基于分解的灰度图像二维阈值选取算法

Decomposition Based TWo-dimensional Threshold Algorithm for Gray Images

作为一维Otsu法的推广,二维Otsu法综合考虑了像素点的灰度信息及其邻域灰度的均值信息,可以有效地滤除噪声.其快速算法采用递归的方式构建查找表,将算法的时间复杂性由O(L4)降到O(L2)提出基于分解的阈值选取算法,求解两个一维Otsu法的阈值来替代原始的二维Otsu法的最佳阈值,指出在原算法的假设成立的条件下,该方法可以得到与原二维Otsu法相同的分割阈值,而算法的时间复杂性可以进一步降低到O(L).而在实际中,原算法的假设一般不成立.本文的实验结果表明此时该阈值选取方法也可以在保证原二维Otsu算法良好的抗噪性的前提下,计算阈值所需的时间更短、空间更小,且阈值化结果也可以达到或优于二维Otsu算法的结果.

Abstract As a generalization of 1D Otsu algorithm, 2D Otsu algorithm considers both the gray value of a pixel and the average gray value of its neighborhood, thus is more robust to noise. By constructing look-up tables recursively, its fast algorithm reduces its complexity from O（L^4） to O（L^2）. Based on the decomposition of 2D Otsu algorithm, a method of calculating the optimal threshold of two 1D Otsu algorithms independently, instead of the optimal threshold of 2D Otsu algorithm, is proposed. When the hypothesis of original 2D Otsu algorithm holds, we point out that the threshold computed by our method is exactly the same as that of 2D Otsu algorithm, while the computational complexity is reduced to O（L）. As for real images, the hypothesis of 2D Otsu algorithm always fails, whereas experimental results show that the proposed threshold algorithm still outperforms original 2D Otsu algorithm. Without losing the robustness to noise, this method needs less time and space, and produces a comparable or better segmentation result.