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 language | English |
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Title of host publication | ACM SIGGRAPH 2010 Papers |
Editors | Hugues Hoppe |
Place of Publication | New York, NY, USA |
Publisher | Association for Computing Machinery, Inc |
Number of pages | 10 |
ISBN (Print) | 9781450302104 |
DOIs | |
Publication status | Published - 26 Jul 2010 |
Event | The 37th International Conference and Exhibition on Computer Graphics and Interactive Techniques, SIGGRAPH 2010 - Los Angeles, United States Duration: 25 Jul 2010 → 29 Jul 2010 Conference number: 37 http://s2010.siggraph.org/index.html |
Publication series
Name | SIGGRAPH '10 |
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Publisher | Association for Computing Machinery |
Conference
Conference | The 37th International Conference and Exhibition on Computer Graphics and Interactive Techniques, SIGGRAPH 2010 |
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Abbreviated title | SIGGRAPH 2010 |
Country/Territory | United States |
City | Los Angeles |
Period | 25/07/10 → 29/07/10 |
Internet address |
Keywords / Materials (for Non-textual outputs)
- multi-resolution
- heat kernel
- matrix exponential
- heat diffusion