Biharmonic Distance Björn Häfner Fakultät für Mathematik - Technische Universität München

This report investigates the paper Lipman et al. Biharmonic distance, who introduced a new distance measure, called biharmonic. We examine the approach of the distance, which is based on the Green’s kernel of the Bi-Laplacian in the continuous and the discrete setting. For the discrete setting we have two different methods of calculation, an approximate as well as an exact computation. Furthermore, we proof and evaluate the biharmonic distance’s properties on the basis of being a metric, gradual, locally isotropic, globally shape-aware, isometry invariant, insensitive to noise and topology, practical to compute, parameter free. Geodesic, diffusion and commute-time distance are shortly introduced to study the differences between the biharmonic distance based on the properties above. The entire report is based on the publication of Lipman et al. 2010 [1]. For this reason it will not be specifically cited within the report.