Wavelet-Based Multifractal Formalism to Assist in Diagnosis in Digitized Mammograms

Abstract

We apply the 2D wavelet transform (WTMM) method to perform a multifractal analysis of digitized mammograms. We show that normal regions display monofractal scaling properties as characterized by the socalled Hurst exponent H 0¡ 3 ¢ 0¡ 1 in fatty areas which look like antipersistent self-similar random surfaces, while H 0¡ 65 ¢ 0¡ 1 in dense areas which exibit long-range correlations and possibly multifractal scaling properties. We further demonstrate that the 2D WTMM method provides a very efficient way to detect tumors as well as microcalcifications (MC) which correspond to much stronger singularities than those involved in the background tissue roughness fluctuations. These preliminary results indicate that the texture discriminatory power of the 2D WTMM method may lead to significant improvement in computer-assisted diagnosis in digitized mammograms.

Statistical Tests of Anisotropy for Fractional Brownian Textures. Application to Full-field Digital Mammography

“…In particular, some of these investigators used the fractal dimension as an indicator of mammogram density [17,18,19]. More recently, some authors studied more deeply the stochastic nature of mammogram density by using stochastic models such as 1/f noise models related to fractional Brownian fields [16,30,33,40]. As in the work presented here, these authors went into much efforts to measure model parameters on mammograms and to empirically validate models.…”

“…Measurements of Hurst-related parameters on full-field digital mammograms and film mammograms have been reported independently in several papers [16,17,19,30,33,40]. Caldwell et al [19] and Byng et al [17,18] [30].…”

Local regularity for texture segmentation: Combining wavelet leaders and proximal minimization

“…In a variety of applications of possibly very different natures, the relevant information characterizing textures, and thus conveying the information to be analyzed, consists of the fluctuations across space of their local regularity. This is notably the case for biomedical textures such as bone [6] or breast [7] (see also [8] for a review), for surface imagery [9], for satellite imagery [10], or for image registration [11,12].…”

A Multiscale Wavelet-Based Test for Isotropy of Random Fields on a Regular Lattice

“…These images have been modeled as isotropic fractional Brownian fields, which are a subclass of intrinsically stationary random fields (see, e.g., [4,21,22,28]). In Section VII we compared the Richard-Bierme (RB) test for isotropy to our wavelet-based test.…”