Jaynes E T.On the Rationale of Maximum-Entropy Methods.Proc of IEEE,1982,70(9): 939-952
[2]
Shore J E,Johnson R W.Axiomatic Derivation of the Principle of Maximum Entropy and the Principle of Minimum Cross Entropy.IEEE Trans on Information Theory,1980,26(1): 26-37
[3]
Kapur J N.Maximum Entropy Models in Science and Engineering.New Delhi,USA: Wiley Eastern,1989
[4]
Wong A K C,Sahoo P K.A Gray-Level Threshold Selection Method Based on Maximum Entropy Principle.IEEE Trans on Systems,Man and Cybernetics,1989,19(4): 866-871
[5]
Zhu Wei,Xu Yuru,Qin Zaibai.New Thresholding Method Using Two-Dimensional Tsallis Entropy.Computer Engineering and Application,2007,43(27): 54-58 (in Chinese)(朱 炜,徐玉如,秦再白.一种新的基于二维Tsallis熵的阈值方法.计算机工程与应用,2007,43(27): 54-58)
[6]
Feng Duan,Feng Shaotong.The World of Entropy.Beijing,China: Science Press,2005 (in Chinese)(冯 端,冯少彤.溯源探幽——熵的世界.北京:科学出版社,2005)
[7]
Tsallis C.Possible Generalization of Boltzman-Gibbs Statistics.Journal of Statistical Physics,1988,52(1/2): 479-487
[8]
Skilling J.Classic Maximum Entropy // Skillings J,ed.Maximum Entropy and Bayesian Methods,Dordrecht,Netherland.Kluwer Academic,1988: 45-52
[9]
Brink A D,Pendock N E.Minimum Cross-Entropy Threshold Selection.Pattern Recognition,1996,29(1): 179-188
[10]
Cao Jiannong.Image Segmentation Based on Boltzmann Entropy.Postdoctoral Research Report.Xian,China: Xian Institute of Surveying and Mapping,2010 (in Chinese)(曹建农 基于玻耳兹曼熵分析的图像分割方法研究.博士后研究工作报告.西安:西安测绘研究所,2010)
[11]
Sahoo P K,Arora G.Image Thresholding Using Two-Dimensional Tsallis-Havrda-Charvat Entropy.Pattern Recognition Letters,2006,27(6): 520-528
[12]
Tang Yinggan,Di Qiuyan,Guan Xinping.Method for Thresholding Image Segmentation Based on Minimum Tsallis-Cross Entropy.Chinese Journal of Scientific Instrument,2008,29(9): 1868-1872 (in Chinese)(唐英干,邸秋艳,关新平,等.基于最小Tsallis交叉熵的阈值图像分割方法.仪器仪表学报,2008,29(9): 1868-1872)
[13]
Xue Jinghao,Zhang Yujin,Lin Xinggang.Image Segmentation Algorithms Based on Cross Entropy and Fuzzy Divergence.Acta Electronica Sinica,1999,10(10): 131-134 (in Chinese)(薛景浩,章毓晋,林行刚.图像分割中的交叉熵和模糊散度算法.电子学报,1999,10(10): 131-134)
[14]
Malik N A,Lim J S.Properties of Two-Dimensional Maximum Entropy Power Spectral Estimation // Proc of the IEEE International Conference on Acoustics,Speech and Signal Processing.Cambridge,USA: Massachusetts Institute of Technology,1982,VII: 788-798
[15]
Liu Jianzhang.A Fast Algorithms of Image Thresholding Based on Two-Dimensional Entropy.Pattern Recognition and Artificial Intelligence,1991,4(3): 46-53 (in Chinese)(刘健庄.基于二维熵的图像阈值选择快速算法.模式识别与人工智能,1991,4(3): 46-53)
[16]
Chen W T,Wen C H,Yang C W.A Fast Two-Dimensional Entropic Thresholding Algorithm.Pattern Recognition,1994,27(7): 885-893
[17]
Gong Jian,Li Liyuan,Chen Weinan.A Fast Two Dimensional Entropic Thresholding Method.Journal of Southeast University,1996,26(4): 31-36 (in Chinese)(龚 坚,李立源,陈维南.二维熵阈值分割的快速算法.东南大学学报,1996,26(4): 31-36)
[18]
Zhang Yijun,Wu Xuejing,Xia Liangzheng.A Fast Recurring Algorithm for Two-Dimensional Entropic Thresholding for Image Segmentation.Pattern Recognition and Artificial Intelligence,1997,10(3): 259-264 (in Chinese)(张毅军,吴雪菁,夏良正.二维图像阈值分割的快速递推算法.模式识别与人工智能,1997,10(3): 259-264)
[19]
Liu Jingnan,Chen Congyan,Yu Lingling.A Fast Two-Dimensional Entropy Threshold Method.Application Research of Computers,2002,19(1): 67-68,70 (in Chinese)(刘京南,陈从颜,余玲玲,等.一种快速二维熵阈值分割算法.计算机应用研究,2002,19(1): 67-68,70)
[20]
Mei Rong,Jiang Changsheng,Chen Mou.2D Minimum Cross Entropy Based on Genetic Algorithm for Dynamic Image Segmentation.Electronics Optics & Control,2005,12(1): 30-34 (in Chinese)(梅 蓉,姜长生,陈 谋.基于遗传算法的二维最小交叉熵的动态图像分割.电光与控制,2005,12(1): 30-34)
[21]
Qiao Weiwei,Wu Chengmao.Two-Dimensional Thresholding Segmentation Method Based on Maximum Inter-Class Cross Entropy.Journal of Northwest University: Natural Science Edition,2008,38(3): 374-378 (in Chinese)(乔韡韡,吴成茂.二维最大类间交叉熵阈值分割法.西北大学学报:自然科学版,2008,38(3): 374-378)
[22]
Fu Xiaowei,Ding Mingyue,Zhou Chengping,et al.Multi-Threshold Image Segmentation with Improved Quantum-Inspired Genetic Algorithm.Proc of SPIE,2009,7495: 749518
[23]
Imtiaz H,Fattah S A.A Face Recognition Scheme Based on Spectral Domain Feature Extraction // Proc of the 6th International Conference on Electrical & Computer Engineering.Wuhan,China,2010: 514-517
[24]
Hao Y,Qiu-sheng W,Hai-wen Y.An Improved Image Segmentation Algorithm and Measurement Methods for Asphalt Mixtures // Proc of the 5th IEEE International Conference on Cybernetics and Intelligent Systems.Singapore,Singapore,2011: 36-41
[25]
Hao Jiasheng,Shen Yi,Xu Hongbing,et al.A Region Entropy Based Objective Evaluation Method for Image Segmentation // Proc of the International Instrumentation and Measurement Technology Conference.Singapore,Singapore,2009: 363-367
[26]
Shi Hang,Zou Yuexian,Wang Yiyan,et al.A Robust Traffic Parameter Extraction Method Using Texture and Entropy // Proc of the IEEE Intelligent Vehicles Symposium.Xi’an,China,2009: 237-241
[27]
Quweider M K.An Expanded Histogram Approach for Multilevel Image Thresholding // Proc of the 20th International Conference on Electronics Communications and Computers.Puebla,Mexico,2010: 109-113
[28]
Chang Faliang,Liu Jing,Qiao Yizheng.Self-Adaptive Threshold Segmentation for Color Image Using Two-Dimensional Entropy Method Based on Genetic Algorithm.Control and Decision,2005,20(6): 674-678 (in Chinese)(常发亮,刘 静,乔谊正.基于遗传算法的彩色图像二维熵多阈值自适应分割.控制与决策,2005,20(6): 674-678)
[29]
Xu Dong,Tang Xudong.Multi-Threshold Image Segmentation Based on Two-Dimensional Tsallis // Proc of the 3rd IEEE International Conference on Computer Science and Information Technology.Beijing,China,2010,VI: 1-5
[30]
Sin C E,Leung C K.Image Segmentation by Changing Template Block by Block.Electrical and Electronic Technology,2001,1: 302-305
[31]
Tian Xiaoguang,Hou Xiaorong.A Tsallis-Entropy Image Thresholding Method Based on Two-Dimensional Histogram Oblique Segmentation // Proc of the WASE International Conference on Information Engineering.Taiyuan,China,2009,I: 164-168
[32]
Li Gang,Fan Xiaoping,Li Yan.The Thresholding Methods Based on Two-Dimensional Non-Extensive Entropy // Proc of the 1st International Congress on Image and Signal Processing.Sanya,China,2008,III: 729-733
[33]
Zhang Yufei,Wu Yiquan.Wu Shihua,et al.Multilevel Thresholding Based on Exponential Cross Entropy and Niche Chaotic Particle Swarm Optimization.Lecture Notes in Electrical Engineering,2011,121: 617-624
[34]
Amani A A ,Ali E Z .Image Segmentation Using Minimum Cross-Entropy Thresholding // Proc of the IEEE International Conference on Systems,Man and Cybernetics.San Antonio,USA,2009: 1776-1781
[35]
Fu Xiaowei,Ding Mingyue.A Multi-Threshold Image Segmentation Method with Adaptive Fuzzy Entropy // Proc of the 2nd International Conference on Future Information Technology and Management Engineering.Sanya,China,2009: 171-174
[36]
Tian Junwei,Huang Yongxuan,Yu Yalin.A Fast FCM Cluster Multi-Threshold Image Segmentation Algorithm Based on Entropy Constraint.Pattern Recognition and Artificial Intelligence,2008,21(2): 221-226 (in Chinese)(田军委,黄永宣,于亚琳.基于熵约束的快速FCM 聚类多阈值图像分割算法.模式识别与人工智能,2008,21(2): 221-226)
[37]
Jurio A,Pagola M,Bustince H.Ignorance-Based Fuzzy Clustering Algorithm.International Journal of Computational Intelligence and Applications,2010,9(3): 225-239
[38]
Lin Aiying,Wu Lili,Zheng Baozhou,et al.The Combination of Local Fuzzy-Entropy-Based Transition Region Extraction with Otsu Thresholding Method for Image Segmentation // Proc of the 2nd International Congress on Image and Signal.Tianjing,China,2009: 1-4
[39]
Gerbrands J J.Segmentation of Noise Images.Ph.D Dissertation.Delft,Netherlands: Delft University,1988
[40]
Zhang Y J,Gerbrands J J.Transition Region Determination Based Thresholding.Pattern Recognition Letters,1991,12(1): 2935-2941
[41]
Pun T.A New Method for Grey-Level Picture Thresholding Using the Entropy of the Histogram.Signal Processing,1980,2(3): 223-237
[42]
Kapur J N,Shahoo 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
[43]
Abutaleb A S.Automatic Thresholding of Gray-Level Pictures Using Two-Dimensional Entropy.Computer Vision,Graphics and Image Processing,1989,47(1): 22-32
[44]
Pal N R,Pal S K.A Review on Image Segmentation Techniques.Pattern Recognition,1993,26(9): 1277-1294
[45]
Sahoo P K,Soltani S,Wong A K C,et al.A Survey of Thresholding Techniques.Computer Vision,Graphics and Image Processing,1988,41(2): 233-260
[46]
Pal N R,Pal S K.Entropic Thresholding.Signal Process,1989,16(2): 97-108
[47]
Wong A K C,Sahoo P K.A Gray-Level Threshold Selection Method Based on Maximum Entropy Principle.IEEE Trans on Systems,Man and Cybernetics,1989,19(4): 422-429
[48]
Ternigan M E,Dastous F.Entropy-Based Texture Analysis in the Spatial Frequency Domain.IEEE Trans on Patter Analysis and Machine Intelligence,1984,6(2): 237-243
[49]
Brink A D.Thresholding of Digital Images Using of Two-Dimensional Entropies.Pattern Recognition,1992,25(8): 803-808
[50]
Johannsen G,Bille J.A Threshold Selection Method Using Information Measures // Proc of the 6th International Conference on Pattern Recognition.Munich,Germany,1982: 140-143
[51]
de Albuquerque M P,Esquef I A,Gesualdi Mello A R,et al.Image Thresholding Using Tsallis Entropy.Pattern Recognition Letters,2004,25(9): 1059-1065
[52]
Wang Shitong,Chung F L.Note on the Equivalence Relationship between Renyi-Entropy Based and Tsallis-Entropy Based Image Thresholding.Pattern Recognition Letters,2005,26(14): 2309-2312
[53]
Li C H,Lee C K.Segmentation of Die Patterns Using Minimum Cross Entropy // Proc of the International Conference on Industrial Electronics,Control,Instrumentation and Automation.San Diego,USA,1992,II: 721-724
[54]
Li C H,Lee C K.Minimum Cross Entropy Thresholding.Pattern Recognition,1993,26(4): 617-625
[55]
Xue Jinghao,Zhang Yujin,Lin Xinggang.Image Thresholding Based on Maximum Between-Class Posterior Cross Entropy.Journal of Image and Graphics,1994,4(2): 110-114 (in Chinese)(薛景浩,章毓晋,林行刚.基于最大类间后验交叉熵的阈值化分割算法.中国图像图形学报,1994,4(2): 110-114)
[56]
Cao Jiannong.Image Segmentation of Maximum Cross Entropy Based on Histogram Reconstruction.Journal of Computer Application,2011,31(12): 3373-3377 (in Chinese)(曹建农.基于直方图重构的极大交叉熵图像分割方法.计算机应用,2011,31(12): 3373-3377)
[57]
Al-Attas R.Multi-Level Minimum Cross Entropy Thresholding Using Gamma Distribution.Master Dissertation.Riyadh,Kingdom of Saudi Arabia: King Saud University,2007
Al-Attas R,El-Zaart A.Thresholding of Medical Images Using Minimum Cross Entropy // Proc of the Kuala Lumpur International Conference on Biomedical Engineering.Kuala Lumpur,Malaysia,2006: 312-315
[60]
Al-Osaimi G,El-Zaart A.Minimum Cross Entropy Thresholding for SAR Images // Proc of the 3rd International Conference on Information and Communication Technologies: From Theory to Applications.Damascus,Syria,2008: 1-6
[61]
Wu Jue,Chung A C S.Markov Random Field Energy Minimization via Iterated Cross Entropy with Partition Strategy // Proc of the IEEE International Conference on Acoustics,Speech and Signal Processing.Honolulu,USA,2007,I: 457-460
[62]
Tupin F,Sigelle M,Maitre H.Definition of a Spatial Entropy and Its Use for Texture Discrimination // Proc of the International Conference on Image Processing.Vancouver,Canada,2000,1: 725-728
[63]
Cao Jiannong.Image Segmentation Based on Boltzmann Entropy.Application Research of Computers,2011,28(10): 3920-3924 (in Chinese)(曹建农.基于玻耳兹曼熵分析的图像分割方法研究.计算机应用研究,2011,28(10): 3920-3924)
[64]
Sezgin M,Kocaeli G,Sankur B.Survey over Image Thresholding Techniques and Quantitative Performance Evaluation.Journal of Electronic Imaging,2004,13(1): 146-165
[65]
Chang C,Du Y,Wang J,et al.Survey and Comparative Analysis of Entropy and Relative Entropy Thresholding Techniques.Vision,Image and Signal Processing,2006,153(6): 837-850
[66]
Shannon C E.A Mathematical Theory of Communication.Bell System Technical Journal,1948,27(3): 379-423
[67]
Shannon C E,Weaver W.The Mathematical Theory of Communication.Urbana,USA: University of Illinois Press,1949
[68]
Pal N R,Sankar K.Pal Entropy: A New Definition and Its Applications.IEEE Trans on Systems,Man and Cybernetics,1991,21(5): 1260-1270
[69]
Gonzalez R C,Woods R E.Digital Image Processing.3rd Edition.New York,USA: Addison-Wesley,1992
[70]
Pun T.Entropic Thresholding: A New Approach.Signal Processing,1981,16(3): 210-239
Cho S,Haralick R,Yi S.Improvement of Kittler and Illingworths Minimum Error Thresholding.Pattern Recognition,1989,22(5): 609-617
[77]
Otsu N.A Threshold Selection Method from Gray-Level Histogram.IEEE Trans on Systems,Man and Cybernetics,1979,9(1): 62-66
[78]
Pal N R.On Minimum Cross-Entropy Thresholding.Pattern Recognition,1996,29(4): 575-580
[79]
Lu Jun,Wang Runsheng.An Improved Approach to Minimum Cross-Entropy Thresholding.Computer Engineering and Science,1999,21(4): 69-73 (in Chinese)(陆 军,王润生 一种改进的最小互熵门限法.计算机工程与科学,1999,21(4): 69-73)
[80]
Jaynes E T.Information Theory and Statistical Mechanics.Physical Reviews,1957,106(4): 620-630
