基于多项式一致逼近的多阈值图像分割算法

doi:10.11959/j.issn.1000-436x.2016196

摘要/Abstract

摘要：

针对传统多阈值图像分割算法的计算复杂性，以及由图像直方图中毛刺的干扰带来的算法不稳定等缺点，提出一种基于伯恩斯坦多项式一致逼近的多阈值图像分割算法。首先根据逼近论中的威尔斯托拉斯定理构造图像直方图曲线的伯恩斯坦多项式，然后将图像直方图的峰谷值计算问题化简为伯恩斯坦多项式的极值问题，该极值问题可由伯恩斯坦多项式函数的一次、二次微分导出，最后依据这些极值和极性应用分类算法自动标注图像直方图的实际峰谷值，由此完成基于多阈值的图像分割。实验结果表明所提算法不受直方图中毛刺的干扰，算法整体稳定，冗余计算少，时间复杂度小，用时少，效率高，逼近性能和分割效果更好。

关键词: 图像分割, 图像直方图, 阈值, 一致逼近, 伯恩斯坦多项式, 距离空间

Abstract:

Aiming at those shortcomings of previous multi-threshold image segmentation algorithm such as large complexity and instability caused by the image histogram glitch interference,a new multi-threshold image segmentation algorithm was proposed using Bernstein polynomial to uniformly approximate histogram curve.First,according to the approximation theory of Weierstrass to construct Bernstein polynomial for the histogram curve,then more difficult peak value calculating of the histogram was reduced to the Bernstein polynomial extremal generating,that was exported easily by the first and second derivative of Bernstein polynomial function,and finally obtain the actual peak value of the image histogram by picking up these extremes and polar values and filtering through classification algorithm,and finish multi-threshold image segmentation.Experimental results show that the algorithm is insensitive for histogram glitch interference,the overall is stable,the redundant computation and time complexity are smaller,with less time and high efficiency,the approximate performance and segmentation effect are better.

Key words: image segmentation, image histogram, threshold, uniform approximation, Bernstein polynomial, distance space

卫颜俊,冯博琴,伍卫国. 基于多项式一致逼近的多阈值图像分割算法[J]. 通信学报, 2016, 37(10): 56-64.

Yan-jun WEI,Bo-qin FENG,Wei-guo WU. Multi-threshold algorithm about image segmentation based on polynomial uniform approximation[J]. Journal on Communications, 2016, 37(10): 56-64.

图/表 9

图1

图2

图3

图4

图5

图6

图7

表1

图8

参考文献 19

[1]	RAFAEL C , RICHARD E . Digital image processing second edition[M]. Publishing House of Electronics Industry, 2002: 567-642.
[2]	程宏煌, 戴卫恒, 姚趁趁 . 图像分割方法综述[J]. 电信快报, 2000,1(10): 39-41. CHENG H H , DAI W H , YAO C C . Image segmentation techniques[J]. Telecom Express, 2000,1(10): 39-41.
[3]	周鲜成 . 图像分割方法及其应用研究综述[J]. 信息技术, 2007,1(12): 11-14. ZHOU X C . Study of image segmentation methods and their applications[J]. Information Technology, 2007,1(12): 11-14.
[4]	CHIN Y H , MON J W . Image segmentation[D]. Madison:University of Wisconsin- Madison, 2006.
[5]	CHRISTIAN R , LOIC P , NASSIR N . Image segmentation in twenty questions[C]// CVPR2015, 2015.
[6]	YATHARTH S . Algorithms for image segmentation[D]. Pilani:Birla Institute of Technology and Science, 2006.
[7]	SHEN T Z , FANG Z W , WU L Y ,et al. A new adaptive image segmentation method[J]. Journal of Beijing Institute of Technology, 1998,7(3): 316-321.
[8]	王亮申, 欧宗瑛, 侯杰 ,等. 基于遗传算法的最优直方图阈值图像分割算法[J]. 数据采集与处理, 2005,20(2): 130-134. WANG L S , OU Z Y , HOU J ,et al. Image segmentation based on optimal histogram threshold by improved genetic algorithms[J]. Journal of Data Acquisition ＆ Processing, 2005,20(2): 130-134.
[9]	李哲学, 陈树越 . 快速多阈值图像分割法[J]. 计算机应用, 2010,30(5): 1336-1343. LI Z X , CHEN S Y . Fast multi-thresholding approach[J]. Journal of Computer Applications, 2010,30(5): 1336-1343.
[10]	安丰玲, 梁德群, 王胜军 ,等. 基于多阈值分割的图像区间均衡增强[C]// 第十二届全国图像图形学学术会议. 2005: 15-19. AN F L , LIANG D Q , WANG S J ,et al. Image region equalization enhancement based on multi-thresholds segmentation[C]// The 12th National Conference on Image and Graphics. 2005: 15-19.
[11]	邢延超, 谈正 . 基于多阈值融合的图像分割[J]. 计算机学报, 2004,27(2): 252-256. XING Y Q , TAN Z . Multi-threshold fusion based image segmentation[J]. Chinese Journal of Computers, 2004,27(2): 252-256.
[12]	曹增强, 范忠诚 . 一种去除图像毛刺的快速算法[J]. 数据采集与处理, 1992,7(3): 235-240. CAO Z Q , FAN Z C . An algorithm for fast eliminating image thorns[J]. Journal of Data Acquisition ＆ Processing, 1992,7(3): 235-240.
[13]	黄琴波 . 结合特定理论的图像分割方法[J]. 电子科技, 2010,23(12): 92-95. HUANG Q B . Survey on the methods of image segmentation research[J]. Electronic Sci.＆Tech, 2010,23(12): 92-95.
[14]	许新征, 丁世飞, 史忠植 ,等. 图像分割的新理论和新方法[J]. 电子学报, 2010,28(2A): 76-82. XU X Z , DING S F , SHI Z Z ,et al. New theories and methods of image segmentation[J]. Acta Electronica Sinica, 2010,28(2A): 76-82.
[15]	庞永锋, 杨威, 孙燕 ,等. 应用泛函分析基础[M]. 西安: 西安电子科技大学出版社, 2015: 89-118. PANG Y F , YANG W , SUN Y ,et al. Fundamentals of applied functional analysis[M]. Xi’an: Xidian University PressPress, 2015: 89-118.
[16]	蒋尔雄, 赵风光, 苏仰锋 . 数值逼近:第2版[M]. 上海: 复旦大学出版社, 2008: 96-136. JIANG E X , ZHAO F G , SU Y F . Numerical approximation:2nd edition[M]. Shanghai: Fudan University PressPress, 2008: 96-136.
[17]	程东旭, 杜娅丽 . 基于样条插值的图像分割算法研究[J]. 中原工学院学报, 2015,26(1): 9-12. CHENG D X , DU Y L . Image segmentation algorithm study based on spline interpolation[J]. Journal of Zhongyuan University of Technology, 2015,26(1): 9-12.
[18]	陈争光, 杨冬风, 冯晓娟 . 三次样条在图像多阈值分割中的应用[J]. 黑龙江八一农垦大学学报, 2010,22(5): 88-90. CHEN Z G , YANG D F , FENG X J . Application of cubic spline in image multi-threshold segmentation[J]. Journal of Heilongjiang Bayi Agricultural University, 2010,22(5): 88-90.
[19]	莫国瑞, 刘开第 . 函数逼近论方法[M]. 北京: 科学出版社, 2003: 1-28. MO G R , LIU K D . Function approximation theory method[M]. Beijing: Science PressPress, 2003: 1-28.

名称	平滑滤波	目标选择	效果	用时/ms
双峰法	需要	单目标	一般	96
迭代法	需要	单目标	一般	72
Otsu法	需要	单目标	好	111
最大熵法	需要	多目标	好	92
本文方法	不必	多目标	好	28