Choice of a 2-D Causal Autoregressive texture model using information criteria

In the context of parametric modeling for image processing, we derive an estimation method for both the order and the parameters of 2-D causal autoregressive model with different geometries of support. Model parameters are estimated from a lattice representation, i.e. based on reflection coefficients. Lattice parameter estimation algorithms offer advantages compared to the Yule-Walker method: they do not require matrix inversion and their computation are robust and fast. For order selection, Information Criterion (IC) methods are the most commonly used. Therefore our order selection method is based on the combination of an IC and the prediction errors of models computed from the lattice parameter estimation algorithm. In this paper, we favour two consistent criteria compared to the non-consistent Akaike criterion: the first criterion is a 2-D extension of Bayesian Information Criterion (BIC); the second criterion, noted $phi_beta$, extended here to the 2-D case, is a generalization drawn on Rissanen's works. Simulations are provided on synthetic and natural textures with Quarter Plane support and Non-Symmetrical Half Plane support. We validate our results on natural textures using the Kullback divergence. The results show the interest of the combination of 2-DFLRLS algorithm and $phi_beta$ criterion to characterize natural textures.