Basic objects characterization and polyhedral surfaces reconstruction in discrete geometry.

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 talk, 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 that are developped in this talk:
- a study of basic discrete objects like discrete lines and planes
is proposed, and we present an algorithm to "recognize" those objects;
- thoses primitives 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.