Hyperbolic wavelet leaders for anisotropic multifractal texture analysis

Abstract : Scale invariance has proven a crucial concept in texture mod-eling and analysis. Isotropic and self-similar fractional Brow-nian fields (2D-fBf) are often used as the natural reference process to model scale free textures. Its analysis is standardly conducted using the 2D discrete wavelet transform. Generalizations of 2D-fBf were considered independently in two respects: Anisotropy in the texture is allowed while preserving exact self-similarity, analysis then needs to be conducted using the 2D-Hyperbolic wavelet transform ; Multifractality enables more versatile scale free models but requires isotropy, analysis is then achieved using wavelet leaders. The present paper proposes a first unifying extension, which is enabled through the following two key contributions: The definition of 2D process that incorporates jointly anisotropy and multi-fractality : The definition of the corresponding analysis tool, the hyperbolic wavelet leaders. Their relevance are studied by numerical simulations using synthetic scale free textures.
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Stéphane Roux, Patrice Abry, Béatrice Vedel, S Jaffard, H Wendt. Hyperbolic wavelet leaders for anisotropic multifractal texture analysis. IEEE International Conference on Image Processing, Sep 2016, Phoenix, AZ, United States. pp.3558 - 3562, ⟨10.1109/ICIP.2016.7533022⟩. ⟨hal-01445950⟩

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