A multi-resolution approach to heat kernels on discrete surfaces

Handle URI:
http://hdl.handle.net/10754/597320
Title:
A multi-resolution approach to heat kernels on discrete surfaces
Authors:
Vaxman, Amir; Ben-Chen, Mirela; Gotsman, Craig
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.
Publisher:
Association for Computing Machinery (ACM)
Journal:
ACM Transactions on Graphics
Issue Date:
26-Jul-2010
DOI:
10.1145/1778765.1778858
Type:
Article
ISSN:
0730-0301
Sponsors:
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.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorVaxman, Amiren
dc.contributor.authorBen-Chen, Mirelaen
dc.contributor.authorGotsman, Craigen
dc.date.accessioned2016-02-25T12:30:37Zen
dc.date.available2016-02-25T12:30:37Zen
dc.date.issued2010-07-26en
dc.identifier.citationVaxman 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.en
dc.identifier.issn0730-0301en
dc.identifier.doi10.1145/1778765.1778858en
dc.identifier.urihttp://hdl.handle.net/10754/597320en
dc.description.abstractStudying 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.en
dc.description.sponsorshipThanks 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.en
dc.publisherAssociation for Computing Machinery (ACM)en
dc.subjectHeat diffusionen
dc.subjectHeat kernelen
dc.subjectMatrix exponentialen
dc.subjectMulti-resolutionen
dc.titleA multi-resolution approach to heat kernels on discrete surfacesen
dc.typeArticleen
dc.identifier.journalACM Transactions on Graphicsen
dc.contributor.institutionTechnion - Israel Institute of Technology, Haifa, Israelen
dc.contributor.institutionStanford University, Palo Alto, United Statesen
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