Features are derived from wavelet transforms of images containing a
mixture of textures. In each case, the texture mixture is segmented, based on a 10-dimensional feature vector associated with every pixel. We show that the quality of the resulting segmentations can be characterized using the Potts or Ising spatial homogeneity parameter. This measure is defined from the segmentation labels. In order to have a better measure which takes into account both the segmentation labels and the input data, we determine the likelihood of the observed data given the model, which in turn is directly related to the Bayes information criterion, BIC. Finally we discuss how BIC is used as an approximation in model assessment using a Bayes factor.
We address the problems of (1) segmenting coarse from fine granularity materials, and (2) discriminating between materials of different granularities. For the former we use wavelet features, and an enhanced version of the widely used EM algorithm. A weighted Gaussian mixture model is used, with a second order spatial neighborhood. For granularity discrimination we investigate the use of multiresolution entropy. We illustrate the good results obtained with a number of practical cases.