Géométrie discrète et morphologie mathématique

Head:	TAJINE Mohamed
Permanent staff:	BAUDRIER Etienne, DA COL-JACOB Marie Andrée, MAZO Loïc, NAEGEL Benoît, RONSE Christian, TAJINE Mohamed
Doctoral students:	Yves Michels, Minh-Son Phan
Post-doctoral researcher:	Odyssée Merveille

Objectives

This theme regroups activities on geometrical, topological, algebraic and discrete models in imaging.

In Discrete Geometry, we study digital geometries and topologies, as well as discrete tomography. The mathematical tools that we develop are adapted to image analysis and synthesis. Our aims are, on the one hand to build a robust and performing algorithmic in imaging, controlling processing errors related to the use of real numbers, and on the other hand to develop tools for studying different properties (differential, geometrical and topological) of both discrete and Euclidean objects. More generally, we study the transfers of properties between Euclidean spaces representing "reality" and discrete spaces belonging to the computer.

In Mathematical Morphology, we study the construction of new operators for morphological image processing, and the extension of the morphology to new types of objects. Work is also conducted on connected operators, component trees and connective image segmentation, as well as the application of mathematical morphology to color or multispectral images.

The preferred application area is currently biomedical imaging, but we are also pursuing work in remote sensing imagery.

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