TY - JOUR
T1 - A multi-resolution approach to heat kernels on discrete surfaces
AU - Vaxman, Amir
AU - Ben-Chen, Mirela
AU - Gotsman, Craig
N1 - 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.
PY - 2010/7/26
Y1 - 2010/7/26
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/597320
UR - https://dl.acm.org/doi/10.1145/1778765.1778858
UR - http://www.scopus.com/inward/record.url?scp=77956369714&partnerID=8YFLogxK
U2 - 10.1145/1778765.1778858
DO - 10.1145/1778765.1778858
M3 - Article
SN - 0730-0301
VL - 29
SP - 1
JO - ACM Transactions on Graphics
JF - ACM Transactions on Graphics
IS - 4
ER -