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Proceedings Paper

Laplace-Beltrami eigenfunctions for 3D shape matching
Author(s): Jason C. Isaacs
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Paper Abstract

Assuming that a 2D surface is a representation of a manifold embedded in 3-space then metrics of the eigenfunctions of the diffusion maps of that manifold represent the shape of that manifold with invariance to rotation, scale, and translation. Diffusion maps is said to preserve the local proximity between data points by constructing a representation for the underlying manifold by an approximation of the Laplace-Beltrami operator acting on the graph of this surface. This work examines 3D shape clustering problems using metrics of the projections onto the natural and nodal sets of the Laplace-Betrami eigenfunctions for shape analysis of closed surfaces. Results demonstrate that the metrics allow for good class separation over multiple targets with noise.

Paper Details

Date Published: 23 May 2011
PDF: 10 pages
Proc. SPIE 8017, Detection and Sensing of Mines, Explosive Objects, and Obscured Targets XVI, 80170Q (23 May 2011); doi: 10.1117/12.885642
Show Author Affiliations
Jason C. Isaacs, Naval Surface Warfare Ctr. (United States)

Published in SPIE Proceedings Vol. 8017:
Detection and Sensing of Mines, Explosive Objects, and Obscured Targets XVI
Russell S. Harmon; John H. Holloway; J. Thomas Broach, Editor(s)

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