NEW MODELS AND TECHNIQUES FOR THE SYNTHESIS, ESTIMATION, IDENTIFICATION, AND SEGMENTATION OF RANDOM FIELDS
Abstract
Random fields models have arisen in important applications in many diverse fields, including image synthesis and analysis. The understanding and processing of images is limited by the types of underlying models that are hypothesized to evoke the image. Hence, new models and associated techniques are developed. The new results are in these main areas: (1) New random fields models; (2) Associated synthesis, estimation, and identification in terms of a new mathematical formulation; (3) New models and techniques for segmentation. The new class of models includes the traditional models, but extends these to comprise a substantially larger new class. Thus, new image textures are representable with convenient small-order parametrizations. In particular, representations with significant correlations between distant locations are achieved. The algorithms for synthesis, estimation, and identification, however, require only about the same amount of time as for the classical models. Indeed, a closed-form algorithm was found for choosing among models with different directionalities. To facilitate the analysis of such problems, the new mathematical notation is aimed at simplifying the difficulties due to the multidimensional nature of random fields models. Many results of one-dimensional theory are thereby easily provable in two or more dimensions. The results make possible the desired statistical operations with the new models. New methods are also developed for segmentation. This, perhaps a more recent image operation of growing importance, is basic to artificial intelligence approaches to image analysis. It is shown that segmentation based on different random fields models is readily achievable even though the segments may be identical in mean and variance. The results follow from the statistically advantageous capability of representing a wide variety of image textures with a small number of parameters.
Degree
Ph.D.
Subject Area
Electrical engineering
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