三维Otsu阈值分割方法的递推算法

Recursive Algorithm for Three-Dimensional Otsu's Thresholding Segmentation Method

一维和二维Otsu法是常用的阈值分割方法,二维Otsu法对含噪图像的分割效果要优于一维Otsu法,但它存在的问题是"对象区域和背景区域上的概率和近似为1"的假设的普适性不够,鉴于此景晓军等人提出了三维Otsu法及其递归算法,使得对低对比度、低信噪比的图像有较好的分割效果.本文指出了景晓军等人给出的递推公式的错误,并进行了修正.鉴于他们给出的递推公式并不是真正意义的递推公式,本文给出了新的递推公式.实验结果表明,本文提出的递推公式进一步减少了运算时间.另外,本文还指出三维Otsu法对于叠加了混合噪声的图像有较好的分割效果.

One-dimensional（1-D） and two-dimensional （2-D）Otsu＇ s methods are two common thresholding segmentation methods.2-D Otsu＇ s method is superior to 1-D Otsu＇ s method for images with noise.A basic assumption for 2-D Otsu＇ s method is that ＂the probability sum of the object and background regions is close to 1＂, this assumption could not be effective in some cases, thus Jing et al.introduced three-dimensional （3-D） Otsu＇ s method and gave a recursive algorithm.3-D Otsu＇s method behaves well for images with low SNR and low contrast. In this paper, the mistakes in Jing＇s recursive formulas are pointed out and a corrected version is given. Because the existed recursive algorithm can not be considered as a real recursive algorithm, we propose a new recursive algorithm. Experimental results show that the computing time of our method is less than that of Jing＇ s method, in addition we point out that 3-D Otsu＇s method can obtain better segmentation results for images with mixture noises.