Laplace-Beltrami Eigenfunction Metrics and Geodesic Shape Distance Features for Shape Matching in Synthetic Aperture Sonar
Abstract
Assuming that a 1D curve is a representation of a manifold embedded in a 2D-space, the metrics of the eigenfunctions of the weighted graph-Laplacian and diffusion operator of that manifold are then a representation of the shape of that manifold with invariance to rotation, scale, and translation. In this work, we employ spectral metrics of the eigenfunctions of the Laplace-Beltrami operator compared with geodesic shape distance features for shape analysis of closed curves extracted from 2-D synthetic aperture sonar imagery. Results demonstrate that the spectral eigenfunction diffusion metric and the geodesic distance allow for good class separation over multiple noisy target shapes with a computational advantage to the eigenfunction method.
Cite
Text
Isaacs. "Laplace-Beltrami Eigenfunction Metrics and Geodesic Shape Distance Features for Shape Matching in Synthetic Aperture Sonar." IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, 2011. doi:10.1109/CVPRW.2011.5981743Markdown
[Isaacs. "Laplace-Beltrami Eigenfunction Metrics and Geodesic Shape Distance Features for Shape Matching in Synthetic Aperture Sonar." IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, 2011.](https://mlanthology.org/cvprw/2011/isaacs2011cvprw-laplacebeltrami/) doi:10.1109/CVPRW.2011.5981743BibTeX
@inproceedings{isaacs2011cvprw-laplacebeltrami,
title = {{Laplace-Beltrami Eigenfunction Metrics and Geodesic Shape Distance Features for Shape Matching in Synthetic Aperture Sonar}},
author = {Isaacs, Jason C.},
booktitle = {IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops},
year = {2011},
pages = {14-20},
doi = {10.1109/CVPRW.2011.5981743},
url = {https://mlanthology.org/cvprw/2011/isaacs2011cvprw-laplacebeltrami/}
}