Giovedì 24 maggio, alle ore 16 in Aula B, si svolge il seminario “Optimal mass transport and application to surface reconstruction and inter-surface mapping“, tenuto da Pierre Alliez.
Abstract: Optimal transport is a powerful mathematical tool at the interface between calculus of variations, probability and partial differential equations. In the recent past concepts from finite dimensional classical geometry have been successfully transferred to infinite-dimensional spaces, where shapes are seen as probability densities, or where raw measurements are seen as discrete measures, i.e., distribution of masses. After having impacted image analysis, optimal transport may reveal relevant for geometry processing as well, opening the door to solving increasingly complex problems.
In the first part of my talk I will describe a framework for robust shape reconstruction, where we reformulate shape reconstruction and simplification as a transportation problem between measures. Our formulation departs from the common way to state the transportation problem in the sense that we do not know the target measure but instead need to solve for it. This approach brings forth a unified treatment of noise, outliers, sharp features and boundaries. In the second part of my talk I will present a novel approach for computing a homeomorphic map between two discrete surfaces. While most previous approaches compose maps over intermediate domains which result in suboptimal inter-surface mapping, we directly optimize a map by computing a mass transport plan between two surfaces.
Pierre Alliez is Senior Researcher and team leader at Inria Sophia-Antipolis – Mediterranee (see https://team.inria.fr/titane/
). He has authored many scientific publications and several book chapters on mesh compression, surface reconstruction, mesh generation, surface remeshing and mesh parameterization. He is an associate editor of the Computational Geometry Algorithms Library (http://www.cgal.org
). He was awarded in 2011-2015 a Consolidator Grant from the European Research Council on Robust Geometry Processing. https://team.inria.fr/titane/pierre-alliez/
Per ulteriori informazioni e per validità come attività seminariale per gli studenti della magistrale, contattare il Prof. Riccardo Scateni.