In this paper, we describe a statistical framework for the analysis of anisotropy of image texture. This framework is based on the modeling of the image by two kinds of non-stationary anisotropicGaussian field with stationary increments and spectral density: the extended fractional Brownian field (EFBF) and a specific Gaussian operator scaling field (GOSF), which both correspond to a generalization of the fractional Brownian field. In this framework, we tackle anisotropy analysis using some directional processes that are either defined as a restriction of the image on an oriented line or as a projection of the image along a direction. In the context of EFBF and GOSF, we specify links between the regularity of line and projection processes and model parameters, and explain how field anisotropy can be apprehended from the analysis of process regularity. Adapting generalized quadratic variations, we also define some estimators of the regularity of line and projection processes, and study their convergence to field model parameters. Estimators are also evaluated on simulated data, and applied for illustration to medical images of the breast and the bone.