Parameter estimation for stochastic texture models

• Main Author: Acuna, Carmen Olga
• Language: ENG
• Published: ScholarWorks@UMass Amherst 1988
• Subjects: Statistics
• Online Access: https://scholarworks.umass.edu/dissertations/AAI8906247

We regard texture as a realization of a stochastic process defined on the square lattice. The model chosen is a Markov Random Field, which incorporates both local and global interactions, and it is a modification of the autobinomial model introduced by Besag (1974) and used by Cross and Jain (1983) for texture generation and synthesis. A Monte Carlo procedure called the Gibbs sampler is used to generate realizations from the model. Examples show how the parameters of the Markov random field control the strength, direction, and range of the clustering in the image. The problem of estimating the model parameters from a sample of independent realizations of the process is studied. The traditional maximum likelihood estimator is found to be consistent and asymptotically normal, but not computationally feasible. An alternative method of estimation, bivariate pseudolikelihood, is proposed. Although computationally intense, this method is much easier to implement than maximum likelihood. Consistency of the estimators is investigated under two different sets of assumptions. Experiments are performed to assess the accuracy of the estimates. In addition, the estimated parameters are used to generate images that are visually compared to those arising from the original model.