分解的二维倒数交叉熵图像阈值选取

Shannon熵常用于表示信息平均不确定性，但因其定义基于对数函数故存在零点处无意义的缺陷，且二维交叉熵法中若能避免对数运算可使处理速度进一步提升。据此，本文提出了基于分解的二维倒数交叉熵图像阈值选取方法。首先定义了倒数交叉熵，依据分割前后图像之间的最小倒数交叉熵选取阈值；然后给出了二维倒数交叉熵定义及其阈值选取公式，提出了二维倒数交叉熵阈值选取的分解算法。通过求解两个一维倒数交叉熵的最佳阈值，再将其组合获得二维倒数交叉熵最佳阈值，由此将二维运算分解为两个一维运算，算法的计算复杂度从O(L4)降低到O(L)。大量实验结果表明，与基于粒子群优化(Particle Swarm Optimization, PSO)的二维最大Shannon熵法、基于粒子群优化的二维Shannon交叉熵法以及二维指数交叉熵法相比，本文方法的分割效果和运行速度均有优势。 

Image Threshold Selection Using Two-dimensional Reciprocal Cross Entropy Based on Decomposition

Though Shannon entropy is usually used to measure information uncertainty, it has the drawback of undefined value at zero because of its definition based on logarithm. And the computation speed of two-dimensional cross entropy method can be further improved if avoiding logarithmic operations. Thus two-dimensional reciprocal cross entropy thresholding method based on decomposition is proposed. Firstly, the reciprocal cross entropy is defined. The threshold is selected according to the minimum reciprocal cross entropy between the original image and its segmented image. Then, the definition of two-dimensional reciprocal cross entropy and its threshold selection formula are given. And the decomposition algorithm of two-dimensional reciprocal cross entropy thresholding is proposed. The optimal threshold of two-dimensional reciprocal cross entropy is obtained by combining two optimal thresholds computed by one-dimensional reciprocal cross entropy method. As a result, two-dimensional operations are decomposed into two one-dimensional operations. The computation is reduced from O(L4) to O(L). A large number of experimental results show that , compared with the two-dimensional maximum Shannon entropy method based on particle swarm optimization (PSO), two-dimensional Shannon cross entropy method based on PSO and the two-dimensional exponential cross entropy method, the two-dimensional reciprocal cross entropy thresholding method based on decomposition proposed in this paper can achieve better results and the computation speed is improved.