基于类间和类内方差的快速二维阈值分割法

为了提高二维阈值分割法的处理速度，提出二维类间方差最大法的快速实现方法.首先，将二维最佳阈值（s*，t*）的求解拆分成两个一维最佳阈值s*和t*的求解，并引入类内距离的定义，提出新的最佳阈值判别式.其次，将原二维直方图分成M×M个区域，合并每个区域为一点，并构建新的二维直方图，在其上应用本文改进的阈值判别式D（s*，t*）求解，得到分割阈值所在的区域编号.最后，在该区域内再次使用D（s*，t*）求解得到原始图像的最佳分割阈值.理论分析及针对不同信噪比的多幅图像的实验结果表明，本文方法的分割错误率低于原始二维Otsu法，且将原算法的时间复杂度由O（L4）降为O（L1/2），空间复杂度由S（L2）降为S（2L）. 

Fast Method for 2 D 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).