Function spaces vs. Scaling functions: Some issues in image classification

Stéphane Jaffard (1) , Patrice Abry (2) , Stéphane Roux (2)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 Phys-ENS - Laboratoire de Physique de l'ENS Lyon

Criteria based on the computation of fractal dimensions have been used in order to perform image analysis and classification; we show that such criteria often amount to deter- mine the regularity of the image in some classes of function spaces, and that looking for richer criteria naturally leads to the introduction of new classes of function spaces. We will investigate the properties of some of these classes, and show which type of additional information they yield for the initial image.

Domaines: Analyse classique [math.CA]

Stéphane Jaffard, Patrice Abry, Stéphane Roux. Function spaces vs. Scaling functions: Some issues in image classification. Maïtine Bergounioux. Mathematical Image processing, springer, pp.1--40, 2011. ⟨hal-00798459v2⟩