A multi-resolution approach to heat kernels on discrete surfaces

Amir Vaxman, Mirela Ben-Chen, Craig Gotsman

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

8 Scopus citations

Abstract

Studying the behavior of the heat diffusion process on a manifold is emerging as an important tool for analyzing the geometry of the manifold. Unfortunately, the high complexity of the computation of the heat kernel - the key to the diffusion process - limits this type of analysis to 3D models of modest resolution. We show how to use the unique properties of the heat kernel of a discrete two dimensional manifold to overcome these limitations. Combining a multi-resolution approach with a novel approximation method for the heat kernel at short times results in an efficient and robust algorithm for computing the heat kernels of detailed models. We show experimentally that our method can achieve good approximations in a fraction of the time required by traditional algorithms. Finally, we demonstrate how these heat kernels can be used to improve a diffusion-based feature extraction algorithm.

Original languageEnglish (US)
Title of host publicationACM SIGGRAPH 2010 Papers, SIGGRAPH 2010
EditorsHugues Hoppe
PublisherAssociation for Computing Machinery, Inc
ISBN (Electronic)9781450302104
DOIs
StatePublished - Jul 26 2010
Externally publishedYes
Event37th International Conference and Exhibition on Computer Graphics and Interactive Techniques, SIGGRAPH 2010 - Los Angeles, United States
Duration: Jul 26 2010Jul 30 2010

Publication series

NameACM SIGGRAPH 2010 Papers, SIGGRAPH 2010

Other

Other37th International Conference and Exhibition on Computer Graphics and Interactive Techniques, SIGGRAPH 2010
Country/TerritoryUnited States
CityLos Angeles
Period7/26/107/30/10

All Science Journal Classification (ASJC) codes

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

Keywords

  • Heat diffusion
  • Heat kernel
  • Matrix exponential
  • Multi-resolution

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