An Optimal Transport Approach to Robust Reconstruction and Simplification of 2D Shapes
Identifieur interne : 000015 ( Main/Corpus ); précédent : 000014; suivant : 000016An Optimal Transport Approach to Robust Reconstruction and Simplification of 2D Shapes
Auteurs : Fernando De Goes ; David Cohen-Steiner ; Pierre Alliez ; Mathieu DesbrunSource :
- Computer Graphics Forum [ 0167-7055 ] ; 2011-08.
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.
Url:
DOI: 10.1111/j.1467-8659.2011.02033.x
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