ANALYSIS OF VARIANCE IN IMAGE PROCESSING OF CORRELATED DATA (MARKOV, TENSOR PRODUCT SPACES, TEXTURE, EDGE DETECTION)

This dissertation provides a framework for the design and analysis of ANOVA-type image processing techniques in the presence of correlated data. Both grey-level and texture segmentation problems can be encompassed by the test statistics described. Insight into the interaction of a defined image parameter space and the operators associated with the chosen test statistic was demonstrated. For the first time, the probabilities were obtained analytically.; Two general theorems on the interaction of the parameters inherent in correlation image data and the operators associated with the ANOVA approach were applied to the design of a generalized form of ANOVA (GANOVA), i.e., The Independence and Parameter Space Dimensionality Reduction Theorems. The former guarantees the existence of independent quadratic forms for which the associated operators retain the same hypothesis/alternative segmentation capability as ANOVA while the latter relates the operators of a vector (image parameter) space to a set of operators in a vector space of reduced dimensionality. In addition, several unique texture generation schemes were presented. The resultant texture realizations provide good visual agreement with real scenes, e.g., rough seas, windswept cloud formations and plaid materials.; The probability of edge detection of ANOVA and GANOVA, as applied to Markov scenes, was found to be a function of the correlation coefficient. A minimum probability was obtained at a correlation distance equal to the mask size. In addition, an operator limited only to a positive semi-definite form, as in GANOVA, provides a reduction in the spatial connectivity of false edge pixels, thereby providing increased object detection capability.; It was also found that GANOVA operators can be designed for invariance to the correlation coefficient. This property is useful in grey-level discrimination where the edges lie in areas possessing different textures.; Finally, ANOVA and GANOVA possess the previously mentioned characteristics given a Bose-Einstein distribution. The results indicate a degree of robustness to changes in the underlying statistics. The Bose-Einstein statistical model affords a meaningful analysis of ANOVA techniques because the stochastic properties of electro-optical imaging systems are well represented by it.