指纹图像增强
|
摘要
自动指纹识别技术是应用最为广泛的一种生物特征识别技术。包括指纹图像预处理、指纹增强、指纹二值化、指纹细化、特征提取、特征匹配六个阶段。己有很多文献对其进行了深入研究。在实际工作中,特别是在刑事案件现场采集的嫌疑人的指纹图像经常是模糊或残缺的,无法直接用于识别工作,识别前,需要对模糊或残缺的指纹图像进行计算机某种处理,使模糊的指纹图像清晰化,使残缺的指纹图像得到修补。在处理很模糊的指纹图和残缺的指纹图像时,文献已报道的指纹图像处理方法的效果不能满足公安刑侦工作需要。为此,我们对模糊或残缺的指纹图像增强进行了深入研究,提出了新的处理方法。他们是:
(1)在指纹增强技术方面,提出了基于STFT(Short Time Fourier Transform)的指纹图像迭代滤波方法,对模糊或残缺的指纹图像增强的效果较文献已报道的处理方法有很明显的提高。
(2)在指纹区域掩膜技术方面,提出了指纹图像面积归一化的区域掩膜快速实现方法,大大地减少了计算机的运算量和使处理任何尺寸大小的指纹图像都可以使用相同的参数。
(3)在指纹图像的二值化技术方面,提出基于STFT边缘区域阈值的快速二值化方法,大大减少了计算量,与其他已有的方法相比,效果有了很大提高。另外,我们还提出了改进的指纹图像增强步骤。
本论文共分六章。第一章,介绍课题研究背景与研究意义、国内外研究现状、目前指纹图像增强存在的问题及解决方案和论文创新处。第二章,介绍指纹识别背景知识。第三章,介绍流行的指纹图像增强方法和我们提出的增强方法。第四章,介绍典型的指纹图像的二值化和细化方法和我们提出的二值化方法。第五章,介绍典型的指纹图像分割法和我们提出的分割方法。第六章,是总结与探讨。
In the recent years, automatic fingerprint identification technique (AFIT),as a kind of biometrics technology, has been applied the most widely. It mainly includes six phases: preprocessing, enhancement, binarization, thinning, feature extraction and matching. It has been intensively studied in the literatures. In practice, especially the suspects’fingerprint images acquired at crime scenes could not be used for identification directly. It needs some computer processing to make them clear enough to use them. The results gotten by the methods reported in the literatures could not satisfy police needs. So, we intensively studied the methods for fingerprint enhancement and deliver new approaches. The approaches are:
(1) In fingerprint enhancement, a novel approach of iteration for fingerprint enhancement based on STFT(Short Time Fourier Transform) was proposed. This method gets much better result than the other existing methods.
(2) In fingerprint area mask, a novel approach of fast getting fingerprint area mask based on fingerprint image area equalization was proposed. This method reduces largely computer’s computation and makes processing parameters the same to all kind of size image.
(3) In fingerprint image binarization, a novel approach of fingerprint image fast binarization based on STFT marginal area pixel threshold was proposed. This method reduces largely computation and gets better result than the other existing methods.
Besides, we proposed a advanced method of fingerprint enhancement steps.
This paper is divided into six chapters. The first chapter was the brief introduction about our research background and significance, the status in quo of the study in the world, existing problems, our solutions and the innovative methods. In the second chapter, basic concepts about fingerprint recognition and identification were introduced. In the third chapter, some typical fingerprint enhancement methods and our method were introduced. In the fourth chapter, some typical fingerprint binarization and thinning methods as well as our method were introduced. In the fifth chapter, some typical fingerprint segmentation methods and our method were introduced. The final sixth chapter is conclusion and discussion.
(1)在指纹增强技术方面,提出了基于STFT(Short Time Fourier Transform)的指纹图像迭代滤波方法,对模糊或残缺的指纹图像增强的效果较文献已报道的处理方法有很明显的提高。
(2)在指纹区域掩膜技术方面,提出了指纹图像面积归一化的区域掩膜快速实现方法,大大地减少了计算机的运算量和使处理任何尺寸大小的指纹图像都可以使用相同的参数。
(3)在指纹图像的二值化技术方面,提出基于STFT边缘区域阈值的快速二值化方法,大大减少了计算量,与其他已有的方法相比,效果有了很大提高。另外,我们还提出了改进的指纹图像增强步骤。
本论文共分六章。第一章,介绍课题研究背景与研究意义、国内外研究现状、目前指纹图像增强存在的问题及解决方案和论文创新处。第二章,介绍指纹识别背景知识。第三章,介绍流行的指纹图像增强方法和我们提出的增强方法。第四章,介绍典型的指纹图像的二值化和细化方法和我们提出的二值化方法。第五章,介绍典型的指纹图像分割法和我们提出的分割方法。第六章,是总结与探讨。
In the recent years, automatic fingerprint identification technique (AFIT),as a kind of biometrics technology, has been applied the most widely. It mainly includes six phases: preprocessing, enhancement, binarization, thinning, feature extraction and matching. It has been intensively studied in the literatures. In practice, especially the suspects’fingerprint images acquired at crime scenes could not be used for identification directly. It needs some computer processing to make them clear enough to use them. The results gotten by the methods reported in the literatures could not satisfy police needs. So, we intensively studied the methods for fingerprint enhancement and deliver new approaches. The approaches are:
(1) In fingerprint enhancement, a novel approach of iteration for fingerprint enhancement based on STFT(Short Time Fourier Transform) was proposed. This method gets much better result than the other existing methods.
(2) In fingerprint area mask, a novel approach of fast getting fingerprint area mask based on fingerprint image area equalization was proposed. This method reduces largely computer’s computation and makes processing parameters the same to all kind of size image.
(3) In fingerprint image binarization, a novel approach of fingerprint image fast binarization based on STFT marginal area pixel threshold was proposed. This method reduces largely computation and gets better result than the other existing methods.
Besides, we proposed a advanced method of fingerprint enhancement steps.
This paper is divided into six chapters. The first chapter was the brief introduction about our research background and significance, the status in quo of the study in the world, existing problems, our solutions and the innovative methods. In the second chapter, basic concepts about fingerprint recognition and identification were introduced. In the third chapter, some typical fingerprint enhancement methods and our method were introduced. In the fourth chapter, some typical fingerprint binarization and thinning methods as well as our method were introduced. In the fifth chapter, some typical fingerprint segmentation methods and our method were introduced. The final sixth chapter is conclusion and discussion.
引文
[1] N.K. Ratha, K. Karu, S. Chen, A.K. Jain, A real-time matching system for large fingerprint databases, IEEE Transaction on Pattern Analysis and Machine Intelligence 18 (8) (1996) 799–813.
[2] L.C. Jain, U. Halici, I. Hayashi, S.B. Lee, S. Tsutsui, Intelligent Biometric Techniques in Fingerprint and Face Recognition, CRC Press, 1999.
[3] Bazen A.M. and Gerez S.H. Segmentation of fingerprint images. In: the 12th Annual Workshop on Circuits, Systems and Signal Processing. Veldhoven, the Netherlands, Nov. 2001, 276-280.
[4] Chen X.J. , Tian J. , Cheng J.G. et al. Segmentation of fingerprint images using linear classifier. EURASIP Journal on Applied Signal Processing, Brno, Czech Republic, Apr. 2004, 480-494.
[5] Maio D. and Maltoni D. Direct gray scale minutiae detection in fingerprints. IEEE Transaction on Pattern Analysis and Machine Intelligence, 1997, 19(1): 27-40.
[6] Chikkerur S. , Wu C.H. and Govindaraju V. A systematic approch for feature extraction in fingerprint images. In: ICBA 2004. Florida, USA, Dec. 16-19, 2004, 344-350.
[7] N. Otsu,“A Threshold Selection Method from Gray-Level Histogram”,IEEE Trans. Systems Man, and Cybernetics, Vol. 9, pp. 62-66, 1979.
[8] Hong L. , Wan Y. and Jain A.K. Fingerprint image enhancement: algorithm and performance evaluation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1998, 20(8): 777-789.
[9] Areekul V. , Watchareeruetai U. and Tantaratana S. Fast separabale gabor filter for fingerprint enhancement. In: ICBA 2004. Hong Kong, China, July 15-17, 2004, 403-409.
[10] Yang J. W. , Liu L.F. , Jiang T.Z. et al. A modified gabor filter design method for fingerprint image enhancement. Pattern Recognition, 2003, 24(12): 1805-1817.
[11] Kim B.G. , Kim H.J. and Park D.J. New enhancement algorithm for fingerprint images. Pattern Recognition, 2002, 3: 879-882.
[12] Luo X.P. and Tian J. Knowledge based fingerprint image enhancement. In: ICPR 2000. Barcelona, Spain, Sep. 3-7, 2000, 783-786.
[13] Xie M.H. and Wang Z.M. Fingerprint enhancement based on edge-direct diffusion. In: Proceedings of the Third International Conference on Image and Graphics. Hong Kong, China, Dec. 18-20, 2004, 274-277.
[14] Sherlock B. , Monro D. and Millard K. Fingerprint enhancement by directional Fourier filtering. IEEE Proceeding-Vision, Image and Signal Processing, 1994,141920: 87-89.
[15] Willis A. J. and Myer L. A cost-effective fingerprint recognition system for use with Low-qulity prints and damaged fingertips. Pattern Recognition, 2001, 34(2): 255-270.
[16] Zhu G. C. and Zhang C. A top-down fingerprint enhancement method based onFourier analysis. In: Advances in Biometric Person Authentication, The 5th Chinese Conference on Biometric Recognition, Proc. Guang Zhou, China, Dec. 13-14, 2004, 439-448.
[17] Sharat Chikkerur Alexander N. Cartwright Venu Govindaraju. Fingerprint Enhancement Using STFT Analysis. Center for Unified Biometrics and Sensors, University at Buffalo, NY, USA. 2 May 2006.
[18] He Y. L. , Tian J. , Luo X.P. et al. Image enhancement and minutia matching in Fingerprint Verification. Pattern Recognition Letter, 2003, 24: 1349-1360.
[19] Ceng G. Z. and Hall R. W. Parallel thinning with tow-subiteration algorithms. Communications of the ACM, 1989, 32: 359-373.
[20] D. Maltoni, D. Maio, A.K. Jain, S. Prabhakar, Handbook of Fingerprint Recognition (Second Edition), Springer, London, 2009.
[21] Shen wei ChenXia and JunShen Robust detection of singular points for fingerprint recongnition Signal Processing and Its Applications, 2003, Processedings. Seventh international Symposium on Volume 2, 14 July 2003. Vol. 2:439-422
[22] Yilong Yin, Jie Tian, Xiukun Yang. Ridge Distance Estimation in Fingerprint Images: Algorithm and Performance Evaluaion, EURASIP Journal on Aplied Signal Processing, 2003, No. 4, pp: 495-502.
[23] L. O’Gormann, J.V.Nickerson, An approach to fingerprint filter design, Pattern Recognition, 1989, 22 (1) 29–38
[24] S. Greenberg, M. Aladjem, D. Kogan, I. Dimitrov, Fingerprint image enhancement using filtering techniques, in: International Conference on Pattern Recognition, 2000, Vol. 3, pp. 326–329.
[25] L. Hong, Y. Wang, A. K. Jain, Fingerprint image enhancement: Algorithm and performance evaluation, Transactions on PAMI, 1998, 21 (4) 777–789.
[26] Sharat Chikkerur Alexander N. Cartwright Venu Govindaraju. Fingerprint Enhancement Using STFT Analysis. Center for Unified Biometrics and Sensors, University at Buffalo, NY, USA. 2 May 2006.
[27] B.G.Sherlock, D.M.Monro, K.Millard, Fingerprint enhancement by directional fourier filtering, in: Visual Image Signal Processing, 1994, Vol. 141, pp. 87–94,.
[28] A. K. Jain, Fundamentals of digital image processing, Prentice Hall International, 1989.
[29] N. Otsu, A Threshold Selection Method from Gray-Level Histogram, IEEE Trans. Systems Man, and Cybernetics, 1979,Vol. 9, pp. 62-66.
[30]唐为方陈旭,两种常见指纹图象细化算法的改进,山东轻工业学院学报,2005,19(1):25一30.
[31] Lam, L., Seong-Whan Lee, and Ching Y. Suen, Thinning Methodologies-A Comprehensive Survey, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol 14, No. 9, September 1992, page 879, bottom of first column through top of second column.
[32] Fingerprint verification competition, http://bias.csr.unibo.it/fvc2002/.
[33] Sharath Pankanti, Salil Prabhakar, and Anil K. Jain. On the individuality of fingerprints. IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.24, no. 8, pp. 1010–1025, 2002.
[34] N.K. Ratha, R.M. Bolle, Fingerprint Image Quality Estimation, IBM Computer Science Research Report RC 21622, 1999
[35] E. Lim, X. Jiang, W. Yau, Fingerprint quality and validity analysis, IEEE International Conference on Image Processing (ICIP 2002), 1 2002 pp. 22–25.
[36] R. Bolle, S. Pankanti, Y.-S. Yao, System and Method for Determining the Quality of Fingerprint Images, US Patent Number US 596356, 1999
[37] L.L. Shen, A. Kot, W.M. Koo, Quality measures of fingerprint images. The 3rd International Conference Audio- and Video-based Biometric Person Authentication (AVBPA 2001), 2001, pp. 182–271.
[38] H.C. Lee, R.E. Gaensslen, Advances in Fingerprint Technology, CRC Press, 2001.
[39] A.K. Jain, S. Pankanti, S. Prabhakar, A. Ross, Recent advances in fingerprint verification, 3rd International Conference on Audio- and Video-Based Person Authentication, 2001, pp. 182–191.
[40] F. Galton, Finger Prints, Macmillan, London, 1892.
[41] N. Ikeda, M. Nakanishi, K. Fujii, T. Hatano, S. Shigematsu, T. Adachi, Y. Okazaki, H. Kyuragi, Fingerprint image enhancement by pixel-parallel processing, 16th International Conference on Pattern Recognition, 2002, pp. 752–755.
[42] M. Sezgin and B. Sankur,“Survey over Image Thresholding Techniques and Quantitative Performance Evaluation”, Journal of Electronic Imaging, Vol. 13, pp. 146-165 , 2004.
[43] N. Otsu,“A Threshold Selection Method from Gray-Level Histogram”, IEEE Trans. Systems Man, and Cybernetics, Vol. 9, pp. 62-66, 1979.
[44] B. Yu, A.K. Jain and M. Mohiuddin,“Address Block Location on Complex Mail Pieces”, Proceeding of International Conference Document Analysis and Recognition, pp. 897-901, 1997.
[45] O.D. Trier and A.K. Jain,“Goal-Directed Evaluation of Binarization Methods”, IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 17, No. 12, pp. 1191-1201, 1995.
[46] T. Kurita, N. Otsu and N. Abdelmalek,“Maximum Likelihood Thresholding Based on Population Mixture Models”, Pattern Recognition, Vol. 25, No.10, pp. 1231-1240, 1992.
[47] J.N. Kapur, P.K. Sahoo, and A.K.C. Wong,“A New Method for Gray- evel Picture Thresholding Using the Entropy of the Histogram”, Computer Vision, Graphics, and Image Processing, vol. 29, pp. 273-285, 1985.
[48] A.S. Abutaleb,“Automatic Thresholding of Gray-Level Pictures Using Two Dimensional Entropy”, Computer Vision, Graphics, and Image Processing, vol. 47, pp. 22-32, 1989.
[49] J. Kittler and J. Illingworth,“Minimum Error Thresholding”, Pattern Recognition, Vol. 19, No. 1, pp. 41-47, 1986.
[50] T.X. Zhang, J.X. Peng and Z.J. Li,“An Adaptive Image Segmentation Method with Visual Nonlinearity Characteristics”, IEEE Trans. On SMC-Part B, Vol. 26, No. 4, pp. 619 -627, 1996.
[51] M. Zhou:“Low SNR Infrared Weak Target Image Segmentation Algorithm”, Laser and Infrared, Vol. 34, No. 3, pp. 225-228, 2004.
[2] L.C. Jain, U. Halici, I. Hayashi, S.B. Lee, S. Tsutsui, Intelligent Biometric Techniques in Fingerprint and Face Recognition, CRC Press, 1999.
[3] Bazen A.M. and Gerez S.H. Segmentation of fingerprint images. In: the 12th Annual Workshop on Circuits, Systems and Signal Processing. Veldhoven, the Netherlands, Nov. 2001, 276-280.
[4] Chen X.J. , Tian J. , Cheng J.G. et al. Segmentation of fingerprint images using linear classifier. EURASIP Journal on Applied Signal Processing, Brno, Czech Republic, Apr. 2004, 480-494.
[5] Maio D. and Maltoni D. Direct gray scale minutiae detection in fingerprints. IEEE Transaction on Pattern Analysis and Machine Intelligence, 1997, 19(1): 27-40.
[6] Chikkerur S. , Wu C.H. and Govindaraju V. A systematic approch for feature extraction in fingerprint images. In: ICBA 2004. Florida, USA, Dec. 16-19, 2004, 344-350.
[7] N. Otsu,“A Threshold Selection Method from Gray-Level Histogram”,IEEE Trans. Systems Man, and Cybernetics, Vol. 9, pp. 62-66, 1979.
[8] Hong L. , Wan Y. and Jain A.K. Fingerprint image enhancement: algorithm and performance evaluation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1998, 20(8): 777-789.
[9] Areekul V. , Watchareeruetai U. and Tantaratana S. Fast separabale gabor filter for fingerprint enhancement. In: ICBA 2004. Hong Kong, China, July 15-17, 2004, 403-409.
[10] Yang J. W. , Liu L.F. , Jiang T.Z. et al. A modified gabor filter design method for fingerprint image enhancement. Pattern Recognition, 2003, 24(12): 1805-1817.
[11] Kim B.G. , Kim H.J. and Park D.J. New enhancement algorithm for fingerprint images. Pattern Recognition, 2002, 3: 879-882.
[12] Luo X.P. and Tian J. Knowledge based fingerprint image enhancement. In: ICPR 2000. Barcelona, Spain, Sep. 3-7, 2000, 783-786.
[13] Xie M.H. and Wang Z.M. Fingerprint enhancement based on edge-direct diffusion. In: Proceedings of the Third International Conference on Image and Graphics. Hong Kong, China, Dec. 18-20, 2004, 274-277.
[14] Sherlock B. , Monro D. and Millard K. Fingerprint enhancement by directional Fourier filtering. IEEE Proceeding-Vision, Image and Signal Processing, 1994,141920: 87-89.
[15] Willis A. J. and Myer L. A cost-effective fingerprint recognition system for use with Low-qulity prints and damaged fingertips. Pattern Recognition, 2001, 34(2): 255-270.
[16] Zhu G. C. and Zhang C. A top-down fingerprint enhancement method based onFourier analysis. In: Advances in Biometric Person Authentication, The 5th Chinese Conference on Biometric Recognition, Proc. Guang Zhou, China, Dec. 13-14, 2004, 439-448.
[17] Sharat Chikkerur Alexander N. Cartwright Venu Govindaraju. Fingerprint Enhancement Using STFT Analysis. Center for Unified Biometrics and Sensors, University at Buffalo, NY, USA. 2 May 2006.
[18] He Y. L. , Tian J. , Luo X.P. et al. Image enhancement and minutia matching in Fingerprint Verification. Pattern Recognition Letter, 2003, 24: 1349-1360.
[19] Ceng G. Z. and Hall R. W. Parallel thinning with tow-subiteration algorithms. Communications of the ACM, 1989, 32: 359-373.
[20] D. Maltoni, D. Maio, A.K. Jain, S. Prabhakar, Handbook of Fingerprint Recognition (Second Edition), Springer, London, 2009.
[21] Shen wei ChenXia and JunShen Robust detection of singular points for fingerprint recongnition Signal Processing and Its Applications, 2003, Processedings. Seventh international Symposium on Volume 2, 14 July 2003. Vol. 2:439-422
[22] Yilong Yin, Jie Tian, Xiukun Yang. Ridge Distance Estimation in Fingerprint Images: Algorithm and Performance Evaluaion, EURASIP Journal on Aplied Signal Processing, 2003, No. 4, pp: 495-502.
[23] L. O’Gormann, J.V.Nickerson, An approach to fingerprint filter design, Pattern Recognition, 1989, 22 (1) 29–38
[24] S. Greenberg, M. Aladjem, D. Kogan, I. Dimitrov, Fingerprint image enhancement using filtering techniques, in: International Conference on Pattern Recognition, 2000, Vol. 3, pp. 326–329.
[25] L. Hong, Y. Wang, A. K. Jain, Fingerprint image enhancement: Algorithm and performance evaluation, Transactions on PAMI, 1998, 21 (4) 777–789.
[26] Sharat Chikkerur Alexander N. Cartwright Venu Govindaraju. Fingerprint Enhancement Using STFT Analysis. Center for Unified Biometrics and Sensors, University at Buffalo, NY, USA. 2 May 2006.
[27] B.G.Sherlock, D.M.Monro, K.Millard, Fingerprint enhancement by directional fourier filtering, in: Visual Image Signal Processing, 1994, Vol. 141, pp. 87–94,.
[28] A. K. Jain, Fundamentals of digital image processing, Prentice Hall International, 1989.
[29] N. Otsu, A Threshold Selection Method from Gray-Level Histogram, IEEE Trans. Systems Man, and Cybernetics, 1979,Vol. 9, pp. 62-66.
[30]唐为方陈旭,两种常见指纹图象细化算法的改进,山东轻工业学院学报,2005,19(1):25一30.
[31] Lam, L., Seong-Whan Lee, and Ching Y. Suen, Thinning Methodologies-A Comprehensive Survey, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol 14, No. 9, September 1992, page 879, bottom of first column through top of second column.
[32] Fingerprint verification competition, http://bias.csr.unibo.it/fvc2002/.
[33] Sharath Pankanti, Salil Prabhakar, and Anil K. Jain. On the individuality of fingerprints. IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.24, no. 8, pp. 1010–1025, 2002.
[34] N.K. Ratha, R.M. Bolle, Fingerprint Image Quality Estimation, IBM Computer Science Research Report RC 21622, 1999
[35] E. Lim, X. Jiang, W. Yau, Fingerprint quality and validity analysis, IEEE International Conference on Image Processing (ICIP 2002), 1 2002 pp. 22–25.
[36] R. Bolle, S. Pankanti, Y.-S. Yao, System and Method for Determining the Quality of Fingerprint Images, US Patent Number US 596356, 1999
[37] L.L. Shen, A. Kot, W.M. Koo, Quality measures of fingerprint images. The 3rd International Conference Audio- and Video-based Biometric Person Authentication (AVBPA 2001), 2001, pp. 182–271.
[38] H.C. Lee, R.E. Gaensslen, Advances in Fingerprint Technology, CRC Press, 2001.
[39] A.K. Jain, S. Pankanti, S. Prabhakar, A. Ross, Recent advances in fingerprint verification, 3rd International Conference on Audio- and Video-Based Person Authentication, 2001, pp. 182–191.
[40] F. Galton, Finger Prints, Macmillan, London, 1892.
[41] N. Ikeda, M. Nakanishi, K. Fujii, T. Hatano, S. Shigematsu, T. Adachi, Y. Okazaki, H. Kyuragi, Fingerprint image enhancement by pixel-parallel processing, 16th International Conference on Pattern Recognition, 2002, pp. 752–755.
[42] M. Sezgin and B. Sankur,“Survey over Image Thresholding Techniques and Quantitative Performance Evaluation”, Journal of Electronic Imaging, Vol. 13, pp. 146-165 , 2004.
[43] N. Otsu,“A Threshold Selection Method from Gray-Level Histogram”, IEEE Trans. Systems Man, and Cybernetics, Vol. 9, pp. 62-66, 1979.
[44] B. Yu, A.K. Jain and M. Mohiuddin,“Address Block Location on Complex Mail Pieces”, Proceeding of International Conference Document Analysis and Recognition, pp. 897-901, 1997.
[45] O.D. Trier and A.K. Jain,“Goal-Directed Evaluation of Binarization Methods”, IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 17, No. 12, pp. 1191-1201, 1995.
[46] T. Kurita, N. Otsu and N. Abdelmalek,“Maximum Likelihood Thresholding Based on Population Mixture Models”, Pattern Recognition, Vol. 25, No.10, pp. 1231-1240, 1992.
[47] J.N. Kapur, P.K. Sahoo, and A.K.C. Wong,“A New Method for Gray- evel Picture Thresholding Using the Entropy of the Histogram”, Computer Vision, Graphics, and Image Processing, vol. 29, pp. 273-285, 1985.
[48] A.S. Abutaleb,“Automatic Thresholding of Gray-Level Pictures Using Two Dimensional Entropy”, Computer Vision, Graphics, and Image Processing, vol. 47, pp. 22-32, 1989.
[49] J. Kittler and J. Illingworth,“Minimum Error Thresholding”, Pattern Recognition, Vol. 19, No. 1, pp. 41-47, 1986.
[50] T.X. Zhang, J.X. Peng and Z.J. Li,“An Adaptive Image Segmentation Method with Visual Nonlinearity Characteristics”, IEEE Trans. On SMC-Part B, Vol. 26, No. 4, pp. 619 -627, 1996.
[51] M. Zhou:“Low SNR Infrared Weak Target Image Segmentation Algorithm”, Laser and Infrared, Vol. 34, No. 3, pp. 225-228, 2004.