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

摘要： 变精度粗糙集是解决模糊决策问题的重要工具，图像边缘信息本身就具有一定的不确定性和模糊性，而图像分割的效果直接依赖于对图像边缘像素的判断精度，因此变精度粗糙集可以更精确地表达图像边缘。将经典图像粗糙集模型扩展到图像变精度粗糙集模型，并将其应用于灰度图像边缘判定问题，利用变精度粗糙集的上下近似定义，构造了变精度灰色形态学算子，依据灰度图像粗糙熵的定义，提出一种基于VPRS粗糙熵的图像分割算法。针对噪声图像，该方法用变精度粗糙集模型判断目标、背景和边界像素集，在不同参数下判断近似集时容忍部分噪声点的存在，从而可获得较好的灰色边缘图像。实验结果说明，由于变精度灰度形态学算子避免了复杂参数优化过程，算法时间执行效率高；同时由于粗糙形态学算子对噪声的优良处理能力，新算法具有较好的噪声鲁棒性。

关键词: 变精度粗糙集, 图像分割, 灰色形态学算子