Mathematical Morphology Theory And Its Applications In Color Image Processing

Mathematical morphology is a novel theory of nonlinear image processing and analysis. Abandoning the traditional numerical modeling and analysis viewpoint, it describes and analyzes images from sets theory points. Its principle idea is using a structuring element which carries object characters to probe images and gather information in images.As the framework and basis of this thesis, mathematical morphology on complete lattices is discussed in detail firstly. Then, in the framework of complete lattice theory, the classical binary morphology and gray morphology are extended to a more general mathematical concept——Abelian group. Specifically, the classical binary morphology and gray mrophology are discussed as examples of morphology in Abelian group. New proofs of important theorems and properties are depicted, including the famous representation theorem for morphological operators.The focus of this paper is on studying vector morphology used in color image processing and discussing its applications. As a combination of reduced ordering and conditional ordering, the total ordering based on distance of vectors is defined firstly. Vector morphology and soft vector morphology based on this ordering are creatively proposed. The comparative study of their properties is explored. As a consequence, the applications of denoising and edge extraction in color images are investigated. The experimental results show that the soft vector morphology based on the distance total ordering can preserve more detail of images and have more insensitive to impulse noises and the shape changes of objects.