Gradient meshes are powerful vector graphic primitives known for producing smooth and detailed color transitions. However, their fixed rectangular topology complicates editing, as adding detail in one region introduces control points across the entire mesh. To improve editability and better support artist workflows, we propose a simplification method for gradient meshes based on local refinement. Our method transforms a traditional, globally-refined mesh into a locally-refined one by iteratively merging adjacent faces and eliminating redundant data while preserving visual quality. We achieve this by rasterizing the mesh and applying established visual quality metrics to ensure consistency with the original. Additionally, we offer artists control over the simplification process by introducing an error threshold, allowing them to balance the level of simplification with visual fidelity. Finally, we conduct a thorough comparison of various mesh simplification strategies to analyze the trade-offs between simplification quality and speed so as to inform users to the optimal one that they can use to obtain the desired trade-off.

Among recent graph drawing (GD) methods, tsNET creates high quality layouts but suffers from a very high runtime due to its underlying reliance on the t-SNE projection technique. We address this problem by presenting NNP-NET, a method that adapts NNP, a projection technique that can project high-dimensional datasets linearly in the data size, to handle both unweighted and weighted graphs, with layout quality being very close to the ground-truth tsNET. We also exploit NNP's built-in out-of-sample ability to enable NNP-NET to project time-dependent (dynamic) graphs while striking a good balance between layout stability and good layout quality. We show experiments that outline how NNP-NET can handle very large graphs - up to 50 million nodes and 108 million edges faster than all other comparable methods we are aware of while also yielding good quality metric values.

Fluid simulation is a central topic in computer graphics, encompassing a wide range of methodologies for modeling Newtonian, non-Newtonian, and viscoelastic behaviors across both single-phase and multiphase settings. Existing single-phase frameworks have achieved high visual fidelity, yet multiphase simulations remain limited in accurately capturing complex phase interactions, particularly under high-viscosity-ratio or viscoelastic conditions. To address these challenges, we develop a unified multiphase viscoelastic formulation capable of handling diverse fluid types-including Newtonian, shear-dependent non-Newtonian, and viscoelastic flows-within a single consistent framework. The formulation extends mixture-model approaches through a multi-mode conformation tensor representation, which enhances numerical stability via phase-level stress corrections and efficiently captures a broad spectrum of rheological behaviors. Compared with existing techniques, our framework achieves improved momentum-mass consistency and numerical stability, maintaining physically plausible results across wide viscosity ranges, advancing the state of the art in multiphase viscoelastic fluid simulation.

tsNET is a recent graph drawing (GD) method that creates high quality layouts but suffers from a very high runtime. We present a new GD method, NNP-NET, which reduces tsNET’s time complexity to generate layouts for very large graphs in seconds. Additionally, we extend tsNET to support drawing graphs with edge weights. We accomplish this by replacing tsNET’s t-SNE projection with Neural Network Projection (NNP), a fast dimensionality reduction (DR) method that can imitate any given DR method. Our experiments show that NNP-NET gets good quality results when compared to other state-of-the art GD methods while yielding a better computational scalability.

Graph drawings are commonly used to visualize relational data. User understanding and performance are linked to the quality of such drawings, which is measured by quality metrics. The tacit knowledge in the graph drawing community about these quality metrics is that they are not always able to accurately capture the quality of graph drawings. In particular, such metrics may rate drawings with very poor quality as very good. In this work we make this tacit knowledge explicit by showing that we can modify existing graph drawings into arbitrary target shapes while keeping one or more quality metrics almost identical. This supports the claim that more advanced quality metrics are needed to capture the "goodness" of a graph drawing and that we cannot confidently rely on the value of a single (or several) certain quality metrics.

Simulating the interactions between fluids and porous media has attracted significant attention in computer graphics. A key challenge in this domain is modeling the Poro-Elasto-Capillary (PEC) coupling effect which describes the intricate interplay of three physical phenomena in soft porous materials: pore-structure evolution, elastic deformation, and wetting driven by capillary pressure. These phenomena collectively govern dynamic behavior such as the softening and fracturing of biscuits upon water absorption or the swelling of cellulose sponges due to liquid infiltration. Most existing simulation methods model porous media either as static grids or as solid particles with augmented water content attributes, failing to capture the full spectrum of PEC-driven effects due to the lack of physical modeling for elasticity, dynamic porosity changes, and capillary interactions. We propose a multiphase particle-based framework to holistically simulate PEC coupling effects with porous media. We develop a physics-driven model that captures elasticity and dynamic pore-structure evolution under capillary action, enabling realistic simulation of softening and swelling. We derive a saturation-aware pressure Poisson equation to enforce fluid incompressibility within and around the porous medium, ensuring accurate capillary-driven flow while preserving mass and momentum. Finally, we propose a representative elementary volume-based formulation to unify the modeling of homogeneous macro-porous media and cavity-embedded structures, enhancing the representation of pore-scale PEC effects. Comparisons with prior work and real footage show the advantages of our approach in achieving visually realistic fluid-porous media interactions.

Inverse projections enable a variety of tasks such as the exploration of classifier decision boundaries, creating counterfactual explanations, and generating synthetic data. Yet, many existing inverse projection methods are difficult to implement, challenging to predict, and sensitive to parameter settings. To address these, we propose to invert distance-preserving projections like Multidimensional Scaling (MDS) projections by using multilateration – a method used for geopositioning. Our approach finds data values for locations where no data point is projected under the key assumption that a given projection technique preserves pairwise distances among data samples in the low-dimensional space. Being based on a geometrical relationship, our technique is more interpretable than comparable machine learning-based approaches and can invert 2-dimensional projections up to D − 1 dimensional spaces if given at least D data points. We compare several strategies for multilateration point selection, show the application of our technique on three additional projection techniques apart from MDS, and use established quality metrics to evaluate its accuracy in comparison to existing inverse projections. We also show its application to computing decision maps for exploring the behavior of trained classification models. When the projection to invert captures data distances well, our inverse performs similarly to existing approaches while being interpretable and considerably simpler to compute.

Image representations of the behavior of trained machine learning classification models can help machine learning engineers examine various aspects of a model such as how it partitions its data space into decision zones separated by decision boundaries; how training samples support the decision in various parts of the data space; and how close training data is to decision boundaries. Yet, for an image of n × n pixels, all current methods that create such images have a computational complexity of O ( n 2 ) which precludes their use in interactive visual analytics scenarios. We present a set of techniques for the fast computation of such image-based classifier representations. Compared to earlier work in this area, we accelerate both so-called decision maps, that compute categorical labels, and classifier maps, that compute real-valued quantities, in O ( ( log n ) 2 ) time. Practically, our method has a speed-up of about one order of magnitude and yields results very similar to the ground-truth maps; has no free parameters; is model agnostic; and is simple to implement. We demonstrate our method on several combinations of maps, datasets, and classification models. • We present FastDBM, a fast method for computing 2D maps (images) that match ground-truth results while avoiding costly per-pixel evaluations. • Our method generalizes earlier approaches from categorical to real-valued functions, supporting any (smooth) function. • We evaluate FastDBM with 3 projection techniques, 4 inverse projection techniques, 4 datasets, and 6 classifiers, showing consistent speedups and high-quality results.

Abstract High‐dimensional data analysis often uses dimensionality reduction (DR, also called projection) to map data patterns to human‐digestible visual patterns in a 2D scatterplot. Yet, DR methods may fail to show true data patterns and/or create visual patterns that do not represent any data patterns. Projection Quality Metrics (PQMs) are used as objective measures to gauge the above process: the higher a projection's scores in PQMs, the more it is deemed faithful to the data it represents. We show that, while PQMs can be used as exclusion criteria — low values usually mean poor projections — the converse does not always hold. For this, we develop a technique to automatically generate projections that score similar or even higher PQM values than projections created by well‐known techniques, but show different, often confusing, visual patterns. Our results show that accepted PQMs cannot be used as an exclusive way to tell whether a projection yields accurate and interpretable visual patterns — in this sense, PQMs play a role akin to that of summary statistics in exploratory data analysis. We also show that not all studied metrics can befooled equally well, suggesting a ranking of metrics in their ability to reliably capture quality.

Abstract Graph drawings using a node‐link metaphor and straight edges are widely used to represent and understand relational data. While such drawings are typically created in 2D, 3D representations have also gained popularity. When exploring 3D drawings, finding viewpoints that help understanding the graph's structure is crucial. Finding good viewpoints also allows using the 3D drawings to generate good 2D graph drawings. In this work, we tackle the problem of automatically finding high‐quality viewpoints for 3D graph drawings. We propose and evaluate strategies based on sampling, gradient descent, and evolutionary‐inspired meta‐heuristics. Our results show that most strategies quickly converge to high‐quality viewpoints within a few dozen function evaluations, with meta‐heuristic approaches showing robust performance regardless of the quality metric.

ABSTRACT High‐accuracy point cloud (self‐) reconstruction is crucial for point cloud editing, translation, and unsupervised representation learning. However, existing point cloud reconstruction methods often sacrifice many geometric details. Altough many techniques have proposed how to construct better point cloud decoders, only a few have designed point cloud encoders from a reconstruction perspective. We propose an autodecoder architecture to achieve detail‐preserving point cloud reconstruction while bypassing the performance bottleneck of the encoder. Our architecture is theoretically applicable to any existing point cloud decoder. For training, both the weights of the decoder and the pre‐initialised latent codes, corresponding to the input points, are updated simultaneously. Experimental results demonstrate that our autodecoder achieves an average reduction of 24.62% in Chamfer Distance compared to existing methods, significantly improving reconstruction quality on the ShapeNet dataset. Furthermore, we verify the effectiveness of our autodecoder in point cloud generation, upsampling, and unsupervised representation learning to demonstrate its performance on downstream tasks, which is comparable to the state‐of‐the‐art methods. We will make our code publicly available after peer review.

We present a Lagrangian dynamic importance Monte Carlo method without non-trivial random walks for solving the Velocity-Vorticity Poisson Equation (VVPE) in Smoothed Particle Hydrodynamics (SPH) for vortical flows. Key to our approach is the use of the Kinematic Vorticity Number (KVN) to detect vortex cores and to compute the KVN-based importance of each particle when solving the VVPE. We use Adaptive Kernel Density Estimation (AKDE) to extract a probability density distribution from the KVN for the the Monte Carlo calculations. Even though the distribution of the KVN can be non-trivial, AKDE yields a smooth and normalized result which we dynamically update at each time step. As we sample actual particles directly, the Lagrangian attributes of particle samples ensure that the continuously evolved KVN-based importance, modeled by the probability density distribution extracted from the KVN by AKDE, can be closely followed. Our approach enables effective vortical flow simulations with significantly reduced computational overhead and comparable quality to the classic Biot-Savart law that in contrast requires expensive global particle querying.

Bone cement filling is an important method for preventing osteoporosis and treating fractures. In bone cement filling surgery, the preparation and dosage of the cement usually depend on specific product manuals and the doctor’s experience. If bone cement is not used properly, it may cause additional damage. For teaching and auxiliary medical purposes, for example, assisting doctors to observe the possible flow of bone cement, this paper proposes a multiphase non-Newtonian fluid simulation method to simulate and visualize the flow behavior during the wet sand phase of bone cement blending and polymerization. Our method enables showing intuitively the application process of bone cement under different scene settings to obtain dynamic bone cement effects with high stability and performance. Compared with other methods, our method can simulate highly viscous mixed fluids efficiently and robustly, which supports our method’s usage in the aforementioned training and experimentation scenarios.

Multidimensional projections are effective techniques for depicting high-dimensional data. The point patterns created by such techniques, or a technique’s visual signature , depend — apart from the data themselves — on the technique design and its parameter settings. Controlling such visual signatures — something that only few projections allow — can bring additional freedom for generating insightful depictions of the data. We present a novel projection technique — ShaRP — that allows explicit control on such visual signatures in terms of shapes of similar-value point clusters (settable to rectangles, triangles, ellipses, and convex polygons) and the projection space (2D or 3D Euclidean or S 2 ). We show that ShaRP scales computationally well with dimensionality and dataset size, provides its signature-control by a small set of parameters, allows trading off projection quality to signature enforcement, and can be used to generate decision maps to explore the behavior of trained machine-learning classifiers.

We present a set of interactive visual analysis techniques aiming at explaining data patterns in multidimensional projections. Our novel techniques include a global value-based encoding that highlights point groups having outlier values in any dimension as well as several local tools that provide details on the statistics of all dimensions for a user-selected projection area. Our techniques generically apply to any projection algorithm and scale computationally well to hundreds of thousands of points and hundreds of dimensions. We describe a user study that shows that our visual tools can be quickly learned and applied by users to obtain non-trivial insights in real-world multidimensional datasets. We also show how our techniques can help understanding a real-world dataset containing quantitative, ordinal, and categorical attributes.

Abstract As the complexity of machine learning (ML) models increases and their application in different (and critical) domains grows, there is a strong demand for more interpretable and trustworthy ML. A direct, model‐agnostic, way to interpret such models is to train surrogate models—such as rule sets and decision trees—that sufficiently approximate the original ones while being simpler and easier‐to‐explain. Yet, rule sets can become very lengthy, with many if–else statements, and decision tree depth grows rapidly when accurately emulating complex ML models. In such cases, both approaches can fail to meet their core goal—providing users with model interpretability. To tackle this, we propose DeforestVis, a visual analytics tool that offers summarization of the behaviour of complex ML models by providing surrogate decision stumps (one‐level decision trees) generated with the Adaptive Boosting (AdaBoost) technique. DeforestVis helps users to explore the complexity versus fidelity trade‐off by incrementally generating more stumps, creating attribute‐based explanations with weighted stumps to justify decision making, and analysing the impact of rule overriding on training instance allocation between one or more stumps. An independent test set allows users to monitor the effectiveness of manual rule changes and form hypotheses based on case‐by‐case analyses. We show the applicability and usefulness of DeforestVis with two use cases and expert interviews with data analysts and model developers.

Abstract Explaining Machine Learning (ML) — and especially Deep Learning (DL) — classifiers' decisions is a subject of interest across fields due to the increasing ubiquity of such models in computing systems. As models get increasingly complex, relying on sophisticated machinery to recognize data patterns, explaining their behavior becomes more difficult. Directly visualizing classifier behavior is in general infeasible, as they create partitions of the data space, which is typically high dimensional. In recent years, Decision Boundary Maps (DBMs) have been developed, taking advantage of projection and inverse projection techniques. By being able to map 2D points back to the data space and subsequently run a classifier, DBMs represent a slice of classifier outputs. However, we recognize that DBMs without additional explanatory views are limited in their applicability. In this work, we propose augmenting the naive DBM generating process with views that provide more in‐depth information about classifier behavior, such as whether the training procedure is locally stable. We describe our proposed views — which we term Differentiable Decision Boundary Maps — over a running example, explaining how our work enables drawing new and useful conclusions from these dense maps. We further demonstrate the value of these conclusions by showing how useful they would be in carrying out or preventing a dataset poisoning attack. We thus provide evidence of the ability of our proposed views to make DBMs significantly more trustworthy and interpretable, increasing their utility as a model understanding tool.

Abstract Node‐link diagrams are a widely used metaphor for creating visualizations of relational data. Most frequently, such techniques address creating 2D graph drawings, which are easy to use on computer screens and in print. In contrast, 3D node‐link graph visualizations are far less used, as they have many known limitations and comparatively few well‐understood advantages. A key issue here is that such 3D visualizations require users to select suitable viewpoints. We address this limitation by studying the ability of layout techniques to produce high‐quality views of 3D graph drawings. For this, we perform a thorough experimental evaluation, comparing 3D graph drawings, rendered from a covering sampling of all viewpoints, with their 2D counterparts across various state‐of‐the‐art node‐link drawing algorithms, graph families, and quality metrics. Our results show that, depending on the graph family, 3D node‐link diagrams can contain a many viewpoints that yield 2D visualizations that are of higher quality than those created by directly using 2D node‐link diagrams. This not only sheds light on the potential of 3D node‐link diagrams but also gives a simple approach to produce high‐quality 2D node‐link diagrams.

Abstract For vortex particle methods relying on SPH‐based simulations, the direct approach of iterating all fluid particles to capture velocity from vorticity can lead to a significant computational overhead during the Biot‐Savart summation process. To address this challenge, we present a Monte Carlo vortical smoothed particle hydrodynamics (MCVSPH) method for efficiently simulating turbulent flows within an SPH framework. Our approach harnesses a Monte Carlo estimator and operates exclusively within a pre‐sampled particle subset, thus eliminating the need for costly global iterations over all fluid particles. Our algorithm is decoupled from various projection loops which enforce incompressibility, independently handles the recovery of turbulent details, and seamlessly integrates with state‐of‐the‐art SPH‐based incompressibility solvers. Our approach rectifies the velocity of all fluid particles based on vorticity loss to respect the evolution of vorticity, effectively enforcing vortex motions. We demonstrate, by several experiments, that our MCVSPH method effectively preserves vorticity and creates visually prominent vortical motions.

Abstract We propose an SPH‐based method for simulating viscoelastic non‐Newtonian fluids within a multiphase framework. For this, we use mixture models to handle component transport and conformation tensor methods to handle the fluid's viscoelastic stresses. In addition, we consider a bonding effects network to handle the impact of microscopic chemical bonds on phase transport. Our method supports the simulation of both steady‐state viscoelastic fluids and discontinuous shear behavior. Compared to previous work on single‐phase viscous non‐Newtonian fluids, our method can capture more complex behavior, including material mixing processes that generate non‐Newtonian fluids. We adopt a uniform set of variables to describe shear thinning, shear thickening, and ordinary Newtonian fluids while automatically calculating local rheology in inhomogeneous solutions. In addition, our method can simulate large viscosity ranges under explicit integration schemes, which typically requires implicit viscosity solvers under earlier single‐phase frameworks.

Physics-based fluid simulation has played an increasingly important role in the computer graphics community. Recent methods in this area have greatly improved the generation of complex visual effects and its computational efficiency. Novel techniques have emerged to deal with complex boundaries, multiphase fluids, gas–liquid interfaces, and fine details. The parallel use of machine learning, image processing, and fluid control technologies has brought many interesting and novel research perspectives. In this survey, we provide an introduction to theoretical concepts underpinning physics-based fluid simulation and their practical implementation, with the aim for it to serve as a guide for both newcomers and seasoned researchers to explore the field of physics-based fluid simulation, with a focus on developments in the last decade. Driven by the distribution of recent publications in the field, we structure our survey to cover physical background; discretization approaches; computational methods that address scalability; fluid interactions with other materials and interfaces; and methods for expressive aspects of surface detail and control. From a practical perspective, we give an overview of existing implementations available for the above methods.

Is it true that if citizens understand hurricane probabilities, they will make more rational decisions for evacuation? Finding answers to such questions is not straightforward in the literature because the terms "judgment" and "decision making" are often used interchangeably. This terminology conflation leads to a lack of clarity on whether people make suboptimal decisions because of inaccurate judgments of information conveyed in visualizations or because they use alternative yet currently unknown heuristics. To decouple judgment from decision making, we review relevant concepts from the literature and present two preregistered experiments (N = 601) to investigate if the task (judgment versus decision making), the scenario (sports versus humanitarian), and the visualization (quantile dotplots, density plots, probability bars) affect accuracy. While experiment 1 was inconclusive, we found evidence for a difference in experiment 2. Contrary to our expectations and previous research, which found decisions less accurate than their direct-equivalent judgments, our results pointed in the opposite direction. Our findings further revealed that decisions were less vulnerable to status-quo bias, suggesting decision makers may disfavor responses associated with inaction. We also found that both scenario and visualization types can influence people's judgments and decisions. Although effect sizes are not large and results should be interpreted carefully, we conclude that judgments cannot be safely used as proxy tasks for decision making, and discuss implications for visualization research and beyond. Materials and preregistrations are available at https://osf.io/ufzp5/?view_only=adc0f78a23804c31bf7fdd9385cb264f.

Particle-based simulations have become increasingly popular in real-time applications due to their efficiency and adaptability, especially for generating highly dynamic fluid effects. However, the swift and stable simulation of interactions among distinct fluids continues to pose challenges for current mixture model techniques. When using a single-mixture flow field to represent all fluid phases, numerical discontinuities in phase fields can result in significant losses of dynamic effects and unstable conservation of mass and momentum. To tackle these issues, we present an advanced implicit mixture model for smoothed particle hydrodynamics. Instead of relying on an explicit mixture field for all dynamic computations and phase transfers between particles, our approach calculates phase momentum sources from the mixture model to derive explicit and continuous velocity phase fields. We then implicitly obtain the mixture field using a phase-mixture momentum-mapping mechanism that ensures conservation of incompressibility, mass, and momentum. In addition, we propose a mixture viscosity model and establish viscous effects between the mixture and individual fluid phases to avoid instability under extreme inertia conditions. Through a series of experiments, we show that, compared to existing mixture models, our method effectively improves dynamic effects while reducing critical instability factors. This makes our approach especially well-suited for long-duration, efficiency-oriented virtual reality scenarios.

Software visualization (softvis) and information visualization (infovis) have a long, interconnected, and complex joint history. Originally appearing as a subdomain of infovis which focuses on solving problems coming from the software engineering domain, softvis has grown in the last two decades to become a selfstanding field with distinct challenges, key results, events, and community. In the same time, the independent growth of the two fields has made the transfer of ideas, techniques, methods, application cases, and researchers between the two domains increasingly challenges. In this talk, I will present a history of this highly dynamic process and argue about the need for raprochemment of infovis and softvis. This need is supported by two key aspects identified and further discussed: (1) Complementarity of the two fields advocates for more interaction, as shown by success stories from softvis which led to entirely novel branches of development into the infovis field and, conversely, recent key developments in infovis which offer strong potential to be picked up to address existing key challenges in softvis. (2) Commonality, in terms of both fields essentially aiming to solve very similar visualization problems that address very similar data and using related visualization pipelines, advocates on an increasingly joint approach in their further development.

The use of social media has become so popular that people share photos every day on them. Automatic face recognition and tagging of people's photos have caused privacy preservation issues and some methods have been proposed for hiding the identity of presented people in these images. Blurring and blacking the face area, adding physical adversarial patches to the face, and adding adversarial masks are some proposed methods for this purpose. However, these methods particularly suffer from dissimilarity of the input and output images and inadequate performance in identity concealment from automatic face recognition (AFR) systems. In this paper, we propose the Generative Mask-guided Face Image Manipulation (GMFIM) model based on Generative Adversarial Networks (GANs) to apply imperceptible edits to the input face image to preserve the identity of the person in the image. Our model consists of a face mask module, a GAN-based optimization module, and a merge module. Different criteria are considered in the objective function of the optimization step to produce high-quality images that are as similar as possible to the input image while they cannot be recognized by AFR systems. The results of the experiments on different datasets show that our model provides promising results in terms of the quality of the generated images and the identity concealment performance.

Projection techniques are often used to visualize high-dimensional data, allowing users to better understand the overall structure of multi-dimensional spaces on a 2D screen. Although many such methods exist, comparably little work has been done on generalizable methods of inverse-projection - the process of mapping the projected points, or more generally, the projection space back to the original high-dimensional space. In this article we present NNInv, a deep learning technique with the ability to approximate the inverse of any projection or mapping. NNInv learns to reconstruct high-dimensional data from any arbitrary point on a 2D projection space, giving users the ability to interact with the learned high-dimensional representation in a visual analytics system. We provide an analysis of the parameter space of NNInv, and offer guidance in selecting these parameters. We extend validation of the effectiveness of NNInv through a series of quantitative and qualitative analyses. We then demonstrate the method's utility by applying it to three visualization tasks: interactive instance interpolation, classifier agreement, and gradient visualization.

The ability to edit an image using intuitive commands and primitives is a desired feature for any image editing software. In this paper, we combine recent results in medial axes with the well-established morphological tree representations to develop an interactive image editing tool that provides global and local image manipulation using high-level primitives. We propose a new way to render interactive morphological trees using icicle plots and introduce different ways of manipulating spline-based medial axis transforms for grayscale and colored image editing. Different applications of the tool, such as watermark removal, image deformation, dataset augmentation for machine learning, artistic illumination manipulation, image rearrangement, and clothing design, are described and showcased on examples.

Abstract Projection algorithms such as t‐SNE or UMAP are useful for the visualization of high dimensional data, but depend on hyperparameters which must be tuned carefully. Unfortunately, iteratively recomputing projections to find the optimal hyperparameter values is computationally intensive and unintuitive due to the stochastic nature of such methods. In this paper we propose HyperNP, a scalable method that allows for real‐time interactive hyperparameter exploration of projection methods by training neural network approximations. A HyperNP model can be trained on a fraction of the total data instances and hyperparameter configurations that one would like to investigate and can compute projections for new data and hyperparameters at interactive speeds. HyperNP models are compact in size and fast to compute, thus allowing them to be embedded in lightweight visualization systems. We evaluate the performance of HyperNP across three datasets in terms of performance and speed. The results suggest that HyperNP models are accurate, scalable, interactive, and appropriate for use in real‐world settings.

Abstract We propose USTNet, a novel deep learning approach designed for learning shape‐to‐shape translation from unpaired domains in an unsupervised manner. The core of our approach lies in disentangled representation learning that factors out the discriminative features of 3D shapes into content and style codes. Given input shapes from multiple domains, USTNet disentangles their representation into style codes that contain distinctive traits across domains and content codes that contain domain‐invariant traits. By fusing the style and content codes of the target and source shapes, our method enables us to synthesize new shapes that resemble the target style and retain the content features of source shapes. Based on the shared style space, our method facilitates shape interpolation by manipulating the style attributes from different domains. Furthermore, by extending the basic building blocks of our network from two‐class to multi‐class classification, we adapt USTNet to tackle multi‐domain shape‐to‐shape translation. Experimental results show that our approach can generate realistic and natural translated shapes and that our method leads to improved quantitative evaluation metric results compared to 3DSNet. Codes are available at https://Haoran226.github.io/USTNet .

Infographics range from minimalism that aims to convey the raw data to elaborately decorated, or embellished, graphics that aim to engage readers by telling a story. Several studies have shown evidence to negative, but also positive, effects on embellishments. We conducted a set of experiments to gauge more precisely how embellishments affect how people relate to infographics and make sense of the conveyed story. By analyzing questionnaires, interviews, and eye-tracking data simplified by bundling, we show that, within bounds, embellishments have a positive effect on how users get engaged in understanding an infographic, with very limited downside. To our knowledge, our work is the first that fuses the aforementioned three information sources to understand infographics. Our findings can help to design more fine-grained studies to quantify the effects of embellishments and also to design infographics that effectively use the embellishments’ positive aspects identified. I think the contribution does not appear well in the abstract. It’s not just that the visual embellishments are positive. We show a methodology that allows us to see what these effects are (in addition to engagement, memorization and recall) at several levels (scales, interviews, eye tracking) which are therefore physiological and emotional. We could include this idea in the abstract?

Multidimensional projections (MPs) are effective methods for visualizing high-dimensional datasets to find structures in the data like groups of similar points and outliers. The insights obtained from MPs can be amplified by complementing these techniques by several so-called explanatory mechanisms. We present and discuss a set of six such mechanisms that explain MPs in terms of similar dimensions, local dimensionality, and dimension correlations. We implement our explanatory tools using an image-based approach, which is efficient to compute, scales well visually for large and dense MP scatterplots, and can handle any projection technique. We demonstrate how the provided explanatory views can be combined to augment each other’s value and thereby lead to refined insights in the data for several high-dimensional datasets, and how these insights correlate with known facts about the data under study.

Medial axes are well-known descriptors used for representing, manipulating, and compressing binary images. In this paper, we present a full pipeline for computing a stable and accurate piece-wise B-spline representation of Medial Axis Transforms (MATs) of binary images. A comprehensive evaluation on a benchmark shows that our method, called Spline-based Medial Axis Transform (SMAT), achieves very high compression ratios while keeping quality high. Compared with the regular MAT representation, the SMAT yields a much higher compression ratio at the cost of a slightly lower image quality. We illustrate our approach on a multi-scale SMAT representation, generating super-resolution images, and free-form binary image deformation.

Abstract A major issue in smoothed particle hydrodynamics (SPH) approaches is the numerical dissipation during the projection process, especially under coarse discretizations. High‐frequency details, such as turbulence and vortices, are smoothed out, leading to unrealistic results. To address this issue, we introduce a vorticity refinement (VR) solver for SPH fluids with negligible computational overhead. In this method, the numerical dissipation of the vorticity field is recovered by the difference between the theoretical and the actual vorticity, so as to enhance turbulence details. Instead of solving the Biot‐Savart integrals, a stream function, which is easier and more efficient to solve, is used to relate the vorticity field to the velocity field. We obtain turbulence effects of different intensity levels by changing an adjustable parameter. Since the vorticity field is enhanced according to the curl field, our method can not only amplify existing vortices, but also capture additional turbulence. Our VR solver is straightforward to implement and can be easily integrated into existing SPH methods.

Abstract Projections aim to convey the relationships and similarity of high‐dimensional data in a low‐dimensional representation. Most such techniques are designed for static data. When used for time‐dependent data, they usually fail to create a stable and suitable low dimensional representation. We propose two dynamic projection methods (PCD‐tSNE and LD‐tSNE) that use global guides to steer projection points. This avoids unstable movement that does not encode data dynamics while keeping t‐SNE's neighborhood preservation ability. PCD‐tSNE scores a good balance between stability, neighborhood preservation, and distance preservation, while LD‐tSNE allows creating stable and customizable projections. We compare our methods to 11 other techniques using quality metrics and datasets provided by a recent benchmark for dynamic projections.

Dimensionality reduction methods, also known as projections, are frequently used in multidimensional data exploration in machine learning, data science, and information visualization. Tens of such techniques have been proposed, aiming to address a wide set of requirements, such as ability to show the high-dimensional data structure, distance or neighborhood preservation, computational scalability, stability to data noise and/or outliers, and practical ease of use. However, it is far from clear for practitioners how to choose the best technique for a given use context. We present a survey of a wide body of projection techniques that helps answering this question. For this, we characterize the input data space, projection techniques, and the quality of projections, by several quantitative metrics. We sample these three spaces according to these metrics, aiming at good coverage with bounded effort. We describe our measurements and outline observed dependencies of the measured variables. Based on these results, we draw several conclusions that help comparing projection techniques, explain their results for different types of data, and ultimately help practitioners when choosing a projection for a given context. Our methodology, datasets, projection implementations, metrics, visualizations, and results are publicly open, so interested stakeholders can examine and/or extend this benchmark.

We present co-skeletons, a new method that computes consistent curve skeletons for 3D shapes from a given family. We compute co-skeletons in terms of sampling density and semantic relevance, while preserving the desired characteristics of traditional, per-shape curve skeletonization approaches. We take the curve skeletons extracted by traditional approaches for all shapes from a family as input, and compute semantic correlation information of individual skeleton branches to guide an edge-pruning process via skeleton-based descriptors, clustering, and a voting algorithm. Our approach achieves more concise and family-consistent skeletons when compared to traditional per-shape methods. We show the utility of our method by using co-skeletons for shape segmentation and shape blending on real-world data.

Abstract Animated visualizations are one of the methods for finding and understanding complex structures of time‐dependent vector fields. Many visualization designs can be used to this end, such as streamlines, vector glyphs, and image‐based techniques. While all such designs can depict any vector field, their effectiveness in highlighting particular field aspects has not been fully explored. To fill this gap, we compare three animated vector field visualization techniques, OLIC, IBFV, and particles, for a critical point detection‐and‐classification task through a user study. Our results show that the effectiveness of the studied techniques depends on the nature of the critical points. We use these results to design a new flow visualization technique that combines all studied techniques in a single view by locally using the most effective technique for the patterns present in the flow data at that location. A second user study shows that our technique is more efficient and less error prone than the three other techniques used individually for the critical point detection task.

Abstract Dimensionality reduction methods are an essential tool for multidimensional data analysis, and many interesting processes can be studied as time‐dependent multivariate datasets. There are, however, few studies and proposals that leverage on the concise power of expression of projections in the context of dynamic/temporal data. In this paper, we aim at providing an approach to assess projection techniques for dynamic data and understand the relationship between visual quality and stability. Our approach relies on an experimental setup that consists of existing techniques designed for time‐dependent data and new variations of static methods. To support the evaluation of these techniques, we provide a collection of datasets that has a wide variety of traits that encode dynamic patterns, as well as a set of spatial and temporal stability metrics that assess the quality of the layouts. We present an evaluation of 9 methods, 10 datasets, and 12 quality metrics, and elect the best‐suited methods for projecting time‐dependent multivariate data, exploring the design choices and characteristics of each method. Additional results can be found in the online benchmark repository. We designed our evaluation pipeline and benchmark specifically to be a live resource, open to all researchers who can further add their favorite datasets and techniques at any point in the future.

Abstract Rectangular treemaps are often the method of choice to visualize large hierarchical datasets. Nowadays such datasets are available over time, hence there is a need for (a) treemaps that can handle time‐dependent data, and (b) corresponding quality criteria that cover both a treemap's visual quality and its stability over time. In recent years a wide variety of (stable) treemapping algorithms has been proposed, with various advantages and limitations. We aim to provide insights to researchers and practitioners to allow them to make an informed choice when selecting a treemapping algorithm for specific applications and data. To this end, we perform an extensive quantitative evaluation of rectangular treemaps for time‐dependent data. As part of this evaluation we propose a novel classification scheme for time‐dependent datasets. Specifically, we observe that the performance of treemapping algorithms depends on the characteristics of the datasets used. We identify four potential representative features that characterize time‐dependent hierarchical datasets and classify all datasets used in our experiments accordingly. We experimentally test the validity of this classification on more than 2000 datasets, and analyze the relative performance of 14 state‐of‐the‐art rectangular treemapping algorithms across varying features. Finally, we visually summarize our results with respect to both visual quality and stability to aid users in making an informed choice among treemapping algorithms. All datasets, metrics, and algorithms are openly available to facilitate reuse and further comparative studies.

Principal curves are a long-standing and well-known method for summarizing large scatterplots. They are defined as self-consistent curves (or curve sets in the more general case) that locally pass through the middle of the scatterplot data. However, computing principal curves that capture well complex scatterplot topologies and are robust to noise is hard and/or slow for large scatterplots. We present a fast and robust approach for computing principal graphs (a generalization of principal curves for more complex topologies) inspired by the similarity to medial descriptors (curves locally centered in a shape). Compared to state-of-the-art methods for computing principal graphs, we outperform these in terms of computational scalability and robustness to noise and resolution. We also demonstrate the advantages of our method over other scatterplot summarization approaches.

Finding the ideal number of layers and size for each layer is a key challenge in deep neural network design. Two approaches for such networks exist: filter learning and architecture learning. While the first one starts with a given architecture and optimizes model weights, the second one aims to find the best architecture. Recently, several visual analytics (VA) techniques have been proposed to understand the behavior of a network, but few VA techniques support designers in architectural decisions. We propose a hybrid methodology based on VA to improve the architecture of a pre-trained network by reducing/increasing the size and number of layers. We introduce Activation Occurrence Maps that show how likely each image position of a convolutional kernel’s output activates for a given class, and Class Selectivity Maps, that show the selectiveness of different positions in a kernel’s output for a given label. Both maps help in the decision to drop kernels that do not significantly add to the network’s performance, increase the size of a layer having too few kernels, and add extra layers to the model. The user interacts from the first to the last layer, and the network is retrained after each layer modification. We validate our approach with experiments in models trained with two widely-known image classification datasets and show how our method helps to make design decisions to improve or to simplify the architectures of such models.

• High-dimensional descriptors. • Machine-learned descriptors. • Texture retrieval.

Abstract Origin‐destination (OD) trails describe movements across space. Typical visualizations thereof use either straight lines or plot the actual trajectories. To reduce clutter inherent to visualizing large OD datasets, bundling methods can be used. Yet, bundling OD trails in urban traffic data remains challenging. Two specific reasons hereof are the constraints implied by the underlying road network and the difficulty of finding good bundling settings. To cope with these issues, we propose a new approach called Route Aware Edge Bundling (RAEB). To handle road constraints, we first generate a hierarchical model of the road‐and‐trajectory data. Next, we derive optimal bundling parameters, including kernel size and number of iterations, for a user‐selected level of detail of this model, thereby allowing users to explicitly trade off simplification vs accuracy. We demonstrate the added value of RAEB compared to state‐of‐the‐art trail bundling methods on both synthetic and real‐world traffic data for tasks that include the preservation of road network topology and the support of multiscale exploration.

Occlusion is an issue in volumetric visualization as it prevents direct visualization of the region of interest. While many techniques such as transfer functions, volume segmentation or view distortion have been developed to address this, there is still room for improvement to better support the understanding of objects' vicinity. However, most existing Focus+Context fail to solve partial occlusion in datasets where the target and the occluder are very similar density-wise. For these reasons, we investigate a new technique which maintains the general structure of the investigated volumetric dataset while addressing occlusion issues. With our technique, the user interactively defines an area of interest where an occluded region or object is partially visible. Then our lens starts pushing at its border occluding objects, thus revealing hidden volumetric data. Next, the lens is modified with an extended field of view (fish-eye deformation) to better see the vicinity of the selected region. Finally, the user can freely explore the surroundings of the area under investigation within the lens. To provide real-time exploration, we implemented our lens using a GPU accelerated ray-casting framework to handle ray deformations, local lighting, and local viewpoint manipulation. We illustrate our technique with five application scenarios in baggage inspection, 3D fluid flow visualization, chest radiology, air traffic planning, and DTI fiber exploration.

Dynamic treemaps are one of the methods of choice for displaying large hierarchies that change over time, such as those encoding the structure of evolving software systems. While quality criteria (and algorithms that optimize for them) are known for static trees, far less has been studied for treemapping dynamic trees. We address this gap by proposing a methodology and associated quality metrics to measure the quality of dynamic treemaps for the specific use-case and context of software evolution visualization. We apply our methodology on a benchmark containing a wide range of real-world software repositories and 12 well-known treemap algorithms. Based on our findings, we discuss the observed advantages and limitations of various treemapping algorithms for visualizing software structure evolution, and propose ways for users to choose the most suitable treemap algorithm based on the targeted criteria of interest.

Bundling visually aggregates curves to reduce clutter and help finding important patterns in trail-sets or graph drawings. We propose a new approach to bundling based on functional decomposition of the underling dataset. We recover the functional nature of the curves by representing them as linear combinations of piecewise-polynomial basis functions with associated expansion coefficients. Next, we express all curves in a given cluster in terms of a centroid curve and a complementary term, via a set of so-called principal component functions. Based on the above, we propose a two-fold contribution: First, we use cluster centroids to design a new bundling method for 2D and 3D curve-sets. Secondly, we deform the cluster centroids and generate new curves along them, which enables us to modify the underlying data in a statistically-controlled way via its simplified (bundled) view. We demonstrate our method by applications on real-world 2D and 3D datasets for graph bundling, trajectory analysis, and vector field and tensor field visualization.

Scatterplot matrices (SPLOMs) are widely used for exploring multidimensional data. Scatterplot diagnostics (scagnostics) approaches measure characteristics of scatterplots to automatically find potentially interesting plots, thereby making SPLOMs more scalable with the dimension count. While statistical measures such as regression lines can capture orientation, and graph-theoretic scagnostics measures can capture shape, there is no scatterplot characterization measure that uses both descriptors. Based on well-known results in shape analysis, we propose a scagnostics approach that captures both scatterplot shape and orientation using skeletons (or medial axes). Our representation can handle complex spatial distributions, helps discovery of principal trends in a multiscale way, scales visually well with the number of samples, is robust to noise, and is automatic and fast to compute. We define skeleton-based similarity metrics for the visual exploration and analysis of SPLOMs. We perform a user study to measure the human perception of scatterplot similarity and compare the outcome to our results as well as to graph-based scagnostics and other visual quality metrics. Our skeleton-based metrics outperform previously defined measures both in terms of closeness to perceptually-based similarity and computation time efficiency.

Edge bundling techniques provide a visual simplification of cluttered graph drawings or trail sets. While many bundling techniques exist, only few recent ones can handle large datasets and also allow selective bundling based on edge attributes. We present a new technique that improves on both above points, in terms of increasing both the scalability and computational speed of bundling, while keeping the quality of the results on par with state-of-the-art techniques. For this, we shift the bundling process from the image space to the spectral (frequency) space, thereby increasing computational speed. We address scalability by proposing a data streaming process that allows bundling of extremely large datasets with limited GPU memory. We demonstrate our technique on several real-world datasets and by comparing it with state-of-the-art bundling methods.

Abstract We propose a new graph layout method based on a modification of the t‐distributed Stochastic Neighbor Embedding (t‐SNE) dimensionality reduction technique. Although t‐SNE is one of the best techniques for visualizing high‐dimensional data as 2D scatterplots, t‐SNE has not been used in the context of classical graph layout. We propose a new graph layout method, tsNET, based on representing a graph with a distance matrix, which together with a modified t‐SNE cost function results in desirable layouts. We evaluate our method by a formal comparison with state‐of‐the‐art methods, both visually and via established quality metrics on a comprehensive benchmark, containing real‐world and synthetic graphs. As evidenced by the quality metrics and visual inspection, tsNET produces excellent layouts.

Abstract Bundling techniques provide a visual simplification of a graph drawing or trail set, by spatially grouping similar graph edges or trails. This way, the structure of the visualization becomes simpler and thereby easier to comprehend in terms of assessing relations that are encoded by such paths, such as finding groups of strongly interrelated nodes in a graph, finding connections between spatial regions on a map linked by a number of vehicle trails, or discerning the motion structure of a set of objects by analyzing their paths. In this state of the art report, we aim to improve the understanding of graph and trail bundling via the following main contributions. First, we propose a data‐based taxonomy that organizes bundling methods on the type of data they work on (graphs vs trails, which we refer to as paths). Based on a formal definition of path bundling, we propose a generic framework that describes the typical steps of all bundling algorithms in terms of high‐level operations and show how existing method classes implement these steps. Next, we propose a description of tasks that bundling aims to address. Finally, we provide a wide set of example applications of bundling techniques and relate these to the above‐mentioned taxonomies. Through these contributions, we aim to help both researchers and users to understand the bundling landscape as well as its technicalities.

In machine learning, pattern classification assigns high-dimensional vectors (observations) to classes based on generalization from examples. Artificial neural networks currently achieve state-of-the-art results in this task. Although such networks are typically used as black-boxes, they are also widely believed to learn (high-dimensional) higher-level representations of the original observations. In this paper, we propose using dimensionality reduction for two tasks: visualizing the relationships between learned representations of observations, and visualizing the relationships between artificial neurons. Through experiments conducted in three traditional image classification benchmark datasets, we show how visualization can provide highly valuable feedback for network designers. For instance, our discoveries in one of these datasets (SVHN) include the presence of interpretable clusters of learned representations, and the partitioning of artificial neurons into groups with apparently related discriminative roles.

Abstract Given a shape, a skeleton is a thin centered structure which jointly describes the topology and the geometry of the shape. Skeletons provide an alternative to classical boundary or volumetric representations, which is especially effective for applications where one needs to reason about, and manipulate, the structure of a shape. These skeleton properties make them powerful tools for many types of shape analysis and processing tasks. For a given shape, several skeleton types can be defined, each having its own properties, advantages, and drawbacks. Similarly, a large number of methods exist to compute a given skeleton type, each having its own requirements, advantages, and limitations. While using skeletons for two‐dimensional (2D) shapes is a relatively well covered area, developments in the skeletonization of three‐dimensional (3D) shapes make these tasks challenging for both researchers and practitioners. This survey presents an overview of 3D shape skeletonization. We start by presenting the definition and properties of various types of 3D skeletons. We propose a taxonomy of 3D skeletons which allows us to further analyze and compare them with respect to their properties. We next overview methods and techniques used to compute all described 3D skeleton types, and discuss their assumptions, advantages, and limitations. Finally, we describe several applications of 3D skeletons, which illustrate their added value for different shape analysis and processing tasks.

Computing skeletons of 2D shapes, and medial surface and curve skeletons of 3D shapes, is a challenging task. In particular, there is no unified framework that detects all types of skeletons using a single model, and also produces a multiscale representation which allows to progressively simplify, or regularize, all skeleton types. In this paper, we present such a framework. We model skeleton detection and regularization by a conservative mass transport process from a shape's boundary to its surface skeleton, next to its curve skeleton, and finally to the shape center. The resulting density field can be thresholded to obtain a multiscale representation of progressively simplified surface, or curve, skeletons. We detail a numerical implementation of our framework which is demonstrably stable and has high computational efficiency. We demonstrate our framework on several complex 2D and 3D shapes.

Medial representations have been widely used for many shape analysis and processing tasks. Large and complex 3D shapes are, in this context, a challenging case. Recently, several methods have been proposed that extract point-based medial surfaces with high accuracy and computational scalability. However, the resulting medial clouds are of limited use for shape processing due to the difficulty of computing refined medial features from such clouds. In this paper, we show how to bridge the gap between having a raw medial cloud and enriching this cloud with feature points, medial-point classification, medial axis decomposition into sheets, robust regularization, and Y-network extraction. We further show how such properties can be used to support several shape processing sample applications including edge detection and shape segmentation, for a wide range of complex 3D shapes.

Visualizing very large graphs by edge bundling is a promising method, yet subject to several challenges: speed, clutter, level-of-detail, and parameter control. We present CUBu, a framework that addresses the above problems in an integrated way. Fully GPU-based, CUBu bundles graphs of up to a million edges at interactive framerates, being over 50 times faster than comparable state-of-the-art methods, and has a simple and intuitive control of bundling parameters. CUBu extends and unifies existing bundling techniques, offering ways to control bundle shapes, separate bundles by edge direction, and shade bundles to create a level-of-detail visualization that shows both the graph core structure and its details. We demonstrate CUBu on several large graphs extracted from real-life application domains.

Edge bundling methods reduce visual clutter of dense and occluded graphs. However, existing bundling techniques either ignore edge properties such as direction and data attributes, or are otherwise computationally not scalable, which makes them unsuitable for tasks such as exploration of large trajectory datasets. We present a new framework to generate bundled graph layouts according to any numerical edge attributes such as directions, timestamps or weights. We propose a GPU-based implementation linear in number of edges, which makes our algorithm applicable to large datasets. We demonstrate our method with applications in the analysis of aircraft trajectory datasets and eye-movement traces.

Interactive data exploration and manipulation are often hindered by dataset sizes. For 3D data, this is aggravated by occlusion, important adjacencies, and entangled patterns. Such challenges make visual interaction via common filtering techniques hard. We describe a set of realtime multi-dimensional data deformation techniques that aim to help users to easily select, analyze, and eliminate spatial-and-data patterns. Our techniques allow animation between view configurations, semantic filtering and view deformation. Any data subset can be selected at any step along the animation. Data can be filtered and deformed to reduce occlusion and ease complex data selections. Our techniques are simple to learn and implement, flexible, and real-time interactive with datasets of tens of millions of data points. We demonstrate our techniques on three domain areas: 2D image segmentation and manipulation, 3D medical volume exploration, and astrophysical exploration.

We present SolidSDD, an integrated tool for the extraction and visual analysis of code clones. SolidSDD aims to simplify and speed up the entire process of clone extraction from code bases written in C, C++, Java, and C#, and visual analysis of the extracted results. To this end, we combine several scalable visualization techniques such as hierarchical edge bundles, table lenses, annotated text views, and linked views. We demonstrate SolidSDD for both fine-grained clone analysis and aggregated report production tasks on several large-scale code bases.

Abstract We present a method for extracting complex manifolds with an arbitrary number of (self‐) intersections from unoriented point clouds containing large amounts of noise. Manifolds are formed in a three‐step process. First, small flat neighbourhoods of all possible orientations are created around all points. Next, neighbourhoods are assembled into larger quasi‐flat patches, whose overlaps give the global connectivity structure of the point cloud. Finally, curved manifolds are extracted from the patch connectivity graph via a multiple‐source flood fill. The manifolds can be reconstructed into meshed surfaces using standard existing surface reconstruction methods. We demonstrate the speed and robustness of our method on several point clouds, with applications in point cloud segmentation, denoising and medial surface reconstruction.

Depicting change captured by dynamic graphs and temporal paths, or trails, is hard. We present two techniques for simplified visualization of such data sets using edge bundles. The first technique uses an efficient image-based bundling method to create smoothly changing bundles from streaming graphs. The second technique adds edge-correspondence data atop of any static bundling algorithm, and is best suited for graph sequences. We show how these techniques can produce simplified visualizations of streaming and sequence graphs. Next, we show how several temporal attributes can be added atop of our dynamic graphs. We illustrate our techniques with data sets from aircraft monitoring, software engineering, and eye-tracking of static and dynamic scenes.

Dynamic graphs are increasingly pervasive in modern information systems. However, understanding how a graph changes in time is difficult. We present here two techniques for simplified visualization of dynamic graphs using edge bundles. The first technique uses a recent image-based graph bundling method to create smoothly changing bundles from streaming graphs. The second technique incorporates additional edge-correspondence data and is thereby suited to visualize discrete graph sequences. We illustrate our methods with examples from real-world large dynamic graph datasets.

Understanding the execution of programs by means of program traces is a key strategy in software comprehension. An important task in this context is comparing two traces in order to find similarities and differences in terms of executed code, execution order, and execution duration. For large and complex program traces, this is a difficult task due to the cardinality of the trace data. In this paper, we propose a new visualization method based on icicle plots and edge bundles. We address visual scalability by several multiscale visualization metaphors, which help users navigating from the main differences between two traces to intermediate structural-difference levels, and, finally fine-grained function call levels. We show how our approach, implemented in a tool called TRACEDIFF, is applicable in several scenarios for trace difference comprehension on real-world trace datasets.

Abstract We present a set of interactive techniques for the visual analysis of multi‐dimensional categorical data. Our approach is based on multiple correspondence analysis (MCA), which allows one to analyse relationships, patterns, trends and outliers among dependent categorical variables. We use MCA as a dimensionality reduction technique to project both observations and their attributes in the same 2D space. We use a treeview to show attributes and their domains, a histogram of their representativity in the data set and as a compact overview of attribute‐related facts. A second view shows both attributes and observations. We use a Voronoi diagram whose cells can be interactively merged to discover salient attributes, cluster values and bin categories. Bar chart legends help assigning meaning to the 2D view axes and 2D point clusters. We illustrate our techniques with real‐world application data.

We present a GPU-based framework for extracting surface and curve skeletons of 3D shapes represented as large polygonal meshes. We use an efficient parallel search strategy to compute point-cloud skeletons and their distance and feature transforms (FTs) with user-defined precision. We regularize skeletons by a new GPU-based geodesic tracing technique which is orders of magnitude faster and more accurate than comparable techniques. We reconstruct the input surface from skeleton clouds using a fast and accurate image-based method. We also show how to reconstruct the skeletal manifold structure as a polygon mesh and the curve skeleton as a polyline. Compared to recent skeletonization methods, our approach offers two orders of magnitude speed-up, high-precision, and low-memory footprints. We demonstrate our framework on several complex 3D models.

Abstract We present a fast and simple method to compute bundled layouts of general graphs. For this, we first transform a given graph drawing into a density map using kernel density estimation. Next, we apply an image sharpening technique which progressively merges local height maxima by moving the convolved graph edges into the height gradient flow. Our technique can be easily and efficiently implemented using standard graphics acceleration techniques and produces graph bundlings of similar appearance and quality to state‐of‐the‐art methods at a fraction of the cost. Additionally, we show how to create bundled layouts constrained by obstacles and use shading to convey information on the bundling quality. We demonstrate our method on several large graphs.

In this paper, we present a novel approach for constructing bundled layouts of general graphs. As layout cues for bundles, we use medial axes, or skeletons, of edges which are similar in terms of position information. We combine edge clustering, distance fields, and 2D skeletonization to construct progressively bundled layouts for general graphs by iteratively attracting edges towards the centerlines of level sets of their distance fields. Apart from clustering, our entire pipeline is image-based with an efficient implementation in graphics hardware. Besides speed and implementation simplicity, our method allows explicit control of the emphasis on structure of the bundled layout, i.e. the creation of strongly branching (organic-like) or smooth bundles. We demonstrate our method on several large real-world graphs.

We present MoleView, a novel technique for interactive exploration of multivariate relational data. Given a spatial embedding of the data, in terms of a scatter plot or graph layout, we propose a semantic lens which selects a specific spatial and attribute-related data range. The lens keeps the selected data in focus unchanged and continuously deforms the data out of the selection range in order to maintain the context around the focus. Specific deformations include distance-based repulsion of scatter plot points, deforming straight-line node-link graph drawings, and as varying the simplification degree of bundled edge graph layouts. Using a brushing-based technique, we further show the applicability of our semantic lens for scenarios requiring a complex selection of the zones of interest. Our technique is simple to implement and provides real-time performance on large datasets. We demonstrate our technique with actual data from air and road traffic control, medical imaging, and software comprehension applications.

Abstract We present a new approach aimed at understanding the structure of connections in edge‐bundling layouts. We combine the advantages of edge bundles with a bundle‐centric simplified visual representation of a graph's structure. For this, we first compute a hierarchical edge clustering of a given graph layout which groups similar edges together. Next, we render clusters at a user‐selected level of detail using a new image‐based technique that combines distance‐based splatting and shape skeletonization. The overall result displays a given graph as a small set of overlapping shaded edge bundles. Luminance, saturation, hue, and shading encode edge density, edge types, and edge similarity. Finally, we add brushing and a new type of semantic lens to help navigation where local structures overlap. We illustrate the proposed method on several real‐world graph datasets.

We present a new method for the combined visualization of software architecture diagrams, such as UML class diagrams or component diagrams, and software metrics defined on groups of diagram elements. Our method extends an existing rendering technique for the so-called areas of interest in system architecture diagrams to visualize several metrics, possibly having missing values, defined on overlapping areas of interest. For this, we use a solution that combines texturing, blending, and smooth scattered-data point interpolation. Our new method simplifies the task of visually correlating the distribution and outlier values of a multivariate metric dataset with a system's structure. We demonstrate the application of our method on component and class diagrams extracted from real-world systems.

We present a new patch-type segmentation method for 3D voxel shapes based on the medial surface, also called surface skeleton. The boundaries of the simplified fore- and background skeletons map one-to-one to increasingly fuzzy, soft convex, respectively concave, edges of the shape. Using this property, we build a method for segmentation of 3D shapes which has several desirable properties. Our method robustly segments both noisy shapes and shapes with soft edges which vanish over low-curvature regions. As the segmentation is based on the skeleton, it reflects the symmetry of the input shape. Finally, multiscale segmentations can be obtained by varying the simplification level of the skeleton. We present a voxel-based implementation of our approach and demonstrate it on several examples.

Abstract We present a new method for decomposing a 3D voxel shape into disjoint segments using the shape's simplified surface‐skeleton. The surface skeleton of a shape consists of 2D manifolds inside its volume. Each skeleton point has a maximally inscribed ball that touches the boundary in at least two contact points. A key observation is that the boundaries of the simplified fore‐ and background skeletons map one‐to‐one to increasingly fuzzy, soft convex, respectively concave, edges of the shape. Using this property, we build a method for segmentation of 3D shapes which has several desirable properties. Our method segments both noisy shapes and shapes with soft edges which vanish over low‐curvature regions. Multiscale segmentations can be obtained by varying the simplification level of the skeleton. We present a voxel‐based implementation of our approach and illustrate it on several realistic examples.

Abstract We present a part‐type segmentation method for articulated voxel‐shapes based on curve skeletons. Shapes are considered to consist of several simpler, intersecting shapes. Our method is based on the junction rule: the observation that two intersecting shapes generate an additional junction in their joined curve‐skeleton near the place of intersection. For each curve‐skeleton point, we construct a piecewise‐geodesic loop on the shape surface. Starting from the junctions, we search along the curve skeleton for points whose associated loops make for suitable part cuts. The segmentations are robust to noise and discretization artifacts, because the curve skeletonization incorporates a single user‐parameter to filter spurious curve‐skeleton branches. Furthermore, segment borders are smooth and minimally twisting by construction. We demonstrate our method on several real‐world examples and compare it to existing part‐type segmentation methods.

Abstract Understanding detailed changes done to source code is of great importance in software maintenance. We present Code Flows, a method to visualize the evolution of source code geared to the understanding of fine and mid‐level scale changes across several file versions. We enhance an existing visual metaphor to depict software structure changes with techniques that emphasize both following unchanged code as well as detecting and highlighting important events such as code drift, splits, merges, insertions and deletions. The method is illustrated with the analysis of a real‐world C++ code system.

We present a practical algorithm for computing robust multiscale curve and surface skeletons of 3D objects of genus zero. Based on a model that follows an advection principle, we assign to each point on the skeleton a part of the object surface, called the collapse. The size of the collapse is used as a uniform importance measure for the curve and surface skeleton, so that both can be simplified by imposing a single threshold on this intuitive measure. The simplified skeletons are connected by default, without special precautions, due to the monotonicity of the importance measure. The skeletons possess additional desirable properties: They are centered, robust to noise, hierarchical, and provide a natural skeleton-to-boundary mapping. We present a voxel-based algorithm that is straightforward to implement and simple to use. We illustrate our method on several realistic 3D objects.

We present an effective framework for segmenting 3D shapes into meaningful components using the curve skeleton. Our algorithm identifies a number of critical points on the curve skeleton, either fully automatically as the junctions of the curve skeleton, or based on user input. We use these points to construct a partitioning of the object surface using geodesies. Because it is based on the curve skeleton, our segmentation intrinsically reflects the shape symmetry and topology. By using geodesies we obtain segments that have smooth, minimally twisting borders. Finally, we present a hierarchical segmentation of shapes which reflects the hierarchical structure of the curve skeleton. We describe a voxel-based implementation of our method which is robust and noise resistant, computationally efficient, able to handle shapes of complex topology, and which delivers level- of-detail segmentations. We demonstrate the framework on various real-world 3D shapes.

We present a set of techniques and design principles for the visualization of large dynamic software logs consisting of attributed change events, such as obtained from instrumenting programs or mining software repositories. We enhance the visualization scalability with importance-based antialiasing techniques that guarantee visibility of several types of events. We present a hierarchical clustering method that uncovers several patterns of interest in the event logs, such as same-lifetime memory allocations and software releases. We visualize the clusters using a new type of technique called interleaved cushions. We demonstrate our methods on two real-world problems: the monitoring of a dynamic memory allocator and the analysis of a software repository.

We present a framework for visualizing large tabular data that combines two views: the table view and the treemap view. The table view extends the known table lens as follows: We cluster related elements to reduce subsampling artifacts and achieve table size independent rendering time; we use multiple-column sorting to create scenariospecific data hierarchies on the fly; and we use shaded cushions to show data structure and variation. Hierarchies built in the table view are shown in a customizable treemap view. One can choose both layout and rendering by a few clicks, effectively creating visual scenarios on-the-fly. We illustrate our framework on real-life stock data.

Many software projects use Software Configuration Management systems to support their development process. Such systems accumulate in time large amounts of information useful for process accounting and auditing. We study how software developers can get insight in this information in order to understand the project context and the product artifacts. To this end, we propose several new techniques for visual mining of project evolution. Central to our approach is a file-based evolution visualization, where each project is shown as a set of horizontal stripes depicting files along the time axis. We propose several mechanisms for interactively building layouts in this display, and for correlating the evolution with the results of various software metrics. We demonstrate the usefulness of our approach on real- life data sets.

Abstract A widely used architecture for the development of software systems is the component‐based application framework. Such frameworks offer two mechanisms. First, they provide component integration and interoperability services which make it possible to extend the framework with various third‐party components. Second, they provide mechanisms to customize the integrated components to the specific needs of applications to be built using the framework. This paper describes an architectural pattern for designing such frameworks so that the appropriate mix of fixed and flexible elements can be integrated into architectures that maximize scalability and extensibility. The pattern is illustrated by frameworks developed for three different application domains: electronic design automation, scientific visualization and numerical simulation, and industrial control systems. Copyright © 2005 John Wiley & Sons, Ltd.

The source code of software systems changes many times during the system lifecycle. We study how developers can get insight in these changes in order to understand the project context and the product artifacts. For this we propose new techniques for code evolution representation and visualization interaction from a version-centric perspective. Central to our approach is a line-based display of the changing code, where each file version is shown as a column and the horizontal axis shows time. We propose a version centric layout of line representations and a constrained interaction scheme that makes it easy to navigate. Additionally, we describe a cushion based technique to enhance visualization with information about stable evolution areas. We demonstrate the usefulness of our approach on real- life data sets.

We present a framework for processing point-based surfaces via partial differential equations (PDEs). Our framework allows an efficient and effective way to bring well-established PDE-based surface processing techniques to the field of point-based representations. We demonstrate the method by a PDE-based surface fairing application

This work presents a tool for light-shading in a distributed environment. A parallelization method based on a concurrent model is described. The purpose of this work is to lower the image generation time in the complex 3D scenes synthesis process. The experimental results concerning the speedup of light shading algorithm are also presented.

We present a novel multiscale approach for flow visualization. We define a local alignment tensor that encodes a measure for alignment to the direction of a given flow field. This tensor induces an anisotropic differential operator on the flow domain, which is discretized with a standard finite element technique. The entries of the corresponding stiffness matrix represent the anisotropically weighted couplings of adjacent nodes of the domain mesh. We use an algebraic multigrid algorithm to generate a hierarchy of fine to coarse descriptions for the above coupling data. This hierarchy comprises a set of coarse grid nodes, a multiscale of basis functions and their corresponding supports. We use these supports to obtain a multilevel decomposition of the flow structure. Standard streamline icons are used to visualize this decomposition at any user-selected level of detail. The method provides a single framework for vector field decomposition independent on the domain dimension or mesh type. Applications are shown in 2D, for flow fields on curved surfaces, and for 3D volumetric flow fields.

The stable local classification of discrete surfaces with respect to features such as edges and corners or concave and convex regions, respectively, is as quite difficult as well as indispensable for many surface processing applications. Usually, the feature detection is done via a local curvature analysis. If concerned with large triangular and irregular grids, e.g., generated via a marching cube algorithm, the detectors are tedious to treat and a robust classification is hard to achieve. Here, a local classification method on surfaces is presented which avoids the evaluation of discretized curvature quantities. Moreover, it provides an indicator for smoothness of a given discrete surface and comes together with a built-in multiscale. The proposed classification tool is based on local zero and first moments on the discrete surface. The corresponding integral quantities are stable to compute and they give less noisy results compared to discrete curvature quantities. The stencil width for the integration of the moments turns out to be the scale parameter. Prospective surface processing applications are the segmentation on surfaces, surface comparison, and matching and surface modeling. Here, a method for feature preserving fairing of surfaces is discussed to underline the applicability of the presented approach.

We present a tool for texture mapping in a distributed environment. A parallelization method based on the master-slave model is described. Our purpose is to lower the image generation time in the complex 3D scenes synthesis process. The experimental results concerning the speedup of texture mapping algorithm are also presented.

As Resource Description Framework (RDF) reaches maturity, there is an increasing need for tools that support it. A common and natural representation for RDF data is a directed labeled graph. Although there are tools to edit and/or browse RDF graph representations, we found their architecture rigid and not easily amenable to producing effective visual representations, especially for large RDF graphs. We discuss here how GViz, a general purpose graph visualisation tool, allows the easy construction and fine-tuning of various visual exploratory scenarios for RDF data. GViz's extended ability of customizing the visualisation's icons showed to be very useful in the context of RDF graph structures visualisation. Among the presented applications, we mention customizable selections, schema-instance comparison, instances comparison, and schemas comparison (schema evolution). GViz proved to be able not only to visualize large RDF data models, but also to be very flexible in designing scenario-specific queries to support the exploration process.

We present a hardware-accelerated method for visualizing 3D flow fields. The method is based on insertion, advection, and decay of dye. To this aim, we extend the texture-based IBFV technique presented by van Wijk (2001) for 2D flow visualization in two main directions. First, we decompose the 3D flow visualization problem in a series of 2D instances of the mentioned IBFV technique. This makes our method benefit from the hardware acceleration the original IBFV technique introduced. Secondly, we extend the concept of advected gray value (or color) noise by introducing opacity (or matter) noise. This allows us to produce sparse 3D noise pattern advections, thus address the occlusion problem inherent to 3D flow visualization. Overall, the presented method delivers interactively animated 3D flow, uses only standard OpenGL 1.1 calls and 2D textures, and is simple to understand and implement.

The visualization of scalar functions of two variables is a classic and ubiquitous application. We present a new method to visualize such data. The method is based on a nonlinear mapping of the function to a height field, followed by visualization as a shaded mountain landscape. The method is easy to implement and efficient, and leads to intriguing and insightful images: The visualization is enriched by adding ridges. Three types of applications are discussed: visualization of iso-levels, clusters (multivariate data visualization), and dense contours (flow visualization).

A new method for the simplification of flow fields is presented. It is based on continuous clustering. A well-known physical clustering model, the Cahn-Hilliard (1958) model, which describes phase separation, is modified to reflect the properties of the data to be visualized. Clusters are defined implicitly as connected components of the positivity set of a density function. An evolution equation for this function is obtained as a suitable gradient flow of an underlying anisotropic energy functional, where time serves as the scale parameter. The evolution is characterized by a successive coarsening of patterns, during which the underlying simulation data specifies preferable pattern boundaries. We introduce specific physical quantities in the simulation to control the shape, orientation and distribution of the clusters as a function of the underlying flow field. In addition, the model is expanded, involving elastic effects. In the early stages of the evolution, a shear-layer-type representation of the flow field can thereby be generated, whereas, for later stages, the distribution of clusters can be influenced. Furthermore, we incorporate upwind ideas to give the clusters an oriented drop-shaped appearance. We discuss the applicability of this new type of approach mainly for flow fields, where the cluster energy penalizes cross-streamline boundaries. However, the method also carries provisions for other fields as well. The clusters can be displayed directly as a flow texture. Alternatively, the clusters can be visualized by iconic representations, which are positioned by using a skeletonization algorithm.

A new method for the simplification of flow fields is presented. It is based on continuous clustering. A well-known physical clustering model, the Cahn Hilliard model (J. Cahn and J. Hilliard, 1958), which describes phase separation, is modified to reflect the properties of the data to be visualized. Clusters are defined implicitly as connected components of the positivity set of a density function. An evolution equation for this function is obtained as a suitable gradient flow of an underlying anisotropic energy functional. Here, time serves as the scale parameter. The evolution is characterized by a successive coarsening of patterns: the actual clustering, and meanwhile the underlying simulation data specifies preferable pattern boundaries. The authors discuss the applicability of this new type of approach mainly for flow fields, where the cluster energy penalizes cross streamline boundaries, but the method also carries provisions in other fields as well. The clusters are visualized via iconic representations. A skeletonization algorithm is used to find suitable positions for the icons.

Vector field visualization remains a difficult task. Many local and global visualization methods for vector fields such as flow data exist, but they usually require extensive user experience on setting the visualization parameters in order to produce images communicating the desired insight. We present a visualization method that produces simplified but suggestive images of the vector field automatically, based on a hierarchical clustering of the input data. The resulting clusters are then visualized with straight or curved arrow icons. The presented method has a few parameters with which users can produce various simplified vector field visualizations that communicate different insights on the vector data.