二维直方图θ-划分Tsallis熵阈值分割算法

Image Thresholding based on 2-D Histogram θ-Division and Tsallis Entropy

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Tsallis熵与传统的Shannon熵相比,具有普适性且更为有效,本文提出了适用面更广的基于二维直方图θ-划分和最大Tsallis熵的图像阈值分割算法。首先给出了二维直方图θ-划分方法,采用四条平行斜线及一条法线与灰度级轴成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=450的特例;然后导出了二维直方图θ-划分最大Tsallis熵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Tsallis熵法相比,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,且所需运行时间及存储空间也大为减少。

In view of the obvious wrong segmentation in commonly used 2-D histogram region division and the non-universality of oblique segmentation method for image thresholding proposed recently, considering that Tsallis entropy has universality and it is more efficient than Shannon entropy, in this paper a much more widely suitable thresholding method is proposed based on 2-D histogram θ-divi- sion and maximum Tsallis entropy. Firstly the 2-D histogram θ-division method is given. The region is divided by four parallel oblique lines and a line. Angel between its normal line and gray level axis is θ degree. 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 0=45^0 of the proposed method. Then the formulae and its fast recursive algorithm of the method are deduced. Finally the seg- mented results and running time with different θ values arc listed in the experimental result, which show that the segmented image a- chieves more accurate borders with smaller θ value while obtains better anti-noise with larger θvalue. It can be selected according to the real image characteristics and the requirement of segmented result. Compared with the conventional 2-D Tsallis entropy method, the pro- posed method not only achieves more accurate segmentation result and more robust anti-noise, but also significantly reduces the running time and memory space.