Wavelet methods for the statistical analysis of image texture

This thesis considers the application of locally stationary wavelet-based stochastic models to the analysis of image texture. In the first part we propose a test of stationarity for spatial data on a regular grid. This test is then incorporated into a segmentation framework in order to determine the number of textures contained within an image, a key feature to many texture segmentation approaches. These novel methods are subsequently applied to various texture analysis problems arising from work with an industrial collaborator. The second part of this thesis considers the modelling of the spectral structure of a non-stationary multivariate image, i.e. an image containing different colour channels. We propose a multivariate locally stationary wavelet-based modelling framework which permits a measure of dependence between pairs of channels. The performance of this modelling approach is then assessed using various colour texture examples encountered by an industrial collaborator