Heat kernel smoothing using laplace-beltrami eigenfunctions

Authors:
Seongho Seo;Moo K. Chung;Houri K. Vorperian
Affiliations:
Department of Brain and Cognitive Sciences, Seoul National University, Korea;Department of Brain and Cognitive Sciences Seoul National University, Korea and Department of Biostatistics and Medical Informatics and Waisman Laboratory for Brain Imaging and Behavior;Vocal Tract Development Laboratory, Waisman Center, University of Wisconsin, Madison, WI
Venue:
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part III
Year:
2010

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Abstract

We present a novel surface smoothing framework using the Laplace-Beltrami eigenfunctions. The Green's function of an isotropic diffusion equation on a manifold is constructed as a linear combination of the Laplace-Beltraimi operator. The Green's function is then used in constructing heat kernel smoothing. Unlike many previous approaches, diffusion is analytically represented as a series expansion avoiding numerical instability and inaccuracy issues. This proposed framework is illustrated with mandible surfaces, and is compared to a widely used iterative kernel smoothing technique in computational anatomy. The MATLAB source code is freely available at http://brainimaging.waisman.wisc. edu/~chung/lb.