STOCHASTIC MODELS IN IMAGE ANALYSIS AND PROCESSING

This study is concerned with the analysis and processing of one-dimensional image boundaries and two-dimensional images using a class of stochastic models. For the boundary data, univariate and multivariate circular autoregressive models (CAR) are suggested. Methods of estimation of parameters of the model and a decision rule for the choice of appropriate order of the model are given. Features that are independent of the transformations of boundaries are derived for the classification of boundaries. Two optimal stochastic data compression schemes using FFT are included. Two non-equivalent two-dimensional generalizations of CAR models leading to simultaneous autoregressive (SAR) and conditional Markov (CM) models on finite lattices are used for the representation of images. In these models, the observation at one location is written as a finite sum of observations at locations in all directions and a noise sequence. The noise sequence is white for SAR models and colored for CM models. Expressions for the spectral density and autocorrelation functions are given for SAR and CM models. An iterative estimation scheme is given for SAR models, which yields approximate likelihood estimates in Gaussian case. A consistent but not efficient estimation scheme is given for arbitrary Gaussian CM models, which is shown to be more efficient than the popular coding estimate for a simple CM model. Using asymptotic Bayes decision theory, transitive, consistent and parsimonious decision rules are derived for choosing an appropriate SAR or CM model. The usefulness of the estimation methods and the decision rule is illustrated using synthetic data from known models. Two applications are illustrated. Minimum mean square error filters, using FFT are designed without requiring the prototype of the original for the restoration of images degraded by a known point spread function and additive white noise of unknown variance. The results of fitting SAR models to textures like cork, grass, etc., are given. The synthetic textures corresponding to the fitted models are similar to the original