Laplace-Beltrami spectra for shape comparison of surfaces in 3D using the closest point method

The need to compare separate objects arises in a wide range of applications. In one approach for comparing objects, `Shape-DNA´ is constructed to give a numerical fingerprint representing an individual object. Shape-DNA is a cropped set of eigenvalues of the Laplace-Beltrami operator for the surface of the object. In this paper, we compute the Shape-DNA of surfaces using the closest point method. Our approach may be applied to a variety of surface representations including triangulations, point clouds and certain analytical shapes. A 2D multidimensional scaling plot illustrates that similar objects form groups based on the Shape-DNAs. Our method has the benefit that it may be applied to surfaces defined by dense point clouds without requiring the construction of point connectivity.