Self-similar anisotropic texture analysis : the hyperbolic wavelet transform contribution

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...

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Veröffentlicht in:IEEE transactions on image processing : a publication of the IEEE Signal Processing Society. - 1992. - 22(2013), 11 vom: 17. Nov., Seite 4353-63
1. Verfasser: Roux, Stéphane G (VerfasserIn)
Weitere Verfasser: Clausel, Marianne, Vedel, Béatrice, Jaffard, Stéphane, Abry, Patrice
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 2013
Zugriff auf das übergeordnete Werk:IEEE transactions on image processing : a publication of the IEEE Signal Processing Society
Schlagworte:Journal Article
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520 |a 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 
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700 1 |a Clausel, Marianne  |e verfasserin  |4 aut 
700 1 |a Vedel, Béatrice  |e verfasserin  |4 aut 
700 1 |a Jaffard, Stéphane  |e verfasserin  |4 aut 
700 1 |a Abry, Patrice  |e verfasserin  |4 aut 
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