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

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

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

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

In this paper, we propose F2-Bubbles, a set overlay visualization technique that addresses overlapping artifacts and supports interactive editing with intelligent suggestions. The core of our method is a new, efficient set overlay construction algorithm that approximates the optimal set overlay by considering set elements and their non-set neighbors. Thanks to the efficiency of the algorithm, interactive editing is achieved, and with intelligent suggestions, users can easily and flexibly edit visualizations through direct manipulations with local adaptations. A quantitative comparison with state-of-the-art set visualization techniques and case studies demonstrate the effectiveness of our method and suggests that F2-Bubbles is a helpful technique for set visualization.

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

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

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

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

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

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

Colormaps are a vital method for users to gain insights into data in a visualization. With a good choice of colormaps, users are able to acquire information in the data more effectively and efficiently. In this survey, we attempt to provide readers with a comprehensive review of colormap generation techniques and provide readers a taxonomy which is helpful for finding appropriate techniques to use for their data and applications. Specifically, we first briefly introduce the basics of color spaces including color appearance models. In the core of our paper, we survey colormap generation techniques, including the latest advances in the field by grouping these techniques into four classes: procedural methods, user-study based methods, rule-based methods, and data-driven methods; we also include a section on methods that are beyond pure data comprehension purposes. We then classify colormapping techniques into a taxonomy for readers to quickly identify the appropriate techniques they might use. Furthermore, a representative set of visualization techniques that explicitly discuss the use of colormaps is reviewed and classified based on the nature of the data in these applications. Our paper is also intended to be a reference of colormap choices for readers when they are faced with similar data and/or tasks.

Abstract Multivariate volume visualization is important for many applications including petroleum exploration and medicine. State‐of‐the‐art tools allow users to interactively explore volumes with multiple linked parameter‐space views. However, interactions in the parameter space using trial‐and‐error may be unintuitive and time consuming. Furthermore, switching between different views may be distracting. In this paper, we propose GuideME: a novel slice‐guided semiautomatic multivariate volume exploration approach. Specifically, the approach comprises four stages: attribute inspection, guided uncertainty‐aware lasso creation, automated feature extraction and optional spatial fine tuning and visualization. Throughout the exploration process, the user does not need to interact with the parameter views at all and examples of complex real‐world data demonstrate the usefulness, efficiency and ease‐of‐use of our method.

Multivariate volumetric datasets are important to both science and medicine. We propose a transfer function (TF) design approach based on user selected samples in the spatial domain to make multivariate volumetric data visualization more accessible for domain users. Specifically, the user starts the visualization by probing features of interest on slices and the data values are instantly queried by user selection. The queried sample values are then used to automatically and robustly generate high dimensional transfer functions (HDTFs) via kernel density estimation (KDE). Alternatively, 2D Gaussian TFs can be automatically generated in the dimensionality reduced space using these samples. With the extracted features rendered in the volume rendering view, the user can further refine these features using segmentation brushes. Interactivity is achieved in our system and different views are tightly linked. Use cases show that our system has been successfully applied for simulation and complicated seismic data sets.

Creating realistic virtual humans has been a challenging objective in the areas of computer science research and technology industry. While there are a number of aspects to create realistic virtual humans, this paper focuses on the comprehensive integrated framework of modeling virtual humans with high level autonomy, which aim to reproduce human-like believable behaviors and movements of virtual humans in virtual environment. In the framework, the perception module enables virtual human to explore the virtual environment and gets vision and audition information; the decision networks based behavioral decision-making module allows virtual human react appropriately to the perceived surrounding environment; the hierarchical movement animation control module is designed to generate autonomous character navigation and realistic motions for character animation in virtual environment. The integrated framework presented is tested in the simulated virtual environment.