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## Image thresholding based on θ-division of 2-D histogram and maximum Shannon entropy

Wu Yi-Quan, Zhang Jin-Kuang
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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,提出了适用面更广的基于二维直方图θ划分和最大Shannon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Shannon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Shannon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小.

#### Abstract

In view of the obvious wrong segmentation in commonly used region division of 2-D histogram and the non- universality of oblique segmentation method for image thresholding proposed recently, in this paper a much more widely suitable thresholding method is proposed based on the θ-division of 2-D histogram and the maximum Shannon entropy criterion. Firstly, the θ-division method of 2-D histogram is given. The region is divided by four parallel oblique lines and a line, where the angle between its normal line and gray level axis is θ degrees. Image thresholding is performed according to pixel's weighted average value of gray level and neighbour average gray level. The oblique segmentation method can be regarded as a special case of the proposed method at θ=45°. Then the formulae and its fast recursive algorithm of the method are deduced. Finally the segmented results and the running time at different values of θ are listed, which show that the segmented images achieve more accurate borders at smaller values of θ and the anti-noise is better at larger values of θ. The value of θ can be selected according to the real image characteristics and the requirements of segmented results. Compared with the algorithm of conventional 2-D maximum Shannon entropy method, the proposed method not only achieves more accurate segmentation results and more robust anti-noise, but also reduces the running time and memory space significantly.

#### 作者及机构信息

###### 1. 南京航空航天大学信息科学与技术学院,南京 210016
• 基金项目: 国家自然科学基金(批准号:60872065)资助的课题.

#### 参考文献

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#### 施引文献

•  [1] Liang Y M, Zhai H C, Chang S J, Zhang S Y 2003 Acta Phys. Sin. 52 2655(in Chinese)[梁艳梅、翟宏琛、常胜江、张思远 2003 物理学报 52 2655] [2] Tang Y G, Di Q Y, Zhao L X, Guan X P 2009 Acta Phys. Sin. 58 9(in Chinese)[唐英干、邸秋艳、赵立兴、关新平 2009 物理学报 58 9] [3] Guo H T, Tian T, Wang L Y, Zhang C T 2006 Acta Optica Sinica 26 506(in Chinese)[郭海涛、田 坦、王连玉、张春田 2006 光学学报 26 506 ] [4] Wu Y Q, Zhu Z D 1993 Journal of Data Acquisition and Processing 8 193(in Chinese)[吴一全、朱兆达1993 数据采集与处理 8 193] [5] Wu Y Q, Zhu Z D 1993 Journal of Data Acquisition and Processing 8 268(in Chinese)[吴一全、朱兆达 1993 数据采集与处理 8 268] [6] Sezgin M, Sankur B 2004 Electronic Imaging 13 146 [7] Bardera A, Boada I, Feixas M, Sbert M 2009 Journal of Signal Processing Systems 54 205 [8] Kapur J N, Sahoo P K, Wong A K C 1985 Computer Vision, Graphics and Image Processing 29 273 [9] Xing X S 2004 Acta Phys. Sin. 53 2852(in Chinese)[邢修三 2004 物理学报 53 2852 ] [10] Abutaleb A S 1989 Pattern Recognition 47 22 [11] Brink A D 1992 Pattern Recognition 25 803 [12] Chen W T, Wen C H, Yang C W 1994 Pattern Recognition 27 885 [13] Gong J, Li L Y, Chen W N 1996 Journal of Southeast University 26 31(in Chinese)[龚 坚、李立源、陈维南1996 东南大学学报 26 31] [14] Zhang Y J, Wu X J, Xia L Z. 1997 Pattern Recognition and Artificial Intelligence 10 259(in Chinese)[张毅军、吴雪菁、夏良正1997 模式识别与人工智能 10 259] [15] Yan X Q, Ye L Q, Liu J L, Gu W K 1998 Pattern Recognition and Artificial Intelligence 11 352(in Chinese)[严学强、叶秀清、刘济林、顾伟康 1998 模式识别与人工智能 11 352] [16] Du F, Shi W K. 2005 Pattern Recognition Letters 26 597 [17] Cao Z H, Li Y J, Zhang K 2007 Scope on Acta Photonica Sinica 36 2377 [18] Du F, Shi W K, Deng Y, Zhu Z F 2005 J. Infrared Millim. Waves 24 370 (in Chinese) [杜 峰、施文康、邓 勇、朱振幅 2005 红外与毫米波学报 24 370] [19] Wu Y Q, Pan Z, Wu W Y 2009 Pattern Recognition and Artificial Intelligence 22 162(in Chinese)[吴一全、潘喆、吴文怡 2009 模式识别与人工智能 22 162]
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##### 出版历程
• 收稿日期:  2009-08-12
• 修回日期:  2009-11-27
• 刊出日期:  2010-04-05

## 二维直方图θ划分最大Shannon熵图像阈值分割

• 1. 南京航空航天大学信息科学与技术学院,南京 210016
基金项目: 国家自然科学基金(批准号:60872065)资助的课题.

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