Since existing algorithms cannot solve the threshold segmentation problem of mixed noise images a 3D minimum error threshold algorithm is proposed in this paper. Using gray distribution information of pixels and relevant information of neighboring pixels

it combines image gray

mean and median values to construct a 3D 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 calculation method based on decomposition is proposed. It calculates three 1D optimal thresholds

instead of one 3D optimal threshold. Its time complexity is reduced to

and space cost is reduced to . Experimental results show that the proposed algorithm outperforms those 2D threshold methods for different types of noised image and non-uniform illuminating images. Especially for mixed noise image

its advantage is more obvious.