Robust Shape Reconstruction and Optimal Transportation

Pierre Alliez (1) , Simon Giraudot (1) , David Cohen-Steiner (2)

1 TITANE - Geometric Modeling of 3D Environments
2 GEOMETRICA - Geometric computing

We describe a framework for robust shape reconstruction from raw point sets, based on optimal transportation between measures, where the input point sets are seen as distribution of masses. In addition to robustness to defect-laden point sets, hampered with noise and outliers, our approach can reconstruct smooth closed shapes as well as piecewise smooth shapes with boundaries.

Domaines: Géométrie algorithmique [cs.CG]; Géométrie algébrique [math.AG]

Pierre Alliez, Simon Giraudot, David Cohen-Steiner. Robust Shape Reconstruction and Optimal Transportation. Courbure discrète : théorie et applications, Jan 2014, Marseille, France. ⟨hal-01090630v2⟩