Fast method for 2D threshold segmentation algorithm based on inter-class and intra-class variances

In order to shorten the running time of 2D threshold segmentation algorithm, a fast implementation of 2D Otsu was developed. First, a two-dimensional optimal threshold (s*, t*) was split into two one-dimensional optimal thresholds, s* and t*. The intra-class variance was defined to propose a new optimal discriminant D(s*, t*). Then the original 2D histogram was divided into M×M regions, and each region was combined as a point to form a new 2D histogram. Based on this new 2D histogram, the discriminant D(s*, t*) was solved to determine the region that corresponds to the optimal threshold, and last the optimal threshold was calculated using D(s*, t*). The theoretical analysis and experimental results of some images with different signal-to-noise ratios (SNRs) show that the segmentation error rate of the proposed algorithm is lower than the original two-dimensional Otsu method. The time complexity of the proposed method is reduced from O(L4) to O(L1/2), and space complexity is reduced from S(L2) to S(2L).