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

Fernando de Goes 1 David Cohen-Steiner 2 Pierre Alliez 2 Mathieu Desbrun 1
1 CS CALTECH - Computer Science Department
2 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : 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.
Keywords : Shape reconstruction optimal transportation
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Fernando de Goes, David Cohen-Steiner, Pierre Alliez, Mathieu Desbrun. An Optimal Transport Approach to Robust Reconstruction and Simplification of 2D Shapes. Computer Graphics Forum, Wiley, 2011, Eurographics Symposium on Geometry Processing 2011, 30 (5), pp.1593-1602. ⟨hal-00758019⟩

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