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Tensor Field Visualization,
Topological Data Analysis
Probabilistic Asymptotic Decider for Topological Ambiguity Resolution in Level-Set Extraction for Uncertain 2D Data|
T. Athawale, C. R. Johnson. In IEEE Transactions on Visualization and Computer Graphics, Vol. 25, No. 1, IEEE, pp. 1163-1172. Jan, 2019.
We present a framework for the analysis of uncertainty in isocontour extraction. The marching squares (MS) algorithm for isocontour reconstruction generates a linear topology that is consistent with hyperbolic curves of a piecewise bilinear interpolation. The saddle points of the bilinear interpolant cause topological ambiguity in isocontour extraction. The midpoint decider and the asymptotic decider are well-known mathematical techniques for resolving topological ambiguities. The latter technique investigates the data values at the cell saddle points for ambiguity resolution. The uncertainty in data, however, leads to uncertainty in underlying bilinear interpolation functions for the MS algorithm, and hence, their saddle points. In our work, we study the behavior of the asymptotic decider when data at grid vertices is uncertain. First, we derive closed-form distributions characterizing variations in the saddle point values for uncertain bilinear interpolants. The derivation assumes uniform and nonparametric noise models, and it exploits the concept of ratio distribution for analytic formulations. Next, the probabilistic asymptotic decider is devised for ambiguity resolution in uncertain data using distributions of the saddle point values derived in the first step. Finally, the confidence in probabilistic topological decisions is visualized using a colormapping technique. We demonstrate the higher accuracy and stability of the probabilistic asymptotic decider in uncertain data with regard to existing decision frameworks, such as deciders in the mean field and the probabilistic midpoint decider, through the isocontour visualization of synthetic and real datasets.
CPU Isosurface Ray Tracing of Adaptive Mesh Refinement Data|
F. Wang, I. Wald, Q. Wu, W. Usher, C. R. Johnson. In IEEE Transactions on Visualization and Computer Graphics, Vol. 25, No. 1, IEEE, pp. 1142-1151. Jan, 2019.
Adaptive mesh refinement (AMR) is a key technology for large-scale simulations that allows for adaptively changing the simulation mesh resolution, resulting in significant computational and storage savings. However, visualizing such AMR data poses a significant challenge due to the difficulties introduced by the hierarchical representation when reconstructing continuous field values. In this paper, we detail a comprehensive solution for interactive isosurface rendering of block-structured AMR data. We contribute a novel reconstruction strategy—the octant method—which is continuous, adaptive and simple to implement. Furthermore, we present a generally applicable hybrid implicit isosurface ray-tracing method, which provides better rendering quality and performance than the built-in sampling-based approach in OSPRay. Finally, we integrate our octant method and hybrid isosurface geometry into OSPRay as a module, providing the ability to create high-quality interactive visualizations combining volume and isosurface representations of BS-AMR data. We evaluate the rendering performance, memory consumption and quality of our method on two gigascale block-structured AMR datasets.
|A statistical framework for quantification and visualisation of positional uncertainty in deep brain stimulation electrodes,
T. M. Athawale, K. A. Johnson, C. R. Butson, C. R. Johnson. In Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization, Taylor & Francis, pp. 1-12. 2018.
Deep brain stimulation (DBS) is an established therapy for treating patients with movement disorders such as Parkinson's disease. Patient-specific computational modelling and visualisation have been shown to play a key role in surgical and therapeutic decisions for DBS. The computational models use brain imaging, such as magnetic resonance (MR) and computed tomography (CT), to determine the DBS electrode positions within the patient's head. The finite resolution of brain imaging, however, introduces uncertainty in electrode positions. The DBS stimulation settings for optimal patient response are sensitive to the relative positioning of DBS electrodes to a specific neural substrate (white/grey matter). In our contribution, we study positional uncertainty in the DBS electrodes for imaging with finite resolution. In a three-step approach, we first derive a closed-form mathematical model characterising the geometry of the DBS electrodes. Second, we devise a statistical framework for quantifying the uncertainty in the positional attributes of the DBS electrodes, namely the direction of longitudinal axis and the contact-centre positions at subvoxel levels. The statistical framework leverages the analytical model derived in step one and a Bayesian probabilistic model for uncertainty quantification. Finally, the uncertainty in contact-centre positions is interactively visualised through volume rendering and isosurfacing techniques. We demonstrate the efficacy of our contribution through experiments on synthetic and real datasets. We show that the spatial variations in true electrode positions are significant for finite resolution imaging, and interactive visualisation can be instrumental in exploring probabilistic positional variations in the DBS lead.
Exploration of periodic flow fields|
A. Sanderson, X. Tricoche. In 18th International Symposium on Flow Visualization, 2018.
One of the difficulties researchers face when exploring flow fields is understanding the respective strengths and limitations of the visualization and analysis techniques that can be applied to their particular problem. We consider in this paper the visualization of doubly periodic flow fields. Specifically, we compare and contrast two traditional visualization techniques, the Poincaré plot and the finite-time Lyapunov exponent (FTLE) plot with a technique recently proposed by the authors, which enhances the Poincaré plot with analytical results that reveal the topology. As is often the case, no single technique achieves a holistic visualization of the flow field that would address all the needs of the analysis. Instead, we show that additional insight can be gained from applying them in combination.
Association Rules-Based Multivariate Analysis and Visualization of Spatiotemporal Climate Data|
F. Wang, W. Li, S. Wang, C.R. Johnson. In ISPRS International Journal of Geo-Information, Vol. 7, No. 7, MDPI AG, pp. 266. July, 2018.
Understanding atmospheric phenomena involves analysis of large-scale spatiotemporal multivariate data. The complexity and heterogeneity of such data pose a significant challenge in discovering and understanding the association between multiple climate variables. To tackle this challenge, we present an interactive heuristic visualization system that supports climate scientists and the public in their exploration and analysis of atmospheric phenomena of interest. Three techniques are introduced: (1) web-based spatiotemporal climate data visualization; (2) multiview and multivariate scientific data analysis; and (3) data mining-enabled visual analytics. The Arctic System Reanalysis (ASR) data are used to demonstrate and validate the effectiveness and usefulness of our method through a case study of "The Great Arctic Cyclone of 2012". The results show that different variables have strong associations near the polar cyclone area. This work also provides techniques for identifying multivariate correlation and for better understanding the driving factors of climate phenomena.
Juniper: A Tree+ Table Approach to Multivariate Graph Visualization|
C. Nobre, M. Streit, A. Lex. In CoRR, 2018.
Analyzing large, multivariate graphs is an important problem in many domains, yet such graphs are challenging to visualize. In this paper, we introduce a novel, scalable, tree+table multivariate graph visualization technique, which makes many tasks related to multivariate graph analysis easier to achieve. The core principle we follow is to selectively query for nodes or subgraphs of interest and visualize these subgraphs as a spanning tree of the graph. The tree is laid out in a linear layout, which enables us to juxtapose the nodes with a table visualization where diverse attributes can be shown. We also use this table as an adjacency matrix, so that the resulting technique is a hybrid node-link/adjacency matrix technique. We implement this concept in Juniper, and complement it with a set of interaction techniques that enable analysts to dynamically grow, re-structure, and aggregate the tree, as well as change the layout or show paths between nodes. We demonstrate the utility of our tool in usage scenarios for different multivariate networks: a bipartite network of scholars, papers, and citation metrics, and a multitype network of story characters, places, books, etc.
Discrete Stratified Morse Theory: A User's Guide|
K Knudson, B Wang. In CoRR, 2018.
Inspired by the works of Forman on discrete Morse theory, which is a combinatorial adaptation to cell complexes of classical Morse theory on manifolds, we introduce a discrete analogue of the stratified Morse theory of Goresky and MacPherson (1988). We describe the basics of this theory and prove fundamental theorems relating the topology of a general simplicial complex with the critical simplices of a discrete stratified Morse function on the complex. We also provide an algorithm that constructs a discrete stratified Morse function out of an arbitrary function defined on a finite simplicial complex; this is different from simply constructing a discrete Morse function on such a complex. We borrow Forman's idea of a "user's guide," where we give simple examples to convey the utility of our theory.
MOG: Mapper on Graphs for Relationship Preserving Clustering|
M. Hajij, B. Wang, P. Rosen. In CoRR, 2018.
The interconnected nature of graphs often results in difficult to interpret clutter. Typically techniques focus on either decluttering by clustering nodes with similar properties or grouping edges with similar relationship. We propose using mapper, a powerful topological data analysis tool, to summarize the structure of a graph in a way that both clusters data with similar properties and preserves relationships. Typically, mapper operates on a given data by utilizing a scalar function defined on every point in the data and a cover for scalar function codomain. The output of mapper is a graph that summarize the shape of the space. In this paper, we outline how to use this mapper construction on an input graphs, outline three filter functions that capture important structures of the input graph, and provide an interface for interactively modifying the cover. To validate our approach, we conduct several case studies on synthetic and real world data sets and demonstrate how our method can give meaningful summaries for graphs with various complexities
Visual Exploration of Semantic Relationships in Neural Word Embeddings|
S. Liu, P.T. Bremer, J.J. Thiagarajan, V. Srikumar, B. Wang, Y. Livnat, V. Pascucci. In IEEE Transactions on Visualization and Computer Graphics, Vol. 24, No. 1, IEEE, pp. 553--562. Jan, 2018.
Constructing distributed representations for words through neural language models and using the resulting vector spaces for analysis has become a crucial component of natural language processing (NLP). However, despite their widespread application, little is known about the structure and properties of these spaces. To gain insights into the relationship between words, the NLP community has begun to adapt high-dimensional visualization techniques. In particular, researchers commonly use t-distributed stochastic neighbor embeddings (t-SNE) and principal component analysis (PCA) to create two-dimensional embeddings for assessing the overall structure and exploring linear relationships (e.g., word analogies), respectively. Unfortunately, these techniques often produce mediocre or even misleading results and cannot address domain-specific visualization challenges that are crucial for understanding semantic relationships in word embeddings. Here, we introduce new embedding techniques for visualizing semantic and syntactic analogies, and the corresponding tests to determine whether the resulting views capture salient structures. Additionally, we introduce two novel views for a comprehensive study of analogy relationships. Finally, we augment t-SNE embeddings to convey uncertainty information in order to allow a reliable interpretation. Combined, the different views address a number of domain-specific tasks difficult to solve with existing tools.
A virtual reality visualization tool for neuron tracing|
W Usher, P Klacansky, F Federer, PT Bremer, A Knoll, J. Yarch, A. Angelucci, V. Pascucci . In IEEE Transactions on Visualization and Computer Graphics, Vol. 24, No. 1, IEEE, pp. 994--1003. Jan, 2018.
racing neurons in large-scale microscopy data is crucial to establishing a wiring diagram of the brain, which is needed to understand how neural circuits in the brain process information and generate behavior. Automatic techniques often fail for large and complex datasets, and connectomics researchers may spend weeks or months manually tracing neurons using 2D image stacks. We present a design study of a new virtual reality (VR) system, developed in collaboration with trained neuroanatomists, to trace neurons in microscope scans of the visual cortex of primates. We hypothesize that using consumer-grade VR technology to interact with neurons directly in 3D will help neuroscientists better resolve complex cases and enable them to trace neurons faster and with less physical and mental strain. We discuss both the design process and technical challenges in developing an interactive system to navigate and manipulate terabyte-sized image volumes in VR. Using a number of different datasets, we demonstrate that, compared to widely used commercial software, consumer-grade VR presents a promising alternative for scientists.
Visual Detection of Structural Changes in Time-Varying Graphs Using Persistent Homology|
M. Hajij, B. Wang, C. Scheidegger, P. Rosen. In 2018 IEEE Pacific Visualization Symposium (PacificVis), IEEE, April, 2018.
Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we propose a novel method using persistent homology to quantify structural changes in time-varying graphs. Specifically, we transform each instance of the time-varying graph into a metric space, extract topological features using persistent homology, and compare those features over time. We provide a visualization that assists in time-varying graph exploration and helps to identify patterns of behavior within the data. To validate our approach, we conduct several case studies on real-world datasets and show how our method can find cyclic patterns, deviations from those patterns, and one-time events in time-varying graphs. We also examine whether a persistence-based similarity measure satisfies a set of well-established, desirable properties for graph metrics.
OpenSpace: Changing the Narrative of Public Dissemination in Astronomical Visualization from What to How|
A. Bock, E. Axelsson, C. Emmart, M. Kuznetsova, C. Hansen, A. Ynnerman. In IEEE Computer Graphics and Applications, Vol. 38, No. 3, IEEE, pp. 44--57. May, 2018.
We present the development of an open-source software called OpenSpace that bridges the gap between scientific discoveries and public dissemination and thus paves the way for the next generation of science communication and data exploration. We describe how the platform enables interactive presentations of dynamic and time-varying processes by domain experts to the general public. The concepts are demonstrated through four cases: Image acquisitions of the New Horizons and Rosetta spacecraft, the dissemination of space weather phenomena, and the display of high-resolution planetary images. Each case has been presented at public events with great success. These cases highlight the details of data acquisition, rather than presenting the final results, showing the audience the value of supporting the efforts of the scientific discovery.
Outcomes of an electronic social network intervention with neuro-oncology patient family caregivers|
M. Reblin, D. Ketcher, P. Forsyth, E. Mendivil, L. Kane, J. Pok, M. Meyer, Y.Wu, J. Agutter. In Journal of Neuro-Oncology, Springer Nature, pp. 1--7. May, 2018.
TopoMS: Comprehensive topological exploration for molecular and condensed‐matter systems|
H. Bhatia, A.G. Gyulassy, V. Lordi, J.E. Pask, V. Pascucci, P.T. Bremer. In Journal of Computational Chemistry, Vol. 39, No. 16, Wiley, pp. 936--952. March, 2018.
We introduce TopoMS, a computational tool enabling detailed topological analysis of molecular and condensed‐matter systems, including the computation of atomic volumes and charges through the quantum theory of atoms in molecules, as well as the complete molecular graph. With roots in techniques from computational topology, and using a shared‐memory parallel approach, TopoMS provides scalable, numerically robust, and topologically consistent analysis. TopoMS can be used as a command‐line tool or with a GUI (graphical user interface), where the latter also enables an interactive exploration of the molecular graph. This paper presents algorithmic details of TopoMS and compares it with state‐of‐the‐art tools: Bader charge analysis v1.0 (Arnaldsson et al., 01/11/17) and molecular graph extraction using Critic2 (Otero‐de‐la‐Roza et al., Comput. Phys. Commun. 2014, 185, 1007). TopoMS not only combines the functionality of these individual codes but also demonstrates up to 4× performance gain on a standard laptop, faster convergence to fine‐grid solution, robustness against lattice bias, and topological consistency. TopoMS is released publicly under BSD License. © 2018 Wiley Periodicals, Inc.
Research and Education in Computational Science and Engineering|
U. Ruede, K. Willcox, L. C. McInnes, H. De Sterck, G. Biros, H. Bungartz, J. Corones, E. Cramer, J. Crowley, O. Ghattas, M. Gunzburger, M. Hanke, R. Harrison, M. Heroux, J. Hesthaven, P. Jimack, C. Johnson, K. E. Jordan, D. E. Keyes, R. Krause, V. Kumar, S. Mayer, J. Meza, K. M. Mrken, J. T. Oden, L. Petzold, P. Raghavan, S. M. Shontz, A. Trefethen, P. Turner, V. Voevodin, B. Wohlmuth,, C. S. Woodward. In SIAM Review, Vol. 60, No. 3, SIAM, pp. 707--754. Jan, 2018.
This report presents challenges, opportunities and directions for computational science and engineering (CSE) research and education for the next decade. Over the past two decades the field of CSE has penetrated both basic and applied research in academia, industry, and laboratories to advance discovery, optimize systems, support decision-makers, and educate the scientific and engineering workforce. Informed by centuries of theory and experiment, CSE performs computational experiments to answer questions that neither theory nor experiment alone is equipped to answer. CSE provides scientists and engineers with algorithmic inventions and software systems that transcend disciplines and scales. CSE brings the power of parallelism to bear on troves of data. Mathematics-based advanced computing has become a prevalent means of discovery and innovation in essentially all areas of science, engineering, technology, and society; and the CSE community is at the core of this transformation. However, a combination of disruptive developments—including the architectural complexity of extreme-scale computing, the data revolution and increased attention to data-driven discovery, and the specialization required to follow the applications to new frontiers—is redefining the scope and reach of the CSE endeavor. With these many current and expanding opportunities for the CSE field, there is a growing demand for CSE graduates and a need to expand CSE educational offerings. This need includes CSE programs at both the undergraduate and graduate levels, as well as continuing education and professional development programs, exploiting the synergy between computational science and data science. Yet, as institutions consider new and evolving educational programs, it is essential to consider the broader research challenges and opportunities that provide the context for CSE education and workforce development.
|Revisiting Abnormalities in Brain Network Architecture Underlying Autism Using Topology-Inspired Statistical Inference,
S. Palande, V. Jose, B. Zielinski, J. Anderson, P.T. Fletcher, B. Wang. In Connectomics in NeuroImaging, Springer International Publishing, pp. 98--107. 2017.
A large body of evidence relates autism with abnormal structural and functional brain connectivity. Structural covariance MRI (scMRI) is a technique that maps brain regions with covarying gray matter density across subjects. It provides a way to probe the anatomical structures underlying intrinsic connectivity networks (ICNs) through the analysis of the gray matter signal covariance. In this paper, we apply topological data analysis in conjunction with scMRI to explore network-specific differences in the gray matter structure in subjects with autism versus age-, gender- and IQ-matched controls. Specifically, we investigate topological differences in gray matter structures captured by structural covariance networks (SCNs) derived from three ICNs strongly implicated in autism, namely, the salience network (SN), the default mode network (DMN) and the executive control network (ECN). By combining topological data analysis with statistical inference, our results provide evidence of statistically significant network-specific structural abnormalities in autism, from SCNs derived from SN and ECN. These differences in brain architecture are consistent with direct structural analysis using scMRI (Zielinski et al. 2012).
Worksheets for Guiding Novices through the Visualization Design Process|
S. McKenna, A. Lex, M. Meyer. In CoRR, 2017.
For visualization pedagogy, an important but challenging notion to teach is design, from making to evaluating visualization encodings, user interactions, or data visualization systems. In our previous work, we introduced the design activity framework to codify the high-level activities of the visualization design process. This framework has helped structure experts' design processes to create visualization systems, but the framework's four activities lack a breakdown into steps with a concrete example to help novices utilizing this framework in their own real-world design process. To provide students with such concrete guidelines, we created worksheets for each design activity: understand, ideate, make, and deploy. Each worksheet presents a high-level summary of the activity with actionable, guided steps for a novice designer to follow. We validated the use of this framework and the worksheets in a graduate-level visualization course taught at our university. For this evaluation, we surveyed the class and conducted 13 student interviews to garner qualitative, open-ended feedback and suggestions on the worksheets. We conclude this work with a discussion and highlight various areas for future work on improving visualization design pedagogy.
Exploration of Heterogeneous Data Using Robust Similarity|
M. Mirzargar, R.T. Whitaker, R.M. Kirby. In CoRR, 2017.
Heterogeneous data pose serious challenges to data analysis tasks, including exploration and visualization. Current techniques often utilize dimensionality reductions, aggregation, or conversion to numerical values to analyze heterogeneous data. However, the effectiveness of such techniques to find subtle structures such as the presence of multiple modes or detection of outliers is hindered by the challenge to find the proper subspaces or prior knowledge to reveal the structures. In this paper, we propose a generic similarity-based exploration technique that is applicable to a wide variety of datatypes and their combinations, including heterogeneous ensembles. The proposed concept of similarity has a close connection to statistical analysis and can be deployed for summarization, revealing fine structures such as the presence of multiple modes, and detection of anomalies or outliers. We then propose a visual encoding framework that enables the exploration of a heterogeneous dataset in different levels of detail and provides insightful information about both global and local structures. We demonstrate the utility of the proposed technique using various real datasets, including ensemble data.
Visualizing Sensor Network Coverage with Location Uncertainty|
T. Sodergren, J. Hair, J.M. Phillips, B. Wang. In CoRR, Vol. abs/1710.06925, 2017.
We present an interactive visualization system for exploring the coverage in sensor networks with uncertain sensor locations. We consider a simple case of uncertainty where the location of each sensor is confined to a discrete number of points sampled uniformly at random from a region with a fixed radius. Employing techniques from topological data analysis, we model and visualize network coverage by quantifying the uncertainty defined on its simplicial complex representations. We demonstrate the capabilities and effectiveness of our tool via the exploration of randomly distributed sensor networks.
Visualization in Meteorology---A Survey of Techniques and Tools for Data Analysis Tasks|
M. Rautenhaus, M. Böttinger, S. Siemen, R. Hoffman, R.M. Kirby, M. Mirzargar, N. Rober, R. Westermann. In IEEE Transactions on Visualization and Computer Graphics, IEEE, pp. 1--1. 2017.
This article surveys the history and current state of the art of visualization in meteorology, focusing on visualization techniques and tools used for meteorological data analysis. We examine characteristics of meteorological data and analysis tasks, describe the development of computer graphics methods for visualization in meteorology from the 1960s to today, and visit the state of the art of visualization techniques and tools in operational weather forecasting and atmospheric research. We approach the topic from both the visualization and the meteorological side, showing visualization techniques commonly used in meteorological practice, and surveying recent studies in visualization research aimed at meteorological applications. Our overview covers visualization techniques from the fields of display design, 3D visualization, flow dynamics, feature-based visualization, comparative visualization and data fusion, uncertainty and ensemble visualization, interactive visual analysis, efficient rendering, and scalability and reproducibility. We discuss demands and challenges for visualization research targeting meteorological data analysis, highlighting aspects in demonstration of benefit, interactive visual analysis, seamless visualization, ensemble visualization, 3D visualization, and technical issues.