基于二维相关性的图像分割及快速递推算法

Two-dimensional Correlation Based Image Segmentation and Its Fast Recursive Algorithm

基于二维直方图提出了二维相关性的阈值分割算法。首先,通过邻域平均得到原始图像的平滑图像,由原始图像和平滑图像构造二维直方图,然后根据相关性最大准则选择最佳的二维阈值向量。由于该方法同时考虑了图像像素的灰度信息及其空间邻域信息,与一维阈值相比能得到更好的分割效果。同时为降低二维阈值算法的复杂性,提出了快速递推算法。该算法将二维相关性的计算写成递推形式,减少了大量的重复计算,使得算法的复杂性从O(L4)降低到O(L2),计算时间大为减少,有利于该算法的实时应用。

A two-dimensional correlation image thresholding algorithm is proposed on the basis of the two-di- mensional histogram. First, a smoothed image is obtained using the neighbor smoothing technique. The two- dimensional histogram is constructed using the gray value and average gray value of a pixel. The two-dimen- sional threshold is obtained according to the maximum correlation criterion. Compared to the one-dimensional case, the two-dimensional correlation thresholding method can get better segmentation results, because it con- siders not only image-pixel gray information but also spatial neighbor information. To reduce computation com- plexity, a fast recursive algorithm is presented. In the fast recursive algorithm, the computation of two-dimen- sional correlation is written in the recursive form. Many repeated calculations are avoided. The computation complexity is reduced from O（L^4） to O（L^2）. The computation time is also reduced dramatically. This facilitates the recursive algorithm application in the real-time image processing system.