A multi-resolution approach to heat kernels on discrete surfaces

Amir Vaxman, Mirela Ben-Chen, Craig Gotsman

Research output: Contribution to journalArticlepeer-review

47 Scopus citations


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. © 2010 ACM.
Original languageEnglish (US)
Pages (from-to)1
JournalACM Transactions on Graphics
Issue number4
StatePublished - Jul 26 2010
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: Thanks to Irad Yavneh for helpful numerical discussions. This work was partially supported by NSF grants 0808515 and 0914833, and by a joint Stanford-KAUST collaborative grant.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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