An Optimal Transport Approach to Robust Reconstruction and Simplification of 2D Shapes
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Date
2011
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and Blackwell Publishing Ltd.
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.
Description
@article{10.1111:j.1467-8659.2011.02033.x,
journal = {Computer Graphics Forum},
title = {{An Optimal Transport Approach to Robust Reconstruction and Simplification of 2D Shapes}},
author = {Goes, Fernando de and Cohen-Steiner, David and Alliez, Pierre and Desbrun, Mathieu},
year = {2011},
publisher = {The Eurographics Association and Blackwell Publishing Ltd.},
ISSN = {1467-8659},
DOI = {10.1111/j.1467-8659.2011.02033.x}
}