An Optimal Transport Approach to Robust Reconstruction and Simplification of 2D Shapes

English

Séminaire Géométrie-Images

20/06/2011 - 15:00 Mr Pierre Alliez (INRIA Sophia-Antipolis) Grand Amphi de l'INRIA Rhône-Alpes, Montbonnot

We propose a robust 2D shape reconstruction and simplification algorithm which takes as input a defect-laden point set with noise and outliers. We introduce an optimal-transport driven approach where the input point set, considered as a sum of Dirac measures, is approximated by a simplicial complex considered as a sum of uniform measures on 0- and 1-simplices. A fine-to-coarse scheme is devised to construct the resulting simplicial complex through greedy decimation of a Delaunay triangulation of the input point set. Our method performs well on a variety of examples ranging from line drawings to grayscale images, with or without noise, features, and boundaries.