Image Thresholding Based on Two-dimensional Histogram θ-division and Maximum Between-cluster Deviation Criterion
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摘要: 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.
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关键词:
- 图像处理 /
- 阈值分割 /
- 二维直方图区域θ-划分 /
- 最大类间平均离差 /
- 递推算法
Abstract: 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 between-cluster 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.
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