Two-dimensional exponential cross entropy image thresholding based on decomposition

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(L⁴) 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.