Three Dimensional Minimum Error Threshold Algorithm and Its Fast Recursive Method

The threshold segmentation of mixed noise image can not be solved by existing algorithms efficiently. A 3D minimum error thresholding algorithm is proposed. Using gray distribution information of pixels and relevant information of neighboring pixels, it combines information of image gray, mean and median to construct a three-dimensional observation space, and then defines a 3D optimal threshold discriminant based on the relative entropy. Furthermore, in order to improve its processing speed, the fast recursive formulas are also given. Its time complexity is O(L3). Experimental results show that the proposed algorithm outperforms those 2D thresholding methods not only for different types of noised image, but also for non-uniform illuminating images. Especially for mixed noise image, its advantage is more obvious.