An Optimal Transport Approach to Robust Reconstruction and Simplification of 2D Shapes - Archive ouverte HAL Access content directly
Journal Articles Computer Graphics Forum Year : 2011

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

(1) , (2) , (2) , (1)
1
2
Fernando de Goes
  • Function : Author
  • PersonId : 873934
David Cohen-Steiner
  • Function : Author
  • PersonId : 945335
Pierre Alliez
Mathieu Desbrun

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.
Fichier principal
Vignette du fichier
DCAD11.pdf (2.03 Mo) Télécharger le fichier
Vignette du fichier
sgp11.jpg (49.59 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Format : Figure, Image
Loading...

Dates and versions

hal-00758019 , version 1 (27-05-2013)

Identifiers

  • HAL Id : hal-00758019 , version 1

Cite

Fernando de Goes, David Cohen-Steiner, Pierre Alliez, Mathieu Desbrun. An Optimal Transport Approach to Robust Reconstruction and Simplification of 2D Shapes. Computer Graphics Forum, 2011, Eurographics Symposium on Geometry Processing 2011, 30 (5), pp.1593-1602. ⟨hal-00758019⟩
243 View
480 Download

Share

Gmail Facebook Twitter LinkedIn More