Smooth 2D Coordinate Systems on Discrete Surfaces

Colin Cartade (1) , Rémy Malgouyres (2) , Christian Mercat (3, 4) , Chafik Samir (5)

1 LIMOS - Laboratoire d'Informatique, de Modélisation et d'optimisation des Systèmes
2 LIMOS - Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes
3 ICJ - Institut Camille Jordan
4 EA S2HEP - Sciences et Société ; Historicité, Éducation et Pratiques
5 ISIT - Image Science for Interventional Techniques

We introduce a new method to compute conformal param- eterizations using a recent definition of discrete conformity, and estab- lish a discrete version of the Riemann mapping theorem. Our algorithm can parameterize triangular, quadrangular and digital meshes. It can be adapted to preserve metric properties. To demonstrate the efficiency of our method, many examples are shown in the experiment section.

Domaines: Traitement des images [eess.IV]

Colin Cartade, Rémy Malgouyres, Christian Mercat, Chafik Samir. Smooth 2D Coordinate Systems on Discrete Surfaces. 14th International Workshop on Combinatorial Image Analysis, Apr 2011, Nancy, France. pp.59-70, ⟨10.1007/978-3-642-19867-0_5⟩. ⟨hal-00659011⟩