Two dimensional blind Volterra signal modelling for texture feature extraction using nonlinear constrained optimisation

In this paper the problem of image modelling is examined from a higher order statistical perspective. We consider images that exhibit textural properties and the objective is to develop analysis techniques through which robust texture characteristics are extracted. We assume that an 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 second and third order 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. Knowledge about the robustness of the statistical measurements of the image is incorporated into the problem.