Self-Similar Anisotropic Texture Analysis: The Hyperbolic Wavelet Transform Contribution - Laboratoire d'Analyse et de Mathématiques Appliquées Accéder directement au contenu
Article Dans Une Revue IEEE Transactions on Image Processing Année : 2013

Self-Similar Anisotropic Texture Analysis: The Hyperbolic Wavelet Transform Contribution

Résumé

Textures in images can often be well modeled using self-similar processes while they may simultaneously display anisotropy. The present contribution thus aims at studying jointly selfsimilarity and anisotropy by focusing on a specific classical class of Gaussian anisotropic selfsimilar processes. It will be first shown that accurate joint estimates of the anisotropy and selfsimilarity parameters are performed by replacing the standard 2D-discrete wavelet transform with the hyperbolic wavelet transform, which permits the use of different dilation factors along the horizontal and vertical axes. Defining anisotropy requires a reference direction that needs not a priori match the horizontal and vertical axes according to which the images are digitized; this discrepancy defines a rotation angle. Second, we show that this rotation angle can be jointly estimated. Third, a nonparametric bootstrap based procedure is described, which provides confidence intervals in addition to the estimates themselves and enables us to construct an isotropy test procedure, which can be applied to a single texture image. Fourth, the robustness and versatility of the proposed analysis are illustrated by being applied to a large variety of different isotropic and anisotropic self-similar fields. As an illustration, we show that a true anisotropy built-in self-similarity can be disentangled from an isotropic self-similarity to which an anisotropic trend has been superimposed.

Dates et versions

hal-00918538 , version 1 (13-12-2013)

Identifiants

Citer

Stéphane G. Roux, Marianne Clausel, Béatrice Vedel, Stéphane Jaffard, Patrice Abry. Self-Similar Anisotropic Texture Analysis: The Hyperbolic Wavelet Transform Contribution. IEEE Transactions on Image Processing, 2013, 22 (11), pp.4353-4363. ⟨10.1109/TIP.2013.2272515⟩. ⟨hal-00918538⟩
320 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More