Anisotropic textures with arbitrary orientation

We present a Markov random field (MRF) model for digital images capable of representing anisotropic textures with arbitrary orientations. The discrete Hamiltonian is obtained through finite difference discretization of a continuous elliptic operator on R-2, together with a polynomial perturbation. We present the solution of a non-linear system of algebraic equations that estimates the orientation angle and the elliptic operator parameters in terms of the estimated discrete Hamiltonian parameters. We perform experiments of simulation and retrieval of parameters using, respectively, the Gibbs sampler algorithm and the variational estimators for MRF. We use also the estimation algorithm to identify relative rotation of digital images of the same realistic picture scanned at various different orientations.