Nous avons l’immense plaisir d’accueillir Pierre Alliez de l’Inria Sophia Antipolis le mardi 19 avril. Celui-ci nous présentera :
Inter-surface Mapping through Optimal Transportation
We present a novel approach to creating a homeomorphic map between two surfaces. While most previous approaches compose maps over intermediate domains, we directly optimize a map between two surfaces by computing a variance-minimizing mass transport plan. We solve this non-linear problem, which is akin to minimizing the Dirichlet energy of both the map and its inverse, using two alternating convex optimization problems for which efficient numerical algorithms exist. A coarse-to-fine approach based on fast evaluation of geodesic distances through diffusion distances is then employed to provide a robust and efficient inter-surface mapping algorithm that naturally finds correspondences between surfaces, with little to no user interaction.