Locally Parallel Texture Modeling

Pierre Maurel 1 Jean-François Aujol 2 Gabriel Peyré 3
1 VisAGeS - Vision, Action et Gestion d'informations en Santé
INSERM - Institut National de la Santé et de la Recherche Médicale : U746, Inria Rennes – Bretagne Atlantique , IRISA-D5 - SIGNAUX ET IMAGES NUMÉRIQUES, ROBOTIQUE
Abstract : This article presents a new adaptive framework for locally parallel texture modeling. Oscillating patterns are modeled with functionals that constrain the local Fourier decomposition of the texture. We first introduce a texture functional which is a weighted Hilbert norm. The weights on the local Fourier atoms are optimized to match the local orientation and frequency of the texture. This adaptive model is used to solve image processing inverse problems, such as image decomposition and inpainting. The local orientation and frequency of the texture component are adaptively estimated during the minimization process. To improve inpainting performances over large missing regions, we introduce a higly non-convex generalization of our texture model. This new model constrains the amplitude of the texture and it allows one to impose an arbitrary oscillation profile. Numerical results illustrate the effectiveness of the method.
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Pierre Maurel, Jean-François Aujol, Gabriel Peyré. Locally Parallel Texture Modeling. SIAM Journal on Imaging Sciences, Society for Industrial and Applied Mathematics, 2011, 4 (1), pp.413-447. ⟨hal-00415779v2⟩

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