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III: Small: Visualizing Robust Features in Vector and Tensor Fields

Award Number and Duration

NSF IIS 1910733

September 1, 2019 to August 31, 2022 (plus 2-Year NCE)

PI and Point of Contact

Bei Wang
Assistant Professor
School of Computing and Scientific Computing and Imaging Institute
University of Utah
beiwang AT sci.utah.edu
http://www.sci.utah.edu/~beiwang

Overview

Vector and tensor fields provide a powerful language to describe physical phenomena in many scientific applications. In atmospheric sciences, vectors are used to represent air movements with speed and directions and to capture typical and atypical atmospheric conditions. In materials science, stress and strain tensors are used to specify the behaviors of material bodies experiencing deformations and to facilitate the study of material strength. The main objective of this project is to define and quantify robust features in vector and tensor fields and to derive scientifically meaningful visualization for knowledge discovery. Robust features are objects, structures, or regions of interest that are stable under small perturbations of the data that arise from measurement noise, numerical instability or simulation uncertainty. Robust features are defined and evaluated via close collaborations with domain scientists to help them discriminate spurious from essential structures in the data. In materials science, the extraction of robust features in stress tensor fields will help the materials scientists better characterize and predict 3D cracking for manufacturing stronger materials. In neuroscience, quantifying the robustness of degenerate elements in brain imaging will offer new metrics and visualization in characterizing tissue microstructure for disease diagnostics. In bioengineering, robust vortex extraction and tracking of 3D conduction velocity fields in the heart will help bioengineers develop new metrics that detect and characterize ischemic stress associated with a heart attack. In atmospheric sciences, extracting and visualizing robust features in wind data will help the atmospheric scientists establish situation awareness of hazardous weather conditions such as wildfires and to provide wildfire weather forecasting and resource planning for firefighting personnel. This project will also provide a unique environment for multidisciplinary activities and training opportunities for students in integrating visualization with scientific applications.

This project will establish a new approach to feature-based visualization with three interconnected aims. First, it will derive novel mathematical formulations of robust features for vector and tensor fields and their ensembles. Second, it will develop new robustness-driven algorithms in feature extraction, tracking, simplification, visual representation, and uncertainty visualization. Third, it will apply and evaluate the proposed framework via close collaborations with scientists in four high-impact application areas: materials science, neuroscience, bioengineering, and atmospheric sciences. Using simulated micro-mechanical fields in an uncracked polycrystal, the project will integrate robust features with visualization to improve the interpretability of micro-mechanical fields and the prediction of fatigue-failure surfaces. Using diffusion tensor imaging (DTI) from the Human Connectome Project, the project will investigate quantifiable characteristics of crossing fibers as part of a long-term goal for deep brain stimulator placement. Using 3D conduction velocity generated in volumes of swine and canine tissues, the project will generate feature-based signatures from vortex stability and evolution and use them, in the long term, for disease diagnostics and medical intervention. Using ensemble datasets generated from the High-Resolution Rapid Refresh Model (HRRR), the project will use robust features in the visualization and statistical analysis of atmospheric models to identify atypical atmospheric conditions for wildfire weather assessment. The research results will be instantiated by a collection of research papers and open-source software tools targeting the communities of collaborating scientists and the large research community. These software tools will be made available via GitHub under MIT or BSD licenses.

Broader Impacts

This project will have a large impact on application domains via multidisciplinary collaborations. The extraction and visualization of robust features in stress tensor fields will help the materials scientist better characterize and predict 3D cracking. Quantifying the robustness of degenerate elements will offer new metrics and visualization in characterizing tissue microstructure in neuroscience. In bioengineering, robust vortex extraction and tracking of 3D conduction velocity fields in the heart will help researchers develop new metrics that detect and characterize ischemic stress. Finally, extracting and visualizing robust features across ensemble members will help researchers understand the uncertainty and predictability of an ensemble for reanalysis in wildfire weather forecasting.

This project provides a unique environment for multidisciplinary activities and training opportunities for students in integrating visualization with domain applications. The research will be integrated into undergraduate and graduate levels courses on the topic of topological data analysis and data visualization. The PI will integrate data visualization research with educational outreach by collaborating with Hi-GEAR (Girls Engineering Abilities Realized) Camp for K-12 education; develop new undergraduate data science curriculum by engaging the students at a mathematical, application and data storytelling level; and promote data visualization as part of the core data science training for graduate students. The PI will continue to actively recruit and mentor minority and women students to participate in the research project.

Awards

Visual Computer Cover of the Year 2023, by Daniel Klötzl, Tim Krake, Youjia Zhou, Ingrid Hotz, Bei Wang, Daniel Weiskopf, 2023.
Visual Computer Second Best Paper Award at Computer Graphics International (CGI), 2022.
Honorable Mention Paper Award at IEEE Workshop on Topological Data Analysis and Visualization (TopoInVis), 2022.
Nithin Chalapathi: Finalist in the Computing Research Association (CRA) Outstanding Undergraduate Researcher Awards, 2021.

Publications and Manuscripts

Year 5 (2023 - 2024)
PDF Distributed Augmentation, Hypersweeps, and Branch Decomposition of Contour Trees for Scientific Exploration.
Mingzhe Li, Hamish Carr, Oliver Rubel, Bei Wang, Gunther H. Weber.
IEEE Visualization Conference (IEEE VIS), accepted, 2024.
IEEE Transactions on Visualization and Computer Graphics (TVCG), accepted, 2024.
arXiv:2408.04836
PDF Fast Comparative Analysis of Merge Trees Using Locality-Sensitive Hashing.
Weiran Lyu, Raghavendra Sridharamurthy, Jeff M. Phillips, Bei Wang.
IEEE Visualization Conference (IEEE VIS), accepted, 2024.
IEEE Transactions on Visualization and Computer Graphics (TVCG), accepted, 2024.

PDF Labeled Interleaving Distance for Reeb Graphs.
Fangfei Lan, Salman Parsa, Bei Wang.
Journal of Applied and Computational Topology, accepted, 2024.
arXiv:2306.01186
PDF Labeled Interleaving Distance for Reeb Graphs (Abstract).
Fangfei Lan, Salman Parsa, Bei Wang.
International Symposium on Computational Geometry (SOCG) Young Researcher Forum (YRF), 2024.

PDF Measure-Theoretic Reeb Graphs and Reeb Spaces.
Qingsong Wang, Guanquan Ma, Raghavendra Sridharamurthy, Bei Wang.
International Symposium on Computational Geometry (SOCG), 2024.
DOI:10.4230/LIPIcs.SoCG.2024.80
arXiv:2401.06748.
PDF Topological Characterization and Uncertainty Visualization of Atmospheric Rivers.
Fangfei Lan, Brandi Gamelin, Lin Yan, Jiali Wang, Bei Wang, Hanqi Guo.
Eurographics Conference on Visualization (EuroVis), 2024.
Computer Graphics Forum, 43(3), e15084, 2024.
DOI:10.1111/cgf.15084

PDF TROPHY: A Topologically Robust Physics-Informed Tracking Framework for Tropical Cyclone.
Lin Yan, Hanqi Guo, Tom Peterka, Bei Wang, Jiali Wang.
IEEE Visualization Conference (IEEE VIS), 2023.
IEEE Transactions on Visualization and Computer Graphics (TVCG), 30, pages 1249-1259, 2024.
Supplementary Material.
DOI:10.1109/TVCG.2023.3326905
arXiv:2307.15243.
PDF TopoSZ: Preserving Topology in Error-Bounded Lossy Compression.
Lin Yan, Xin Liang, Hanqi Guo, Bei Wang.
IEEE Visualization Conference (IEEE VIS), 2023.
IEEE Transactions on Visualization and Computer Graphics (TVCG), 30, pages 1302-1312, 2024.
Supplementary Material.
DOI:10.1109/TVCG.2023.3326920
arXiv:2304.11768.
PDF Comparing Morse Complexes Using Optimal Transport: An Experimental Study.
Mingzhe Li, Carson Storm, Austin Yang Li, Tom Needham, Bei Wang.
IEEE Visualization and Visual Analytics (VIS) Short Paper, pages 41-45, 2023.
Supplementary Material.
DOI:10.1109/VIS54172.2023.00017
PDF Combinatorial Exploration of Morse-Smale Functions on the Sphere via Interactive Visualization.
 Youjia Zhou, Janis Lazovskis, Michael J. Catanzaro, Matthew Zabka, Bei Wang.
IEEE Workshop on Topological Data Analysis and Visualization (TopoInVis) at IEEE VIS, pages 51-60, 2023.
DOI:10.1109/TopoInVis60193.2023.00012
arXiv:1912.09580.
PDF Comparing Mapper Graphs of Artificial Neuron Activations.
 Youjia Zhou, Helen Jenne, Davis Brown, Madelyn Shapiro, Brett Jefferson, Cliff Joslyn, Gregory Henselman-Petrusek, Brenda Praggastis, Emilie Purvine, Bei Wang.
IEEE Workshop on Topological Data Analysis and Visualization (TopoInVis) at IEEE VIS, pages 41-50, 2023.
DOI:10.1109/TopoInVis60193.2023.00011
PDF Hypergraph Co-Optimal Transport: Metric and Categorical Properties.
Samir Chowdhury, Tom Needham, Ethan Semrad, Bei Wang, Youjia Zhou.
Journal of Applied and Computational Topology, 2023.
DOI:10.1007/s41468-023-00142-9
arXiv:2112.03904
Year 4 (2022 - 2023)

PDF Multilevel Robustness for 2D Vector Field Feature Tracking, Selection, and Comparison.
 Lin Yan, Paul Aaron Ullrich, Luke P. Van Roekel, Bei Wang, Hanqi Guo.
Computer Graphics Forum, 42(6), e14799, 2023.
DOI: 10.1111/cgf.14799
arXiv:2209.11708

PDF Flexible and Probabilistic Topology Tracking with Partial Optimal Transport.
Mingzhe Li, Xinyuan Yan, Lin Yan, Tom Needham, Bei Wang.
Manuscript, 2023.
arXiv:2302.02895.

PDF TopoBERT: Exploring the Topology of Fine-Tuned Word Representations.
Archit Rathore, Yichu Zhou, Vivek Srikumar, Bei Wang.
Information Visualization, 22(3), pages 186-208, 2023.
DOI: 10.1177/14738716231168671

PDF Meta-diagrams for 2-parameter persistence.
Nate Clause, Tamal K. Dey, Facundo Mémoli, Bei Wang.
International Symposium on Computational Geometry (SOCG), 2023.
DOI:10.4230/LIPIcs.SoCG.2023.25
Year 3 (2021 - 2022)

PDF Visual Computer Cover of the Year 2023.
Daniel Klötzl, Tim Krake, Youjia Zhou, Ingrid Hotz, Bei Wang, Daniel Weiskopf.
Visual Computer, 2023.
Based on Local Bilinear Computation of Jacobi Sets, Visual Computer 38, pages 3435-3448, 2022.
PDF Uncertainty Visualization for Graph Coarsening.
 Fangfei Lan, Sourabh Palande, Michael Young, Bei Wang.
IEEE International Conference on Big Data (IEEE BigData), pages 2922-2931, 2022.
DOI: 10.1109/BigData55660.2022.10021039
PDF Local Bilinear Computation of Jacobi Sets
 Daniel Klötzl, Tim Krake, Youjia Zhou, Ingrid Hotz, Bei Wang, Daniel Weiskopf.
Computer Graphics International (CGI), 2022.
Visual Computer, 38, pages 3435-3448, 2022.
DOI: 10.1007/s00371-022-02557-4
Visual Computer Second Best Paper Award.
PDF Reduced Connectivity for Local Bilinear Jacobi Sets.
Daniel Klötzl, Tim Krake, Youjia Zhou, Jonathan Stober, Kathrin Schulte, Ingrid Hotz, Bei Wang, Daniel Weiskopf.
IEEE Workshop on Topological Data Analysis and Visualization (TopoInVis) at IEEE VIS, 2022.
arXiv:2208.07148
DOI: 10.1109/TopoInVis57755.2022.00011
Honorable Mention Paper Award.
PDF Adaptive Covers for Mapper Graphs Using Information Criteria.
 Nithin Chalapathi, Youjia Zhou, Bei Wang.
IEEE International Conference on Big Data, Workshop on Applications of Topological Data Analysis to Big Data, 2021.
DOI: 10.1109/BigData52589.2021.9671324

Year 2 (2020 - 2021)
PDF Uncertainty Visualization of 2D Morse Complex Ensembles Using Statistical Summary Maps.
Tushar Athawale, Dan Maljovec, Lin Yan, Chris R. Johnson, Valerio Pascucci, Bei Wang.
IEEE Transactions on Visualization and Computer Graphics (TVCG), 28(4), pages 1955-1966, 2022.
DOI: 10.1109/TVCG.2020.3022359
PDF Scalar Field Comparison with Topological Descriptors: Properties and Applications for Scientific Visualization.
Lin Yan, Talha Bin Masood, Raghavendra Sridharamurthy, Farhan Rasheed, Vijay Natarajan, Ingrid Hotz, Bei Wang.
Eurographics Conference on Visualization (EuroVis), 2021.
Computer Graphics Forum, 40(3), pages 599-633, 2021.
DOI: 10.1111/cgf.14331

PDF TopoAct: Visually Exploring the Shape of Activations in Deep Learning.
 Archit Rathore, Nithin Chalapathi, Sourabh Palande, Bei Wang.
Computer Graphics Forum, 40(1), pages 382-397, 2021.
Supplemental Material.
DOI: 10.1111/cgf.14195
arXiv:1912.06332.
Year 1 (2019 - 2020)
PDF State of the Art in Time-Dependent Flow Topology: Interpreting Physical Meaningfulness Through Mathematical Properties.
Roxana Bujack, Lin Yan, Ingrid Hotz, Christoph Garth, Bei Wang.
Eurographics Conference on Visualization (EuroVis) STAR
Computer Graphics Forum, 2020.
DOE: 10.1111/cgf14037
PDF Moduli Spaces of Morse Functions for Persistence.
Michael J. Catanzaro, Justin Curry, Brittany Terese Fasy, Janis Lazovskis, Greg Malen, Hans Riess, Bei Wang, Matthew Zabka.
Journal of Applied and Computational Topology, 2020.
DOI: 10.1007/s41468-020-00055-x.
arXiv:1909.10623.
PDF Mathematical Foundations in Visualization.
Ingrid Hotz, Roxana Bujack, Christoph Garth, Bei Wang.
In Foundations of Data Visualization, Springer, to appear, 2020
Editors: Min Chen, Helwig Hauser, Penny Rheingans, Gerik Scheuermann.
DOI: 10.1007/978-3-030-34444-3_5.
PDF A Visual Exploration and Design of Morse Vector Fields (Abstract).
Youjia Zhou, Janis Lazovskis, Michael J. Catanzaro, Matthew Zabka, Bei Wang.
Algebraic Topology: Methods, Computation, & Science (ATMCS), poster, 2020.
Conference cancelled due to COVID-19.

Software Downloads

MVF Designer: Design and Visualization of Morse Vector Fields.
https://github.com/zhou325/VIS-MSVF

 MVF Designer is an interactive tool that enables the design and analysis of 2D Morse vector fields via elementary moves.

Presentations, Educational Development and Broader Impacts

Year 4 (2022 - 2023)

  1. Bei Wang, Invited Talk, BSV Research Seminar on Computer Graphics, Image Processing, and Visualization, University of Leipzig, Leipzig, Germany, November 8, 2023.
    Complex data visualization: climate simulations, high-dimensional point clouds, hypergraphs and beyond.

  2. Bei Wang, Co-organizer, A Hands-on TTK Tutorial for Absolute Beginners at IEEE VIS Conference, October 22, 2023.

  3. Bei Wang, Invited Talk, Dagstuhl Seminar on Computational Geometry of Earth System Analysis, August 21, 2023.
    Topological Characterization and Uncertainty Visualization of Atmospheric Rivers.
Year 4 (2022 - 2023)

  1. Bei Wang, Invited Talk, 7th Workshop on Geometry and Machine Learning at the International Symposium on Computational Geometry (SOCG), June 10-15, 2023.

  2. Bei Wang, Session Chairs, full paper session and Young Researchers Forum at the International Symposium on Computational Geometry (SOCG), June 10-15, 2023.

  3. Workshop: Dagstuhl Seminar: Topological Data Analysis and Applications, May 7-12, 2023.
    Organizers: Bei Wang, Ulrich Bauer, Vijay Natarajan.

  4. Bei Wang Invited Talk, Colorado State University Topology Seminar, April 18, 2023.

  5. Bei Wang Invited Talk, Northeastern Topology Seminar, April 11, 2023.

  6. Bei Wang Invited Talk, Institute for Mathematical and Statistical Innovation (IMSI), Randomness in Topology and its Applications workshop, March 21, 2023.

  7. Bei Wang Keynote Talk, Machine Learning on Higher-Order Structured data (ML-HOS) Workshop at ICDM 2022. Hypergraph Co-Optimal Transport, November 28, 2022.

  8. Bei Wang Invited Talk, Dagstuhl Seminar on Set Visualization and Uncertainty, Germany. Visualizing Hypergraphs With Connections to Uncertainty Visualization. November 13-18, 2022.

  9. Bei Wang Invited Talk, Stochastic Seminar, Department of Mathematics, University of Utah, November 4, 2022.

  10. Workshop: Topological Analysis of Ensemble Scalar Data with TTK, A Sequel at IEEE VIS Conference, October 16-21, 2022.
    Organizers: Bei Wang, Christoph Garth, Charles Gueunet, Pierre Guillou, Federico Iuricich, Joshua A Levine, Jonas Lukasczyk, Mathieu Pont, Julien Tierny, Jules Vidal, Florian Wetzels.

  11. Bei Wang Invited Talk, Mini Symposium on Statistics and Machine Learning in Topological and Geometric Data Analysis at SIAM Conference on Mathematics of Data Science (MDS22), September 29, 2022.

Year 3 (2021 - 2022)

  1. Workshop: AWM Research Symposium Special Session on Topological Data Analysis, June 16-19, 2022.
    Organizers: Bei Wang, Radmila Sazdanovic, Lori Ziegelmeier

  2. Workshop: Topological Data Visualization Workshop, May 16-20, 2022.
    Organizers: Bei Wang, Isabel Darcy.

  3. Bei Wang Outreach: Hi-GEAR (Girls Engineering Abilities Realized) Visual Camp, Computer Science, July 11, 2022.

  4. Tutorial: Topological Analysis of Ensemble Scalar Data with TTK at IEEE VIS Conference, October 24-29, 2021.
    Organizers: Bei Wang, Christoph Garth, Charles Gueunet, Pierre Guillou, Lutz Hofmann, Joshua A Levine, Jonas Lukasczyk, Julien Tierny, Jules Vidal, Florian Wetzels.

  5. Bei Wang Invited Talk: Department of Energy Computer Graphics Forum, August 30, 2022.

  6. Bei Wang Invited Talk: Utah Center for Data Science (UCDS) Data Science Seminar, August 24, 2022.

  7. Bei Wang Invited Talk: Applied Topology in Frontier Sciences. Applied, Combinatorial and Toric Topology. Institute for Mathematical Sciences, Singapore, July 18 to 22, 2022.

  8. Bei Wang Invited Talk: Spring Western AMS Sectional Meeting, special session on Computational Topology and Applications, May 14-15, 2022.

  9. Bei Wang Invited Talk: Women in Data Science Ames Regional Event at the Iowa State University, April 21, 2022.

  10. Bei Wang Invited Talk: University of Iowa Mathematical Biology Seminar, April 18, 2022.

  11. Bei Wang Invited Talk: Colloquium Talk at Department of Computational Mathematics, Science, and Engineering (CMSE), Michigan State University, April 4, 2022.

  12. Bei Wang Invited Talk: Joint Mathematics Meetings AMS Special Session on Combinatorial Approaches to Topological Structures and Applications, April 9, 2022.

  13. Bei Wang Invited Talk: Joint Mathematics Meetings AWS Special Session on Women in Computational Topology, April 9, 2022.

  14. Bei Wang Invited Talk: Visualization Seminar at the University of Utah, March 23, 2022.

  15. Bei Wang Invited Talk: Workshop on Algebraic Combinatorics and Category Theory in Topological Data Analysis, March 12, 2022.

  16. Bei Wang Invited Talk: Institute for Mathematical and Statistical Innovation (IMSI), the Mathematics of Soft Matter Structure and Dynamics workshop, February 28, 2022.

  17. Bei Wang Invited Talk: TDA Week, Japan, February 18, 2022.

  18. Bei Wang Distinguished Seminar Speaker: SIAM Pacific Northwest (PNW) Distinguished Seminar, February 15, 2022.

  19. Bei Wang Invited Talk: Computational Persistence Workshop, November 3, 2021.

Year 2 (2020 - 2021)

  1. Lin Yan Conference Talk (virtual) at 23rd EG Conference on Visualization (EuroVis), June 14-18, 2021.

  2. Bei Wang Invited Talk (virtual) at ILJU POSTECH MINDS Workshop on Topological Data Analysis and Machine Learning, July 6-9, 2021.

  3. Bei Wang Invited Talk (virtual) at Mathematics for Artificial Reasoning in Science (MARS) Seminar at Pacific Northwest National Laboratory (PNNL), Jan. 20, 2021.

  4. Tushar Athawale Conference Talk (virtual, TVCG page) at IEEE Visualization Conference, Oct 24-29, 2020.

  5. Bei Wang Outreach: Hi-GEAR (Girls Engineering Abilities Realized) Visual Camp, Computer Science, June 18, 2021.

Year 1 (2019 - 2020)

  1. Workshop: Application Spotlights: Challenges in the Visualization of Bioelectric Fields for Cardiac and Neural Research at IEEE VIS Conference, October 25-30, 2020.
    Organizers: Bei Wang, Rob MacLeod, Wilson Good.

  2. Lin Yan, Nithin Chalapathi, Bei Wang Outreach: Hi-GEAR (Girls Engineering Abilities Realized) Visual Camp, Computer Science -- Data Visualization Board, July 7-9, 2020.

  3. Bei Wang Invited Talk (virtual) at GAMES: Graphics And Mixed Environment Seminar, July 2, 2020.

  4. Bei Wang Invited Talk (virtual) at Applied Algebraic Topology Research Network, May 20, 2020.

  5. Bei Wang Guest Lecture (virtual) on data visualization for Dr. David Millman's class (graduate and undergraduate students) at Montana State University, April 28, 2020.

  6. Bei Wang Visit collaborators at Los Alamos National Lab (LANL), Jan 23-25, 2020.

Students

Current Students

Weiran Lyu, PhD
School of Computing and Scientific Computing and Imaging Institute
University of Utah

Mingzhe Li, PhD
School of Computing and Scientific Computing and Imaging Institute
University of Utah

Former Students

Youjia Zhou, PhD, graduated Spring 2023
School of Computing and Scientific Computing and Imaging Institute
University of Utah

Austin Li, BS, graduated Spring 2023 (REU)
School of Computing
University of Utah

Carson Storm, BS, graduated Spring 2023 (REU)
School of Computing
University of Utah

Archit Rathore, PhD, defended Summer 2022, graduated Spring 2023
School of Computing and Scientific Computing and Imaging Institute
University of Utah

Lin Yan, PhD, graduated Spring 2022
School of Computing and Scientific Computing and Imaging Institute
University of Utah

Nithin Chalapathi, BS, graduated Spring 2021 (REU)
School of Computing
University of Utah

Collaborators

Current Collaborators

Dr. Jacob Dean Hochhalter, Assistant Professor, Department of Mechanical Engineering; University of Utah.

Dr. Rob MacLeod, SCI Institute Associate Director; Faculty, SCI Institute; Professor of Bioengineering; Research Associate Professor of Internal Medicine; University of Utah.

Dr. Ashley D. Spear, Assistant Professor, Department of Mechanical Engineering; University of Utah.

Dr. Pania Newell, Assistant Professor, Department of Mechanical Engineering; University of Utah.

Dr. John Horel, Professor, Chair, Department of Atmospheric Sciences; University of Utah.

Former Collaborators

Dr. Wenda Tan, Assistant Professor, Department of Mechanical Engineering; University of Utah. Now at University of Michigan.

Dr. Christopher Butson, Director of Neuromodulation Research; Faculty, Scientific Computing and Imaging (SCI) Institute; Associate Professor, Department of Biomedical Engineering; University of Utah. Now at University of Florida.

Acknowledgement

This material is based upon work supported or partially supported by the National Science Foundation under Grant No.1910733.

Any opinions, findings, and conclusions or recommendations expressed in this project are those of author(s) and do not necessarily reflect the views of the National Science Foundation.

Web page last update: March 7, 2023.