关键词: 变精度粗糙集, 图像分割, 灰色形态学算子

Abstract: The theory of Variable Precision Rough Set（VPRS） is the important tool to solve the problem of fuzzy decision. The image edge information itself has certain uncertainty and fuzziness. The image segmentation effect depends directly on the extraction accuracy of the image edge, so VPRS model can more accurately express image edge. In this paper, the classical image rough set model is extended to the variable precision rough set model, that is applied to gray image edge decision problem, by using the upper and lower approximate definitions of rough sets of variable precision. The definition of the gray image variable accuracy roughness is expanded, and the variable precision gray morphological operator is constructed. Based on those, a grey image segmentation algorithm is proposed. In the case of the noise image, the new method with VPRS will be better able to determine the target, background, and the boundary, and it will allow for the presence of a bit of noise in the approximate set at different parameters, so as to obtain a better gray edge image. The experimental results show that the algorithm has high efficiency due to the fact that the variable precision gray morphology operator can avoid the complex parameter optimization process. Meanwhile, it has better noise robustness because of its excellent ability to handle noise.

Key words: Variable Precision Rough Set（VPRS）, image segmentation, grey morphology operator