Mathematical Morphology Based On Rough Set Research And Applications

This thesis reviews the principles and properties of mathematical morphology and rough sets theory. Based on the investigation of the links between both the domains, we establish the equivalence between some morphological operators and rough sets. According to this, a novel mathematical morphology ?mathematical morphology based on rough sets is proposed. Integrating the quality of rough sets which is good at dealing with imprecise data with that of mathematical morphology, describing object structure quantificationally, it overcomes the subjectivity of fuzzy mathematical morphology and provides a very powerful and flexible tool for image processing.To verify the validity of the new method, some applications of mathematical morphology based on rough sets for image processing such as morphological filters, skeletonization, object reconstruction and edge detection are presented. Simulation examples show that the mathematical morphology based on rough sets possesses good properties such as robust to noise, precision, easy for parallel processing compared with the traditional morphological operators. The performance of the mathematical morphology based on rough sets is much better than the traditional mathematical morphology.