Laplace-Beltrami eigenfunction metrics and geodesic shape distance features for shape matching in synthetic aperture sonar

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.