Simulation of oriented patterns with prescribed local orientation using anisotropic Gaussian fields

We consider a stochastic framework for oriented texture modeling. We study a large class of generalized Gaussian fields, called Generalized Anisotropic Fractional Brownian Fields (GAFBF), which combines a local version of an Anisotropic Fractional Brownian Fields (AFBF) with Multifractional Brownian Fields (MBF). This mixture enables to control both the local orientation and the roughness of the texture. A second model based on fields deformation and called Warped Anisotropic Fractional Brownian Fields (WAFBF) is also studied. In this paper, we first establish theoretical results of these new stochastic models, and describe their properties. The notion of orientation for localizable random fields we introduced in our previous works is relevant to give explicit formulas for the orientations of these two models, insuring the control of the expected one. Furthermore, we investigate different ways to simulate a collection of textures with prescribed local orientation and roughness. These procedures serve for concretely observe the behavior of these fields ans as a benchmark for the validation of anisotropy detection tools. We finally propose methods for estimating the anisotropy of a specific AFBF and for characterizing the probability distribution of orientation estimators.