Critical Point Cancellation in 3D Vector Fields: Robustness and Discussion

Skraba, Primoz; Rosen, Paul; Wang, Bei; Chen, Guoning; Bhatia, Harsh; Pascucci, Valerio

doi:10.1109/TVCG.2016.2534538

Title: Critical Point Cancellation in 3D Vector Fields: Robustness and Discussion

Abstract

Vector field topology has been successfully applied to represent the structure of steady vector fields. Critical points, one of the essential components of vector field topology, play an important role in describing the complexity of the extracted structure. Simplifying vector fields via critical point cancellation has practical merit for interpreting the behaviors of complex vector fields such as turbulence. However, there is no effective technique that allows direct cancellation of critical points in 3D. This work fills this gap and introduces the first framework to directly cancel pairs or groups of 3D critical points in a hierarchical manner with a guaranteed minimum amount of perturbation based on their robustness, a quantitative measure of their stability. In addition, our framework does not require the extraction of the entire 3D topology, which contains non-trivial separation structures, and thus is computationally effective. Furthermore, our algorithm can remove critical points in any subregion of the domain whose degree is zero and handle complex boundary configurations, making it capable of addressing challenging scenarios that may not be resolved otherwise. Here, we apply our method to synthetic and simulation datasets to demonstrate its effectiveness.

Authors:

Skraba, Primoz ^[1]; Rosen, Paul ^[2]; Wang, Bei ^[3]; Chen, Guoning ^[4]; Bhatia, Harsh ^[5]; Pascucci, Valerio ^[3]

Jozef Stefan Inst. (IJS), Ljubljana (Slovenia)
Univ. of South Florida, Tampa, FL (United States)
Univ. of Utah, Salt Lake City, UT (United States)
Univ. of Houston, TX (United States)
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Publication Date:: Mon Feb 29 00:00:00 EST 2016

Research Org.:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States); Univ. of Utah, Salt Lake City, UT (United States)

Sponsoring Org.:: National Science Foundation (NSF); USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1416501

Alternate Identifier(s):: OSTI ID: 1326229

Report Number(s):: LLNL-JRNL-733787; DOE-UTAH-PASCUCCI-0017
Journal ID: ISSN 1077-2626

Grant/Contract Number:: AC52-07NA27344; AC0705ID14517; NA0002375

Resource Type:: Accepted Manuscript

Journal Name:: IEEE Transactions on Visualization and Computer Graphics

Additional Journal Information:: Journal Volume: 22; Journal Issue: 6; Journal ID: ISSN 1077-2626

Publisher:: IEEE

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; three-dimensional displays; robustness; topology; visualization; complexity theory; electronic mail; merging; computational topology; flow visualization; vector field simplification; 97 MATHEMATICS AND COMPUTING

Citation Formats


                    Skraba, Primoz, Rosen, Paul, Wang, Bei, Chen, Guoning, Bhatia, Harsh, and Pascucci, Valerio. Critical Point Cancellation in 3D Vector Fields: Robustness and Discussion.  United States: N. p., 2016. 
Web.  doi:10.1109/TVCG.2016.2534538.

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                    Skraba, Primoz, Rosen, Paul, Wang, Bei, Chen, Guoning, Bhatia, Harsh, & Pascucci, Valerio. Critical Point Cancellation in 3D Vector Fields: Robustness and Discussion.  United States.  https://doi.org/10.1109/TVCG.2016.2534538

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                    Skraba, Primoz, Rosen, Paul, Wang, Bei, Chen, Guoning, Bhatia, Harsh, and Pascucci, Valerio. Mon .  
"Critical Point Cancellation in 3D Vector Fields: Robustness and Discussion".  United States.  https://doi.org/10.1109/TVCG.2016.2534538.  https://www.osti.gov/servlets/purl/1416501.

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@article{osti_1416501,

  title        = {Critical Point Cancellation in 3D Vector Fields: Robustness and Discussion},

  author       = {Skraba, Primoz and Rosen, Paul and Wang, Bei and Chen, Guoning and Bhatia, Harsh and Pascucci, Valerio},

  abstractNote = {Vector field topology has been successfully applied to represent the structure of steady vector fields. Critical points, one of the essential components of vector field topology, play an important role in describing the complexity of the extracted structure. Simplifying vector fields via critical point cancellation has practical merit for interpreting the behaviors of complex vector fields such as turbulence. However, there is no effective technique that allows direct cancellation of critical points in 3D. This work fills this gap and introduces the first framework to directly cancel pairs or groups of 3D critical points in a hierarchical manner with a guaranteed minimum amount of perturbation based on their robustness, a quantitative measure of their stability. In addition, our framework does not require the extraction of the entire 3D topology, which contains non-trivial separation structures, and thus is computationally effective. Furthermore, our algorithm can remove critical points in any subregion of the domain whose degree is zero and handle complex boundary configurations, making it capable of addressing challenging scenarios that may not be resolved otherwise. Here, we apply our method to synthetic and simulation datasets to demonstrate its effectiveness.},

  doi          = {10.1109/TVCG.2016.2534538},

  journal      = {IEEE Transactions on Visualization and Computer Graphics},

  number       = 6,

  volume       = 22,

  place        = {United States},

  year         = {Mon Feb 29 00:00:00 EST 2016},

  month        = {Mon Feb 29 00:00:00 EST 2016}

}

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Works referencing / citing this record:

A Survey of Topology-based Methods in Visualization
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Robust Extraction and Simplification of 2D Symmetric Tensor Field Topology
posted_content, February 2021

Jankowai, Jochen; Wang, Bei; Hotz, Ingrid
OSF Preprints
DOI: 10.31219/osf.io/k67qg

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