A two-dimensional autoregressive modelling technique using a constrained optimisation formulation and the minimum hierarchical clustering scheme

The problem of texture characterisation is attempted using a two-dimensional (2-D) autoregressive (AR) modelling technique. Each distinct texture is represented by a different set of 2-D AR model coefficients. A method to estimate AR model coefficients is proposed by relating the extended Yule-Walker system of equations in the third-order statistical domain to the same system in the second-order statistical domain using a constrained optimisation formulation. This method is applied to an image with a constant texture in block-by-block process, so that a number of sets of AR model coefficients are obtained. The minimum hierarchical clustering technique and a weighting scheme are then applied to these sets of coefficients, in order to obtain the final estimation.