Parametric estimation for Gaussian operator scaling random fields and anisotropy analysis of bone radiograph textures

In this paper, we consider a stochastic anisotropic model for trabecular bone x-ray images. In [1], a fractal analysis based on isotropic Fractional Brownian Fields was proposed to characterize bone microarchitecture. However anisotropy measurement is of special interest for the diagnosis of osteoporosis [7]. We propose to model trabecular bone radiographs by operator scaling Gaussian random fields which are anisotropic generalizations of the Fractional Brownian Field. We construct consistent estimators for these models and apply them on trabecular bone x-ray images. Our first results suggest that these models are relevant for this modeling.