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

Author: de Goes, Fernando Ferrari

Year: 2011

Degree: Master's thesis

Advisor: Desbrun, Mathieu

Committee Member: Unknown, Unknown

Option: Computer Science

DOI: 10.7907/YKZF-VX90

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.

Files

• pwsrec.pdf (application/pdf)