基于分解的二维指数交叉熵图像阈值分割

Two-dimensional exponential cross entropy image thresholding based on decomposition

尽管用对数定义的Shannon熵是测度信息不确定性的有效方法,但存在无定义值和零值的问题,且现有的二维Shannon交叉熵法其运行速度仍有提升空间。为此,提出了一维和二维指数交叉熵阈值分割算法。首先给出了指数交叉熵的定义,并导出了一维指数交叉熵阈值选取方法;然后将其推广提出了基于分解的二维指数交叉熵阈值分割算法。通过分别求原像素灰度级图像和邻域平均灰度级图像的一维指数交叉熵最佳阈值,并将其组合求解二维指数交叉熵最佳阈值,从而将二维运算转换到两个一维空间上,大大缩小了搜索空间,使计算复杂度由O(L^4)降为O(L)。实验结果表明,与最近提出的二维Shannon交叉熵法及二维Tsallis交叉熵法相比,所提出的方法能够得到更为优越的分割效果,且运行时间大幅减少。

Although the Shannon entropy defined by logarithm is effectively used to measure information uncertain,there exists problem of undefined value and zero value.The computation speed of the existing two-dimensional Shannon cross entropy method can be further improved.Thus,one-dimensional and two-dimensional exponential cross entropy thresholding method is proposed.Firstly,a new definition of the exponential cross entropy is given.One-dimensional exponential cross entropy method for threshold selection is derived. Then,it is extended and two-dimensional exponential cross entropy thresholding method based on decomposition is proposed.The optimal threshold of one-dimensional exponential cross entropy method for pixel grey-level image or neighborhood average grey-level image is computed,respectively.And they are combined to obtain the optimal threshold of two-dimensional exponential cross entropy method.The computation of two-dimensional exponential cross entropy method is converted into two one-dimensional spaces.As a result, the search space is significantly reduced.The computation complexity is reduced from O（L^4） to O（L）.The experimental results show that,compared with the proposed recently two-dimensional Shannon cross entropy method and the two-dimensional Tsallis cross entropy method,the two-dimensional exponential cross entropy thresholding method based on decomposition proposed in this paper can achieve superior segmented results and greatly reduce the running time.