Goes, Fernando deCohen-Steiner, DavidAlliez, PierreDesbrun, MathieuMario Botsch and Scott Schaefer2015-02-272015-02-2720111467-8659https://doi.org/10.1111/j.1467-8659.2011.02033.xWe 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.