Inverse problem formulation for regularity estimation in images

Nelly Pustelnik (1) , Patrice Abry (1) , Herwig Wendt (2, 3) , Nicolas Dobigeon (2, 4)

1 Phys-ENS - Laboratoire de Physique de l'ENS Lyon
2 IRIT-SC - Signal et Communications
3 CNRS - Centre National de la Recherche Scientifique
4 Toulouse INP - Institut National Polytechnique (Toulouse)

The identification of texture changes is a challenging problem that can be addressed by considering local regularity fluctuations in an image. This work develops a procedure for local regularity estimation that combines a convex optimization strategy with wavelet leaders, specific wavelet coefficients recently introduced in the context of multifractal analysis. The proposed procedure is formulated as an inverse problem that combines the joint estimation of both local regularity exponent and of the optimal weights underlying regularity measurement. Numerical experiments using synthetic texture indicate that the performance of the proposed approach compares favorably against other wavelet based local regularity estimation formulations. The method is also illustrated with an example involving real-world texture.

Mots clés: Convex optimization; Variational approach; Wavelet leaders; Local regularity

Domaines: Synthèse d'image et réalité virtuelle [cs.GR]; Traitement du signal et de l'image [eess.SP]; Traitement des images [eess.IV]; Vision par ordinateur et reconnaissance de formes [cs.CV]; Intelligence artificielle [cs.AI]

Nelly Pustelnik, Patrice Abry, Herwig Wendt, Nicolas Dobigeon. Inverse problem formulation for regularity estimation in images. International Conference on Image Processing (ICIP 2014), Oct 2014, Paris, France. pp. 6081-6085. ⟨hal-01399871⟩