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中文摘要：
首先,定义了灰度熵并导出了相应的二维灰度熵阈值选取公式;其次,利用高速收敛PSO算法寻找二维灰度熵法的最佳阈值,并采用递推方式避免迭代过程中适应度函数的重复计算;最后,将二维灰度熵的运算转换到两个一维空间上,计算复杂度由O（L2）进一步降为O（L）。实验结果表明,与基于粒子群的二维最大Shannon熵法相比,所提出的两种方法的分割效果具有明显优势,且运行时间大幅减少。
英文摘要：
The method of threshold selection based on two-dimensional maximal Shannon entropy only depends on the probability information from gray histogram of image,and does not immediately consider the uniformity of within-cluster gray scale.Thus a two-dimensional gray entropy thresholding method based on particle swarm optimization（PSO） with high speed convergence or decomposition is proposed.Firstly,gray entropy is defined and the corresponding formulae for threshold selection based on two-dimensional gray entropy is derived.Then,particle swarm optimization algorithm with high speed convergence are used to find the optimal threshold of two-dimensional gray entropy method.The recursive algorithm is adopted to avoid the repetitive computation of fitness function in iterative procedure.As a result,the computing speed is improved greatly.Finally,the computations of two-dimensional gray entropy are converted into two one-dimensional spaces,which make the computation complexity further reduced from O（L2） to O（L）.The experimental results show that,compared with two-dimensional maximal Shannon entropy thresholding based on PSO,the proposed two methods can have much superior segmentation performance and their running time is reduced significantly.
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