Analysis of Anisotropic Brownian Textures and Application to Lesion Detection in Mammograms

In Image Analysis, Texture Analysis is an important issue which is being motivated by a wide range of applications. In this paper, we focus on the description of irregular anisotropic textures which often appear in medical images. We present a probabilistic framework where images are viewed as realizations of some extended fractional Brownian fields. We then propose a texture analysis which is based on quadratic variations of image increments. Specific to our approach, these variations are computed in several directions. In this way, they can provide us with useful information about directional properties of textures. We formulate an asymptotical result linking variations to their scale and orientation. From this asymptotic relationship, we derive two statistical indices which can be used for describing both the texture irregularity and anisotropy. Finally, we plug these indices into a classifier to detect lesions in mammograms. We evaluate the classifier on the MIAS database using ROC curves, and obtain an AUC of 0.81 for lesions of all types.