Order selection of 2-D AR model using a lattice representation and information criteria for texture analysis

In the context of parametric modeling for image processing, we use a lattice representation, i.e. based on reflection coefficients, to derive an estimation method for both the parameters and the order of the 2-D Quarter Plane Autoregressive model. The method is based on the combination of an Information Criterion (IC) and the prediction errors of models computed from a lattice parameter estimation algorithm. In this paper, we propose the use of two criteria which are consistent conversely the Akaike one: the Kashyap and Chelappa criterion is a 2-D extension of Bayesian Information Criterion (BIC); the second criteria, called φβ criterion, which is extended here to the 2-D case, is a generalization drawn on Rissanen´s works. Simulations are provided on synthetic and natural textures. The results show the interest of using lattice estimation algorithm and φβ criterion to a characterization of textures.