Elliptic operator for shape analysis
Many shape analysis methods treat the geometry of an object as a metric space that can be captured by the Laplace Beltrami operator. In this paper, we propose to adapt a classical operator from quantum mechanics to the field of shape analysis where we suggest to integrate a scalar function through a unified elliptical Hamiltonian operator. We study the addition of a potential function to the Laplacian as a generator for dual spaces in which shape processing is performed. Then, we evaluate the resulting spectral basis for different applications such as mesh compression and shape matching. The suggested operator is shown to produce better functional spaces to operate with, as demonstrated by the proposed framework that outperforms existing spectral methods, for example, when applied to shape matching benchmarks.
ArXiv