归一化互信息量最大化导向的自动阈值选择方法
|
摘要
当前景或背景的灰度分布呈现为非正态分布特征时,比如极值、瑞利、贝塔或均匀分布,将所选阈值与最优阈值之差控制在10个灰度级内并非易事.为了在统一框架内处理不同灰度分布情形下的阈值选择问题,提出了一种归一化互信息量最大化导向的自动阈值选择方法.该方法先采用多尺度梯度乘变换规范化输入图像,获得具有单峰长拖尾灰度分布的规范图像;然后对不同阈值对应的二值图像进行轮廓提取,获得不同的轮廓图像;最后计算规范图像和不同轮廓图像之间的归一化互信息量,并以最大值对应的阈值作为最终阈值.在具有不同灰度分布模式的9幅合成图像和59幅真实世界图像上,将提出的方法和1种人工阈值方法及4种自动阈值方法进行了比较.实验结果表明,提出的方法虽然在计算效率方面不优于4个自动方法,但在分割的适应性和精确度方面优势明显:对前述不同灰度分布情形,其所选阈值与最优阈值之差都在9个灰度级内.
When the gray level distribution of foreground or background appears a non-normal distribution, such as extreme value, Rayleigh, beta or uniform distribution, it is challenging to keep the difference between the selected threshold and the optimal threshold under control within 10 gray levels. To deal with the issue of threshold selection in different gray level distributions within a unified framework, we propose an automatic method of threshold selection that is guided by maximizing normalized mutual information. Firstly, this method applies a multiscale gradient multiplication to an input image, which produces a normalized image with a single-peaked trailing distribution. Then, the binary images corresponding to different thresholds are subjected to contour extraction to produce different contour images. Finally,normalized mutual information between the normalized image and different contour images is calculated and the threshold corresponding to maximum is taken as the final threshold. The proposed method is compared with a manual thresholding method and 4 automatic ones on 9 synthetic images and 59 real-world ones with different distributions. The results show that the proposed method is not superior to these 4 automatic methods in computational efficiency, but it has a significant advantage in the adaptability and accuracy of segmentation: in the case of the aforementioned different gray level distributions, the differences between its selected thresholds and the optimal ones are all within 9 gray levels.
When the gray level distribution of foreground or background appears a non-normal distribution, such as extreme value, Rayleigh, beta or uniform distribution, it is challenging to keep the difference between the selected threshold and the optimal threshold under control within 10 gray levels. To deal with the issue of threshold selection in different gray level distributions within a unified framework, we propose an automatic method of threshold selection that is guided by maximizing normalized mutual information. Firstly, this method applies a multiscale gradient multiplication to an input image, which produces a normalized image with a single-peaked trailing distribution. Then, the binary images corresponding to different thresholds are subjected to contour extraction to produce different contour images. Finally,normalized mutual information between the normalized image and different contour images is calculated and the threshold corresponding to maximum is taken as the final threshold. The proposed method is compared with a manual thresholding method and 4 automatic ones on 9 synthetic images and 59 real-world ones with different distributions. The results show that the proposed method is not superior to these 4 automatic methods in computational efficiency, but it has a significant advantage in the adaptability and accuracy of segmentation: in the case of the aforementioned different gray level distributions, the differences between its selected thresholds and the optimal ones are all within 9 gray levels.
引文
1 Sezgin M, Sankur B. Survey over image thresholding techniques and quantitative performance evaluation. Journal of Electronic Imaging, 2004, 13(1):146-165
2 Fan Jiu-Lun, Ren Jing. Symmetric co-occurrence matrix thresholding method based on square distance. Acta Electronica Sinica, 2011, 39(10):2277-2281(范九伦,任静.基于平方距离的对称共生矩阵阈值法.电子学报,2011, 39(10):2277-2281)
3 Long Jian-Wu, Shen Xuan-Jing, Zang Hui, Chen Hai-Peng.An adaptive thresholding algorithm by background estimation in Gaussian scale space. Acta Automatica Sinica, 2014,40(8):1773-1782(龙建武,申铉京,臧慧,陈海鹏.高斯尺度空间下估计背景的自适应阈值分割算法.自动化学报, 2014, 40(8):1773-1782)
4 Wu Yi-Quan, Meng Tian-Liang, Wu Shi-Hua. Research progress of image thresholding methods in recent 20 years(1994-2014). Journal of Data Acquisition&Processing,2015, 30(1):1-23(吴一全,孟天亮,吴诗婳.图像阈值分割方法研究进展20年(1994-2014).数据采集与处理, 2015, 30(1):1-23)
5 Chen Hai-Peng, Shen Xuan-Jing, Long Jian-Wu. Threshold optimization framework of global thresholding algorithms using Gaussian fitting. Journal of Computer Research and Development, 2016, 53(4):892-903(陈海鹏,申铉京,龙建武.采用高斯拟合的全局阈值算法阈值优化框架.计算机研究与发展, 2016, 53(4):892-903)
6 Tao Wen-Bing, Jin Hai. A new image thresholding method based on graph spectral theory. Chinese Journal of Computers, 2007, 30(1):110-119(陶文兵,金海.一种新的基于图谱理论的图像阈值分割方法.计算机学报, 2007, 30(1):110-119)
7 Zou Y B, Liu H, Zhang Q. Image bilevel thresolding based on stable transition region set. Digital Signal Processing,2013, 23(1):126-141
8 Otsu N. A threshold selection method from gray-level histograms. IEEE Transactions on Systems, Man, and Cybernetics, 1979, 9(1):62-66
9 Kittler J, Illingworth J. Minimum error thresholding. Pattern Recognition, 1991, 19(1):41-47
10 Kapur J N, Sahoo P K, Wong A K C. A new method for gray-level picture thresholding using the entropy of the histogram. Computer Vision, Graphics, and Image Processing,1985, 29(3):273-285
11 Li C H, Lee C K. Minimum cross entropy thresholding. Pattern Recognition, 1993, 26(4):617-625
12 Pal N R, Pal S K. Entropic thresholding. Signal Processing,1989, 16(2):97-108
13 de Albuquerque M P, Esquef I A, Gesualdi Mello A R, de Albuquerqueb M P. Image thresholding using Tsallis entropy.Pattern Recognition Letters, 2004, 25(9):1059-1065
14 Sahoo P, Wilkins C, Yeager J. Threshold selection using Renyi s entropy. Pattern Recognition, 1997, 30(1):71-84
15 Nie F Y, Zhang P F, Li J Q, Ding D H. A novel generalized entropy and its application in image thresholding. Signal Processing, 2017, 134:23-34
16 Xu Xiang-Yang, Song En-Min, Jin Liang-Hai. Characteristic analysis of threshold based on Otsu criterion. Acta Electronica Sinica, 2009, 37(12):2716-2719(许向阳,宋恩民,金良海. Otsu准则的阈值性质分析.电子学报,2009, 37(12):2716-2719)
17 Xue J H, Titterington D M. t-test, F-tests and Otsu s methods for image thresholding. IEEE Transactions on Image Processing, 2011, 20(8):2392-2396
18 Xue J H, Titterington D M. Median-based image thresholding. Image and Vision Computing, 2011, 29(9):631-637
19 Cai H M, Yang Z, Cao X H, Xia W M, Xu X Y. A new iterative triclass thresholding technique in image segmentation. IEEE Transactions on Image Processing, 2014, 23(3):1038-1046
20 Fan J L, Lei B. A modified valley-emphasis method for automatic thresholding. Pattern Recognition Letters, 2012,33(6):703-708
21 Lin Q Q, Ou C J. Tsallis entropy and the long-range correlation in image thresholding. Signal Processing, 2012, 92(12):2931-2939
22 Zhang Yu-Jin. A survey on transition region-based techniques for image segmentation. Journal of Computer-Aided Design&Computer Graphics, 2015, 27(3):379-387(章毓晋.图像分割中基于过渡区技术的统计调查.计算机辅助设计与图形学学报, 2015, 27(3):379-387)
23 Yan Cheng-Xin, Sang Nong, Zhang Tian-Xu, Zeng Kun. Image transition region extraction and segmentation based on local complexity. Journal of Infrared and Millimeter Waves,2005, 24(4):312-316(闫成新,桑农,张天序,曾坤.基于局部复杂度的图像过渡区提取与分割.红外与毫米波学报, 2005, 24(4):312-316)
24 Feng Tao, Zhou Zu-An, Liu Qi-Zhen. Analysis of the image transition region processing based on local complexity.Journal of Image and Graphics, 2008, 13(10):1894-1897(冯涛,周祖安,刘其真.基于局部复杂度的图像过渡区处理研究.中国图象图形学报, 2008, 13(10):1894-1897)
25 Wang Yan-Chun, Liang De-Qun, Wang Yan. Transition region extraction and segmentation based on image fuzzy entropy neighborhood unhomogeneity. Acta Electronica Sinica, 2008, 36(12):2445-2449(王彦春,梁德群,王演.基于图像模糊熵邻域非一致性的过渡区提取与分割.电子学报, 2008, 36(12):2445-2449)
26 Liu Jian-Zhuang, Li Wen-Qing. The automatic thresholding of gray-level pictures via two-dimensional Otsu method.Acta Automatica Sinica, 1993, 19(1):101-105(刘健庄,栗文青.灰度图像的二维Otsu自动阈值分割法.自动化学报, 1993, 19(1):101-105)
27 Fan Jiu-Lun, Zhao Feng. Two-dimensional Otsu s curve thresholding segmentation method for gray-level images.Acta Electronica Sinica, 2007, 35(4):751-755(范九伦,赵凤.灰度图像的二维Otsu曲线阈值分割法.电子学报,2007, 35(4):751-755)
28 Fan Jiu-Lun, Lei Bo. Two-dimensional cross-entropy lineartype threshold segmentation method for gray-level images.Acta Electronica Sinica, 2009, 37(3):476-480(范九伦,雷博.灰度图像的二维交叉熵直线型阈值分割法.电子学报, 2009, 37(3):476-480)
29 Fan Jiu-Lun, Lei Bo. Two-dimensional extension of minimum error threshold segmentation method for gray-level images. Acta Automatica Sinica, 2009, 35(4):386-393(范九伦,雷博.灰度图像最小误差阈值分割法的二维推广.自动化学报, 2009, 35(4):386-393)
30 Wu Yi-Quan, Zhang Xiao-Jie, Wu Shi-Hua. Twodimensional symmetric cross-entropy image thresholding.Journal of Image and Graphics, 2011, 16(8):1393-1401(吴一全,张晓杰,吴诗婳. 2维对称交叉熵图像阈值分割.中国图象图形学报, 2011, 16(8):1393-1401)
31 Fan Jiu-Lun, Zhao Feng, Zhang Xue-Feng. Recursive algorithm for three-dimensional Otsu s thresholding segmentation method. Acta Electronica Sinica, 2007, 35(7):1398-1402(范九伦,赵凤,张雪峰.三维Otsu阈值分割方法的递推算法.电子学报, 2007, 35(7):1398-1402)
32 Shen Xuan-Jing, Long Jian-Wu, Chen Hai-Peng, Wei Wei.Otsu thresholding algorithm based on rebuilding and dimension reduction of the 3-dimensional histogram. Acta Electronica Sinica, 2011, 39(5):1108-1114(申铉京,龙建武,陈海鹏,魏巍.三维直方图重建和降维的Otsu阈值分割算法.电子学报, 2011, 39(5):1108-1114)
33 Liu Jin, Jin Wei-Dong. Three-dimensional adaptive minimum error thresholding segmentation algorithm. Journal of Image and Graphics, 2013, 18(11):1416-1424(刘金,金炜东. 3维自适应最小误差阈值分割法.中国图象图形学报, 2013, 18(11):1416-1424)
34 Lu Zhen-Tai, Lv Qing-Wen, Chen Wu-Fan. Unsupervised segmentation of medical image based on maximizing mutual information. Journal of Image and Graphics, 2008, 13(4):658-661(卢振泰,吕庆文,陈武凡.基于最大互信息量的图像自动优化分割.中国图象图形学报, 2008, 13(4):658-661)
35 Strehl A, Ghosh J. Cluster ensembles—a knowledge reuse framework for combining multiple partitions. The Journal of Machine Learning Research, 2002, 3(3):583-617
36 Bemis R. Thresholding tool[Online], available:http://cn.mathworks.com/matlabcentral/fileexchange/6770-thresholding-tool, September 1, 2017.
2 Fan Jiu-Lun, Ren Jing. Symmetric co-occurrence matrix thresholding method based on square distance. Acta Electronica Sinica, 2011, 39(10):2277-2281(范九伦,任静.基于平方距离的对称共生矩阵阈值法.电子学报,2011, 39(10):2277-2281)
3 Long Jian-Wu, Shen Xuan-Jing, Zang Hui, Chen Hai-Peng.An adaptive thresholding algorithm by background estimation in Gaussian scale space. Acta Automatica Sinica, 2014,40(8):1773-1782(龙建武,申铉京,臧慧,陈海鹏.高斯尺度空间下估计背景的自适应阈值分割算法.自动化学报, 2014, 40(8):1773-1782)
4 Wu Yi-Quan, Meng Tian-Liang, Wu Shi-Hua. Research progress of image thresholding methods in recent 20 years(1994-2014). Journal of Data Acquisition&Processing,2015, 30(1):1-23(吴一全,孟天亮,吴诗婳.图像阈值分割方法研究进展20年(1994-2014).数据采集与处理, 2015, 30(1):1-23)
5 Chen Hai-Peng, Shen Xuan-Jing, Long Jian-Wu. Threshold optimization framework of global thresholding algorithms using Gaussian fitting. Journal of Computer Research and Development, 2016, 53(4):892-903(陈海鹏,申铉京,龙建武.采用高斯拟合的全局阈值算法阈值优化框架.计算机研究与发展, 2016, 53(4):892-903)
6 Tao Wen-Bing, Jin Hai. A new image thresholding method based on graph spectral theory. Chinese Journal of Computers, 2007, 30(1):110-119(陶文兵,金海.一种新的基于图谱理论的图像阈值分割方法.计算机学报, 2007, 30(1):110-119)
7 Zou Y B, Liu H, Zhang Q. Image bilevel thresolding based on stable transition region set. Digital Signal Processing,2013, 23(1):126-141
8 Otsu N. A threshold selection method from gray-level histograms. IEEE Transactions on Systems, Man, and Cybernetics, 1979, 9(1):62-66
9 Kittler J, Illingworth J. Minimum error thresholding. Pattern Recognition, 1991, 19(1):41-47
10 Kapur J N, Sahoo P K, Wong A K C. A new method for gray-level picture thresholding using the entropy of the histogram. Computer Vision, Graphics, and Image Processing,1985, 29(3):273-285
11 Li C H, Lee C K. Minimum cross entropy thresholding. Pattern Recognition, 1993, 26(4):617-625
12 Pal N R, Pal S K. Entropic thresholding. Signal Processing,1989, 16(2):97-108
13 de Albuquerque M P, Esquef I A, Gesualdi Mello A R, de Albuquerqueb M P. Image thresholding using Tsallis entropy.Pattern Recognition Letters, 2004, 25(9):1059-1065
14 Sahoo P, Wilkins C, Yeager J. Threshold selection using Renyi s entropy. Pattern Recognition, 1997, 30(1):71-84
15 Nie F Y, Zhang P F, Li J Q, Ding D H. A novel generalized entropy and its application in image thresholding. Signal Processing, 2017, 134:23-34
16 Xu Xiang-Yang, Song En-Min, Jin Liang-Hai. Characteristic analysis of threshold based on Otsu criterion. Acta Electronica Sinica, 2009, 37(12):2716-2719(许向阳,宋恩民,金良海. Otsu准则的阈值性质分析.电子学报,2009, 37(12):2716-2719)
17 Xue J H, Titterington D M. t-test, F-tests and Otsu s methods for image thresholding. IEEE Transactions on Image Processing, 2011, 20(8):2392-2396
18 Xue J H, Titterington D M. Median-based image thresholding. Image and Vision Computing, 2011, 29(9):631-637
19 Cai H M, Yang Z, Cao X H, Xia W M, Xu X Y. A new iterative triclass thresholding technique in image segmentation. IEEE Transactions on Image Processing, 2014, 23(3):1038-1046
20 Fan J L, Lei B. A modified valley-emphasis method for automatic thresholding. Pattern Recognition Letters, 2012,33(6):703-708
21 Lin Q Q, Ou C J. Tsallis entropy and the long-range correlation in image thresholding. Signal Processing, 2012, 92(12):2931-2939
22 Zhang Yu-Jin. A survey on transition region-based techniques for image segmentation. Journal of Computer-Aided Design&Computer Graphics, 2015, 27(3):379-387(章毓晋.图像分割中基于过渡区技术的统计调查.计算机辅助设计与图形学学报, 2015, 27(3):379-387)
23 Yan Cheng-Xin, Sang Nong, Zhang Tian-Xu, Zeng Kun. Image transition region extraction and segmentation based on local complexity. Journal of Infrared and Millimeter Waves,2005, 24(4):312-316(闫成新,桑农,张天序,曾坤.基于局部复杂度的图像过渡区提取与分割.红外与毫米波学报, 2005, 24(4):312-316)
24 Feng Tao, Zhou Zu-An, Liu Qi-Zhen. Analysis of the image transition region processing based on local complexity.Journal of Image and Graphics, 2008, 13(10):1894-1897(冯涛,周祖安,刘其真.基于局部复杂度的图像过渡区处理研究.中国图象图形学报, 2008, 13(10):1894-1897)
25 Wang Yan-Chun, Liang De-Qun, Wang Yan. Transition region extraction and segmentation based on image fuzzy entropy neighborhood unhomogeneity. Acta Electronica Sinica, 2008, 36(12):2445-2449(王彦春,梁德群,王演.基于图像模糊熵邻域非一致性的过渡区提取与分割.电子学报, 2008, 36(12):2445-2449)
26 Liu Jian-Zhuang, Li Wen-Qing. The automatic thresholding of gray-level pictures via two-dimensional Otsu method.Acta Automatica Sinica, 1993, 19(1):101-105(刘健庄,栗文青.灰度图像的二维Otsu自动阈值分割法.自动化学报, 1993, 19(1):101-105)
27 Fan Jiu-Lun, Zhao Feng. Two-dimensional Otsu s curve thresholding segmentation method for gray-level images.Acta Electronica Sinica, 2007, 35(4):751-755(范九伦,赵凤.灰度图像的二维Otsu曲线阈值分割法.电子学报,2007, 35(4):751-755)
28 Fan Jiu-Lun, Lei Bo. Two-dimensional cross-entropy lineartype threshold segmentation method for gray-level images.Acta Electronica Sinica, 2009, 37(3):476-480(范九伦,雷博.灰度图像的二维交叉熵直线型阈值分割法.电子学报, 2009, 37(3):476-480)
29 Fan Jiu-Lun, Lei Bo. Two-dimensional extension of minimum error threshold segmentation method for gray-level images. Acta Automatica Sinica, 2009, 35(4):386-393(范九伦,雷博.灰度图像最小误差阈值分割法的二维推广.自动化学报, 2009, 35(4):386-393)
30 Wu Yi-Quan, Zhang Xiao-Jie, Wu Shi-Hua. Twodimensional symmetric cross-entropy image thresholding.Journal of Image and Graphics, 2011, 16(8):1393-1401(吴一全,张晓杰,吴诗婳. 2维对称交叉熵图像阈值分割.中国图象图形学报, 2011, 16(8):1393-1401)
31 Fan Jiu-Lun, Zhao Feng, Zhang Xue-Feng. Recursive algorithm for three-dimensional Otsu s thresholding segmentation method. Acta Electronica Sinica, 2007, 35(7):1398-1402(范九伦,赵凤,张雪峰.三维Otsu阈值分割方法的递推算法.电子学报, 2007, 35(7):1398-1402)
32 Shen Xuan-Jing, Long Jian-Wu, Chen Hai-Peng, Wei Wei.Otsu thresholding algorithm based on rebuilding and dimension reduction of the 3-dimensional histogram. Acta Electronica Sinica, 2011, 39(5):1108-1114(申铉京,龙建武,陈海鹏,魏巍.三维直方图重建和降维的Otsu阈值分割算法.电子学报, 2011, 39(5):1108-1114)
33 Liu Jin, Jin Wei-Dong. Three-dimensional adaptive minimum error thresholding segmentation algorithm. Journal of Image and Graphics, 2013, 18(11):1416-1424(刘金,金炜东. 3维自适应最小误差阈值分割法.中国图象图形学报, 2013, 18(11):1416-1424)
34 Lu Zhen-Tai, Lv Qing-Wen, Chen Wu-Fan. Unsupervised segmentation of medical image based on maximizing mutual information. Journal of Image and Graphics, 2008, 13(4):658-661(卢振泰,吕庆文,陈武凡.基于最大互信息量的图像自动优化分割.中国图象图形学报, 2008, 13(4):658-661)
35 Strehl A, Ghosh J. Cluster ensembles—a knowledge reuse framework for combining multiple partitions. The Journal of Machine Learning Research, 2002, 3(3):583-617
36 Bemis R. Thresholding tool[Online], available:http://cn.mathworks.com/matlabcentral/fileexchange/6770-thresholding-tool, September 1, 2017.