Adaptive eigensystem truncation for spectral shape signatures

Abstract

ABSTRACTThe ability to compare the shapes of objects is crucial to the practice of engineering design. Spectral shape signatures provide a high-quality similarity measure based on diffusion physics by means of the spectrum of an estimate of the Laplace-Beltrami operator for the surface of an object.However, point cloud and mesh models often have very large intrinsic sizes and subsequently large Laplace-Beltrami estimate matrices. Recommendations from the current spectral shape signature literature are to use only a fixed number of arithmetically greatest eigenvalues and their corresponding eigenvectors in the computation of a spectral shape signature. This recommendation “seems to work well”, but it is not yet understood the degree to which this fixed number of eigenpairs approximates the full spectrum for the purposes of shape similarity measures or even what fixed number to use. Using a fixed number of eigenpairs for all model sizes and samplings also introduces inconsistencies between different samplin...