Laplace-Beltrami eigenfunctions for 3D shape matching

Jason C. Isaacs

doi:10.1117/12.885642

23 May 2011 Laplace-Beltrami eigenfunctions for 3D shape matching

Jason C. Isaacs

Proceedings Volume 8017, Detection and Sensing of Mines, Explosive Objects, and Obscured Targets XVI; 80170Q (2011) https://doi.org/10.1117/12.885642
Event: SPIE Defense, Security, and Sensing, 2011, Orlando, Florida, United States

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.

Citation Download Citation

Jason C. Isaacs "Laplace-Beltrami eigenfunctions for 3D shape matching", Proc. SPIE 8017, Detection and Sensing of Mines, Explosive Objects, and Obscured Targets XVI, 80170Q (23 May 2011); https://doi.org/10.1117/12.885642

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