Research On The Theory And Application Of Soft Multivariate Morphology Based On Fuzzy Logic

Mathematical morphology is a nonlinear technology of image processing and analysis based on rigorous mathematical theory. It has been applied in various areas in image processing extensively and successfully due to its simple, elegant algorithm. Morphology abandons traditional views of numerical modeling and analysis. Instead, a geometric approach is used to describe and analyze the images. Four basic operations, dilation, erosion, opening and closing operation constitute a series of operators of image processing and analysis according to the principles and significance of image processing. A strong and rigorous theory of mathematical morphology has been consitited.Fundamental principles of binary and grayscale mathematical morphology, fuzzy morphology and soft mathematical morphology are introduced in this paper. The definitions, geometric interpretation and mathematical properties of various operations of these kinds of morphology are investigated. Advantages of their applications are analyzed. These discussions are the solid foundation for the research later.This dissertation focuses on studying multivariate morphology and its applications, which extends mathematical morphology to color images. A new definition of vector partial ordering is proposed based on fuzzy evaluation criteria, Its properties are investigated. Meanwhile, a new framework of fuzzy soft multivariate morphology is established. Fundamental vector morphological operators are consititued and their properties are wholly discussed.Based on the rigorous mathematical theory, large number of experiments is implemenyted. Experimental results show that the fuzzy soft multivariate morphology based on fuzzy evaluation criteria not only has better performance, but also has less time complexity of the algorithm than classical color morphology based on other vector orderings in image filtering and edge detection communities.The fuzzy soft multivariate morphological operators proposed in this dissertation inherit the advantages of fuzzy morphology, taking fully into account the ambiguity of images in image processing and analysis. Image details can be maintained very well with the application of fuzzy soft multivariate morphological operators. Furthermore, fuzzy soft multivariate morphological operators own the characteristics of soft mathematical morphology, having certain robustness (stability). In other words, new morphological operators are not sensitive to noises and mini-change of shape of objects in image processing, and are apt to their applications in practice.