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The mathematical morphology have been widely used for signal processing in various field including biology, geography, linguistics, military, chemistry, agriculture, manufacturing, medical, and so on. Due to the reason of lacking flexibility in conventional morphology, concept of the generalized morphology is introduced to enhance the morphological operations. In this dissertation, three topics of the generalized morphology and their applications are presented. The first topic concerns the morphological filtering. Two newly defined morphological filters, order statistic soft morphological and recursive order statistic soft morphological filters, are proposed for better signal reconstruction from noisy environment. These new filters are proved through the experimental results to be better in noise reduction and edge preservation than other conventional filters. Moreover, by the help of the flexibility of these filter''s structure, new image applications can be developed. On the other hand, an efficient class of alternating sequential filters (ASF) in morphology is developed to reduce half of the huge computational complexity residue in the original ASF structure while maintaining comparable filtering performance.
In the second part, we are interested in the motion planning problems in computer vision. Two morphological approaches that offer the shortest paths for moving objects of arbitrary shape allowing rotation and forward/backward movement are proposed. The parallel and simple architecture of the proposed morphological algorithms not only make a feasible and tractable system but also allow to solve more complex/realistic problems whose models are less limited to the realistic hardware.
The third part concerns the topic of pattern recognition. An effect target detection algorithm is proposed and proved that it can be applied to the real imaging systems to detect the desired objects on distorted perspective plane from cluttered background by using the dynamic-varying structuring elements matching. Moreover, the proposed algorithm is shown to have ability in detecting the distortion resulted by the processing process.
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