基于粒子群优化的Fuzzy c-mean聚类算法的基因芯片图像处理
|
摘要
基因中包含着大量的遗传信息,对这些信息的研究有着深远的意义。但是以往的研究方法在处理高通量的基因信息时效率低下,于是80年代中期一种高效准确的基因芯片技术应运生。基因芯片有广泛的应用领域,是科研的一个热点方向。图像处理则是基因芯片应用中不可或缺的一个重要步骤,通过有效的图像处理可高效精确的获得芯片所包含的高通量信息。因此基因芯片的图像处理有着非常重要的研究意义。
本文主要针对基因芯片的图像处理进行研究。对图像处理包含的主要步骤:图像预处理,网格定位,图像分割以及分割效果的评价,信号提取分别进行了介绍。图像预处理和网格定位都是为了分割能够更好更准确的进行。分割是图像处理的难点,分割的好坏直接影响最终信号提取的结果。所以本文将基因芯片图像分割技术作为重点。
本文对于基因芯片的图像分割的整个过程展开了全面的研究,从分割算法到算法的评价都进行了详细的阐述。并且在总结前人的分割算法的基础上,提出了一种基于Fuzzy c-means聚类的自适应基因芯片图像分割方法,并且在此算法的基础上进行了进一步的改进提出了基于粒子群优化的Fuzzy c-means聚类的基因芯片图像分割算法,比原先的聚类方法抗噪能力更强,且不容易陷入局部最优。
为了更客观的评价算法的分割效果,本文介绍了多种分割算法评价准则,并提出了一种使用合成图像对基因表达比率进行最终测量精度评价的准则。最终使用多种评价准则对于常用的基因芯片图像分割方法和本文提出的分割算法进行了评价和比较。
For gene contains a large number of genetic information, researches on it have profound significance. However, early methods can’t fix the problem of low efficiency in dealing with high-throughput information. A gene chip technology with high efficiency and accuracy has been focused from it appears in 1980s to now. Gene chips have been applied in many fields, and image processing is a critical integral step which can obtain information in the gene chip.
The thesis focuses on the image processing of gene chip. The key steps of image processing include image preprocessing, grid location, image segmentation, evaluation of segmentation algorithm and signal extraction, and they are introduced respectively in the thesis. Image preprocessing and gridding are the preparations which facilitate the segmentation. Segmentation is one of the most steps, which can affect the final signal extraction result. The thesis mainly focuses on the segmentation of gene chip image. The entire process of segmentation is introduced, including algorithm and evaluation of algorithm. After summarizing the previous algorithm, an adaptive segmentation algorithm based on Fuzzy c-means clustering is proposed. Besides this, an improved Fuzzy c-means clustering algorithm optimized by particle swarm is also proposed. The improved algorithm has better performance in noisy situation and can’t easily fall into local optimum.
A variety of evaluation criteria for segmentation have been described, and the thesis proposes a novel ultimate measurement accuracy criteria based on gene expression ratio. Using these criteria, segmentation algorithm are evaluated and compared.
本文主要针对基因芯片的图像处理进行研究。对图像处理包含的主要步骤:图像预处理,网格定位,图像分割以及分割效果的评价,信号提取分别进行了介绍。图像预处理和网格定位都是为了分割能够更好更准确的进行。分割是图像处理的难点,分割的好坏直接影响最终信号提取的结果。所以本文将基因芯片图像分割技术作为重点。
本文对于基因芯片的图像分割的整个过程展开了全面的研究,从分割算法到算法的评价都进行了详细的阐述。并且在总结前人的分割算法的基础上,提出了一种基于Fuzzy c-means聚类的自适应基因芯片图像分割方法,并且在此算法的基础上进行了进一步的改进提出了基于粒子群优化的Fuzzy c-means聚类的基因芯片图像分割算法,比原先的聚类方法抗噪能力更强,且不容易陷入局部最优。
为了更客观的评价算法的分割效果,本文介绍了多种分割算法评价准则,并提出了一种使用合成图像对基因表达比率进行最终测量精度评价的准则。最终使用多种评价准则对于常用的基因芯片图像分割方法和本文提出的分割算法进行了评价和比较。
For gene contains a large number of genetic information, researches on it have profound significance. However, early methods can’t fix the problem of low efficiency in dealing with high-throughput information. A gene chip technology with high efficiency and accuracy has been focused from it appears in 1980s to now. Gene chips have been applied in many fields, and image processing is a critical integral step which can obtain information in the gene chip.
The thesis focuses on the image processing of gene chip. The key steps of image processing include image preprocessing, grid location, image segmentation, evaluation of segmentation algorithm and signal extraction, and they are introduced respectively in the thesis. Image preprocessing and gridding are the preparations which facilitate the segmentation. Segmentation is one of the most steps, which can affect the final signal extraction result. The thesis mainly focuses on the segmentation of gene chip image. The entire process of segmentation is introduced, including algorithm and evaluation of algorithm. After summarizing the previous algorithm, an adaptive segmentation algorithm based on Fuzzy c-means clustering is proposed. Besides this, an improved Fuzzy c-means clustering algorithm optimized by particle swarm is also proposed. The improved algorithm has better performance in noisy situation and can’t easily fall into local optimum.
A variety of evaluation criteria for segmentation have been described, and the thesis proposes a novel ultimate measurement accuracy criteria based on gene expression ratio. Using these criteria, segmentation algorithm are evaluated and compared.
引文
[1] Yi W, Yao M, Jiang Z. Fuzzy Particle Swarm Optimization Clustering and Its Application to Image Clustering[Z]. Springer Berlin / Heidelberg, 2006: 4261, 459-467.
[2] Van Der Merwe D W, Engelbrecht A P. Data clustering using particle swarm optimization[C]. 2003.
[3]李瑶.基因芯片与功能基因组[M].化学工业出版社, 2004.
[4]陈忠斌.生物芯片技术[M].化学工业出版社, 2005.
[5]李瑶.基因芯片数据分析与处理[M].化学工业出版社, 2006.
[6] Adams R. B L. Seeded region growing[J]. IEEE T Pattern Anal., 1994, 16: 641-647.
[7] Chen Y. Ratio-based decisions and the quantitative analysis of cDNA microarray images[J]. J. Biomed. Opt., 1997, 2: 364-374.
[8] Bozinov D, Rahnenführer J. Unsupervised technique for robust target separation and analysis of DNA microarray spots through adaptive pixel clustering[J]. Bioinformatics, 2002, 18(5): 747-756.
[9] Demirkaya O. Segmentation of cDNA Microarray spots using markov random field modeling[J]. Bioinformatics, 2005, 21: 2994-3000.
[10] Angulo J, Serra J. Automatic analysis of DNA microarray images using mathematical morphology[J]. Bioinformatics, 2003, 19(5): 553-562.
[11] A Y W. Error measures for scene segmentation[J]. pattern recognition, 1977, 9: 217-231.
[12] Lee U S. comparative performance study of several global thresholding techniques for segmentation[C]. 1990.
[13]章毓晋.图象分割[M].科学出版社, 2001.
[14] Zhang Y J, Gerbrands J J. Comparison of thresholding techniques using synthetic images and ultimate measurement accuracy[C]. 1992.
[15] Zhang Y J. A survey on evaluation methods for image segmentation[J]. Pattern Recognition, 1996, 29(8): 1335-1346.
[16] Pease A C S D S E. Light-generated oligonucleotide arrays for rapid DNA sequence analysis[J]. P Natl Acad Sci. USA, 1994, 91: 5022.
[17] Fodor S P R R P H. Multiplexed biochemical assays with biological chips[J]. Nature, 1993, 364: 555-560.
[18] M Schena D S R D. Quantitative monitoring of gene expression patterns with a complementary DNA Microarray [J]. Science, 1995, 270(20): 467-470.
[19] http://www.mathworks.com/help/toolbox/images/ref/rgb2gray.html[Z].
[20] Rafael C.gonzalez R E W S.数字图像处理[M].电子工业出版社, 2005.
[21]王延翔.基于均值算法的混合噪声图像滤波算法的研究与实现[D].北京邮电大学, 2010.
[22] Vincent J. Critical issues in the processing of cDNA microarray images[D]. Virginia Polytechnic Institute and State University, 2001.
[23] Hirata R, Barrera J, Hashimoto R F, et al. Microarray Gridding by Mathematical Morphology[J]. Graphics, Patterns and Images, SIBGRAPI Conference on, 2001, 0: 112.
[24] Wang X. Quantitative quality control in microarray image processing and data acquistion[J]. Nucleic Acids Res., 2001, 29: 75.
[25]胡宝清.模糊理论基础[M].武汉大学出版社, 2004.
[26] Zhang D, Chen S. Clustering Incomplete Data Using Kernel-Based Fuzzy C-means Algorithm[Z]. Springer Netherlands, 2003: 18, 155-162.
[27]纪震,廖惠连,吴青华.粒子群算法及应用[M].科学出版社, 2009.
[28] Zhang Y J. A survey on evaluation methods for image segmentation[J]. 1996, 29(8): 1335-1346.
[29] Zhang Y J. A review of recent evaluation methods for image segmentation[C]. 2001.
[30] M. D. Levine A N. Dynamic measurement of computer generated image segmentations[J]. IEEE Trans. PAMI-7, 1985: 155-164.
[31] J. S. Weszka A R. Threshold evaluation techniques[J]. IEEE Trans. SMC-8, 1978:622-629.
[32] Matti N, Tommi A, Miika A, et al. Simulation of microarray data with realistic characteristics[Z]. BioMed Central, 2006.
[33] Rahnenfuhrer J, Bozinov D. Hybrid clustering for microarray image analysis combining intensity and shape features[J]. BMC Bioinformatics, 2004, 5(1): 47.
[34] Yi W, Yao M, Jiang Z. Fuzzy Particle Swarm Optimization Clustering and Its Application to Image Clustering[Z]. Springer Berlin / Heidelberg, 2006: 4261, 459-467.
[35] Engelbrecht. image classification using particle swarm optimization[Z].
[36] Bengtsson A, Bengtsson H. Microarray image analysis: background estimation using quantile and morphological filters[J]. BMC Bioinformatics, 2006, 7(1): 96.
[37]王春花.基于模糊C_均值聚类的图像分割技术研究[D].辽宁师范大学, 2005.
[38]李丽丽.模糊C-均值聚类算法及其在图像分割中的应用[D].山东师范大学, 2009.
[39]武拴虎,严洪.一种基于聚类和统计分析DNA基因芯片图像处理算法[J].计算机工程与应用, 2005(2): 22-25.
[40]侯志荣,吕振肃.基于MATLAB的粒子群优化算法及其应用[J].计算机仿真, 2003, 20(10): 68-70.
[41]刘向东,沙秋夫,刘勇奎.基于粒子群优化算法的聚类分析[J].计算机工程, 2006, 32(6): 201-202.
[42]张利彪,周春光,马铭.基于粒子群优化算法的模糊C-均值聚类[J].吉林大学学报, 2006, 44(2): 217-222.
[43] Nikolaos Giannakeas D I F. An automated method for gridding and clustering-based segmentation of cDNA microarray images[J]. Computerized Medical Imaging and Graphics, 2009, 33: 40-49.
[44]李照宇.图像处理在基因芯片分析系统中的应用[D].天津大学, 2003.
[45] Dw Van Der Merwe A E. Data Clustering using Particle Swarm Optimization[J]. 2003.
[46]韦苗苗,江铭炎.基于粒子群优化算法的多阈值图像分割[J].山东大学学报, 2005, 35(6): 118-121.
[47] Ahmed A A, Vias M, Iyer N G, et al. Microarray segmentation methods significantly influence data precision[J]. Nucleic Acids Research, 2004, 32(5): 50.
[48] Yang Y H, Buckley M J, Dudoit S, et al. Comparison of Methods for Image Analysis on cDNA Microarray Data[J]. Journal of Computational and Graphical Statistics, 2002, 11(1): 108-136.
[49] Cardoso J S, Corte-Real L. Toward a generic evaluation of image segmentation[J]. Image Processing, IEEE Transactions on, 2005, 14(11): 1773-1782.
[50] Unnikrishnan R, Pantofaru C, Hebert M. Toward Objective Evaluation of Image Segmentation Algorithms[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2007, 29: 929-944.
[51] Novikov E, Barillot E. An algorithm for automatic evaluation of the spot quality in two-color DNA microarray experiments[J]. BMC Bioinformatics, 2005, 6(1): 293.
[52] Chen W, Fang K. A hybridized clustering approach using particle swarm optimization for image segmentation[C]. 2008.
[53]张石,董建威,佘黎煌.医学图像分割算法的评价方法[J].中国图象图形学报, 2009, 14(9): 1872-1880.
[54]王永莉.医学图像中血管分割算法的研究[D].上海交通大学, 2010.
[55] Kim D, Lee K H, Lee D. A novel initialization scheme for the fuzzy c-means algorithm for color clustering[J]. Pattern Recognition Letters, 2004, 25(2): 227-237.
[56]匡泰,朱清新,孙跃. FCM算法用于灰度图像分割的初始化方法的研究[J].计算机应用, 2006, 26(4): 784-786.
[57]曾璐.彩色图像分割技术研究[D].武汉理工大学, 2010.
[58]李俊,杨新等.定位基因芯片探针点的圆心度方法[J].生物医学工程杂志, 2002, 19(1): 97-100.
[59]孙啸.基因芯片设计及数据分析软件系统[J].东南大学学报, 2000, 30(5): 1-6.
[60]陆琳,孙福军,侯明.基因芯片图像去噪方法研究进展[J].检验检疫科学, 2007, 17(1-2).
[61]宁绍芬.基于FCM聚类的算法改进[D].中国海洋大学, 2009.
[62]孙继勇.基因芯片核心技术及其最新进展[J].国际检验医学杂志, 2009, 30(5):467-468.
[63]袁方,周志勇,宋鑫.初始聚类中心优化的K-means算法[J].计算机工程, 2007, 33(3): 65-66.
[64]邵桂芳,罗林开等.基于数学形态学的基因芯片图像高亮噪声处理[J].信息与控制, 2009, 38(3): 270-275.
[65]李红卫,苑伟政,叶芳.基于数学形态学的微阵列芯片荧光图像处理与分析[J].传感技术学报, 2007, 20(2): 338-342.
[66]林开颜,徐立鸿,吴军辉.快速模糊C均值聚类彩色图像分割方法[J].中国图象图形学报, 2004, 9(2): 159-164.
[67]胡翔宇,唐小萍.生物芯片图像样点的自动识别[J].光电工程, 2006, 33(3): 95-100.
[68]秦明.图像分割技术研究[D].吉林大学, 2010.
[70] Wu K, Yang M. Alternative c-means clustering algorithms[J]. Pattern Recognition, 2002, 35(10): 2267-2278.
[71] Xie X L, Beni G. A Validity Measure for Fuzzy Clustering[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1991, 13: 841-847.
[72] Chen C. Design of PSO-based Fuzzy Classification Systems[J]. Journal of Science and Engineering, 2006, 9(1): 63-70.
[73] Hua J, Liu Z, Xiong Z, et al. Microarray BASICA: background adjustment, segmentation, image compression and analysis of microarray images[C]. 2003.
[74]高新波.模糊聚类分析及其应用[M].西安电子科技大学出版社, 2004.
[75] Milan Sonka V H R B.图像处理、分析与机器视觉(第二版)[M].人民邮电出版社, 2002.
[76] Castleman K R.数字图像处理[M].电子工业出版社, 2002.
[77]张瑜,基因芯片检测仪的图像分析软件设计[D],南京理工大学硕士学位论文,2006.
[2] Van Der Merwe D W, Engelbrecht A P. Data clustering using particle swarm optimization[C]. 2003.
[3]李瑶.基因芯片与功能基因组[M].化学工业出版社, 2004.
[4]陈忠斌.生物芯片技术[M].化学工业出版社, 2005.
[5]李瑶.基因芯片数据分析与处理[M].化学工业出版社, 2006.
[6] Adams R. B L. Seeded region growing[J]. IEEE T Pattern Anal., 1994, 16: 641-647.
[7] Chen Y. Ratio-based decisions and the quantitative analysis of cDNA microarray images[J]. J. Biomed. Opt., 1997, 2: 364-374.
[8] Bozinov D, Rahnenführer J. Unsupervised technique for robust target separation and analysis of DNA microarray spots through adaptive pixel clustering[J]. Bioinformatics, 2002, 18(5): 747-756.
[9] Demirkaya O. Segmentation of cDNA Microarray spots using markov random field modeling[J]. Bioinformatics, 2005, 21: 2994-3000.
[10] Angulo J, Serra J. Automatic analysis of DNA microarray images using mathematical morphology[J]. Bioinformatics, 2003, 19(5): 553-562.
[11] A Y W. Error measures for scene segmentation[J]. pattern recognition, 1977, 9: 217-231.
[12] Lee U S. comparative performance study of several global thresholding techniques for segmentation[C]. 1990.
[13]章毓晋.图象分割[M].科学出版社, 2001.
[14] Zhang Y J, Gerbrands J J. Comparison of thresholding techniques using synthetic images and ultimate measurement accuracy[C]. 1992.
[15] Zhang Y J. A survey on evaluation methods for image segmentation[J]. Pattern Recognition, 1996, 29(8): 1335-1346.
[16] Pease A C S D S E. Light-generated oligonucleotide arrays for rapid DNA sequence analysis[J]. P Natl Acad Sci. USA, 1994, 91: 5022.
[17] Fodor S P R R P H. Multiplexed biochemical assays with biological chips[J]. Nature, 1993, 364: 555-560.
[18] M Schena D S R D. Quantitative monitoring of gene expression patterns with a complementary DNA Microarray [J]. Science, 1995, 270(20): 467-470.
[19] http://www.mathworks.com/help/toolbox/images/ref/rgb2gray.html[Z].
[20] Rafael C.gonzalez R E W S.数字图像处理[M].电子工业出版社, 2005.
[21]王延翔.基于均值算法的混合噪声图像滤波算法的研究与实现[D].北京邮电大学, 2010.
[22] Vincent J. Critical issues in the processing of cDNA microarray images[D]. Virginia Polytechnic Institute and State University, 2001.
[23] Hirata R, Barrera J, Hashimoto R F, et al. Microarray Gridding by Mathematical Morphology[J]. Graphics, Patterns and Images, SIBGRAPI Conference on, 2001, 0: 112.
[24] Wang X. Quantitative quality control in microarray image processing and data acquistion[J]. Nucleic Acids Res., 2001, 29: 75.
[25]胡宝清.模糊理论基础[M].武汉大学出版社, 2004.
[26] Zhang D, Chen S. Clustering Incomplete Data Using Kernel-Based Fuzzy C-means Algorithm[Z]. Springer Netherlands, 2003: 18, 155-162.
[27]纪震,廖惠连,吴青华.粒子群算法及应用[M].科学出版社, 2009.
[28] Zhang Y J. A survey on evaluation methods for image segmentation[J]. 1996, 29(8): 1335-1346.
[29] Zhang Y J. A review of recent evaluation methods for image segmentation[C]. 2001.
[30] M. D. Levine A N. Dynamic measurement of computer generated image segmentations[J]. IEEE Trans. PAMI-7, 1985: 155-164.
[31] J. S. Weszka A R. Threshold evaluation techniques[J]. IEEE Trans. SMC-8, 1978:622-629.
[32] Matti N, Tommi A, Miika A, et al. Simulation of microarray data with realistic characteristics[Z]. BioMed Central, 2006.
[33] Rahnenfuhrer J, Bozinov D. Hybrid clustering for microarray image analysis combining intensity and shape features[J]. BMC Bioinformatics, 2004, 5(1): 47.
[34] Yi W, Yao M, Jiang Z. Fuzzy Particle Swarm Optimization Clustering and Its Application to Image Clustering[Z]. Springer Berlin / Heidelberg, 2006: 4261, 459-467.
[35] Engelbrecht. image classification using particle swarm optimization[Z].
[36] Bengtsson A, Bengtsson H. Microarray image analysis: background estimation using quantile and morphological filters[J]. BMC Bioinformatics, 2006, 7(1): 96.
[37]王春花.基于模糊C_均值聚类的图像分割技术研究[D].辽宁师范大学, 2005.
[38]李丽丽.模糊C-均值聚类算法及其在图像分割中的应用[D].山东师范大学, 2009.
[39]武拴虎,严洪.一种基于聚类和统计分析DNA基因芯片图像处理算法[J].计算机工程与应用, 2005(2): 22-25.
[40]侯志荣,吕振肃.基于MATLAB的粒子群优化算法及其应用[J].计算机仿真, 2003, 20(10): 68-70.
[41]刘向东,沙秋夫,刘勇奎.基于粒子群优化算法的聚类分析[J].计算机工程, 2006, 32(6): 201-202.
[42]张利彪,周春光,马铭.基于粒子群优化算法的模糊C-均值聚类[J].吉林大学学报, 2006, 44(2): 217-222.
[43] Nikolaos Giannakeas D I F. An automated method for gridding and clustering-based segmentation of cDNA microarray images[J]. Computerized Medical Imaging and Graphics, 2009, 33: 40-49.
[44]李照宇.图像处理在基因芯片分析系统中的应用[D].天津大学, 2003.
[45] Dw Van Der Merwe A E. Data Clustering using Particle Swarm Optimization[J]. 2003.
[46]韦苗苗,江铭炎.基于粒子群优化算法的多阈值图像分割[J].山东大学学报, 2005, 35(6): 118-121.
[47] Ahmed A A, Vias M, Iyer N G, et al. Microarray segmentation methods significantly influence data precision[J]. Nucleic Acids Research, 2004, 32(5): 50.
[48] Yang Y H, Buckley M J, Dudoit S, et al. Comparison of Methods for Image Analysis on cDNA Microarray Data[J]. Journal of Computational and Graphical Statistics, 2002, 11(1): 108-136.
[49] Cardoso J S, Corte-Real L. Toward a generic evaluation of image segmentation[J]. Image Processing, IEEE Transactions on, 2005, 14(11): 1773-1782.
[50] Unnikrishnan R, Pantofaru C, Hebert M. Toward Objective Evaluation of Image Segmentation Algorithms[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2007, 29: 929-944.
[51] Novikov E, Barillot E. An algorithm for automatic evaluation of the spot quality in two-color DNA microarray experiments[J]. BMC Bioinformatics, 2005, 6(1): 293.
[52] Chen W, Fang K. A hybridized clustering approach using particle swarm optimization for image segmentation[C]. 2008.
[53]张石,董建威,佘黎煌.医学图像分割算法的评价方法[J].中国图象图形学报, 2009, 14(9): 1872-1880.
[54]王永莉.医学图像中血管分割算法的研究[D].上海交通大学, 2010.
[55] Kim D, Lee K H, Lee D. A novel initialization scheme for the fuzzy c-means algorithm for color clustering[J]. Pattern Recognition Letters, 2004, 25(2): 227-237.
[56]匡泰,朱清新,孙跃. FCM算法用于灰度图像分割的初始化方法的研究[J].计算机应用, 2006, 26(4): 784-786.
[57]曾璐.彩色图像分割技术研究[D].武汉理工大学, 2010.
[58]李俊,杨新等.定位基因芯片探针点的圆心度方法[J].生物医学工程杂志, 2002, 19(1): 97-100.
[59]孙啸.基因芯片设计及数据分析软件系统[J].东南大学学报, 2000, 30(5): 1-6.
[60]陆琳,孙福军,侯明.基因芯片图像去噪方法研究进展[J].检验检疫科学, 2007, 17(1-2).
[61]宁绍芬.基于FCM聚类的算法改进[D].中国海洋大学, 2009.
[62]孙继勇.基因芯片核心技术及其最新进展[J].国际检验医学杂志, 2009, 30(5):467-468.
[63]袁方,周志勇,宋鑫.初始聚类中心优化的K-means算法[J].计算机工程, 2007, 33(3): 65-66.
[64]邵桂芳,罗林开等.基于数学形态学的基因芯片图像高亮噪声处理[J].信息与控制, 2009, 38(3): 270-275.
[65]李红卫,苑伟政,叶芳.基于数学形态学的微阵列芯片荧光图像处理与分析[J].传感技术学报, 2007, 20(2): 338-342.
[66]林开颜,徐立鸿,吴军辉.快速模糊C均值聚类彩色图像分割方法[J].中国图象图形学报, 2004, 9(2): 159-164.
[67]胡翔宇,唐小萍.生物芯片图像样点的自动识别[J].光电工程, 2006, 33(3): 95-100.
[68]秦明.图像分割技术研究[D].吉林大学, 2010.
[70] Wu K, Yang M. Alternative c-means clustering algorithms[J]. Pattern Recognition, 2002, 35(10): 2267-2278.
[71] Xie X L, Beni G. A Validity Measure for Fuzzy Clustering[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1991, 13: 841-847.
[72] Chen C. Design of PSO-based Fuzzy Classification Systems[J]. Journal of Science and Engineering, 2006, 9(1): 63-70.
[73] Hua J, Liu Z, Xiong Z, et al. Microarray BASICA: background adjustment, segmentation, image compression and analysis of microarray images[C]. 2003.
[74]高新波.模糊聚类分析及其应用[M].西安电子科技大学出版社, 2004.
[75] Milan Sonka V H R B.图像处理、分析与机器视觉(第二版)[M].人民邮电出版社, 2002.
[76] Castleman K R.数字图像处理[M].电子工业出版社, 2002.
[77]张瑜,基因芯片检测仪的图像分析软件设计[D],南京理工大学硕士学位论文,2006.