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.