Reversible vectorisation of 3D digital planar curves and applications

Isabelle Sivignon (1) , Florent Dupont (1) , Jean-Marc Chassery (2)

1 M2DisCo - Geometry Processing and Constrained Optimization
2 GIPSA-GPIG - GIPSA - Géométrie, Perception, Images, Geste

This paper tackles the problem of the computation of a planar polygonal curve from a digital planar curve, such that the digital data can be exactly retrieved from the polygonal curve. The proposed transformation also provides an analytical modelling of a digital plane segment as a discrete polygon composed of a face, edges and vertices. A dual space representation of lines and planes is used to ensure that the computed curve remains inside the digital curve, and this tool enables to define a very efficient algorithm. Applied on the digital plane segments resulting from the decomposition of a digital surface, this algorithm provides a set of polygons modelling exactly the digital surface.

Mots clés: discrete polygon; 3D; vectorisation; modelling

Domaines: Traitement du signal et de l'image [eess.SP]

Isabelle Sivignon, Florent Dupont, Jean-Marc Chassery. Reversible vectorisation of 3D digital planar curves and applications. Image and Vision Computing, 2007, 25 (10), pp.1644-1656. ⟨10.1016/j.imavis.2006.06.022⟩. ⟨hal-00105893⟩