| Mathematical morphology is a new subject dealing with image analysis and is based on strict mathematical theory. Its fundamental laws and methods have greatly influenced the theory and techniques of image processing. The essay starts with the initial introduction of mathematical morphology on complete lattices. Then, theoretically, mathematical morphology is stretched from complete lattices to complete semi-lattices and the adjunction of complete semi-lattices is studied. Some qualities of mathematical morphology on complete semi-lattices are discussed and supported. Two examples of difference semi-lattice and reference semi-lattices are also supplied. Finally, the essay introduced the application of mathematical morphology in digital image processing according to the essence of mathematical morphology on complete lattices and complete semi-lattices. Four applicable algorithms are also provided, namely, the detection of holes, the monitor of moving objects and the fast moving part, the abstraction of the edge of image and image enhancement. |
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