基于模糊聚类图像分割方法研究
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摘要
图像分割是从输入图像中提取目标或感兴趣区域的过程,是目标检测和识别过程中的重要步骤。模糊聚类是模糊理论的一个重要的分支,在图像分割中得到广泛应用。本文对应用模糊聚类的图像分割方法进行了探讨,主要研究内容如下:
1)对模糊理论的基本内容进行了系统的介绍,并详细介绍了模糊C-均值(FCM)聚类方法和基于灰度直方图的快速FCM聚类的图像分割算法。
2)本文给出一种将模拟退火(SA)与FCM聚类相结合的算法,可以减少初始聚类中心和隶属度矩阵的选取对算法收敛性的影响。在合理选择冷却进度表的基础上,依据FCM聚类算法建立目标函数,实现了基于SA和FCM聚类的图像分割算法。
3)将核方法的思想推广到FCM聚类,构造了基于Mercer核函数的模糊核C-均值图像分割算法。通过利用Mercer核,将样本从输入空间映射到高维特征空间,使原来没有显现的特征突现出来,取得了很好的图像分割效果。
Image segmentation is the process of detecting objects or interesting areas from input image, and it is an important step in object detection and recognition. Fuzzy clustering is an important branch of fuzzy set theory, and is widely applied in image segmentation. In this dissertation, the application of fuzzy clustering in image segmentation is studied. The main work of this dissertation is summarized as follows:1) The dissertation systematically introduces the fundamental knowledge of fuzzy set theory, fuzzy clustering algorithms and its application in image segmentation— fast fuzzy c-means clustering algorithm based on histogram.2) A fuzzy clustering algorithm is given which combines simulated annealing (SA) and fuzzy c-means (FCM) clustering. This algorithm can reduce the influence of selection of the initial clustering centers value and the membership matrix' elements on the algorithm convergence. Based on choosing reasonable cooling schedule, the objection function for SA is set up according to FCM clustering, and the image segmentation algorithm based on SA and FCM clustering is implemented.3) Based on kernel method, an image segmentation algorithm of fuzzy kernel c-means is proposed. By using Mercer kernel to map the samples from original space to a high-dimension feature space, we can get good results of clustering.
1)对模糊理论的基本内容进行了系统的介绍,并详细介绍了模糊C-均值(FCM)聚类方法和基于灰度直方图的快速FCM聚类的图像分割算法。
2)本文给出一种将模拟退火(SA)与FCM聚类相结合的算法,可以减少初始聚类中心和隶属度矩阵的选取对算法收敛性的影响。在合理选择冷却进度表的基础上,依据FCM聚类算法建立目标函数,实现了基于SA和FCM聚类的图像分割算法。
3)将核方法的思想推广到FCM聚类,构造了基于Mercer核函数的模糊核C-均值图像分割算法。通过利用Mercer核,将样本从输入空间映射到高维特征空间,使原来没有显现的特征突现出来,取得了很好的图像分割效果。
Image segmentation is the process of detecting objects or interesting areas from input image, and it is an important step in object detection and recognition. Fuzzy clustering is an important branch of fuzzy set theory, and is widely applied in image segmentation. In this dissertation, the application of fuzzy clustering in image segmentation is studied. The main work of this dissertation is summarized as follows:1) The dissertation systematically introduces the fundamental knowledge of fuzzy set theory, fuzzy clustering algorithms and its application in image segmentation— fast fuzzy c-means clustering algorithm based on histogram.2) A fuzzy clustering algorithm is given which combines simulated annealing (SA) and fuzzy c-means (FCM) clustering. This algorithm can reduce the influence of selection of the initial clustering centers value and the membership matrix' elements on the algorithm convergence. Based on choosing reasonable cooling schedule, the objection function for SA is set up according to FCM clustering, and the image segmentation algorithm based on SA and FCM clustering is implemented.3) Based on kernel method, an image segmentation algorithm of fuzzy kernel c-means is proposed. By using Mercer kernel to map the samples from original space to a high-dimension feature space, we can get good results of clustering.
引文
[1] 章毓晋.图像分割[M].北京:科学出版社,2001.
[2] 李娟.基于模糊理论的图像分割算法研究.[D]:武汉科技大学信息科学与工程学院,2005.5-20.
[3] Haralick R M, Shapiro L G. Image Segmentation Techniques, CVGIP [J], 1985,29:100-132
[4] Zhang Y J, Gerbrands J J. Objective and Quantitative Segmentation Evaluation And Comparison. Signal Processing [J], 1994,39:43～54
[5] Gonzalez R C, Woods R E. Digital Image Processing [M]. 3rd.ed. AddisonWesley, 1992
[6] Zhang Y J.A Survey on Evaluation Methods for Image Segmentation. Pattern Recognition [J], 1996, 29(8): 1335～1346
[7] Zhang Y J. Quantitative Image Quality Measures and their Applications in Segmentation Evaluation. Journal of Electronics [J], 1997,14:97-103
[8] 林开颜,吴军辉,徐立鸿.彩色图像分割方法综述,中国图像图形学报[J],2005,10(1):1-10
[9] 赵荣椿,迟耀斌,朱重光.图像分割技术进展.中国体视学和图像分析[J],1998,3(2):121-128
[10] 罗希平等.图像分割方法综述.模式识别与人工智能[J],1999,12(3):300-312
[11] Sahoo P K.A Survey of threshold techniques. CVGIP [J], 1988,41(2): 233-260
[12] 吴一全,朱兆达。图像处理中阈值选取方法30年(1962-1992)的进展(一).数据采集与处理[J],1993,8(3):193-201
[13] 吴一全,朱兆达。图像处理中阈值选取方法30年(1962-1992)的进展(二).数据采集与处理[J],1993,8(4):268-281
[14] Weszka J S, Rosefield A. Histogram modification for threshold selection. IEEE-SMC [J], 1979,9:38-72
[15] Nalwa V S, Binford T O. On Detecting Edges. IEEE Trans on Pattern Analysis and Machine Intelligence [J], 1986, 8(6): 699～714
[16] Haralick R M. Digital Step Edges from Zero Crossing of Second Directional Derivatives. IEEE Trans on Pattern Analysis and Machine Intelligence [J], 1984,6(1): 58～68
[17] Chang Y L, Li X B. Adaptive image region-growing. IEEE-IP [J], 1994,3(6):868-872
[18] Horowitz S L, Pavlidis T. Picture segmentation by a tree traversal algorithm. J. ACM [J], 1976,23:368-388
[19] 尹平,王润生.基于边缘信息的分开合并图像分割方法.中国图像图形学报[J],1998,3(6):450-454
[20] Strasters K, Gerbrands J J. Three-Dimensional image segmentation using a split, merge and group approach. Pattern Recognition Letters [J], 1991,12:307-325
[21] Lee C K, Wong S P. A Mathematical Morphological Approach for Segmenting Heavily Noise-corrupted Images. Pattern Recognition [J], 1996, 29(8):1347～1357
[22] 黄风岗,杨国,宋克欧.柔性形态学在图像边缘检测中的应用.中国图像图形学报[J],2000,5A(4):284～287
[23] Cheng K S, et al. The Application of Competitive Hopfield Neural Network to Medical Image Segmentation. IEEE-MI [J], 1996, 15:560～567
[24] 陈燕新,戚飞虎.基于竞争Hopfield网络的自动聚类分割方法.模式识别与人工智能[J],1998,11(2):215～221
[25] 章国宝,叶桦,陈维南.基于正交小波变换的多尺度边缘提取.中国图像图形学报[J],1998,3(8):651～654
[26] 郑宏,潘励.基于遗传算法的图像阈值自动选取.中国图像图形学报[J],1999,4(4):327～330
[27] 薛景浩,章毓晋,林行刚.二维遗传算法用于图像动态分割.自动化学报[J],2000,26(5):327～330
[28] Pal S K, King R A. On edge detection of X -ray image using fuzzy sets. IEEE-PAMI, 1983, 5(1): 69-77
[29] Menhardt W, Imme M. Contour detection using fuzzy sets. Signal Processing IV: Theories and Applications[C], Lacoume J C, etal.eds, 1988,1633-1638
[30] Hall L O, et al. A comparison of neural network and fuzzy clustering techniques in segmenting magnetic resonance images of the brain. IEEE-NN, 1992,5: 672-681
[31] Huang L K, Wang M J. Image thresholding by minimizing the measure of fuzziness. Pattern Recognition, 1995, 28(1): 41-51
[32] Cheng H D, et al. Threshold selection based on fuzzy C-partition entropy approach. Pattern Recognition, 1998,31 (7): 857-870
[33] 杨纶标,高英仪.模糊数学原理与应用,第四版(工科研究生用书)[M].广州:华南理工大学出版社,2005
[34] J C Dunn. A fuzzy relative of the ISODATA process and its use in detecting compact, well-separated clusters [J]. J Cybem. 1974, 3:32-57
[35] J C Bezdek. Pattern recognition with fuzzy objective function algorithms [M]. New York: Plenum, 1981
[36] Tsai D M, Chen Y H.A fast histogram -clustering approach for multi-level thresholding. Pattern Recognition Letters[J], 1992,13:245-252
[37] 叶秀清,顾伟康,肖强.快速模糊图像分割算法.模式识别与人工智能[J],1996,9(1):66-70
[38] 丁震,胡钟山,杨静宇等.一种适用于灰度图像分割的快速FCM算法.模式识别与人工智能[J],1997,10(2):132-139
[39] 丁震,胡钟山,杨静宇等.FCM算法用于灰度图像分割的研究.电子学报[J],1997,25(5):39-43
[40] 胡钟山,丁震,杨静宇等.一种改进的Fuzzy C-Means聚类算法.南京理工大学学报[J],1997,21(8):337-340
[41] 许月芳.基于遗传模糊 C-均值聚类算法的图像分割[J].西北工业大学学报,2002(20):549-553
[42] Richard O.Duda,Peter E.Hart,David GStork.模式分类(第二版)[M].北京:机械工业出版社,2003.
[43] Kirkpatrick S, Gelatt C D and Vecchi M P.Optimization by simulated annealing [J] Science, 1983,220,671-680
[44] 康立山,谢云,尤矢勇等.非数值并行算法(第一册)—模拟退火算法[M].北京:科学出版社,1994
[45] H H Szu, R L Hartley. Fast simulated annealing. Physics Letters A [J], 1987,122:157-162
[46] J W Greens, K J Supowit. Simulated annealing without rejected moves. IEEE Tans On CAD [J], 1986, 5:221-228
[47] D S Johnson, C R Aragon, et al. Optimization by simulated annealing: An experimental evaluation, Part Ⅰ [M], AT&T Bell Lab, N J: Murray Hill, 1987
[48] C Sechen. VLSI placement and global routing using simulated annealing [M]. Kluwer Academic, 1988
[49] John S T, Nello C. Kernel Method for Pattern Analysis [M]. Cambridge University Press, 2004
[50] Girolami M. Mercer Kernel Based Clustering in Feature Space. IEEE Trans on Neural Networks [J], 2002,13(3): 780-784
[51] 张莉,周传达,焦李成.核聚类算法计算机学报[J].,2002,25(6):587-590
[52] 伍忠东,高新东,谢维信.基于核方法的模糊聚类算法.西安电子科技大学学报[J],2004,31(4):533-577
[53] J C Bezdek. Convergence Theory for Fuzzy C Means: Counter examples and Repairs [J]. IEEE Trans on SMC, 1987,17(4): 873-877.
[54] 高新波,裴继红,谢维信.模糊c-均值聚类算法中加权指数m的研究.电子学报 [J], 2000,28(4):80-83
[55] Huntsberges T L, Jacors C L, Cannon R L. Iterative Fuzzy Image Segmentation. Pattern Recognition [J], 1985,18(2): 131-138
[2] 李娟.基于模糊理论的图像分割算法研究.[D]:武汉科技大学信息科学与工程学院,2005.5-20.
[3] Haralick R M, Shapiro L G. Image Segmentation Techniques, CVGIP [J], 1985,29:100-132
[4] Zhang Y J, Gerbrands J J. Objective and Quantitative Segmentation Evaluation And Comparison. Signal Processing [J], 1994,39:43～54
[5] Gonzalez R C, Woods R E. Digital Image Processing [M]. 3rd.ed. AddisonWesley, 1992
[6] Zhang Y J.A Survey on Evaluation Methods for Image Segmentation. Pattern Recognition [J], 1996, 29(8): 1335～1346
[7] Zhang Y J. Quantitative Image Quality Measures and their Applications in Segmentation Evaluation. Journal of Electronics [J], 1997,14:97-103
[8] 林开颜,吴军辉,徐立鸿.彩色图像分割方法综述,中国图像图形学报[J],2005,10(1):1-10
[9] 赵荣椿,迟耀斌,朱重光.图像分割技术进展.中国体视学和图像分析[J],1998,3(2):121-128
[10] 罗希平等.图像分割方法综述.模式识别与人工智能[J],1999,12(3):300-312
[11] Sahoo P K.A Survey of threshold techniques. CVGIP [J], 1988,41(2): 233-260
[12] 吴一全,朱兆达。图像处理中阈值选取方法30年(1962-1992)的进展(一).数据采集与处理[J],1993,8(3):193-201
[13] 吴一全,朱兆达。图像处理中阈值选取方法30年(1962-1992)的进展(二).数据采集与处理[J],1993,8(4):268-281
[14] Weszka J S, Rosefield A. Histogram modification for threshold selection. IEEE-SMC [J], 1979,9:38-72
[15] Nalwa V S, Binford T O. On Detecting Edges. IEEE Trans on Pattern Analysis and Machine Intelligence [J], 1986, 8(6): 699～714
[16] Haralick R M. Digital Step Edges from Zero Crossing of Second Directional Derivatives. IEEE Trans on Pattern Analysis and Machine Intelligence [J], 1984,6(1): 58～68
[17] Chang Y L, Li X B. Adaptive image region-growing. IEEE-IP [J], 1994,3(6):868-872
[18] Horowitz S L, Pavlidis T. Picture segmentation by a tree traversal algorithm. J. ACM [J], 1976,23:368-388
[19] 尹平,王润生.基于边缘信息的分开合并图像分割方法.中国图像图形学报[J],1998,3(6):450-454
[20] Strasters K, Gerbrands J J. Three-Dimensional image segmentation using a split, merge and group approach. Pattern Recognition Letters [J], 1991,12:307-325
[21] Lee C K, Wong S P. A Mathematical Morphological Approach for Segmenting Heavily Noise-corrupted Images. Pattern Recognition [J], 1996, 29(8):1347～1357
[22] 黄风岗,杨国,宋克欧.柔性形态学在图像边缘检测中的应用.中国图像图形学报[J],2000,5A(4):284～287
[23] Cheng K S, et al. The Application of Competitive Hopfield Neural Network to Medical Image Segmentation. IEEE-MI [J], 1996, 15:560～567
[24] 陈燕新,戚飞虎.基于竞争Hopfield网络的自动聚类分割方法.模式识别与人工智能[J],1998,11(2):215～221
[25] 章国宝,叶桦,陈维南.基于正交小波变换的多尺度边缘提取.中国图像图形学报[J],1998,3(8):651～654
[26] 郑宏,潘励.基于遗传算法的图像阈值自动选取.中国图像图形学报[J],1999,4(4):327～330
[27] 薛景浩,章毓晋,林行刚.二维遗传算法用于图像动态分割.自动化学报[J],2000,26(5):327～330
[28] Pal S K, King R A. On edge detection of X -ray image using fuzzy sets. IEEE-PAMI, 1983, 5(1): 69-77
[29] Menhardt W, Imme M. Contour detection using fuzzy sets. Signal Processing IV: Theories and Applications[C], Lacoume J C, etal.eds, 1988,1633-1638
[30] Hall L O, et al. A comparison of neural network and fuzzy clustering techniques in segmenting magnetic resonance images of the brain. IEEE-NN, 1992,5: 672-681
[31] Huang L K, Wang M J. Image thresholding by minimizing the measure of fuzziness. Pattern Recognition, 1995, 28(1): 41-51
[32] Cheng H D, et al. Threshold selection based on fuzzy C-partition entropy approach. Pattern Recognition, 1998,31 (7): 857-870
[33] 杨纶标,高英仪.模糊数学原理与应用,第四版(工科研究生用书)[M].广州:华南理工大学出版社,2005
[34] J C Dunn. A fuzzy relative of the ISODATA process and its use in detecting compact, well-separated clusters [J]. J Cybem. 1974, 3:32-57
[35] J C Bezdek. Pattern recognition with fuzzy objective function algorithms [M]. New York: Plenum, 1981
[36] Tsai D M, Chen Y H.A fast histogram -clustering approach for multi-level thresholding. Pattern Recognition Letters[J], 1992,13:245-252
[37] 叶秀清,顾伟康,肖强.快速模糊图像分割算法.模式识别与人工智能[J],1996,9(1):66-70
[38] 丁震,胡钟山,杨静宇等.一种适用于灰度图像分割的快速FCM算法.模式识别与人工智能[J],1997,10(2):132-139
[39] 丁震,胡钟山,杨静宇等.FCM算法用于灰度图像分割的研究.电子学报[J],1997,25(5):39-43
[40] 胡钟山,丁震,杨静宇等.一种改进的Fuzzy C-Means聚类算法.南京理工大学学报[J],1997,21(8):337-340
[41] 许月芳.基于遗传模糊 C-均值聚类算法的图像分割[J].西北工业大学学报,2002(20):549-553
[42] Richard O.Duda,Peter E.Hart,David GStork.模式分类(第二版)[M].北京:机械工业出版社,2003.
[43] Kirkpatrick S, Gelatt C D and Vecchi M P.Optimization by simulated annealing [J] Science, 1983,220,671-680
[44] 康立山,谢云,尤矢勇等.非数值并行算法(第一册)—模拟退火算法[M].北京:科学出版社,1994
[45] H H Szu, R L Hartley. Fast simulated annealing. Physics Letters A [J], 1987,122:157-162
[46] J W Greens, K J Supowit. Simulated annealing without rejected moves. IEEE Tans On CAD [J], 1986, 5:221-228
[47] D S Johnson, C R Aragon, et al. Optimization by simulated annealing: An experimental evaluation, Part Ⅰ [M], AT&T Bell Lab, N J: Murray Hill, 1987
[48] C Sechen. VLSI placement and global routing using simulated annealing [M]. Kluwer Academic, 1988
[49] John S T, Nello C. Kernel Method for Pattern Analysis [M]. Cambridge University Press, 2004
[50] Girolami M. Mercer Kernel Based Clustering in Feature Space. IEEE Trans on Neural Networks [J], 2002,13(3): 780-784
[51] 张莉,周传达,焦李成.核聚类算法计算机学报[J].,2002,25(6):587-590
[52] 伍忠东,高新东,谢维信.基于核方法的模糊聚类算法.西安电子科技大学学报[J],2004,31(4):533-577
[53] J C Bezdek. Convergence Theory for Fuzzy C Means: Counter examples and Repairs [J]. IEEE Trans on SMC, 1987,17(4): 873-877.
[54] 高新波,裴继红,谢维信.模糊c-均值聚类算法中加权指数m的研究.电子学报 [J], 2000,28(4):80-83
[55] Huntsberges T L, Jacors C L, Cannon R L. Iterative Fuzzy Image Segmentation. Pattern Recognition [J], 1985,18(2): 131-138
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