Research On Digital Morphological Filter Theory And Its Algorithms

Digital morphological filter is an important nonlinear filter. It has found wide applications in many research fields, such as image analysis and processing, computer vision and mode recognition. At present, it is a hot subject of nonlinear research in digital signal processing.There is not a systematic method for morphological filter designing because of the complexion and diversity of nonlinear filter theory and algorithms. Most of existing algorithms are proposed in accordance with a certain practical requirement, lacking penetrating theoretical analysis and having limitation in their applications. The performances of morphological filters depend on the types of their structural elements and morphological transforms. The reasonable choice of morphological filters, the constructing of their good-functioned fast algorithms and deep theoretical analyzing for them are still difficult problems. Starting from the investigation of the fundamental theory of morphological filters and concentrating on the choice of structuring elements and the combinations of morphological transforms, this dissertation systematically researches the principles, structures and algorithms of morphological filters by using the methods of serial/parallel processing, linear weighted combination and adaptive processing. The main contents and contributions of this dissertation are as follows:1. The fundamental theory of digital morphological filters is systematically and completely summarized in this dissertation. On the basis of the methods of signal state modeling and stack filter description, this dissertation researches the root signal characteristics and output statistical properties of traditional morphological filters (including opening, closing, open-closing and clos-opening), and illustrates the relationship between various root signals of above filters and points out that the phenomena of statistical biasing existing in the outputs of traditional morphological filters is the direct reason for their noise-removing efficiencies. In addition, the morphological filtering methods have successfully applied in the waveform restoration of noisy ECG signal and the extraction of geometrical shapes of objects in two-dimensional images.2. In order to reduce the statistical bias in the output of traditional morphological open-closing and clos-opening filters, this dissertation presents a new class of generalized open-closing (GOC) and clos-opening (GCO) morphological filters by using two different sized of structuring elements and proves that this class of filters...