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


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.


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.

Item Type:Thesis (Master's thesis)
Subject Keywords:reconstruction, simplification, optimal transport
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Computer Science
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Desbrun, Mathieu
Thesis Committee:
  • Unknown, Unknown
Defense Date:23 May 2011
Non-Caltech Author Email:fdegoes (AT)
Record Number:CaltechTHESIS:05222011-165117683
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6417
Deposited By: Fernando Ferrari De Goes
Deposited On:23 May 2011 18:51
Last Modified:09 Oct 2019 17:09

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