A wavelet-based method for multifractal image analysis:: From theoretical concepts to experimental applications

The description of the 2D WTMM methodology with test applications to random monofractal and multifractal self-affine surfaces displaying isotropic and aniso-tropic scale similarity properties are discussed. The WTMM representation is considered as a very efficient and accurate numerical tool for scanning the singularities of fractal landscapes. The 2D WTMM method is used as a natural generalization of box-counting algorithms and structure function techniques. The 2D WTMM method is very useful in classifying tissues by quantifying breast density fluctuations in a very accurate way. The detection and segmentation of MC by mixing and combining the 2D WTMM method with neural network techniques cab be used in the diagnosis of digitized mammogram. The 2D WTMM method depends on the computation of partition functions from the WT structure defined by the wavelet transform modulus maxima. The WTMM method provides a necessary generalization of the classical box-counting techniques.