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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 (Estimated)

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.

Publications and Manuscripts

Papers marked with * use alphabetic ordering of authors.
Students are underlined.
Year 1 (2019 - 2020)

Publications

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.
Online Version: https://diglib.eg.org/handle/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.
Online Version: https://doi.org/10.1007/s41468-020-00055-x.
arXiv Version: 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.
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.

Manuscripts

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.
Manuscript under review, 2020.

PDF MVF Designer: Design and Visualization of Morse Vector Fields.
Youjia Zhou, Janis Lazovskis, Michael J. Catanzaro, Matthew Zabka, Bei Wang.
Manuscript in revision, 2019.
arXiv Version: arXiv:1912.09580.
PDF TopoAct: Visually Exploring the Shape of Activations in Deep Learning.
Archit Rathore, Nithin Chalapathi, Sourabh Palande, Bei Wang.
Manuscript under review, 2020.
arXiv Version: arXiv:1912.06332.
Geometry and Topology Aware Merge Tree Metrics for Ensembles.
Lin Yan, Talha Bin Masood, Ingrid Hotz, Bei Wang
Manuscript under review, 2020.
Visualizing Robust Critical Points in Vector Field Ensembles.
Lin Yan, Paul Rosen, Bei Wang.
Manuscript in preparation, 2020.
Comparative Analysis of Joint Tensor Datasets from Deep Brain Stimulation.
Youjia Zhou, Kara Johnson, Christopher R. Butson, Bei Wang.
Manuscript in preparation, 2020.

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 1 (2019 - 2020)
  1. Workshop: Application Spotlights: Challenges in the Visualization of Bioelectric Fields for Cardiac and Neural Research at IEEE VIS, October 25-30, 2020.
    Organizers: Bei Wang, Rob MacLeod, Wilson Good.

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

  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

Lin Yan
School of Computing and Scientific Computing and Imaging Institute
University of Utah
linyan AT sci.utah.edu

Youjia Zhou
School of Computing and Scientific Computing and Imaging Institute
University of Utah
zhou325 AT sci.utah.edu

Archit Rathore
School of Computing and Scientific Computing and Imaging Institute
University of Utah
archit.rathore AT utah.edu

Collaborators

Dr. Christopher Butson, Director of Neuromodulation Research; Faculty, Scientific Computing and Imaging (SCI) Institute; Associate Professor, Department of Biomedical 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. Wenda Tan, 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.

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: June 30, 2020.