysis at three levels: the whole city, the region group, and the regional level. This work proposes a new perspective in crime analysis by creating "what-if" scenarios and allowing decision-makers to anticipate changes that would make a region safer. The tool guides the user in selecting variables with the most significant effect in all city regions. Using a greedy strategy, the system recommends the best variables that may influence crime in unsafe regions as the user explores. Our tool allows for identifying the most appropriate counterfactual explorations at the regional level by grouping them by similarity and determining their feasibility by comparing them with existing examples in other regions. Using crime data from São Paulo, Brazil, we validated our results with case studies. These case studies reveal interesting findings; for example, scenarios that influence crime in a particular unsafe region (or set of regions) might not influence crime in other unsafe regions.

The emergence of distinct machine learning explanation methods has leveraged a number of new issues to be investigated. The disagreement problem is one such issue, as there may be scenarios where the output of different explanation methods disagree with each other. Although understanding how often, when, and where explanation methods agree or disagree is important to increase confidence in the explanations, few works have been dedicated to investigating such a problem. In this work, we proposed Visagreement, a visualization tool designed to assist practitioners in investigating the disagreement problem. Visagreement builds upon metrics to quantitatively compare and evaluate explanations, enabling visual resources to uncover where and why methods mostly agree or disagree. The tool is tailored for tabular data with binary classification and focuses on local feature importance methods. In the provided use cases, Visagreement turned out to be effective in revealing, among other phenomena, how disagreements relate to the quality of the explanations and machine learning model accuracy, thus assisting users in deciding where and when to trust explanations. To assess the effectiveness and practical utility of Visagreement, we conducted an evaluation involving four experts. These experts assessed the tool's Effectiveness, Usability, and Impact on Decision-Making. The experts confirm the Visagreement tool's effectiveness and user-friendliness, making it a valuable asset for analyzing and exploring (dis)agreements.

With the increasing use of black-box Machine Learning (ML) techniques in critical applications, there is a growing demand for methods that can provide transparency and accountability for model predictions. As a result, a large number of local explainability methods for black-box models have been developed and popularized. However, machine learning explanations are still hard to evaluate and compare due to the high dimensionality, heterogeneous representations, varying scales, and stochastic nature of some of these methods. Topological Data Analysis (TDA) can be an effective method in this domain since it can be used to transform attributions into uniform graph representations, providing a common ground for comparison across different explanation methods. We present a novel topology-driven visual analytics tool, Mountaineer, that allows ML practitioners to interactively analyze and compare these representations by linking the topological graphs back to the original data distribution, model predictions, and feature attributions. Mountaineer facilitates rapid and iterative exploration of ML explanations, enabling experts to gain deeper insights into the explanation techniques, understand the underlying data distributions, and thus reach well-founded conclusions about model behavior. Furthermore, we demonstrate the utility of Mountaineer through two case studies using real-world data. In the first, we show how Mountaineer enabled us to compare black-box ML explanations and discern regions of and causes of disagreements between different explanations. In the second, we demonstrate how the tool can be used to compare and understand ML models themselves. Finally, we conducted interviews with three industry experts to help us evaluate our work.

To reduce the number of pending cases and conflicting rulings in the Brazilian Judiciary, the National Congress amended the Constitution, allowing the Brazilian Supreme Court (STF) to create binding precedents (BPs), i.e., a set of understandings that both Executive and lower Judiciary branches must follow. The STF's justices frequently cite the 58 existing BPs in their decisions, and it is of primary relevance that judicial experts could identify and analyze such citations. To assist in this problem, we propose LegalVis, a web-based visual analytics system designed to support the analysis of legal documents that cite or could potentially cite a BP. We model the problem of identifying potential citations (i.e., non-explicit) as a classification problem. However, a simple score is not enough to explain the results; that is why we use an interpretability machine learning method to explain the reason behind each identified citation. For a compelling visual exploration of documents and BPs, LegalVis comprises three interactive visual components: the first presents an overview of the data showing temporal patterns, the second allows filtering and grouping relevant documents by topic, and the last one shows a document's text aiming to interpret the model's output by pointing out which paragraphs are likely to mention the BP, even if not explicitly specified. We evaluated our identification model and obtained an accuracy of 96%; we also made a quantitative and qualitative analysis of the results. The usefulness and effectiveness of LegalVis were evaluated through two usage scenarios and feedback from six domain experts.

Analyzing classification model performance is a crucial task for machine learning practitioners. While practitioners often use count-based metrics derived from confusion matrices, like accuracy, many applications, such as weather prediction, sports betting, or patient risk prediction, rely on a classifier's predicted probabilities rather than predicted labels. In these instances, practitioners are concerned with producing a calibrated model, that is, one which outputs probabilities that reflect those of the true distribution. Model calibration is often analyzed visually, through static reliability diagrams, however, the traditional calibration visualization may suffer from a variety of drawbacks due to the strong aggregations it necessitates. Furthermore, count-based approaches are unable to sufficiently analyze model calibration. We present Calibrate, an interactive reliability diagram that addresses the aforementioned issues. Calibrate constructs a reliability diagram that is resistant to drawbacks in traditional approaches, and allows for interactive subgroup analysis and instance-level inspection. We demonstrate the utility of Calibrate through use cases on both real-world and synthetic data. We further validate Calibrate by presenting the results of a think-aloud experiment with data scientists who routinely analyze model calibration.

We have been honored to oversee the organization of IEEE VIS 2021. This marked the first year in which the SciVis, InfoVis, and VAST conferences were merged into a single, unified IEEE VIS. When we began planning for VIS in 2019, we envisioned a great experience for our community, who would be able to enjoy the innovative scientific program provided by a unified VIS, while delighting in the hospitable and lively atmosphere of New Orleans. But even the best laid plans cannot account for all contingencies. The emergence of the COVID-19 pandemic changed and complicated much in our lives, including the planning for VIS 2021. Moreover, transition to a unified conference was not without its challenges as well. Despite the difficulties, our community showed, once again, its strength and resilience. Our organizing committee created an exciting conference with a rich program full of high-quality research with all challenges being continuously and admirably addressed. As general chairs, our primary responsibility was to watch these wonderful volunteers conduct truly inspiring work under extreme constraints. For this, we are deeply indebted.

Extracting and analyzing crime patterns in big cities is a challenging spatiotemporal problem. The hardness of the problem is linked to two main factors, the sparse nature of the crime activity and its spread in large spatial areas. Sparseness hampers most time series (crime time series) comparison methods from working properly, while the handling of large urban areas tends to render the computational costs of such methods impractical. Visualizing different patterns hidden in crime time series data is another issue in this context, mainly due to the number of patterns that can show up in the time series analysis. In this article, we present a new methodology to deal with the issues above, enabling the analysis of spatiotemporal crime patterns in a street-level of detail. Our approach is made up of two main components designed to handle the spatial sparsity and spreading of crimes in large areas of the city. The first component relies on a stochastic mechanism from which one can visually analyze probable×intensive crime hotspots. Such analysis reveals important patterns that can not be observed in the typical intensity-based hotspot visualization. The second component builds upon a deep learning mechanism to embed crime time series in Cartesian space. From the embedding, one can identify spatial locations where the crime time series have similar behavior. The two components have been integrated into a web-based analytical tool called CriPAV (Crime Pattern Analysis and Visualization), which enables global as well as a street-level view of crime patterns. Developed in close collaboration with domain experts, CriPAV has been validated through a set of case studies with real crime data in São Paulo - Brazil. The provided experiments and case studies reveal the effectiveness of CriPAV in identifying patterns such as locations where crimes are not intense but highly probable to occur as well as locations that are far apart from each other but bear similar crime patterns.

Seeded segmentation methods have gained a lot of attention due to their good performance in fragmenting complex images, easy usability and synergism with graph-based representations. These methods usually rely on sophisticated computational tools whose performance strongly depends on how good the training data reflect a sought image pattern. Moreover, poor adherence to the image contours, lack of unique solution, and high computational cost are other common issues present in most seeded segmentation methods. In this work we introduce Laplacian Coordinates, a quadratic energy minimization framework that tackles the issues above in an effective and mathematically sound manner. The proposed formulation builds upon graph Laplacian operators, quadratic energy functions, and fast minimization schemes to produce highly accurate segmentations. Moreover, the presented energy functions are not prone to local minima, i.e., the solution is guaranteed to be globally optimal, a trait not present in most image segmentation methods. Another key property is that the minimization procedure leads to a constrained sparse linear system of equations, enabling the segmentation of high-resolution images at interactive rates. The effectiveness of Laplacian Coordinates is attested by a comprehensive set of comparisons involving nine state-of-the-art methods and several benchmarks extensively used in the image segmentation literature.

Multidimensional Projection is a fundamental tool for high-dimensional data analytics and visualization. With very few exceptions, projection techniques are designed to map data from a high-dimensional space to a visual space so as to preserve some dissimilarity (similarity) measure, such as the Euclidean distance for example. In fact, although adopting distinct mathematical formulations designed to favor different aspects of the data, most multidimensional projection methods strive to preserve dissimilarity measures that encapsulate geometric properties such as distances or the proximity relation between data objects. However, geometric relations are not the only interesting property to be preserved in a projection. For instance, the analysis of particular structures such as clusters and outliers could be more reliably performed if the mapping process gives some guarantee as to topological invariants such as connected components and loops. This paper introduces TopoMap, a novel projection technique which provides topological guarantees during the mapping process. In particular, the proposed method performs the mapping from a high-dimensional space to a visual space, while preserving the 0-dimensional persistence diagram of the Rips filtration of the high-dimensional data, ensuring that the filtrations generate the same connected components when applied to the original as well as projected data. The presented case studies show that the topological guarantee provided by TopoMap not only brings confidence to the visual analytic process but also can be used to assist in the assessment of other projection methods.

This February 2021 issue of the IEEE Transactions on Visualization and Computer Graphics (TVCG) contains the proceedings of IEEE VIS 2020, held online between 25-30 October 2020, hosted by General Chairs from the University of Utah. With IEEE VIS 2020, the conference series is in its 31st year. IEEE VIS consists of three conferences, held concurrently: the IEEE Visual Analytics Science and Technology Conference (VAST), the IEEE Information Visualization Conference (InfoVis), and the IEEE Scientific Visualization Conference (SciVis). These three conferences are the premier venues for the visualization community to exchange the latest ideas and developments, attracting researchers and practitioners alike.

Boundary detection has long been a fundamental tool for image processing and computer vision, supporting the analysis of static and time-varying data. In this work, we built upon the theory of Graph Signal Processing to propose a novel boundary detection filter in the context of graphs, having as main application scenario the visual analysis of spatio-temporal data. More specifically, we propose the equivalent for graphs of the so-called Laplacian of Gaussian edge detection filter, which is widely used in image processing. The proposed filter is able to reveal interesting spatial patterns while still enabling the definition of entropy of time slices. The entropy reveals the degree of randomness of a time slice, helping users to identify expected and unexpected phenomena over time. The effectiveness of our approach appears in applications involving synthetic and real data sets, which show that the proposed methodology is able to uncover interesting spatial and temporal phenomena. The provided examples and case studies make clear the usefulness of our approach as a mechanism to support visual analytic tasks involving spatio-temporal data.

São Paulo is the largest city in South America, with crime rates that reflect its size. The number and type of crimes vary considerably around the city, assuming different patterns depending on urban and social characteristics of each particular location. Previous works have mostly focused on the analysis of crimes with the intent of uncovering patterns associated to social factors, seasonality, and urban routine activities. Therefore, those studies and tools are more global in the sense that they are not designed to investigate specific regions of the city such as particular neighborhoods, avenues, or public areas. Tools able to explore specific locations of the city are essential for domain experts to accomplish their analysis in a bottom-up fashion, revealing how urban features related to mobility, passersby behavior, and presence of public infrastructures (e.g., terminals of public transportation and schools) can influence the quantity and type of crimes. In this paper, we present CrimAnalyzer, a visual analytic tool that allows users to study the behavior of crimes in specific regions of a city. The system allows users to identify local hotspots and the pattern of crimes associated to them, while still showing how hotspots and corresponding crime patterns change over time. CrimAnalyzer has been developed from the needs of a team of experts in criminology and deals with three major challenges: i) flexibility to explore local regions and understand their crime patterns, ii) identification of spatial crime hotspots that might not be the most prevalent ones in terms of the number of crimes but that are important enough to be investigated, and iii) understand the dynamic of crime patterns over time. The effectiveness and usefulness of the proposed system are demonstrated by qualitative and quantitative comparisons as well as by case studies run by domain experts involving real data. The experiments show the capability of CrimAnalyzer in identifying crime-related phenomena.

The brachial plexus is a complex network of peripheral nerves that enables sensing from and control of the movements of the arms and hand. Nowadays, the coordination between the muscles to generate simple movements is still not well understood, hindering the knowledge of how to best treat patients with this type of peripheral nerve injury. To acquire enough information for medical data analysis, physicians conduct motion analysis assessments with patients to produce a rich dataset of electromyographic signals from multiple muscles recorded with joint movements during real-world tasks. However, tools for the analysis and visualization of the data in a succinct and interpretable manner are currently not available. Without the ability to integrate, compare, and compute multiple data sources in one platform, physicians can only compute simple statistical values to describe patient's behavior vaguely, which limits the possibility to answer clinical questions and generate hypotheses for research. To address this challenge, we have developed MOTION BROWSER, an interactive visual analytics system which provides an efficient framework to extract and compare muscle activity patterns from the patient's limbs and coordinated views to help users analyze muscle signals, motion data, and video information to address different tasks. The system was developed as a result of a collaborative endeavor between computer scientists and orthopedic surgery and rehabilitation physicians. We present case studies showing physicians can utilize the information displayed to understand how individuals coordinate their muscles to initiate appropriate treatment and generate new hypotheses for future research.

Visual analysis of multidimensional data requires expressive and effective ways to reduce data dimensionality to encode them visually. Multidimensional projections (MDP) figure among the most important visualization techniques in this context, transforming multidimensional data into scatter plots whose visual patterns reflect some notion of similarity in the original data. However, MDP come with distortions that make these visual patterns not trustworthy, hindering users to infer actual data characteristics. Moreover, the patterns present in the scatter plots might not be enough to allow a clear understanding of multidimensional data, motivating the development of layout enrichment methodologies to operate together with MDP. This survey attempts to cover the main aspects of MDP as a visualization and visual analytic tool. It provides detailed analysis and taxonomies as to the organization of MDP techniques according to their main properties and traits, discussing the impact of such properties for visual perception and other human factors. The survey also approaches the different types of distortions that can result from MDP mappings and it overviews existing mechanisms to quantitatively evaluate such distortions. A qualitative analysis of the impact of distortions on the different analytic tasks performed by users when exploring multidimensional data through MDP is also presented. Guidelines for choosing the best MDP for an intended task are also provided as a result of this analysis. Finally, layout enrichment schemes to debunk MDP distortions and/or reveal relevant information not directly inferable from the scatter plot are reviewed and discussed in the light of new taxonomies. We conclude the survey providing future research axes to fill discovered gaps in this domain.

The Convolutional Neural Network (CNN) figures among the state-of-the-art Deep Learning (DL) algorithms due to its robustness to support data shift, scale variations, and its capability of extracting relevant information from large-scale input data. However, setting appropriate parameters to define CNN architectures is still a challenging issue, mainly to tackle real-world problems. A typical approach consists in empirically assessing different CNN settings in order to select the most appropriate one. This procedure has clear limitations, including the choice of suitable predefined configurations as well as the high computational cost involved in evaluating each of them. This work presents a novel methodology to tackle the previously mentioned issues, providing mechanisms to estimate effective CNN configurations, including the size of convolutional masks (convolutional kernels) and the number of convolutional units (CNN neurons) per layer. Based on the False Nearest Neighbors (FNN), a well-known tool from the area of Dynamical Systems, the proposed method helps estimating CNN architectures that are less complex and produce good results. Our experiments confirm that architectures estimated through the proposed approach are as effective as the complex ones defined by empirical and computationally intensive strategies.

Dynamic networks naturally appear in a multitude of applications from different fields. Analyzing and exploring dynamic networks in order to understand and detect patterns and phenomena is challenging, fostering the development of new methodologies, particularly in the field of visual analytics. In this work, we propose a novel visual analytics methodology for dynamic networks, which relies on the spectral graph wavelet theory. We enable the automatic analysis of a signal defined on the nodes of the network, making viable the robust detection of network properties. Specifically, we use a fast approximation of a graph wavelet transform to derive a set of wavelet coefficients, which are then used to identify activity patterns on large networks, including their temporal recurrence. The coefficients naturally encode the spatial and temporal variations of the signal, leading to an efficient and meaningful representation. This methodology allows for the exploration of the structural evolution of the network and their patterns over time. The effectiveness of our approach is demonstrated using usage scenarios and comparisons involving real dynamic networks.

Traditional vector field visualization has a close focus on velocity, and is typically constrained to the dynamics of massless particles. In this paper, we present a novel approach to the analysis of the force-induced dynamics of inertial particles. These forces can arise from acceleration fields such as gravitation, but also be dependent on the particle dynamics itself, as in the case of magnetism. Compared to massless particles, the velocity of an inertial particle is not determined solely by its position and time in a vector field. In contrast, its initial velocity can be arbitrary and impacts the dynamics over its entire lifetime. This leads to a four-dimensional problem for 2D setups, and a six-dimensional problem for the 3D case. Our approach avoids this increase in dimensionality and tackles the visualization by an integrated topological analysis approach. We demonstrate the utility of our approach using a synthetic time-dependent acceleration field, a system of magnetic dipoles, and N-body systems both in 2D and 3D.

Abstract This paper presents a novel method to detect free‐surfaces on particle‐based volume representation. In contrast to most particle‐based free‐surface detection methods, which perform the surface identification based on physical and geometrical properties derived from the underlying fluid flow simulation, the proposed approach only demands the spatial location of the particles to properly recognize surface particles, avoiding even the use of kernels. Boundary particles are identified through a Hidden Point Removal (HPR) operator used for visibility test. Our method is very simple, fast, easy to implement and robust to changes in the distribution of particles, even when facing large deformation of the free‐surface. A set of comparisons against state‐of‐the‐art boundary detection methods show the effectiveness of our approach. The good performance of our method is also attested in the context of fluid flow simulation involving free‐surface, mainly when using level‐sets for rendering purposes.

A music piece contains a large amount of information represented as a series of instructions corresponding to notes that must be played at specific times. These simple notes are combined to form complex harmonic structures that can be difficult to identify and analyze. Due to its simplicity and straightforward interpretation, music sheets and piano rolls have been the visual metaphor employed by most music visualization tools to support interpretation. Albeit it can represent all necessary elements to perform a music piece, these metaphors do not explicitly show many of the patterns and structures inherent to music arrangements, such as rhythm progression and harmonic interactions, needing users to create a mental model of them. Moreover, comparing different pieces and visualizing how a particular instrument track relates to the others is an issue not only for music sheet-based techniques, but also for most existing music visualization methods. In this paper, we present a novel visualization framework, called Music Overview, Stability, and Harmony Visualization (MoshViz), which facilitates the visualization and understanding of music renditions, focusing mainly on the visual analysis of specific musical instruments. Our approach creates a high-level model of music data and highlights structures of interest, enabling a detail+overview visualization to assist users in the task of identifying harmonic and melodic patterns. The usefulness and representativeness of MoshViz are confirmed by a set of user tests which demonstrate that the proposed visual metaphor matches, with a high degree of accuracy, the mental model of different users regarding the recognizable patterns of sounds.

Kernel-based methods have experienced a substantial progress in the last years, tuning out an essential mechanism for data classification, clustering and pattern recognition. The effectiveness of kernel-based techniques, though, depends largely on the capability of the underlying kernel to properly embed data in the feature space associated to the kernel. However, visualizing how a kernel embeds the data in a feature space is not so straightforward, as the embedding map and the feature space are implicitly defined by the kernel. In this work, we present a novel technique to visualize the action of a kernel, that is, how the kernel embeds data into a high-dimensional feature space. The proposed methodology relies on a solid mathematical formulation to map kernelized data onto a visual space. Our approach is faster and more accurate than most existing methods while still allowing interactive manipulation of the projection layout, a game-changing trait that other kernel-based projection techniques do not have.

Existing algorithms for building layouts from geometric primitives are typically designed to cope with requirements such as orthogonal alignment, overlap removal, optimal area usage, hierarchical organization, among others. However, most techniques are able to tackle just a few of those requirements simultaneously, impairing their use and flexibility. In this work we propose a novel methodology for building layouts from geometric primitives that concurrently addresses a wider range of requirements. Relying on multidimensional projection and mixed integer optimization, our approach arranges geometric objects in the visual space so as to generate well structured layouts that preserve the semantic relation among objects while still making an efficient use of display area. Moreover, scalability is handled through a hierarchical representation scheme combined with navigation tools. A comprehensive set of quantitative comparisons against existing geometry-based layouts and applications on text, image, and video data set visualization prove the effectiveness of our approach.

Image inpainting is a challenging topic in computer vision that seeks to recover the natural aspect of an image where data has been partially damaged or occluded by undesired objects. A common drawback not addressed by most inpainting methodologies is that the user must manually provide the inpainting mask as input data to the method. Selecting the inpainting mask is tedious, time consuming and it often requires artistic skills to precisely determine the mask. In this work we design a new tool that allows users to easily select the desirable mask. The proposed framework combines the high-adherence on image contours of the Laplacian Coordinates segmentation approach with the efficiency of a recent inpainting technique that unifies anisotropic diffusion, inner product-based filling order mechanism and exemplar-based completion. The user can interact with the object that he/she intends to edit by stroking small parts of the object so as to proceed with the segmentation and inpainting task. Our comparisons show that the proposed framework has good performance in terms of applicability and effectiveness when compared against other existing techniques in the literature.

Abstract Multidimensional projection‐based visualization methods typically rely on clustering and attribute selection mechanisms to enable visual analysis of multidimensional data. Clustering is often employed to group similar instances according to their distance in the visual space. However, considering only distances in the visual space may be misleading due to projection errors as well as the lack of guarantees to ensure that distinct clusters contain instances with different content. Identifying clusters made up of a few elements is also an issue for most clustering methods. In this work we propose a novel multidimensional projection‐based visualization technique that relies on representative instances to define clusters in the visual space. Representative instances are selected by a deterministic sampling scheme derived from matrix decomposition, which is sensitive to the variability of data while still been able to handle classes with a small number of instances. Moreover, the sampling mechanism can easily be adapted to select relevant attributes from each cluster. Therefore, our methodology unifies sampling, clustering, and feature selection in a simple framework. A comprehensive set of experiments validate our methodology, showing it outperforms most existing sampling and feature selection techniques. A case study shows the effectiveness of the proposed methodology as a visual data analysis tool.

Multidimensional projection techniques provide an appealing approach for multivariate data analysis, for their ability to translate high-dimensional data into a low-dimensional representation that preserves neighborhood information. In recent years, pushed by the ever increasing data complexity in many areas, numerous advances in such techniques have been observed, primarily in terms of computational efficiency and support for interactive applications. Both these achievements were made possible due to the introduction of the concept of control points, which are used in many different multidimensional projection techniques. However, little attention has been drawn towards the process of control points selection. In this work we propose a novel multidimensional projection technique based on radial basis functions (RBF). Our method uses RBF to create a function that maps the data into a low-dimensional space by interpolating the previously calculated position of control points. We also present a built-in method for the control points selection based on "forward-selection" and "Orthogonal Least Squares" techniques. We demonstrate that the proposed selection process allows our technique to work with only a few control points while retaining the projection quality and avoiding redundant control points.

Seed-based image segmentation methods have gained much attention lately, mainly due to their good performance in segmenting complex images with little user interaction. Such popularity leveraged the development of many new variations of seed-based image segmentation techniques, which vary greatly regarding mathematical formulation and complexity. Most existing methods in fact rely on complex mathematical formulations that typically do not guarantee unique solution for the segmentation problem while still being prone to be trapped in local minima. In this work we present a novel framework for seed-based image segmentation that is mathematically simple, easy to implement, and guaranteed to produce a unique solution. Moreover, the formulation holds an anisotropic behavior, that is, pixels sharing similar attributes are kept closer to each other while big jumps are naturally imposed on the boundary between image regions, thus ensuring better fitting on object boundaries. We show that the proposed framework outperform state-of-the-art techniques in terms of quantitative quality metrics as well as qualitative visual results.

Abstract Simplicial meshes are useful as discrete approximations of continuous spaces in numerical simulations. In some applications, however, meshes need to be modified over time. Mesh update operations are often expensive and brittle, making the simulations unstable. In this paper we propose a framework for updating simplicial meshes that undergo geometric and topological changes. Instead of explicitly maintaining connectivity information, we keep a collection of weights associated with mesh vertices, using a Weighted Delaunay Triangulation (WDT). These weights implicitly define mesh connectivity and allow direct merging of triangulations. We propose two formulations for computing the weights, and two techniques for merging triangulations, and finally illustrate our results with examples in two and three dimensions.

We propose an approach for verification of volume rendering correctness based on an analysis of the volume rendering integral, the basis of most DVR algorithms. With respect to the most common discretization of this continuous model (Riemann summation), we make assumptions about the impact of parameter changes on the rendered results and derive convergence curves describing the expected behavior. Specifically, we progressively refine the number of samples along the ray, the grid size, and the pixel size, and evaluate how the errors observed during refinement compare against the expected approximation errors. We derive the theoretical foundations of our verification approach, explain how to realize it in practice, and discuss its limitations. We also report the errors identified by our approach when applied to two publicly available volume rendering packages.

Internet users are very familiar with the results of a search query displayed as a ranked list of snippets. Each textual snippet shows a content summary of the referred document (or webpage) and a link to it. This display has many advantages, for example, it affords easy navigation and is straightforward to interpret. Nonetheless, any user of search engines could possibly report some experience of disappointment with this metaphor. Indeed, it has limitations in particular situations, as it fails to provide an overview of the document collection retrieved. Moreover, depending on the nature of the query--for example, it may be too general, or ambiguous, or ill expressed--the desired information may be poorly ranked, or results may contemplate varied topics. Several search tasks would be easier if users were shown an overview of the returned documents, organized so as to reflect how related they are, content wise. We propose a visualization technique to display the results of web queries aimed at overcoming such limitations. It combines the neighborhood preservation capability of multidimensional projections with the familiar snippet-based representation by employing a multidimensional projection to derive two-dimensional layouts of the query search results that preserve text similarity relations, or neighborhoods. Similarity is computed by applying the cosine similarity over a "bag-of-words" vector representation of collection built from the snippets. If the snippets are displayed directly according to the derived layout, they will overlap considerably, producing a poor visualization. We overcome this problem by defining an energy functional that considers both the overlapping among snippets and the preservation of the neighborhood structure as given in the projected layout. Minimizing this energy functional provides a neighborhood preserving two-dimensional arrangement of the textual snippets with minimum overlap. The resulting visualization conveys both a global view of the query results and visual groupings that reflect related results, as illustrated in several examples shown.

Abstract Interactive visualization systems for exploring and manipulating high‐dimensional feature spaces have experienced a substantial progress in the last few years. State‐of‐art methods rely on solid mathematical and computational foundations that enable sophisticated and flexible interactive tools. Current methods are even capable of modifying data attributes during interaction, highlighting regions of potential interest in the feature space, and building visualizations that bring out the relevance of attributes. However, those methodologies rely on complex and non‐intuitive interfaces that hamper the free handling of the feature spaces. Moreover, visualizing how neighborhood structures are affected during the space manipulation is also an issue for existing methods. This paper presents a novel visualization‐assisted methodology for interacting and transforming data attributes embedded in feature spaces. The proposed approach relies on a combination of multidimensional projections and local transformations to provide an interactive mechanism for modifying attributes. Besides enabling a simple and intuitive visual layout, our approach allows the user to easily observe the changes in neighborhood structures during interaction. The usefulness of our methodology is shown in an application geared to image retrieval.

Abstract In this work we propose a new discretization method for the Laplace–Beltrami operator defined on point‐based surfaces. In contrast to the existing point‐based discretization techniques, our approach does not rely on any triangle mesh structure, turning out truly mesh‐free. Based on a combination of Smoothed Particle Hydrodynamics and an optimization procedure to estimate area elements, our discretization method results in accurate solutions while still being robust when facing abrupt changes in the density of points. Moreover, the proposed scheme results in numerically stable discrete operators. The effectiveness of the proposed technique is brought to bear in many practical applications. In particular, we use the eigenstructure of the discrete operator for filtering and shape segmentation. Point‐based surface deformation is another application that can be easily carried out from the proposed discretization method.

We present a benchmark for the evaluation and comparison of algorithms which reconstruct a surface from point cloud data. Although a substantial amount of effort has been dedicated to the problem of surface reconstruction, a comprehensive means of evaluating this class of algorithms is noticeably absent. We propose a simple pipeline for measuring surface reconstruction algorithms, consisting of three main phases: surface modeling, sampling, and evaluation. We use implicit surfaces for modeling shapes which are capable of representing details of varying size and sharp features. From these implicit surfaces, we produce point clouds by synthetically generating range scans which resemble realistic scan data produced by an optical triangulation scanner. We validate our synthetic sampling scheme by comparing against scan data produced by a commercial optical laser scanner, where we scan a 3D-printed version of the original surface. Last, we perform evaluation by comparing the output reconstructed surface to a dense uniformly distributed sampling of the implicit surface. We decompose our benchmark into two distinct sets of experiments. The first set of experiments measures reconstruction against point clouds of complex shapes sampled under a wide variety of conditions. Although these experiments are quite useful for comparison, they lack a fine-grain analysis. To complement this, the second set of experiments measures specific properties of surface reconstruction, in terms of sampling characteristics and surface features. Together, these experiments depict a detailed examination of the state of surface reconstruction algorithms.

Abstract Word clouds have become one of the most widely accepted visual resources for document analysis and visualization, motivating the development of several methods for building layouts of keywords extracted from textual data. Existing methods are effective to demonstrate content, but are not capable of preserving semantic relationships among keywords while still linking the word cloud to the underlying document groups that generated them. Such representation is highly desirable for exploratory analysis of document collections. In this paper we present a novel approach to build document clouds, named ProjCloud that aim at solving both semantical layouts and linking with document sets. ProjCloud generates a semantically consistent layout from a set of documents. Through a multidimensional projection, it is possible to visualize the neighborhood relationship between highly related documents and their corresponding word clouds simultaneously. Additionally, we propose a new algorithm for building word clouds inside polygons, which employs spectral sorting to maintain the semantic relationship among words. The effectiveness and flexibility of our methodology is confirmed when comparisons are made to existing methods. The technique automatically constructs projection based layouts the user may choose to examine in the form of the point clouds or corresponding word clouds, allowing a high degree of control over the exploratory process.

Robust analysis of vector fields has been established as an important tool for deriving insights from the complex systems these fields model. Traditional analysis and visualization techniques rely primarily on computing streamlines through numerical integration. The inherent numerical errors of such approaches are usually ignored, leading to inconsistencies that cause unreliable visualizations and can ultimately prevent in-depth analysis. We propose a new representation for vector fields on surfaces that replaces numerical integration through triangles with maps from the triangle boundaries to themselves. This representation, called edge maps, permits a concise description of flow behaviors and is equivalent to computing all possible streamlines at a user defined error threshold. Independent of this error streamlines computed using edge maps are guaranteed to be consistent up to floating point precision, enabling the stable extraction of features such as the topological skeleton. Furthermore, our representation explicitly stores spatial and temporal errors which we use to produce more informative visualizations. This work describes the construction of edge maps, the error quantification, and a refinement procedure to adhere to a user defined error bound. Finally, we introduce new visualizations using the additional information provided by edge maps to indicate the uncertainty involved in computing streamlines and topological structures.

The broad goals of verifiable visualization rely on correct algorithmic implementations. We extend a framework for verification of isosurfacing implementations to check topological properties. Specifically, we use stratified Morse theory and digital topology to design algorithms which verify topological invariants. Our extended framework reveals unexpected behavior and coding mistakes in popular publicly available isosurface codes.

Creating high-quality quad meshes from triangulated surfaces is a highly nontrivial task that necessitates consideration of various application specific metrics of quality. In our work, we follow the premise that automatic reconstruction techniques may not generate outputs meeting all the subjective quality expectations of the user. Instead, we put the user at the center of the process by providing a flexible, interactive approach to quadrangulation design. By combining scalar field topology and combinatorial connectivity techniques, we present a new framework, following a coarse to fine design philosophy, which allows for explicit control of the subjective quality criteria on the output quad mesh, at interactive rates. Our quadrangulation framework uses the new notion of Reeb atlas editing, to define with a small amount of interactions a coarse quadrangulation of the model, capturing the main features of the shape, with user prescribed extraordinary vertices and alignment. Fine grain tuning is easily achieved with the notion of connectivity texturing, which allows for additional extraordinary vertices specification and explicit feature alignment, to capture the high-frequency geometries. Experiments demonstrate the interactivity and flexibility of our approach, as well as its ability to generate quad meshes of arbitrary resolution with high-quality statistics, while meeting the user’s own subjective requirements.

Robust analysis of vector fields has been established as an important tool for deriving insights from the complex systems these fields model. Many analysis techniques rely on computing streamlines, a task often hampered by numerical instabilities. Approaches that ignore the resulting errors can lead to inconsistencies that may produce unreliable visualizations and ultimately prevent in-depth analysis. We propose a new representation for vector fields on surfaces that replaces numerical integration through triangles with linear maps defined on its boundary. This representation, called edge maps, is equivalent to computing all possible streamlines at a user defined error threshold. In spite of this error, all the streamlines computed using edge maps will be pairwise disjoint. Furthermore, our representation stores the error explicitly, and thus can be used to produce more informative visualizations. Given a piecewise-linear interpolated vector field, a recent result [15] shows that there are only 23 possible map classes for a triangle, permitting a concise description of flow behaviors. This work describes the details of computing edge maps, provides techniques to quantify and refine edge map error, and gives qualitative and visual comparisons to more traditional techniques.

Abstract Multidimensional projection has emerged as an important visualization tool in applications involving the visual analysis of high‐dimensional data. However, high precision projection methods are either computationally expensive or not flexible enough to enable feedback from user interaction into the projection process. A built‐in mechanism that dynamically adapts the projection based on direct user intervention would make the technique more useful for a larger range of applications and data sets. In this paper we propose the Piecewise Laplacian‐based Projection (PLP), a novel multidimensional projection technique, that, due to the local nature of its formulation, enables a versatile mechanism to interact with projected data and to allow interactive changes to alter the projection map dynamically, a capability unique of this technique. We exploit the flexibility provided by PLP in two interactive projection‐based applications, one designed to organize pictures visually and another to build music playlists. These applications illustrate the usefulness of PLP in handling high‐dimensional data in a flexible and highly visual way. We also compare PLP with the currently most promising projections in terms of precision and speed, showing that it performs very well also according to these quality criteria.

Multidimensional projection techniques have experienced many improvements lately, mainly regarding computational times and accuracy. However, existing methods do not yet provide flexible enough mechanisms for visualization-oriented fully interactive applications. This work presents a new multidimensional projection technique designed to be more flexible and versatile than other methods. This novel approach, called Local Affine Multidimensional Projection (LAMP), relies on orthogonal mapping theory to build accurate local transformations that can be dynamically modified according to user knowledge. The accuracy, flexibility and computational efficiency of LAMP is confirmed by a comprehensive set of comparisons. LAMP's versatility is exploited in an application which seeks to correlate data that, in principle, has no connection as well as in visual exploration of textual documents.

We introduce a flexible technique for interactive exploration of vector field data through classification derived from user-specified feature templates. Our method is founded on the observation that, while similar features within the vector field may be spatially disparate, they share similar neighborhood characteristics. Users generate feature-based visualizations by interactively highlighting well-accepted and domain specific representative feature points. Feature exploration begins with the computation of attributes that describe the neighborhood of each sample within the input vector field. Compilation of these attributes forms a representation of the vector field samples in the attribute space. We project the attribute points onto the canonical 2D plane to enable interactive exploration of the vector field using a painting interface. The projection encodes the similarities between vector field points within the distances computed between their associated attribute points. The proposed method is performed at interactive rates for enhanced user experience and is completely flexible as showcased by the simultaneous identification of diverse feature types.

Most multidimensional projection techniques rely on distance (dissimilarity) information between data instances to embed high-dimensional data into a visual space. When data are endowed with Cartesian coordinates, an extra computational effort is necessary to compute the needed distances, making multidimensional projection prohibitive in applications dealing with interactivity and massive data. The novel multidimensional projection technique proposed in this work, called Part-Linear Multidimensional Projection (PLMP), has been tailored to handle multivariate data represented in Cartesian high-dimensional spaces, requiring only distance information between pairs of representative samples. This characteristic renders PLMP faster than previous methods when processing large data sets while still being competitive in terms of precision. Moreover, knowing the range of variation for data instances in the high-dimensional space, we can make PLMP a truly streaming data projection technique, a trait absent in previous methods.

Public genealogical databases are becoming increasingly populated with historical data and records of the current population's ancestors. As this increasing amount of available information is used to link individuals to their ancestors, the resulting trees become deeper and more dense, which justifies the need for using organized, space-efficient layouts to display the data. Existing layouts are often only able to show a small subset of the data at a time. As a result, it is easy to become lost when navigating through the data or to lose sight of the overall tree structure. On the contrary, leaving space for unknown ancestors allows one to better understand the tree's structure, but leaving this space becomes expensive and allows fewer generations to be displayed at a time. In this work, we propose that the H-tree based layout be used in genealogical software to display ancestral trees. We will show that this layout presents an increase in the number of displayable generations, provides a nicely arranged, symmetrical, intuitive and organized fractal structure, increases the user's ability to understand and navigate through the data, and accounts for the visualization requirements necessary for displaying such trees. Finally, user-study results indicate potential for user acceptance of the new layout.

Visual representations of isosurfaces are ubiquitous in the scientific and engineering literature. In this paper, we present techniques to assess the behavior of isosurface extraction codes. Where applicable, these techniques allow us to distinguish whether anomalies in isosurface features can be attributed to the underlying physical process or to artifacts from the extraction process. Such scientific scrutiny is at the heart of verifiable visualization--subjecting visualization algorithms to the same verification process that is used in other components of the scientific pipeline. More concretely, we derive formulas for the expected order of accuracy (or convergence rate) of several isosurface features, and compare them to experimentally observed results in the selected codes. This technique is practical: in two cases, it exposed actual problems in implementations. We provide the reader with the range of responses they can expect to encounter with isosurface techniques, both under "normal operating conditions" and also under adverse conditions. Armed with this information--the results of the verification process--practitioners can judiciously select the isosurface extraction technique appropriate for their problem of interest, and have confidence in its behavior.

The problem of projecting multidimensional data into lower dimensions has been pursued by many researchers due to its potential application to data analysis of various kinds. This paper presents a novel multidimensional projection technique based on least square approximations. The approximations compute the coordinates of a set of projected points based on the coordinates of a reduced number of control points with defined geometry. We name the technique Least Square Projections (LSP). From an initial projection of the control points, LSP defines the positioning of their neighboring points through a numerical solution that aims at preserving a similarity relationship between the points given by a metric in mD. In order to perform the projection, a small number of distance calculations is necessary and no repositioning of the points is required to obtain a final solution with satisfactory precision. The results show the capability of the technique to form groups of points by degree of similarity in 2D. We illustrate that capability through its application to mapping collections of textual documents from varied sources, a strategic yet difficult application. LSP is faster and more accurate than other existing high quality methods, particularly where it was mostly tested, that is, for mapping text sets.

This paper introduces Least Square Projection (LSP), a fast technique for projection of multi-dimensional data onto lower dimensions developed and tested successfully in the context of creation of text maps based on their content. Current solutions are either based on computationally expensive dimension reduction with no proper guarantee of the outcome or on faster techniques that need some sort of post-processing for recovering information lost during the process. LSP is based on least square approximation, a technique originally employed for surface modeling and reconstruction. Least square approximations are capable of computing the coordinates of a set of projected points based on a reduced number of control points with defined geometry. We extend the concept for general data sets. In order to perform the projection, a small number of distance calculations is necessary and no repositioning of the final points is required to obtain a satisfactory precision of the final solution. Textual information is a typically difficult data type to handle, due to its intrinsic dimensionality. We employ document corpora as a benchmark to demonstrate the capabilities of the LSP to group and separate documents by their content with high precision.

Point-based models are gaining lately considerable attention as an alternative to traditional surface meshes. In this context, Point Set Surfaces (PSS) were proposed as a modeling and rendering method with important topological and approximation properties. However, ray-tracing PSS is computationally expensive. Therefore, we propose an interactive ray-tracing algorithm for PSS implemented completely on commodity graphics hardware. We also exploit the advantages of PSS to propose a novel technique for extracting surfaces directly from volumetric data. This technique is based on the well known predictor-corrector principle from the numerical methods for solving ordinary differential equations. Our technique provides good approximations to surfaces defined by a certain property in the volume, such as iso-surfaces or surfaces located at regions of high gradient magnitude. Also, local details of the surfaces could be manipulated by changing the local polynomial approximation and the smoothing parameters used. Furthermore, the surfaces generated are smooth and low frequency noise is naturally handled.

Despite the significant evolution of techniques for 3D-reconstruction from planar cross sections, establishing the correspondence of regions in adjacent slices remains an important issue. In this article, we propose a novel approach for solving the correspondence problem in a flexible manner. We show that from the 3D Delaunay triangulation, it is possible to derive a distance measure among regions lying in adjacent slices. Such distance is used to define a positive integer parameter, called β, responsible for establishing the connections. Varying β thus allows the construction of different models from a given set of cross-sectional regions: small values of β causes closer regions to be connected into a single component, and as β increases, more distant regions are connected together. The algorithm, named β-connection, is described, and examples are provided that illustrate its applicability in solid modeling and model reconstruction from real data. The underlying reconstruction method is effective, which jointly with the β-connection correspondence strategy, improve the usability of volumetric reconstruction techniques considerably.

This paper introduces the concept of digital planar surfaces and corresponding Morse operators. These operators offer a novel and powerful method for construction and de-construction of such surfaces in a way that global topological control of the resulting object is always maintained. In that respect, this paper offers a complete pixel characterization tool. Image handling is a natural application for such approach. We present a novel fast algorithm for image segmentation using Morse operators for digital planar surfaces. It classifies as a region growing technique with added topological control and is extremely useful for applications that need proper object description. Results from real data are stimulating, and show that the segmentation algorithm compares very well with other methods. The topological approach also forms a base for future expansion to applications such as volume segmentation.

This paper presents a novel algorithm for volumetric reconstruction of objects from planar sections using Delaunay triangulation, which solves the main problems posed to models defined by reconstruction, particularly from the viewpoint of producing meshes that are suitable for interaction and simulation tasks. The requirements for these applications are discussed here and the results of the method are presented. Additionally, it is compared to another commonly used reconstruction algorithm based on Delaunay triangulation, showing the advantages of the reconstructions obtained by our technique.