A multi-resolution approach to heat kernels on discrete surfaces

Amir Vaxman, Mirela Ben-Chen, Craig Gotsman

Research output: Contribution to journalArticlepeer-review

43 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)
Article number121
JournalACM Transactions on Graphics
Volume29
Issue number4
DOIs
StatePublished - 2010
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Computer Graphics and Computer-Aided Design

Keywords

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

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