Mathematical Morphology And Its Application

The theory of mathematic morphology is investigated and geometrical meanings and properties of basic morphological operators are induced and summarized. The essence of mathematic morphology to probe signals using structuring element is demonstrated.The applications of mathematic morphology are studied and the main achievements can be summarized as follows. (1) Mathematic morphology is applied to yarn neps detection in textile industry. The concept of generalized structuring element in mathematic morphology is proposed and the generalized morphological structuring element with trapezium pyramidal template is constructed, which enriches the theory of mathematic morphology. The concept of generalized structuring element and the construction approach are innovative points in this dissertation. (2) The applications of mathematic morphology in automatic small target detection in infrared image sequences are studied. An algorithm of automatically detecting small target in infrared image sequences based on gray-scale morphological open by reconstruction operators is presented and infrared image enhancement is implemented using morphological operations, thus further improving the detection performance of the proposed algorithm. The applications of mathematic morphology in infrared target detection are enriched. (3) A method of filtering feedback signals in closed loop control system is proposed and applied to the practical system successfully, which supplies a gap in this application field of mathematic morphology. All those application algorithms above have important values both in academic research and practical application research.The theory of morphological pyramid and the main achievements can be summarized as follows. (1) Multiscale morphological close pyramid with perfect reconstruction is constructed and successfully applied to multiresolution image segmentation. The proposed segmentation algorithm can separate bright component in dark background and dark component in bright background, which is significant in the area of remote sensing image processing. (2) Multiscale flat-SE morphological hybrid pyramid is constructed and successfully applied to filter scanning images. The concept and constructing approach of multiscale flat-SE morphological hybrid pyramid extend the theory of mathematic morphology, which are not involved by reference literature available.The theory of morphological wavelet is investigated and the main achievements can be summarized as follows. (1) The method of constructing nonlinear morphological Haar wavelet is discussed in detail for the first time and morphological Haar wavelet is successfully applied to image decompositions. Morphological Haar wavelet has the advantages of nonlinear, the same value scope of scale signal with original signal, preservation of signal local maximum (minimum) in multiresolution space and ensuring perfect reconstruction, so is more suitable for image compression coding and pattern recognition. (2) A novel approach of constructing morphological wavelet with non-redundancy and perfect reconstruction based on updating-lifting scheme isproposed. The concept of generalized updating operator is presented first and the method of constructing generalized updating operator is discussed, thus developing the theory of mathematic morphology further. The concept and construction method of generalized updating operator are innovative points in this dissertation. (3) A denoising algorithm based on updating-lifting wavelet thresholding is presented and the experimental results show the proposed algorithm is more superior to the denoising method based on traditional wavelet thresholding. The peak signal-noise ratio is improved by 2~5dB and signal-noise ratio 4~7dB.Especially in the case of low signal-noise ratio, the proposed algorithm is much better. This algorithm is important to mathematic morphology and wavelet theory and their applications.