Thesis of Isabelle Sivignon

De la caractérisation des primitives à la reconstruction polyédrique de surfaces en géométrie discrète

Defense date: 04/11/2004

Advisor: Florent Dupont
Coadvisor: Jean-Marc Chassery


Discrete geometry aims at defining geometric objects and properties of the Euclidean space in the discrete space, ensuring as much consistency as possible between the two geometric worlds. In image analysis, problems involving discrete geometry appear as soon as discrete images features detection or coding (for instance) is studied. In this work, we consider several problems of discrete geometry, from basic objects, like lines and planes, caracterization to discrete surface polyhedral reconstruction. This progression is split into two
steps which correspond to the two parts of this document :
– a study of basic discrete objects like discrete lines and planes is proposed, and we present new characterization elements about digital intersections ;
– thoses primitves are then used in order to model complex discrete objects : first, we present some results on discrete surfaces segmentation into discrete planes, and then, we describe new algorithms to achieve a reversible polyhedral reconstruction of discrete surfaces based on the segmentation results.