In view of the inaccurate segmentation in the traditional two-dimensional (2-D) Otsu's thresholding method mainly owing to the supposition that the sum of probabilities of main-diagonal districts in 2-D histogram is approximately one

afast and precise 2-D Otsu's image thresholding method is presented in this paper.A 2-D histogram was created with the select neighborhood and Otsu's method was used on the 2-D histogram in order to obtain better segmentation performance.The probabilities and the mean gray levels in the objects and the background of 2-D histogram main-diagonal districts were calculated preciselyto get a more accurate threshold.The 2-D histogram projection was analyzed to get its features

three theorems were proved

and a novel recursive approach was inferred with the features and the theorems to reduce the computational complexity.Experimental results show that the proposed method achieves more accurate segmentation results and more robust anti-noise than the current 2-D Otsu's thresholding methods

and that its running time is much less

almost the same as that of the current Otsu's recursive algorithm based on 2-D histogram oblique segmentation.