Visualization of Unsteady Flow Using Heat Kernel Signatures

Kairong Jiang, Matthew Berger, Joshua A. Levine

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations


We introduce a new technique to visualize complex flowing phenomena by using concepts from shape analysis. Our approach uses techniques that examine the intrinsic geometry of manifolds through their heat kernel, to obtain representations of such manifolds that are isometry-invariant and multi-scale. These representations permit us to compute heat kernel signatures of each point on that manifold, and we can use these signatures as features for classification and segmentation that identify points that have similar structural properties. Our approach adapts heat kernel signatures to unsteady flows by formulating a notion of shape where pathlines are observations of a manifold living in a high-dimensional space. We use this space to compute and visualize heat kernel signatures associated with each pathline. Besides being able to capture the structural features of a pathline, heat kernel signatures allow the comparison of pathlines from different flow datasets through a shape matching pipeline. We demonstrate the analytic power of heat kernel signatures by comparing both (1) different timesteps from the same unsteady flow as well as (2) flow datasets taken from ensemble simulations with varying simulation parameters. Our analysis only requires the pathlines themselves, and thus it does not utilize the underlying vector field directly. We make minimal assumptions on the pathlines: while we assume they are sampled from a continuous, unsteady flow, our computations can tolerate pathlines that have varying density and potential unknown boundaries. We evaluate our approach through visualizations of a variety of two-dimensional unsteady flows.

Original languageEnglish (US)
Title of host publication2020 IEEE Pacific Visualization Symposium, PacificVis 2020 - Proceedings
EditorsFabian Beck, Jinwook Seo, Chaoli Wang
PublisherIEEE Computer Society
Number of pages10
ISBN (Electronic)9781728156972
StatePublished - Jun 2020
Event13th IEEE Pacific Visualization Symposium, PacificVis 2020 - Tianjin, China
Duration: Apr 14 2020Apr 17 2020

Publication series

NameIEEE Pacific Visualization Symposium
ISSN (Print)2165-8765
ISSN (Electronic)2165-8773


Conference13th IEEE Pacific Visualization Symposium, PacificVis 2020


  • Flow Visualization
  • Heat Kernel Signatures
  • Human-centered computing
  • Pathlines
  • Scientific visualization
  • Shape Analysis
  • Visualization
  • Visualization application domains

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Computer Vision and Pattern Recognition
  • Hardware and Architecture
  • Software


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