Hyperbolic wavelet leaders for anisotropic multifractal texture analysis

Abstract

Scale invariance has proven a crucial concept in texture modeling and analysis. Isotropic and self-similar fractional Brownian 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.