Parameter estimation for excursion set texture models

Abstract We discuss some work which was motivated by the need to synthesize binary images with a structure statistically similar to a given image. Excursion sets of random fields, which are obtained by ‘thresholding’ a random field at some level, have many advantages for this kind of problem. For stationary Gaussian random fields, excursion sets can be easily simulated and the global properties of the simulated images can be directly related to the model parameters. One barrier to the wider application of excursion set texture models is the lack of statistically efficient methods of parameter estimation. We discuss here the use of the EM algorithm for this problem. Markov chain Monte Carlo techniques are used to implement a stochastic version of the EM procedure. A further modification of the algorithm, which introduces no approximations, enables the method to be implemented in problems of typical size. The techniques can be extended to parameter estimation from contour data at more than one level, to the Bayesian analysis of excursion sets, and to the modelling of binary and categorical time series.