中文摘要：

为了快速准确地完成刀具磨损检测系统中刀具磨损图像的分割,提出了分解的二维Renyi交叉熵刀具磨损图像阈值分割方法。首先引入Renyi交叉熵的定义,给出一维Renyi交叉熵阈值选取公式。然后推导出二维Renyi交叉熵阈值选取公式,并采用快速递推公式来降低阈值选取准则函数的计算复杂度。最后提出了二维Renyi交叉熵的分解算法,将二维Renyi交叉熵的运算转化为两个一维Renyi交叉熵的运算,使算法的运算量从O（L4）降为O（L）。针对不同类型的刀具磨损图像的实验表明,所提出的方法与基于粒子群优化的二维最大Shannon交叉熵法、基于粒子群优化的二维Renyi熵法、二维最小Tsallis交叉熵法相比,在分割效果和运行速度上均具有很大优势。

英文摘要：

In order to segment the tool wear image quickly and accurately in tool wear detection system,the decomposed 2D Renyi cross entropy segmentation method of tool wear image is presented. Firstly,Renyi cross entropy is defined,and the 1D Renyi cross entropy thresholding method is presented. Then 2D threshold selection method based on the Renyi cross entropy is derived,and the recursive algorithm is adopted to reduce the computational complexity of criterion function for threshold selection. Finally,the decomposition algorithm of 2D Renyi cross entropy is proposed,and the computation of 2D Renyi cross entropy is converted into two computations of 1D Renyi cross entropy,then the computational complexity is reduced from O（ L4） to O（ L）. A large number of experiments on different kind of tool wear images are processed and then the experimental results are compared with2 D maximum Shannon entropy method based on particle swarm optimization（ PSO）,2D Renyi entropy method based on particle swarm optimization（ PSO） and the 2D minimum Tsallis cross entropy method,the proposed method shows obvious advantages for tool wear image in segmentation results and processing speed.