Laplacian spectral distances and kernels on 3D shapes

•Design and discretization of Laplacian spectral distances on 3D shapes.•Smoothness and shape-intrinsic properties through filtered Laplacian eigenvalues.•Higher approximation accuracy and lower computational cost than previous work.•Spectrum-free computation bypasses computational and storage limit...

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Bibliographic Details
Published in:Pattern recognition letters 2014-10, Vol.47, p.102-110
Main Author: Patané, Giuseppe
Format: Article
Language:English
Subjects:
Biharmonic and diffusion distances
Discrete geometry
Laplace–Beltrami operator
Laplacian matrix
Shape analysis
Spectral distances
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Summary:•Design and discretization of Laplacian spectral distances on 3D shapes.•Smoothness and shape-intrinsic properties through filtered Laplacian eigenvalues.•Higher approximation accuracy and lower computational cost than previous work.•Spectrum-free computation bypasses computational and storage limits. This paper presents an alternative means of deriving and discretizing spectral distances and kernels on a 3D shape by filtering its Laplacian spectrum. Through the selection of a filter map, we design new spectral kernels and distances, whose smoothness and encoding of both local and global properties depend on the convergence of the filtered Laplacian eigenvalues to zero. Approximating the discrete spectral distances through the Taylor approximation of the filter map, the proposed computation is independent of the evaluation of the Laplacian spectrum, bypasses the computational and storage limits of previous work, which requires the selection of a specific subset of eigenpairs, and guarantees a higher approximation accuracy and a lower computational cost.
ISSN:0167-8655
1872-7344
DOI:10.1016/j.patrec.2014.04.003