37-Issue 3
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Item Interactive Analysis of Word Vector Embeddings(The Eurographics Association and John Wiley & Sons Ltd., 2018) Heimerl, Florian; Gleicher, Michael; Jeffrey Heer and Heike Leitte and Timo RopinskiWord vector embeddings are an emerging tool for natural language processing. They have proven beneficial for a wide variety of language processing tasks. Their utility stems from the ability to encode word relationships within the vector space. Applications range from components in natural language processing systems to tools for linguistic analysis in the study of language and literature. In many of these applications, interpreting embeddings and understanding the encoded grammatical and semantic relations between words is useful, but challenging. Visualization can aid in such interpretation of embeddings. In this paper, we examine the role for visualization in working with word vector embeddings. We provide a literature survey to catalogue the range of tasks where the embeddings are employed across a broad range of applications. Based on this survey, we identify key tasks and their characteristics. Then, we present visual interactive designs that address many of these tasks. The designs integrate into an exploration and analysis environment for embeddings. Finally, we provide example use cases for them and discuss domain user feedback.Item Exploring the Visualization Design Space with Repertory Grids(The Eurographics Association and John Wiley & Sons Ltd., 2018) Kurzhals, Kuno; Weiskopf, Daniel; Jeffrey Heer and Heike Leitte and Timo RopinskiThere is an ongoing discussion in the visualization community about the relevant factors that render a visualization effective, expressive, memorable, aesthetically pleasing, etc. These factors lead to a large design space for visualizations. To explore this design space, qualitative research methods based on observations and interviews are often necessary. We describe an interview method that allows us to systematically acquire and assess important factors from subjective answers by interviewees. To this end, we adopt the repertory grid methodology in the context of visualization. It is based on the personal construct theory: each personality interprets a topic based on a set of personal, basic constructs expressed as contrasts. For the individual interpretation of visualizations, this means that these personal terms can be very different, depending on numerous influences, such as the prior experiences of the interviewed person. We present an interviewing process, visual interface, and qualitative and quantitative analysis procedures that are specifically devised to fit the needs of visualization applications. A showcase interview with 15 typical static information visualizations and 10 participants demonstrates that our approach is effective in identifying common constructs as well as individual differences. In particular, we investigate differences between expert and nonexpert interviewees. Finally, we discuss the differences to other qualitative methods and how the repertory grid can be embedded in existing theoretical frameworks of visualization research for the design process.Item Visual and Quantitative Analysis of Great Arteries' Blood Flow Jets in Cardiac 4D PC-MRI Data(The Eurographics Association and John Wiley & Sons Ltd., 2018) Köhler, Benjamin; Grothoff, Matthias; Gutberlet, Matthias; Preim, Bernhard; Jeffrey Heer and Heike Leitte and Timo RopinskiFlow in the great arteries (aorta, pulmonary artery) is normally laminar with a parabolic velocity profile. Eccentric flow jets are linked to various diseases like aneurysms. Cardiac 4D PC-MRI data provide spatio-temporally resolved blood flow information for the whole cardiac cycle. In this work, we establish a time-dependent visualization and quantification of flow jets. For this purpose, equidistant measuring planes are automatically placed along the vessel's centerline. The flow jet position and region with highest velocities are extracted for every plane in each time step. This is done during pre-processing and without user-defined parameters. We visualize the main flow jet as geometric tube. High-velocity areas are depicted as a net around this tube. Both geometries are time-dependent and can be animated. Quantitative values are provided during cross-sectional measuring plane-based evaluation. Moreover, we offer a plot visualization as summary of flow jet characteristics for the selected plane. Our physiologically plausible results are in accordance with medical findings. Our clinical collaborators appreciate the possibility to view the flow jet in the whole vessel at once, which normally requires repeated pathline filtering due to varying velocities along the vessel course. The overview plots are considered as valuable for documentation purposes.Item Landscaper: A Modeling System for 3D Printing Scale Models of Landscapes(The Eurographics Association and John Wiley & Sons Ltd., 2018) Allahverdi, Kamyar; Djavaherpour, Hessam; Mahdavi-Amiri, Ali; Samavati, Faramarz; Jeffrey Heer and Heike Leitte and Timo RopinskiLandscape models of geospatial regions provide an intuitive mechanism for exploring complex geospatial information. However, the methods currently used to create these scale models require a large amount of resources, which restricts the availability of these models to a limited number of popular public places, such as museums and airports. In this paper, we have proposed a system for creating these physical models using an affordable 3D printer in order to make the creation of these models more widely accessible. Our system retrieves GIS relevant to creating a physical model of a geospatial region and then addresses the two major limitations of affordable 3D printers, namely the limited number of materials and available printing volume. This is accomplished by separating features into distinct extruded layers and splitting large models into smaller pieces, allowing us to employ different methods for the visualization of different geospatial features, like vegetation and residential areas, in a 3D printing context. We confirm the functionality of our system by printing two large physical models of relatively complex landscape regions.Item Explorative Blood Flow Visualization using Dynamic Line Filtering based on Surface Features(The Eurographics Association and John Wiley & Sons Ltd., 2018) Behrendt, Benjamin; Berg, Philipp; Beuing, Oliver; Preim, Bernhard; Saalfeld, Sylvia; Jeffrey Heer and Heike Leitte and Timo RopinskiRupture risk assessment is a key to devise patient-specific treatment plans of cerebral aneurysms. To understand and predict the development of aneurysms and other vascular diseases over time, both hemodynamic flow patterns and their effect on the vessel surface need to be analyzed. Flow structures close to the vessel wall often correlate directly with local changes in surface parameters, such as pressure or wall shear stress. Yet, in many existing applications, the analyses of flow and surface features are either somewhat detached from one another or only globally available. Especially for the identification of specific blood flow characteristics that cause local startling parameters on the vessel surface, like elevated pressure values, an interactive analysis tool is missing. The explorative visualization of flow data is challenging due to the complexity of the underlying data. In order to find meaningful structures in the entirety of the flow, the data has to be filtered based on the respective explorative aim. In this paper, we present a combination of visualization, filtering and interaction techniques for explorative analysis of blood flow with a focus on the relation of local surface parameters and underlying flow structures. Coherent bundles of pathlines can be interactively selected based on their relation to features of the vessel wall and further refined based on their own hemodynamic features. This allows the user to interactively select and explore flow structures locally affecting a certain region on the vessel wall and therefore to understand the cause and effect relationship between these entities. Additionally, multiple selected flow structures can be compared with respect to their quantitative parameters, such as flow speed. We confirmed the usefulness of our approach by conducting an informal interview with two expert neuroradiologists and an expert in flow simulation. In addition, we recorded several insights the neuroradiologists were able to gain with the help of our tool.Item Design Factors for Summary Visualization in Visual Analytics(The Eurographics Association and John Wiley & Sons Ltd., 2018) Sarikaya, Alper; Gleicher, Michael; Szafir, Danielle Albers; Jeffrey Heer and Heike Leitte and Timo RopinskiData summarization allows analysts to explore datasets that may be too complex or too large to visualize in detail. Designers face a number of design and implementation choices when using summarization in visual analytics systems. While these choices influence the utility of the resulting system, there are no clear guidelines for the use of these summarization techniques. In this paper, we codify summarization use in existing systems to identify key factors in the design of summary visualizations. We use quantitative content analysis to systematically survey examples of visual analytics systems and enumerate the use of these design factors in data summarization. Through this analysis, we expose the relationship between design considerations, strategies for data summarization in visualization systems, and how different summarization methods influence the analyses supported by systems. We use these results to synthesize common patterns in real-world use of summary visualizations and highlight open challenges and opportunities that these patterns offer for designing effective systems. This work provides a more principled understanding of design practices for summary visualization and offers insight into underutilized approaches.Item Core Lines in 3D Second-Order Tensor Fields(The Eurographics Association and John Wiley & Sons Ltd., 2018) Oster, Timo; Rössl, Christian; Theisel, Holger; Jeffrey Heer and Heike Leitte and Timo RopinskiVortices are important features in vector fields that show a swirling behavior around a common core. The concept of a vortex core line describes the center of this swirling behavior. In this work, we examine the extension of this concept to 3D second-order tensor fields. Here, a behavior similar to vortices in vector fields can be observed for trajectories of the eigenvectors. Vortex core lines in vector fields were defined by Sujudi and Haimes to be the locations where stream lines are parallel to an eigenvector of the Jacobian. We show that a similar criterion applied to the eigenvector trajectories of a tensor field yields structurally stable lines that we call tensor core lines. We provide a formal definition of these structures and examine their mathematical properties. We also present a numerical algorithm for extracting tensor core lines in piecewise linear tensor fields. We find all intersections of tensor core lines with the faces of a dataset using a simple and robust root finding algorithm. Applying this algorithm to tensor fields obtained from structural mechanics simulations shows that it is able to effectively detect and visualize regions of rotational or hyperbolic behavior of eigenvector trajectories.Item Time Lattice: A Data Structure for the Interactive Visual Analysis of Large Time Series(The Eurographics Association and John Wiley & Sons Ltd., 2018) Miranda, Fabio; Lage, Marcos; Doraiswamy, Harish; Mydlarz, Charlie; Salamon, Justin; Lockerman, Yitzchak; Freire, Juliana; Silva, Claudio T.; Jeffrey Heer and Heike Leitte and Timo RopinskiAdvances in technology coupled with the availability of low-cost sensors have resulted in the continuous generation of large time series from several sources. In order to visually explore and compare these time series at different scales, analysts need to execute online analytical processing (OLAP) queries that include constraints and group-by's at multiple temporal hierarchies. Effective visual analysis requires these queries to be interactive. However, while existing OLAP cube-based structures can support interactive query rates, the exponential memory requirement to materialize the data cube is often unsuitable for large data sets. Moreover, none of the recent space-efficient cube data structures allow for updates. Thus, the cube must be re-computed whenever there is new data, making them impractical in a streaming scenario. We propose Time Lattice, a memory-efficient data structure that makes use of the implicit temporal hierarchy to enable interactive OLAP queries over large time series. Time Lattice is a subset of a fully materialized cube and is designed to handle fast updates and streaming data. We perform an experimental evaluation which shows that the space efficiency of the data structure does not hamper its performance when compared to the state of the art. In collaboration with signal processing and acoustics research scientists, we use the Time Lattice data structure to design the Noise Profiler, a web-based visualization framework that supports the analysis of noise from cities. We demonstrate the utility of Noise Profiler through a set of case studies.Item Towards Easy Comparison of Local Businesses Using Online Reviews(The Eurographics Association and John Wiley & Sons Ltd., 2018) Wang, Yong; Haleem, Hammad; Shi, Conglei; Wu, Yanhong; Zhao, Xun; Fu, Siwei; Qu, Huamin; Jeffrey Heer and Heike Leitte and Timo RopinskiWith the rapid development of e-commerce, there is an increasing number of online review websites, such as Yelp, to help customers make better purchase decisions. Viewing online reviews, including the rating score and text comments by other customers, and conducting a comparison between different businesses are the key to making an optimal decision. However, due to the massive amount of online reviews, the potential difference of user rating standards, and the significant variance of review time, length, details and quality, it is difficult for customers to achieve a quick and comprehensive comparison. In this paper, we present E-Comp, a carefully-designed visual analytics system based on online reviews, to help customers compare local businesses at different levels of details. More specifically, intuitive glyphs overlaid on maps are designed for quick candidate selection. Grouped Sankey diagram visualizing the rating difference by common customers is chosen for more reliable comparison of two businesses. Augmented word cloud showing adjective-noun word pairs, combined with a temporal view, is proposed to facilitate in-depth comparison of businesses in terms of different time periods, rating scores and features. The effectiveness and usability of E-Comp are demonstrated through a case study and in-depth user interviews.Item Key Time Steps Selection for Large-Scale Time-Varying Volume Datasets Using an Information-Theoretic Storyboard(The Eurographics Association and John Wiley & Sons Ltd., 2018) Zhou, Bo; Chiang, Yi-Jen; Jeffrey Heer and Heike Leitte and Timo RopinskiKey time steps selection is essential for effective and efficient scientific visualization of large-scale time-varying datasets. We present a novel approach that can decide the number of most representative time steps while selecting them to minimize the difference in the amount of information from the original data.We use linear interpolation to reconstruct the data of intermediate time steps between selected time steps.We propose an evaluation of selected time steps by computing the difference in the amount of information (called information difference) using variation of information (VI) from information theory, which compares the interpolated time steps against the original data. In the one-time preprocessing phase, a dynamic programming is applied to extract the subset of time steps that minimize the information difference. In the run-time phase, a novel chart is used to present the dynamic programming results, which serves as a storyboard of the data to guide the user to select the best time steps very efficiently. We extend our preprocessing approach to a novel out-of-core approximate algorithm to achieve optimal I/O cost, which also greatly reduces the in-core computing time and exhibits a nice trade-off between computing speed and accuracy. As shown in the experiments, our approximate method outperforms the previous globally optimal DTW approach [TLS12] on out-of-core data by significantly improving the running time while keeping similar qualities, and is our major contribution.Item VirtualDesk: A Comfortable and Efficient Immersive Information Visualization Approach(The Eurographics Association and John Wiley & Sons Ltd., 2018) Filho, Jorge A. Wagner; Freitas, Carla M.D.S.; Nedel, Luciana; Jeffrey Heer and Heike Leitte and Timo Ropinski3D representations are potentially useful under many circumstances, but suffer from long known perception and interaction challenges. Current immersive technologies, which combine stereoscopic displays and natural interaction, are being progressively seen as an opportunity to tackle this issue, but new guidelines and studies are still needed, especially regarding information visualization. Many proposed approaches are impractical for actual usage, resulting in user discomfort or requiring too much time or space. In this work, we implement and evaluate an alternative data exploration metaphor where the user remains seated and viewpoint change is only realisable through physical movements. All manipulation is done directly by natural mid-air gestures, with the data being rendered at arm's reach. The virtual reproduction of the analyst's desk aims to increase immersion and enable tangible interaction with controls and two dimensional associated information. A comparative user study was carried out against a desktop-based equivalent, exploring a set of 9 perception and interaction tasks based on previous literature and a multidimensional projection use case. We demonstrate that our prototype setup, named VirtualDesk, presents excellent results regarding user comfort and immersion, and performs equally or better in all analytical tasks, while adding minimal or no time overhead and amplifying user subjective perceptions of efficiency and engagement. Results are also contrasted to a previous experiment employing artificial flying navigation, with significant observed improvements.Item DimSUM: Dimension and Scale Unifying Map for Visual Abstraction of DNA Origami Structures(The Eurographics Association and John Wiley & Sons Ltd., 2018) Miao, Haichao; Llano, Elisa De; Isenberg, Tobias; Gröller, Eduard; Barišic, Ivan; Viola, Ivan; Jeffrey Heer and Heike Leitte and Timo RopinskiWe present a novel visualization concept for DNA origami structures that integrates a multitude of representations into a Dimension and Scale Unifying Map (DimSUM). This novel abstraction map provides means to analyze, smoothly transition between, and interact with many visual representations of the DNA origami structures in an effective way that was not possible before. DNA origami structures are nanoscale objects, which are challenging to model in silico. In our holistic approach we seamlessly combine three-dimensional realistic shape models, two-dimensional diagrammatic representations, and ordered alignments in one-dimensional arrangements, with semantic transitions across many scales. To navigate through this large, two-dimensional abstraction map we highlight locations that users frequently visit for certain tasks and datasets. Particularly interesting viewpoints can be explicitly saved to optimize the workflow. We have developed DimSUM together with domain scientists specialized in DNA nanotechnology. In the paper we discuss our design decisions for both the visualization and the interaction techniques. We demonstrate two practical use cases in which our approach increases the specialists' understanding and improves their effectiveness in the analysis. Finally, we discuss the implications of our concept for the use of controlled abstraction in visualization in general.Item Visualizing Multidimensional Data with Order Statistics(The Eurographics Association and John Wiley & Sons Ltd., 2018) Raj, Mukund; Whitaker, Ross T.; Jeffrey Heer and Heike Leitte and Timo RopinskiMultidimensional data sets are common in many domains, and dimensionality reduction methods that determine a lower dimensional embedding are widely used for visualizing such data sets. This paper presents a novel method to project data onto a lower dimensional space by taking into account the order statistics of the individual data points, which are quantified by their depth or centrality in the overall set. Thus, in addition to conveying relative distances in the data, the proposed method also preserves the order statistics, which are often lost or misrepresented by existing visualization methods. The proposed method entails a modification of the optimization objective of conventional multidimensional scaling (MDS) by introducing a term that penalizes discrepancies between centrality structures in the original space and the embedding. We also introduce two strategies for visualizing lower dimensional embeddings of multidimensional data that takes advantage of the coherent representation of centrality provided by the proposed projection method. We demonstrate the effectiveness of our visualization with comparisons on different kinds of multidimensional data, including categorical and multimodal, from a variety of domains such as botany and health care.Item Analyzing Residue Surface Proximity to Interpret Molecular Dynamics(The Eurographics Association and John Wiley & Sons Ltd., 2018) Lichtenberg, Nils; Menges, Raphael; Ageev, Vladimir; George, Ajay Abisheck Paul; Heimer, Pascal; Imhof, Diana; Lawonn, Kai; Jeffrey Heer and Heike Leitte and Timo RopinskiThe surface of a molecule holds important information about the interaction behavior with other molecules. In dynamic folding or docking processes, residues of amino acids with different properties change their position within the molecule over time. The atoms of the residues that are accessible to the solvent can directly contribute to binding interactions, while residues buried within the molecular structure contribute to the stability of the molecule. Understanding patterns and causality of structural changes is important for experts in the pharmaceutical domain, e.g., in the process of drug design. We apply an iterative computation of the Solvent Accessible Surface in order to extract virtual layers of a molecule. The extraction allows to track the movement of residues in the body of the molecule, with respect to the distance of the residue to the surface or the core during dynamics simulations. We visualize the obtained layer information for the complete time span of the molecular dynamics simulation as a 2D-map and for individual time-steps as a 3D-representation of the molecule. The data acquisition has been implemented alongside with further analysis functionality in a prototypical application, which is available to the public domain. We underline the feasibility of our approach with a study from the pharmaceutical domain, where our approach has been used for novel insights into the folding behavior of μ-conotoxins.Item Chart Constellations: Effective Chart Summarization for Collaborative and Multi-User Analyses(The Eurographics Association and John Wiley & Sons Ltd., 2018) Xu, Shenyu; Bryan, Chris; Li, Jianping Kelvin; Zhao, Jian; Ma, Kwan-Liu; Jeffrey Heer and Heike Leitte and Timo RopinskiMany data problems in the real world are complex and require multiple analysts working together to uncover embedded insights by creating chart-driven data stories. How, as a subsequent analysis step, do we interpret and learn from these collections of charts? We present Chart Constellations, a system to interactively support a single analyst in the review and analysis of data stories created by other collaborative analysts. Instead of iterating through the individual charts for each data story, the analyst can project, cluster, filter, and connect results from all users in a meta-visualization approach. Constellations supports deriving summary insights about prior investigations and supports the exploration of new, unexplored regions in the dataset. To evaluate our system, we conduct a user study comparing it against data science notebooks. Results suggest that Constellations promotes the discovery of both broad and high-level insights, including theme and trend analysis, subjective evaluation, and hypothesis generation.Item Rendering and Extracting Extremal Features in 3D Fields(The Eurographics Association and John Wiley & Sons Ltd., 2018) Kindlmann, Gordon L.; Chiw, Charisee; Huynh, Tri; Gyulassy, Attila; Reppy, John; Bremer, Peer-Timo; Jeffrey Heer and Heike Leitte and Timo RopinskiVisualizing and extracting three-dimensional features is important for many computational science applications, each with their own feature definitions and data types. While some are simple to state and implement (e.g. isosurfaces), others require more complicated mathematics (e.g. multiple derivatives, curvature, eigenvectors, etc.). Correctly implementing mathematical definitions is difficult, so experimenting with new features requires substantial investments. Furthermore, traditional interpolants rarely support the necessary derivatives, and approximations can reduce numerical stability. Our new approach directly translates mathematical notation into practical visualization and feature extraction, with minimal mental and implementation overhead. Using a mathematically expressive domain-specific language, Diderot, we compute direct volume renderings and particlebased feature samplings for a range of mathematical features. Non-expert users can experiment with feature definitions without any exposure to meshes, interpolants, derivative computation, etc. We demonstrate high-quality results on notoriously difficult features, such as ridges and vortex cores, using working code simple enough to be presented in its entirety.Item Visualization of 4D Vector Field Topology(The Eurographics Association and John Wiley & Sons Ltd., 2018) Hofmann, Lutz; Rieck, Bastian; Sadlo, Filip; Jeffrey Heer and Heike Leitte and Timo RopinskiIn this paper, we present an approach to the topological analysis of four-dimensional vector fields. In analogy to traditional 2D and 3D vector field topology, we provide a classification and visual representation of critical points, together with a technique for extracting their invariant manifolds. For effective exploration of the resulting four-dimensional structures, we present a 4D camera that provides concise representation by exploiting projection degeneracies, and a 4D clipping approach that avoids self-intersection in the 3D projection. We exemplify the properties and the utility of our approach using specific synthetic cases.Item Maps and Globes in Virtual Reality(The Eurographics Association and John Wiley & Sons Ltd., 2018) Yang, Yalong; Jenny, Bernhard; Dwyer, Tim; Marriott, Kim; Chen, Haohui; Cordeil, Maxime; Jeffrey Heer and Heike Leitte and Timo RopinskiThis paper explores different ways to render world-wide geographic maps in virtual reality (VR). We compare: (a) a 3D exocentric globe, where the user's viewpoint is outside the globe; (b) a flat map (rendered to a plane in VR); (c) an egocentric 3D globe, with the viewpoint inside the globe; and (d) a curved map, created by projecting the map onto a section of a sphere which curves around the user. In all four visualisations the geographic centre can be smoothly adjusted with a standard handheld VR controller and the user, through a head-tracked headset, can physically move around the visualisation. For distance comparison exocentric globe is more accurate than egocentric globe and flat map. For area comparison more time is required with exocentric and egocentric globes than with flat and curved maps. For direction estimation, the exocentric globe is more accurate and faster than the other visual presentations. Our study participants had a weak preference for the exocentric globe. Generally the curved map had benefits over the flat map. In almost all cases the egocentric globe was found to be the least effective visualisation. Overall, our results provide support for the use of exocentric globes for geographic visualisation in mixed-reality.Item Bladder Runner: Visual Analytics for the Exploration of RT-Induced Bladder Toxicity in a Cohort Study(The Eurographics Association and John Wiley & Sons Ltd., 2018) Raidou, Renata Georgia; Casares-Magaz, Oscar; Amirkhanov, Aleksandr; Moiseenko, Vitali; Muren, Ludvig P.; Einck, John P.; Vilanova, Anna; Gröller, Eduard; Jeffrey Heer and Heike Leitte and Timo RopinskiWe present the Bladder Runner, a novel tool to enable detailed visual exploration and analysis of the impact of bladder shape variation on the accuracy of dose delivery, during the course of prostate cancer radiotherapy (RT). Our tool enables the investigation of individual patients and cohorts through the entire treatment process, and it can give indications of RT-induced complications for the patient. In prostate cancer RT treatment, despite the design of an initial plan prior to dose administration, bladder toxicity remains very common. The main reason is that the dose is delivered in multiple fractions over a period of weeks, during which, the anatomical variation of the bladder - due to differences in urinary filling - causes deviations between planned and delivered doses. Clinical researchers want to correlate bladder shape variations to dose deviations and toxicity risk through cohort studies, to understand which specific bladder shape characteristics are more prone to side effects. This is currently done with Dose-Volume Histograms (DVHs), which provide limited, qualitative insight. The effect of bladder variation on dose delivery and the resulting toxicity cannot be currently examined with the DVHs. To address this need, we designed and implemented the Bladder Runner, which incorporates visualization strategies in a highly interactive environment with multiple linked views. Individual patients can be explored and analyzed through the entire treatment period, while inter-patient and temporal exploration, analysis and comparison are also supported. We demonstrate the applicability of our presented tool with a usage scenario, employing a dataset of 29 patients followed through the course of the treatment, across 13 time points. We conducted an evaluation with three clinical researchers working on the investigation of RT-induced bladder toxicity. All participants agreed that Bladder Runner provides better understanding and new opportunities for the exploration and analysis of the involved cohort data.Item Spatio-Temporal Contours from Deep Volume Raycasting(The Eurographics Association and John Wiley & Sons Ltd., 2018) Frey, Steffen; Jeffrey Heer and Heike Leitte and Timo RopinskiWe visualize contours for spatio-temporal processes to indicate where and when non-continuous changes occur or spatial bounds are encountered. All time steps are comprised densely in one visualization, with contours allowing to efficiently analyze processes in the data even in case of spatial or temporal overlap. Contours are determined on the basis of deep raycasting that collects samples across time and depth along each ray. For each sample along a ray, its closest neighbors from adjacent rays are identified, considering time, depth, and value in the process. Large distances are represented as contours in image space, using color to indicate temporal occurrence. This contour representation can easily be combined with volume rendering-based techniques, providing both full spatial detail for individual time steps and an outline of the whole time series in one view. Our view-dependent technique supports efficient progressive computation, and requires no prior assumptions regarding the shape or nature of processes in the data. We discuss and demonstrate the performance and utility of our approach via a variety of data sets, comparison and combination with an alternative technique, and feedback by a domain scientist.
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