STRUCTURAL INFORMATIVENESS OF MORPHOLOGICAL SHAPE MODELS BASED ON COVERINGS AND MULTI-COVERINGS

The development of new models and techniques for morphological image analysis and the simplicity theory are overviewed. Based on the simplicity theory as an analogue of the probability theory, the structural entropy is defined, as well as the mutual and conditional structural informativeness of morphological shapes. The properties of structural entropy are investigated and proved. It is demonstrated that conditional structural entropy can be used as a functional analogue of the morphological shape correlation coefficient in various shape comparison problems for all types of morphologies with shape models described by coverings. Additionally, the multi-cover model is proposed, for which the simplicity and structural (fractal) entropy are defined. Using the multiplet (multipoint) Hough morphology as an example, the generalized concepts of t-simplicity, structural and fractal t-entropy, hypergraph models, and t-pleted multi-coverings are introduced.