二维直方图θ-划分最大平均离差阈值分割算法

Image Thresholding Based on Two-dimensional Histogram θ-division and Maximum Between-cluster Deviation Criterion

鉴于常用二维直方图区域直分法存在错分,最近提出的斜分法不具普遍性,而基于L1范数的最小一乘准则比最小二乘准则更为合理且简捷,提出了适用面更广的基于二维直方图θ-划分和最大类间平均离差的图像阈值分割算法.首先给出了二维直方图θ-划分方法,采用4条平行斜线及1条其法线与灰度级轴成θ角的直线划分二维直方图区域,按灰度级和邻域平均灰度级的加权和进行阈值分割,斜分法可视为该方法中θ=45°的特例;然后导出了二维直方图θ-划分最大类间平均离差阈值选取公式及其快速递推算法;最后给出了θ取不同值时的分割结果及运行时间.θ取较小值时,边界形状准确性较高,θ取较大值时,抗噪性较强,应用时可根据实际图像特点及需求合理选取θ的值.与常规二维直方图直分最大类间方差法及最大类间平均离差法相比,所需运行时间相近,但本文提出的方法所得分割结果更为准确,抵抗噪声更为稳健,且存储空间也大为减少.

In view of the obvious wrong segmentation in commonly used two-dimensional histogram region division and the non-universality of oblique segmentation method for image thresholding proposed recently,considering that the least absolute criterion based on L1 norm is more reasonable and simpler than least square criterion,in this paper a much more widely suitable thresholding method is proposed based on two-dimensional histogram θ-division and maximum betweencluster deviation criterion.Firstly,the two-dimensional histogram θ-division method is given.The region is divided by four parallel oblique lines and a line.The angel between its normal line and gray level axis is θ.Image thresholding is performed according to pixel s weighted average value of gray level and neighbor average gray level.So the oblique segmentation method can be regarded as a special case with θ = 45° of the proposed method.Then,the formulae and its fast recursive algorithm of the method are deduced.Finally,the segmented results and running time with different θ values are listed as the experimental results,which show that the segmented image achieves more accurate borders with a smaller θ value while obtains better anti-noise with a larger θ value.It can be selected according to the real image characteristics and the requirement of segmented results.Compared with the algorithms of conventional two-dimensional maximum between-cluster variance method and two-dimensional maximum between-cluster deviation method,a similar running time is required,however,the proposed method not only achieves more accurate segmentation results and more robust anti-noise,but also requires much less memory space.