Adaptive eigensystem truncation for spectral shape signatures. Issue 6 (19th September 2017) - Williams, Reed M.; Ilieş, Horea T.
ABSTRACT: The 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 samplings of the same shape at different intrinsic sizes and may cost unnecessary computational effort on resource-limited systems (e.g., drones or robots). In this paper we briefly examine the performance of fixed numbers of eigenpairs on approximating the spectrum of models of different sizes, propose an adaptive cutoff selection method which improves consistency between models for spectral signature use, demonstrate the method on Heat and Wave Kernel signatures (HKS and WKS) for point clouds, and briefly discuss the trade-off between running time and desired error or convergence properties. GRAPHICAL ABSTRACT: