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An Optimal Transport Approach to Robust Reconstruction and Simplification of 2D Shapes
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
Cited literature [30 references]
https://hal.inria.fr/hal-00758019
Contributor : Pierre Alliez <>
Submitted on : Monday, May 27, 2013 - 11:53:13 AM
Last modification on : Saturday, January 27, 2018 - 1:31:40 AM
Long-term archiving on: : Friday, March 31, 2017 - 4:48:00 PM
Contributor : Pierre Alliez <>
Submitted on : Monday, May 27, 2013 - 11:53:13 AM
Last modification on : Saturday, January 27, 2018 - 1:31:40 AM
Long-term archiving on: : Friday, March 31, 2017 - 4:48:00 PM
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DCAD11.pdf
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