Abstract: Image segmentation method based on the classical rough set theory is lacking of accurate classification on the uncertainty of target image edge boundaries, and classical rough set information system which is built for an image with a priori granularity does not reflect the roughness information between different particle size objectives accurately. Based on the theory of approximation set of rough set model, this paper adopts an adaptive optimal graining method on the rough set representation of the image, and then builds the upper and lower approximation sets of the target and background images. According to the approximate set ideas, this paper accurately describes the edge boundaries of the target set, and improves the efficiency of the rough set approximation set maximum rough entropy combined with particle swarm algorithm at the same time, finally obtains the optimal segmentation threshold. The experimental results show that this method is feasible and effective.

Key words: image segmentation, rough set, approximation set, granular computing, particle swarm

摘要： 基于经典粗糙集理论的图像分割方法缺少对目标图像不确定性边界域的精确划分，其根据先验粒度构建的图像粗糙集信息系统，并没有客观准确地反映出不同粒度之间的粗糙性信息。基于粗糙集近似集理论模型，首先采用自适应粒化方法得到图像的最优粒度，接着基于该粒度划分构建图像的目标和背景的上下近似集，再根据近似集思想对目标集合的边界域进行精确刻画，同时结合粒子群算法提高求解粗糙集近似集最大粗糙熵的效率，最终得到图像分割的最优分割阈值，并通过仿真实验表明该方法具有可行性和有效性。

关键词: 图像分割, 粗糙集, 近似集, 粒计算, 粒子群