A multi-resolution approach to heat kernels on discrete surfaces

Type
Article

Authors
Vaxman, Amir
Ben-Chen, Mirela
Gotsman, Craig

Date
2010-07-26

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. © 2010 ACM.

Citation
Vaxman A, Ben-Chen M, Gotsman C (2010) A multi-resolution approach to heat kernels on discrete surfaces. ACM Transactions on Graphics 29: 1. Available: http://dx.doi.org/10.1145/1778765.1778858.

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.

Publisher
Association for Computing Machinery (ACM)

Journal
ACM Transactions on Graphics

DOI
10.1145/1778765.177885810.1145/1833349.1778858

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