Design of data segmentation and data compression operators based on projective morphological decompositions

Problems of morphological data segmentation and compression are addressed within the framework of projective morphology. Schemes for design of morphological segmentation operators with and without the loss of information based on equivalent transformations of bases of morphological decomposition are proposed. The projectivity of the obtained operations of segmentation with information loss is proved for two main classes of operators of morphological projection: minimum-distance (minimum deviation norm) and monotonic projectors. Information—entropy criteria of optimal finding of segmentation parameters are considered. It is shown that the choice of optimal segmentation parameters depends on the informativity (sample size) of the source data.