The cross-entropy in the existing thresholding methods does not satisfy the symmetricity of distance measure. And the computation speed of the algorithms can be further improved. Thus an image threshold selection method based on decomposition and two-dimensional symmetric cross-entropy is proposed in this paper. Firstly, the difference between the segmented image and the original one is measured by the symmetric cross-entropy. The threshold selection formulae are derived based on the one-dimensional and two-dimensional symmetric cross-entropy, respectively. A two-dimensional fast recursive algorithm is given, which makes the computation complexity reduced to O(L2) from O(L4) of full search. Then the computation of two-dimensional symmetric cross-entropy is converted into two one-dimensional spaces and its computation complexity is further reduced to 0 (L). The experimental results show that, compared with the existing threshold selection method based on two-dimensional nonsymmetric cross-entropy, the proposed method has stronger anti-noise and the processing time is significantly reduced. It is an effective threshold selection method based on two-dimensional cross-entropy.%现有阈值分割方法中所用的交叉熵不满足距离度量对称性,且算法运行速度尚有提升空间,为此提出基于分解的2维对称交叉熵图像阈值分割方法.首先通过运用对称交叉熵描述分割前后图像之间的差异程度,分别导出1维和2维对称交叉熵阈值选取公式,给出相应的2维快速递推算法,计算复杂性由穷举搜索的O(L4)降到O(L2)；然后将2维对称交叉熵法的运算转换到两个1维空间上,计算复杂性进一步降低到D(L).实验结果表明,与现有的2维非对称交叉熵法相比,该方法具有更强的抗噪性,运行时间大幅减少,是一种更有效的2维交叉熵阈值分割方法.
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