Estimation of the Hurst Exponent of Noisy or Blurred Fractal Textures. Application to Computer-Aided Mammogram Analysis

One over eight women will be diagnosed with breast cancer in her lifetime. As early detection is key to the survival of the patient, recent works aiming at improving the prognosis of breast cancer focused on upstream assessment of cancer risk, so that women at higher risk are prescribed more frequent screenings. A promising research avenue relies on the characterization of mammographic textures through their fractal attributes. However, the presence of noise or blur in mammograms, inherent to real data acquired in a clinical context, might significantly impairs both the accuracy and the robustness of fractal attribute estimators. The aim of the present work is twofold. First, the sensitivity to noise and blur of two state-of-the-art estimators of the Hurst exponent, a widely used fractal attribute, is quantified on different synthetic texture models. Second, these estimators, respectively based on wavelet leaders and mono-genic wavelets, are applied to real mammograms extracted from the VinDr-Mammo public dataset. The comparison of the estimated Hurst exponents to the values in the literature shows an overestimation of the Hurst exponents of dense tissues from old datasets, suspected to originate from a model mismatch or from a lack of robustness to changes in the screened population.