Two Dimensional Volterra Filter Modelling of Textured Images Using Weighted Constrained Optimisation

Abstract

In this paper the problem of textured image modelling is examined from a higher order statistical perspective. The objective is to develop analysis techniques through which robust texture characteristics are extracted. We assume that the observed image is derived from a Volterra system (filter) that is driven by a Gaussian input image. Both the filter parameters and the input image are unknown and therefore the problem can be classified as blind or unsupervised in nature. In the statistical approach to the solution of the above problem we seek to determine equations that relate the unknown parameters of the Volterra model with the statistical parameters of the “output” image to be modelled. These equations are highly nonlinear and their solution is attempted through a novel weighted constrained optimisation formulation.