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

Citation

de Goes, Fernando Ferrari (2011) An Optimal Transport Approach to Robust Reconstruction and Simplification of 2D Shapes. Master's thesis, California Institute of Technology. doi:10.7907/YKZF-VX90. https://resolver.caltech.edu/CaltechTHESIS:05222011-165117683

Abstract

We present 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.

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