Collaborators:

Marie Rochery, Josiane Zerubia.

Key words:

active contours, quadratic functional, geometry, shape description, level sets, road network extraction.

Resume:

Active contours have been used in numerous applications in image processing and computer vision. They offer great modelling flexibility and can be solved with simple and rapid algorithms. Classically, the energies used are linear functionals on the space of 1-chains. They thus encode essentially pointwise information. This work introduces energies that are quadratic functionals. They can thus encode global information, in particular about shape.

Theory:

An analysis of the different forms of quadratic functional compatible with various invariance requirements, and of the different ways in which data may be introduced into the functionals.

Practice:

1. The study of a particular quadratic geometric term. The quadratic nature of the model necessitates considerably more algorithmic delicacy than in the linear case, requiring the careful study and use of a variety of techniques from level set theory and practice. The energy describes branched shapes.

2. The study of certain quadratic data terms.

3. The application of the above to the problem of road network extraction from remote sensing images.

Preliminary results:

Publications:

• "Étude d'une nouvelle classe de contours actifs pour la détection de routes dans des images de télédétection", Marie Rochery, Ian H. Jermyn, Josiane Zerubia, Proceedings of GRETSI, Paris, France, September 2003.