基于模糊聚类算法的医学图像分割技术研究
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摘要
图像分割技术是计算机视觉、图像理解等领域中最重要的研究课题之一,也是医学图像处理的核心内容和主要课题。医学图像分割是指根据图像中像素的相关特征,将图像分割为互不相交的不同组织或器官。基于医学图像分割技术,可以提取医学图像中感觉兴趣的器官/组织,对病变组织等进行定性和定量分析。同时,医学图像分割又是三维重建等影像处理的基础,分割的效果直接影响到三维模型重建的精确性。因此,研究医学图像分割技术具有非常重要的现实意义和实用价值。
由于医学图像自身的复杂性,医学图像分割技术已经成为制约医学图像处理进一步应用和发展的瓶颈。考虑到医学图像中的强度不一致、部分容积效应和噪声等现象,本文拟对基于模糊聚类算法的医学图像分割技术进行研究。与其他分割方法相比,模糊聚类算法是一种典型的“软分割”方法,它允许像素以不同的隶属度同时隶属于不同的组织和器官,可以有效地解决医学图像中的部分容积效应现象。基于模糊聚类算法对医学图像进行分割时,可以从原图像中保留尽可能多的信息,因而可以获得较好的分割效果。然而,传统的模糊聚类算法由于没有考虑像素的邻域信息,对医学图像中的噪声、伪影等非常敏感,分割效果不是很理想。同时,算法在运行效率上也较为低下,无法满足医学图像处理的实时要求。针对这两个问题,在现有的改进模糊聚类算法的基础上本文重点进行了以下研究工作：
(1)针对FCM算法效率低下的问题,本文从聚类中心计算的角度进行了分析,认为算法效率低下的一个重要原因在于聚类中心的计算需要涉及图像中的所有像素。基于此,本文提出了基于分层技术的图像分割技术,假设聚类中心仅由相应聚类内的像素强度值决定,与隶属于其他聚类的像素无关。算法首先基于阈值分割技术将医学图像粗略地分割为不同的组织／器官,然后基于模糊聚类算法对初略分割的图像进行修正,从而可以提高分割算法的运行效率。
(2)研究了医学图像分割的实时分割技术。针对FCM算法效率低下以及相关改进算法分割效果不理想的问题,本文首先对现有的分割算法进行深入分析,认为运行效率低下的原因是算法没有充分挖掘图像中隐藏的信息。基于相关分析,提出了基于直方图的FCM算法。算法利用峰值检测技术将医学图像的直方图分割为不同的区间,并假设聚类中心取决于相应的区间,与其他区间无关。利用获得的区间在图像的直方图上基于模糊聚类算法对图像进行分割可以进一步提高算法的运行效率。一般情况下可以在0.1秒内完成医学图像的分割,满足医学图像分割的实时性要求。
(3)对基于邻域信息的图像分割技术进行研究。FCM的改进算法FCMS算法在进行图像分割时,采用常数α作为邻域像素对中心像素的影响因子,这样处理可以抑制噪声的影响,然而在对不含噪声的图像进行分割时,目标的边缘部分存在模糊现象。针对该问题,本文在研究过程中基于像素的空间信息和灰度信息提出了像素的相关性模型,并基于像素的相关性对FCMS算法进行了改进。在设计的算法中,用像素之间的相关性作为邻域像素对中心像素的影响因子,这样可以从很大程度上提高算法的分割效果,消除目标对象的模糊现象。
Image segmentation is one of the most important topics in such fields as com-puter vision, image understanding, etc, and is also the core and hot topics in medical imaging. Formally, medical image segmentation is to partition a medical image into non-overlapping different organs or tissues with homogeneous characteristics. By med-ical image segmentation, interesting organ/issue can be retrieved from medical images, and lesions can be analyzed qualitatively and quantitatively. In addition, medical im-age segmentation is the basis of image processing, such as3D reconstruction, and the segmentation results affect the accuracy of reconstruction model directly. Therefore, re-search of medical image segmentation is of important significance and practical value.
Due to the complexity of medical images, medical image segmentation has been one bottleneck to restrict medical applications. Considering such phenomena as intensi-ty inhomogeneity, partial volume effect(PVE) and noise, this paper investigates medical image segmentation based on fuzzy clustering algorithms. Compared with other seg-mentation methods, fuzzy clustering is one typical "soft" algorithm. In fuzzy clustering algorithm, pixels can belong to different organs or tissues concurrently with different membership degrees, and can deal with PVE in medical images. When applied in im-age segmentation, fuzzy clustering method can retain as much information as possible from the original image, and thus can retrieve good results. However, since spatial in-formation is not considered, traditional fuzzy clustering algorithm is sensitive to noise and artifacts in medical images, and performs poor in noisy images. Moreover, the ef-ficiency is very low, and cannot satisfies the requirement of medical image processing. For these two problems, the research of this paper are performed from the following aspects:
(1) Aiming at low efficiency of FCM, this paper analyzes this problem from the aspect of cluster center computation. In this paper, low efficiency is partly due to the fact that cluster center is computed on the basis of all pixels. Based on this, one stratified segmentation technology is proposed in this paper, in which cluster centers are supposed to be based on pixels in corresponding organ/issues, unrelated with pixels belonging to other clusters. In the proposed algorithm, threshold technique is adopted to partition the medical image into different organ/issue roughly, and then FCM is performed to revise the rough results, which will decease the computation and thus improve the efficiency.
(2) This paper investigated the real-time segmentation of medical image segmenta-tion, which can solve low efficiency of FCM and poor result of FCM-related algorithm-s. In this paper, current segmentation algorithms originating from FCM are analyzed deeply, and low efficiency of FCM is due to the fact that the hidden information is not mined sufficiently. Based on this suppose, one improved algorithm based on histogram is proposed, named HisFCM. Peak detection is adopted to partition the histogram of the given image into different intervals, and suppose clustering centers are decided by cor-responding intervals, unrelated to others. Based on these intervals, FCM is performed on the histogram, which can improve the efficiency greatly. Generally, it needs less than0.1s to perform segmentation, which can satisfy the real-time requirement of medical image segmentation.
(3) Image segmentation based on neighbor information is proposed. FCMS is one improved algorithm to enhance the segmentation results of FCM, and one constant a is assigned to reflect the impact of neighbor pixels on central one. By such processing, the algorithm can resist the effect of noise. However, when images without noise are segmented, the pixels along the edge maybe misclassified, and fuzzy phenomena appear. This paper proposed the relevance model based on spatial information and intensity information. Then pixel relevance is adopted to replace the impact factor of neighbor pixels on central one. By such, segmentation results can be improved greatly, and fuzzy phenomena can also be eliminated.
由于医学图像自身的复杂性,医学图像分割技术已经成为制约医学图像处理进一步应用和发展的瓶颈。考虑到医学图像中的强度不一致、部分容积效应和噪声等现象,本文拟对基于模糊聚类算法的医学图像分割技术进行研究。与其他分割方法相比,模糊聚类算法是一种典型的“软分割”方法,它允许像素以不同的隶属度同时隶属于不同的组织和器官,可以有效地解决医学图像中的部分容积效应现象。基于模糊聚类算法对医学图像进行分割时,可以从原图像中保留尽可能多的信息,因而可以获得较好的分割效果。然而,传统的模糊聚类算法由于没有考虑像素的邻域信息,对医学图像中的噪声、伪影等非常敏感,分割效果不是很理想。同时,算法在运行效率上也较为低下,无法满足医学图像处理的实时要求。针对这两个问题,在现有的改进模糊聚类算法的基础上本文重点进行了以下研究工作：
(1)针对FCM算法效率低下的问题,本文从聚类中心计算的角度进行了分析,认为算法效率低下的一个重要原因在于聚类中心的计算需要涉及图像中的所有像素。基于此,本文提出了基于分层技术的图像分割技术,假设聚类中心仅由相应聚类内的像素强度值决定,与隶属于其他聚类的像素无关。算法首先基于阈值分割技术将医学图像粗略地分割为不同的组织／器官,然后基于模糊聚类算法对初略分割的图像进行修正,从而可以提高分割算法的运行效率。
(2)研究了医学图像分割的实时分割技术。针对FCM算法效率低下以及相关改进算法分割效果不理想的问题,本文首先对现有的分割算法进行深入分析,认为运行效率低下的原因是算法没有充分挖掘图像中隐藏的信息。基于相关分析,提出了基于直方图的FCM算法。算法利用峰值检测技术将医学图像的直方图分割为不同的区间,并假设聚类中心取决于相应的区间,与其他区间无关。利用获得的区间在图像的直方图上基于模糊聚类算法对图像进行分割可以进一步提高算法的运行效率。一般情况下可以在0.1秒内完成医学图像的分割,满足医学图像分割的实时性要求。
(3)对基于邻域信息的图像分割技术进行研究。FCM的改进算法FCMS算法在进行图像分割时,采用常数α作为邻域像素对中心像素的影响因子,这样处理可以抑制噪声的影响,然而在对不含噪声的图像进行分割时,目标的边缘部分存在模糊现象。针对该问题,本文在研究过程中基于像素的空间信息和灰度信息提出了像素的相关性模型,并基于像素的相关性对FCMS算法进行了改进。在设计的算法中,用像素之间的相关性作为邻域像素对中心像素的影响因子,这样可以从很大程度上提高算法的分割效果,消除目标对象的模糊现象。
Image segmentation is one of the most important topics in such fields as com-puter vision, image understanding, etc, and is also the core and hot topics in medical imaging. Formally, medical image segmentation is to partition a medical image into non-overlapping different organs or tissues with homogeneous characteristics. By med-ical image segmentation, interesting organ/issue can be retrieved from medical images, and lesions can be analyzed qualitatively and quantitatively. In addition, medical im-age segmentation is the basis of image processing, such as3D reconstruction, and the segmentation results affect the accuracy of reconstruction model directly. Therefore, re-search of medical image segmentation is of important significance and practical value.
Due to the complexity of medical images, medical image segmentation has been one bottleneck to restrict medical applications. Considering such phenomena as intensi-ty inhomogeneity, partial volume effect(PVE) and noise, this paper investigates medical image segmentation based on fuzzy clustering algorithms. Compared with other seg-mentation methods, fuzzy clustering is one typical "soft" algorithm. In fuzzy clustering algorithm, pixels can belong to different organs or tissues concurrently with different membership degrees, and can deal with PVE in medical images. When applied in im-age segmentation, fuzzy clustering method can retain as much information as possible from the original image, and thus can retrieve good results. However, since spatial in-formation is not considered, traditional fuzzy clustering algorithm is sensitive to noise and artifacts in medical images, and performs poor in noisy images. Moreover, the ef-ficiency is very low, and cannot satisfies the requirement of medical image processing. For these two problems, the research of this paper are performed from the following aspects:
(1) Aiming at low efficiency of FCM, this paper analyzes this problem from the aspect of cluster center computation. In this paper, low efficiency is partly due to the fact that cluster center is computed on the basis of all pixels. Based on this, one stratified segmentation technology is proposed in this paper, in which cluster centers are supposed to be based on pixels in corresponding organ/issues, unrelated with pixels belonging to other clusters. In the proposed algorithm, threshold technique is adopted to partition the medical image into different organ/issue roughly, and then FCM is performed to revise the rough results, which will decease the computation and thus improve the efficiency.
(2) This paper investigated the real-time segmentation of medical image segmenta-tion, which can solve low efficiency of FCM and poor result of FCM-related algorithm-s. In this paper, current segmentation algorithms originating from FCM are analyzed deeply, and low efficiency of FCM is due to the fact that the hidden information is not mined sufficiently. Based on this suppose, one improved algorithm based on histogram is proposed, named HisFCM. Peak detection is adopted to partition the histogram of the given image into different intervals, and suppose clustering centers are decided by cor-responding intervals, unrelated to others. Based on these intervals, FCM is performed on the histogram, which can improve the efficiency greatly. Generally, it needs less than0.1s to perform segmentation, which can satisfy the real-time requirement of medical image segmentation.
(3) Image segmentation based on neighbor information is proposed. FCMS is one improved algorithm to enhance the segmentation results of FCM, and one constant a is assigned to reflect the impact of neighbor pixels on central one. By such processing, the algorithm can resist the effect of noise. However, when images without noise are segmented, the pixels along the edge maybe misclassified, and fuzzy phenomena appear. This paper proposed the relevance model based on spatial information and intensity information. Then pixel relevance is adopted to replace the impact factor of neighbor pixels on central one. By such, segmentation results can be improved greatly, and fuzzy phenomena can also be eliminated.
引文
[1]Dzung L Pham, Chenyang Xu, Jerry L Prince. Current methods in medical image segmentation[J]. Annual review of biomedical engineering,2000,2(1):315-337.
[2]王亚丽.PET核医学成像原理分析[J].科技情报开发与经济,2007,17(18)：162-163.
[3]任超世.EIT———一种诱人的医学成像新技术[J].电子科技导报,1996,(5)：9-13.
[4]唐峰,谢晋东,赵雷.医学成像系统显示器性能评价方法[J].中国医学装备,2006,3(1)：27-30.
[5]朱俊杰,章世玲,马成兴.核医学成像技术中计算机的应用[J].核电子学与探测技术,1992,12(4)：236-239.
[6]Isaac Bankman. Handbook of medical image processing and analysis [M]. aca-demic press,2008.
[7]Victor M Spitzer, David G Whitlock. Atlas of the Visible Human male:reverse engineering of the human body[M]. DIANE Publishing Company,2002.
[8]Jianbo Shi, Jitendra Malik. Normalized cuts and image segmentation[J]. Pattern Analysis and Machine Intelligence, IEEE Transactions on,2000,22(8):888-905.
[9]Yuri Boykov, Gareth Funka-Lea. Graph cuts and efficient ND image segmenta-tion[J]. International Journal of Computer Vision,2006,70(2):109-131.
[10]Sara Vicente, Vladimir Kolmogorov, Carsten Rother. Graph cut based image seg-mentation with connectivity priors. In Computer Vision and Pattern Recognition, 2008. CVPR 2008. IEEE Conference on. IEEE,2008,1-8.
[11]Andrew Delong, Yuri Boykov. A scalable graph-cut algorithm for nd grids. In Computer Vision and Pattern Recognition,2008. CVPR 2008. IEEE Conference on. IEEE,2008,1-8.
[12]Xue Bai, Guillermo Sapiro. A geodesic framework for fast interactive image and video segmentation and matting. In Computer Vision,2007. ICCV 2007. IEEE 1 lth International Conference on. IEEE,2007,1-8.
[13]Jue Wang, Michael F Cohen. Image and video matting:a survey[M], volume 3. Now Publishers Inc,2008.
[14]Dorin Comaniciu, Peter Meer. Mean shift:A robust approach toward feature space analysis[J]. Pattern Analysis and Machine Intelligence, IEEE Transactions on,2002,24(5):603-619.
[15]Pedro F Felzenszwalb, Daniel P Huttenlocher. Efficient graph-based image seg-mentation [J]. International Journal of Computer Vision,2004,59(2):167-181.
[16]Leo Grady. Random walks for image segmentation[J]. Pattern Analysis and Machine Intelligence, IEEE Transactions on,2006,28(11):1768-1783.
[17]Ming-Ming Cheng, Guo-Xin Zhang. Connectedness of random walk segmenta-tion[J]. IEEE transactions on pattern analysis and machine intelligence,2011, 33(1):200-202.
[18]Carsten Rother, Vladimir Kolmogorov, Andrew Blake. Grabcut:Interactive fore-ground extraction using iterated graph cuts. In ACM Transactions on Graphics (TOG). ACM,2004, volume 23,309-314.
[19]S. Zheng, Ming-Ming Cheng, J. Warrell, P. Sturgess, V. Vineet, C. Rother, P.H.S. Torr. Dense semantic image segmentation with objects and attributes. In IEEE CVPR.2014.
[20]Ming-Ming Cheng, Niloy J. Mitra, Xiaolei Huang, Philip H. S. Torr, Shi-Min Hu. Salient object detection and segmentation. Technical report, Tsinghua University, 2011. Submission NO. TPAMI-2011-10-0753.
[21]Ming-Ming Cheng, Guo-Xin Zhang, Niloy J. Mitra, Xiaolei Huang, Shi-Min Hu. Global contrast based salient region detection. In IEEE CVPR.2011,409-416.
[22]Ming-Ming Cheng, Jonathan Warrell, Wen-Yan Lin, Shuai Zheng, Vibhav Vi-neet, Nigel Crook. Efficient salient region detection with soft image abstraction. In IEEE ICCV.2013,1529-1536.
[23]吕庆文,陈武凡.基于互信息量的图像分割[J].计算机学报,2006,29(2)：296-301.
[24]唐新亭,张小峰,邹海林.图像分割的最大熵方法的改进[J].计算机工程与应用,2012,48(1)：212-215.
[25]Luminita A Vese, Tony F Chan. A multiphase level set framework for image segmentation using the mumford and shah model[J]. International journal of computer vision,2002,50(3):271-293.
[26]Michael Kass, Andrew Witkin, Demetri Terzopoulos; Snakes:Active contour models[J]. International journal of computer vision,1988,1(4):321-331.
[27]Zexuan Ji, Quansen Sun, Yong Xia, Qiang Chen, Deshen Xia, Dagan Feng. Gen-eralized rough fuzzy c-means algorithm for brain MR image segmentation [J]. Computer methods and programs in biomedicine,2012,108(2)-.644-655.
[28]Zexuan Ji, Yong Xia, Qiang Chen, Quansen Sun, Deshen Xia, David Dagan Feng. Fuzzy c-means clustering with weighted image patch for image segmentation[J]. Applied Soft Computing,2012,12(6):1659-1667.
[29]Hwan Soo Choi, David R Haynor, Yongmin Kim. Partial volume tissue classi-fication of multichannel magnetic resonance images-a mixel model [J]. Medical Imaging, IEEE Transactions on,1991,10(3):395-407.
[30]Koen Van Leemput, Frederik Maes, Dirk Vandermeulen, Paul Suetens. A unify-ing framework for partial volume segmentation of brain mr images [J]. Medical Imaging, IEEE Transactions on,2003,22(1):105-119.
[31]吕庆文,陈武凡.基于互信息熵差测度的医学图像自动优化分割[J].中国科学：E辑,2006,36(6)：657-667.
[32]唐果,赵晓东,汪元美.三维医学图像分割与可视化研究[J].计算机学报,1998,21(3)：204-209.
[33]John Robert Anderson, Ryszard S Michalski, Ryszard Stanislaw Michalski, Jaime Guillermo Carbonell, Tom Michael Mitchell. Machine learning:An ar-tificial intelligence approach[M], volume 2. Morgan Kaufmann,1986.
[34]Christopher M Bishop, et al. Pattern recognition and machine learning[M], vol-ume 1. springer New York,2006.
[35]Richard O Duda, Peter E Hart, David G Stork. Pattern classification[M]. John Wiley & Sons,2012.
[36]Joseph C Dunn. A fuzzy relative of the I SOD ATA process and its use in detect-ing compact well-separated clusters[J].1973.
[37]James Christian Bezdek. Fuzzy mathematics in pattern classification[J].1973.
[38]James C Bezdek. A convergence theorem for the fuzzy ISODATA clustering algorithms.[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1980,2(1):1-8.
[39]James C Bezdek. Pattern recognition with fuzzy objective function algorithm-s[M]. Kluwer Academic Publishers,1981.
[40]Richard J Hathaway, James C Bezdek. Recent convergence results for the fuzzy c-means clustering algorithms [J]. Journal of Classification,1988,5(2):237-247.
[41]John A Hartigan, Manchek A Wong. Algorithm AS 136:A k-means clustering algorithm[J]. Applied statistics,1979,100-108.
[42]Benoit Caldairou, Nicolas Passat, Piotr A Habas, Colin Studholme, Francois Rousseau. A non-local fuzzy segmentation method:Application to brain mri[J]. Pattern Recognition,2011,44(9):1916-1927.
[43]Mohamed N Ahmed, Sameh M Yamany, Nevin Mohamed, Aly A Farag, Thomas Moriarty. A modified fuzzy c-means algorithm for bias field estimation and segmentation of MRI data[J]. Medical Imaging, IEEE Transactions on,2002, 21(3):193-199.
[44]Nevin A Mohamed, MN Ahmed, A Farag. Modified fuzzy c-mean in medi-cal image segmentation. In Acoustics, Speech, and Signal Processing,1999. Proceedings.,1999 IEEE International Conference on. IEEE,1999, volume 6, 3429-3432.
[45]Mohamed N Ahmed, Sameh M Yamany, Aly A Farag, Thomas Moriarty. Bias field estimation and adaptive segmentation of MRI data using a modified fuzzy c-means algorithm. In Computer Vision and Pattern Recognition,1999. IEEE Computer Society Conference on. IEEE,1999, volume 1.
[46]Dao-Qiang Zhang, Song-Can Chen. A novel kernelized fuzzy c-means algorith-m with application in medical image segmentation[J], artificial intelligence in medicine,2004,32(1):37-50.
[47]Stelios Krinidis, Vassilios Chatzis. A robust fuzzy local information c-means clustering algorithm[J]. Image Processing, IEEE Transactions on,2010, 19(5):1328-1337.
[48]Laszlo Szilagyi, Zoltan Benyo, Sandor M Szilagyi, HS Adam. MR brain image segmentfation using an enhanced fuzzy c-means algorithm. In Engineering in Medicine and Biology Society,2003. Proceedings of the 25th Annual Interna-tional Conference of the IEEE. IEEE,2003, volume 1,724-726.
[49]Weiling Cai, Songcan Chen, Daoqiang Zhang. Fast and robust fuzzy c-means clustering algorithms incorporating local information for image segmentation[J]. Pattern Recognition,2007,40(3):825-838.
[50]Lin Zhu, Fu-Lai Chung, Shitong Wang. Generalized fuzzy c-means clustering algorithm with improved fuzzy partitions[J]. Systems, Man, and Cybernetics, Part B:Cybernetics, IEEE Transactions on,2009,39(3):578-591.
[51]Frank Hoppner, Frank Klawonn. Improved fuzzy partitions for fuzzy regression models[J]. International journal of approximate reasoning,2003,32(2):85-102.
[52]Zhang Yang, Fu-Lai Chung, Wang Shitong. Robust fuzzy clustering-based image segmentation[J]. Applied Soft Computing,2009,9(1):80-84.
[53]Huiyu Zhou, Gerald Schaefer, Chunmei Shi. A mean shift based fuzzy c-means algorithm for image segmentation. In Engineering in Medicine and Biology So-ciety,2008. EMBS 2008.30th Annual International Conference of the IEEE. IEEE,2008,3091-3094.
[54]Zhimin Wang, Qing Song, Yeng Chai Soh, Kang Sim. An adaptive spa-tial information-theoretic fuzzy clustering algorithm for image segmentation[J]. Computer Vision and Image Understanding,2013,117(10):1412-1420.
[55]Naosheng Qiao, Beiji Zou. A segmentation method for noisy photoelectric image[J]. Optik-International Journal for Light and Electron Optics,2013, 124(20):4092-^094.
[56]Raghuram Krishnapuram, James M Keller. A possibilistic approach to cluster-ing[J]. Fuzzy Systems, IEEE Transactions on,1993, 1(2):98-110.
[57]Jianzhong Wang, Jun Kong, Yinghua Lu, Miao Qi, Baoxue Zhang. A modi-fied fcm algorithm for MRI brain image segmentation using both local and non-local spatial constraints[J]. Computerized Medical Imaging and Graphics,2008, 32(8):685-698.
[58]王向阳,王春花.基于特征散度的自适应fcm图像分割算法[J].中国图象图形学报,2008,13(5)：906-910.
[59]李艳灵,沈轶.基于空间邻域信息的fcm图像分割算法[J].华中科技大学学报：自然科学版,2009,(6)：56-59.
[60]于剑.论模糊c均值算法的模糊指标[J].计算机学报,2003,26(8)：968-973.
[61]王丽娟,关守义,王晓龙,王熙照.基于属性权重的fuzzy c mean算法[J].计算机学报,2006,29(10)：1797-1803.
[62]于剑,程乾生.关于FCM算法中的权重指数m的一点注记[J].电子学报,2003,21(3)：478-480.
[63]Jian Yu, Cui-Xia Li. Novel cluster validity index for FCM algorithm[J]. Journal of Computer Science and Technology,2006,21(1):137-140.
[64]Jian Yu, Qiansheng Cheng, Houkuan Huang. Analysis of the weighting expo-nent in the FCM[J]. Systems, Man, and Cybernetics, Part B:Cybernetics, IEEE Transactions on,2004,34(1):634-639.
[65]Weina Wang, Yunjie Zhang. On fuzzy cluster validity indices [J]. Fuzzy sets and systems,2007,158(19):2095-2117.
[66]Richard J Hathaway, James C Bezdek, Yingkang Hu. Generalized fuzzy c-means clustering strategies using 1 p norm distances[J]. Fuzzy Systems, IEEE Transac-tions on,2000,8(5):576-582.
[67]王建英,孙德山,张永.基于马氏距离的FCM图像分割算法[J].计算机工程与应用,2010,46(1)：47-49.
[68]Yong Zhang, Zhuoran Li, Jingying Cai, Jianying Wang. Image segmentation based on FCM with mahalanobis distance. In Information Computing and Ap-plications, Springer,2010,205-212.
[69]SR Kannan, R Devi, S Ramathilagam, K Takezawa. Effective FCM noise cluster-ing algorithms in medical images[J]. Computers in biology and medicine,2013, 43(2):73-83.
[70]AN Benaichouche, Hamouche Oulhadj, Patrick Siarry. Improved spatial fuzzy c-means clustering for image segmentation using pso initialization, mahalanobis distance and post-segmentation correction[J]. Digital Signal Processing,2013, 23(5):1390-1400.
[71]Ajay Singh Raghuvanshi, Sudarshan Tiwari, Rajeev Tripathi, Nand Kishor. Op-timal number of clusters in wireless sensor networks:a FCM approach[J]. Inter-national Journal of Sensor Networks,2012,12(1):16-24.
[72]Haojun Sun, Shengrui Wang, Qingshan Jiang. FCM-based model selection al-gorithms for determining the number of clusters [J]. Pattern recognition,2004, 37(10):2027-2037.
[73]Yaonan Wang, Chunsheng Li, Yi Zuo. A selection model for optimal fuzzy clustering algorithm and number of clusters based on competitive comprehensive fuzzy evaluation[J]. Fuzzy Systems, IEEE Transactions on,2009,17(3):568-577.
[74]Keh-Shih Chuang, Hong-Long Tzeng, Sharon Chen, Jay Wu, Tzong-Jer Chen. Fuzzy c-means clustering with spatial information for image segmentation [J]. computerized medical imaging and graphics,2006,30(1):9-15.
[75]Nikhil R Pal, Sankar K Pal. A review on image segmentation techniques [J]. Pattern recognition,1993,26(9):1277-1294.
[76]Robert M Haralick, Linda G Shapiro. Image segmentation techniques [J]. Com-puter vision, graphics, and image processing,1985,29(1):100-132.
[77]林开颜,吴军辉,徐立鸿,et al.彩色图像分割方法综述田.中国图象图形学报,2005,10(1)：1-10.
[78]Lotfi A Zadeh. Fuzzy sets[J]. Information and control,1965,8(3):338-353.
[79]J Valente de Oliveira, Witold Pedrycz, et al. Advances in fuzzy clustering and its applications[M]. Wiley Online Library,2007.
[80]Milind M Mushrif, Ajoy K Ray. Color image segmentation:Rough-set theoretic approach[J]. Pattern Recognition Letters,2008,29(4):483-493.
[81]Pradipta Maji, Sankar K Pal. RFCM:A hybrid clustering algorithm using rough and fuzzy sets[J]. Fundamenta Informaticae,2007,80(4):475-496.
[82]Pradipta Maji, Sankar K Pal. Rough set based generalized fuzzy c-means al-gorithm and quantitative indices [J]. IEEE Transactions on Systems, Man, and Cybernetics, Part B,2007,37(6):1529-1540.
[83]Yong Zhang, Dan Huang, Min Ji, Fuding Xie. Image segmentation using pso and pcm with mahalanobis distance[J]. Expert Systems with Applications,2011, 38(7):9036-9040.
[84]Chao Xu, Peilin Zhang, Bing Li, Dinghai Wu, Hongbo Fan. Vague c-means clustering algorithm[J]. Pattern Recognition Letters,2013,34(5):505-510.
[85]Dao Q Zhang, Song C Chen. Kernel-based fuzzy and possibilistic c-means clus-tering. In Proceedings of the International Conference Artificial Neural Network. 2003,122-125.
[86]SR Kannan, S Ramathilagam, R Devi, Evor Hines. Strong fuzzy c-means in medical image data analysis[J]. Journal of Systems and Software,2012, 85(11):2425-2438.
[87]Nello Cristianini, John Shawe-Taylor. An introduction to support vector ma-chines and other kernel-based learning methods[M]. Cambridge university press, 2000.
[88]徐海祥,喻莉,朱光喜,张翔,田金文.基于支持向量机的磁共振脑组织图像分割[J].中国图象图形学报,2006,10(10)：1275-1280.
[89]James C Bezdek. Cluster validity with fuzzy sets[M]. Taylor & Francis,1973.
[90]Xuanli Lisa Xie, Gerardo Beni. A validity measure for fuzzy clustering[J]. IEEE Transactions on pattern analysis and machine intelligence,1991,13(8):841-847.
[91]Jianqing Liu, Y-H Yang. Multiresolution color image segmentation[J]. Pattern Analysis and Machine Intelligence, IEEE Transactions on,1994,16(7):689-700.
[92]Witold Pedrycz. Knowledge-based clustering:from data to information gran-ules[M]. John Wiley & Sons,2005.
[93]Daniel Graves, Witold Pedrycz. Kernel-based fuzzy clustering and fuzzy clus-tering:A comparative experimental study [J]. Fuzzy sets and systems,2010, 161(4):522-543.
[94]Khang Siang Tan, Nor Ashidi Mat Isa. Color image segmentation using his-togram thresholding-fuzzy c-means hybrid approach[J]. Pattern Recognition, 2011,44(1):1-15.
[95]Chunming Li, Chiu-Yen Kao, John C Gore, Zhaohua Ding. Minimization of region-scalable fitting energy for image segmentation [J]. Image Processing, IEEE Transactions on,2008,17(10):1940-1949.
[96]Stanley Osher, Ronald P Fedkiw. Level set methods:an overview and some recent results[J]. Journal of Computational physics,2001,169(2):463-502.
[97]Stanley Osher Ronald Fedkiw, S Osher. Level set methods and dynamic implicit surfaces[J]. Surfaces,2002,44:77.
[98]Stanley Osher, James A Sethian. Fronts propagating with curvature-dependent speed:algorithms based on hamilton-jacobi formulations [J]. Journal of compu-tational physics,1988,79(1):12-49.
[99]Vicent Caselles, Francine Catte, Tomeu Coll, Francoise Dibos. A geometric model for active contours in image processing[J]. Numerische mathematik,1993, 66(1):1-31.
[100]Ravi Malladi, James A Sethian, Baba C Vemuri. Shape modeling with front propagation:A level set approach[J]. Pattern Analysis and Machine Intelligence, IEEE Transactions on,1995,17(2):158-175.
[101]David Mumford, Jayant Shah. Optimal approximations by piecewise smooth functions and associated variational problems [J]. Communications on pure and applied mathematics,1989,42(5):577-685.
[102]Chunming Li, Chenyang Xu, Changfeng Gui, Martin D Fox. Distance regu-larized level set evolution and its application to image segmentation [J]. Image Processing, IEEE Transactions on,2010,19(12):3243-3254.
[103]Vicent Caselles, Ron Kimmel, Guillermo Sapiro. Geodesic active contours[J]. International journal of computer vision,1997,22(1):61-79.
[104]Xiang-Yang Wang, Juan Bu. A fast and robust image segmentation using fcm with spatial information [J]. Digital Signal Processing,2010,20(4):1173-1182.
[105]T Esch, M Thiel, M Bock, A Roth, S Dech. Improvement of image segmentation accuracy based on multiscale optimization procedure[J]. Geoscience and Remote Sensing Letters, IEEE,2008,5(3):463-467.
[106]Francisco Varela, Jean-Philippe Lachaux, Eugenio Rodriguez, Jacques Martiner-ie. The brain web:phase synchronization and large-scale integration [J]. Nature reviews neuroscience,2001,2(4):229-239.
[107]Brain Web. Simulated brain database[J]. McConnell Brain Imaging Cen-tre, Montreal Neurological Institute, McGill, http://brainweb. bic. mni. mcgill. ca/brainweb,2004.
[108]D. Martin, C. Fowlkes, D. Tal, J. Malik. A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. In Proc.8th Int'l Conf. Computer Vision.2001, volume 2, 416-423.
[109]Howard Besser. Visual access to visual images:the UC berkeley image database project[J]. Library Trends,1990,38(4):787-798.
[2]王亚丽.PET核医学成像原理分析[J].科技情报开发与经济,2007,17(18)：162-163.
[3]任超世.EIT———一种诱人的医学成像新技术[J].电子科技导报,1996,(5)：9-13.
[4]唐峰,谢晋东,赵雷.医学成像系统显示器性能评价方法[J].中国医学装备,2006,3(1)：27-30.
[5]朱俊杰,章世玲,马成兴.核医学成像技术中计算机的应用[J].核电子学与探测技术,1992,12(4)：236-239.
[6]Isaac Bankman. Handbook of medical image processing and analysis [M]. aca-demic press,2008.
[7]Victor M Spitzer, David G Whitlock. Atlas of the Visible Human male:reverse engineering of the human body[M]. DIANE Publishing Company,2002.
[8]Jianbo Shi, Jitendra Malik. Normalized cuts and image segmentation[J]. Pattern Analysis and Machine Intelligence, IEEE Transactions on,2000,22(8):888-905.
[9]Yuri Boykov, Gareth Funka-Lea. Graph cuts and efficient ND image segmenta-tion[J]. International Journal of Computer Vision,2006,70(2):109-131.
[10]Sara Vicente, Vladimir Kolmogorov, Carsten Rother. Graph cut based image seg-mentation with connectivity priors. In Computer Vision and Pattern Recognition, 2008. CVPR 2008. IEEE Conference on. IEEE,2008,1-8.
[11]Andrew Delong, Yuri Boykov. A scalable graph-cut algorithm for nd grids. In Computer Vision and Pattern Recognition,2008. CVPR 2008. IEEE Conference on. IEEE,2008,1-8.
[12]Xue Bai, Guillermo Sapiro. A geodesic framework for fast interactive image and video segmentation and matting. In Computer Vision,2007. ICCV 2007. IEEE 1 lth International Conference on. IEEE,2007,1-8.
[13]Jue Wang, Michael F Cohen. Image and video matting:a survey[M], volume 3. Now Publishers Inc,2008.
[14]Dorin Comaniciu, Peter Meer. Mean shift:A robust approach toward feature space analysis[J]. Pattern Analysis and Machine Intelligence, IEEE Transactions on,2002,24(5):603-619.
[15]Pedro F Felzenszwalb, Daniel P Huttenlocher. Efficient graph-based image seg-mentation [J]. International Journal of Computer Vision,2004,59(2):167-181.
[16]Leo Grady. Random walks for image segmentation[J]. Pattern Analysis and Machine Intelligence, IEEE Transactions on,2006,28(11):1768-1783.
[17]Ming-Ming Cheng, Guo-Xin Zhang. Connectedness of random walk segmenta-tion[J]. IEEE transactions on pattern analysis and machine intelligence,2011, 33(1):200-202.
[18]Carsten Rother, Vladimir Kolmogorov, Andrew Blake. Grabcut:Interactive fore-ground extraction using iterated graph cuts. In ACM Transactions on Graphics (TOG). ACM,2004, volume 23,309-314.
[19]S. Zheng, Ming-Ming Cheng, J. Warrell, P. Sturgess, V. Vineet, C. Rother, P.H.S. Torr. Dense semantic image segmentation with objects and attributes. In IEEE CVPR.2014.
[20]Ming-Ming Cheng, Niloy J. Mitra, Xiaolei Huang, Philip H. S. Torr, Shi-Min Hu. Salient object detection and segmentation. Technical report, Tsinghua University, 2011. Submission NO. TPAMI-2011-10-0753.
[21]Ming-Ming Cheng, Guo-Xin Zhang, Niloy J. Mitra, Xiaolei Huang, Shi-Min Hu. Global contrast based salient region detection. In IEEE CVPR.2011,409-416.
[22]Ming-Ming Cheng, Jonathan Warrell, Wen-Yan Lin, Shuai Zheng, Vibhav Vi-neet, Nigel Crook. Efficient salient region detection with soft image abstraction. In IEEE ICCV.2013,1529-1536.
[23]吕庆文,陈武凡.基于互信息量的图像分割[J].计算机学报,2006,29(2)：296-301.
[24]唐新亭,张小峰,邹海林.图像分割的最大熵方法的改进[J].计算机工程与应用,2012,48(1)：212-215.
[25]Luminita A Vese, Tony F Chan. A multiphase level set framework for image segmentation using the mumford and shah model[J]. International journal of computer vision,2002,50(3):271-293.
[26]Michael Kass, Andrew Witkin, Demetri Terzopoulos; Snakes:Active contour models[J]. International journal of computer vision,1988,1(4):321-331.
[27]Zexuan Ji, Quansen Sun, Yong Xia, Qiang Chen, Deshen Xia, Dagan Feng. Gen-eralized rough fuzzy c-means algorithm for brain MR image segmentation [J]. Computer methods and programs in biomedicine,2012,108(2)-.644-655.
[28]Zexuan Ji, Yong Xia, Qiang Chen, Quansen Sun, Deshen Xia, David Dagan Feng. Fuzzy c-means clustering with weighted image patch for image segmentation[J]. Applied Soft Computing,2012,12(6):1659-1667.
[29]Hwan Soo Choi, David R Haynor, Yongmin Kim. Partial volume tissue classi-fication of multichannel magnetic resonance images-a mixel model [J]. Medical Imaging, IEEE Transactions on,1991,10(3):395-407.
[30]Koen Van Leemput, Frederik Maes, Dirk Vandermeulen, Paul Suetens. A unify-ing framework for partial volume segmentation of brain mr images [J]. Medical Imaging, IEEE Transactions on,2003,22(1):105-119.
[31]吕庆文,陈武凡.基于互信息熵差测度的医学图像自动优化分割[J].中国科学：E辑,2006,36(6)：657-667.
[32]唐果,赵晓东,汪元美.三维医学图像分割与可视化研究[J].计算机学报,1998,21(3)：204-209.
[33]John Robert Anderson, Ryszard S Michalski, Ryszard Stanislaw Michalski, Jaime Guillermo Carbonell, Tom Michael Mitchell. Machine learning:An ar-tificial intelligence approach[M], volume 2. Morgan Kaufmann,1986.
[34]Christopher M Bishop, et al. Pattern recognition and machine learning[M], vol-ume 1. springer New York,2006.
[35]Richard O Duda, Peter E Hart, David G Stork. Pattern classification[M]. John Wiley & Sons,2012.
[36]Joseph C Dunn. A fuzzy relative of the I SOD ATA process and its use in detect-ing compact well-separated clusters[J].1973.
[37]James Christian Bezdek. Fuzzy mathematics in pattern classification[J].1973.
[38]James C Bezdek. A convergence theorem for the fuzzy ISODATA clustering algorithms.[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1980,2(1):1-8.
[39]James C Bezdek. Pattern recognition with fuzzy objective function algorithm-s[M]. Kluwer Academic Publishers,1981.
[40]Richard J Hathaway, James C Bezdek. Recent convergence results for the fuzzy c-means clustering algorithms [J]. Journal of Classification,1988,5(2):237-247.
[41]John A Hartigan, Manchek A Wong. Algorithm AS 136:A k-means clustering algorithm[J]. Applied statistics,1979,100-108.
[42]Benoit Caldairou, Nicolas Passat, Piotr A Habas, Colin Studholme, Francois Rousseau. A non-local fuzzy segmentation method:Application to brain mri[J]. Pattern Recognition,2011,44(9):1916-1927.
[43]Mohamed N Ahmed, Sameh M Yamany, Nevin Mohamed, Aly A Farag, Thomas Moriarty. A modified fuzzy c-means algorithm for bias field estimation and segmentation of MRI data[J]. Medical Imaging, IEEE Transactions on,2002, 21(3):193-199.
[44]Nevin A Mohamed, MN Ahmed, A Farag. Modified fuzzy c-mean in medi-cal image segmentation. In Acoustics, Speech, and Signal Processing,1999. Proceedings.,1999 IEEE International Conference on. IEEE,1999, volume 6, 3429-3432.
[45]Mohamed N Ahmed, Sameh M Yamany, Aly A Farag, Thomas Moriarty. Bias field estimation and adaptive segmentation of MRI data using a modified fuzzy c-means algorithm. In Computer Vision and Pattern Recognition,1999. IEEE Computer Society Conference on. IEEE,1999, volume 1.
[46]Dao-Qiang Zhang, Song-Can Chen. A novel kernelized fuzzy c-means algorith-m with application in medical image segmentation[J], artificial intelligence in medicine,2004,32(1):37-50.
[47]Stelios Krinidis, Vassilios Chatzis. A robust fuzzy local information c-means clustering algorithm[J]. Image Processing, IEEE Transactions on,2010, 19(5):1328-1337.
[48]Laszlo Szilagyi, Zoltan Benyo, Sandor M Szilagyi, HS Adam. MR brain image segmentfation using an enhanced fuzzy c-means algorithm. In Engineering in Medicine and Biology Society,2003. Proceedings of the 25th Annual Interna-tional Conference of the IEEE. IEEE,2003, volume 1,724-726.
[49]Weiling Cai, Songcan Chen, Daoqiang Zhang. Fast and robust fuzzy c-means clustering algorithms incorporating local information for image segmentation[J]. Pattern Recognition,2007,40(3):825-838.
[50]Lin Zhu, Fu-Lai Chung, Shitong Wang. Generalized fuzzy c-means clustering algorithm with improved fuzzy partitions[J]. Systems, Man, and Cybernetics, Part B:Cybernetics, IEEE Transactions on,2009,39(3):578-591.
[51]Frank Hoppner, Frank Klawonn. Improved fuzzy partitions for fuzzy regression models[J]. International journal of approximate reasoning,2003,32(2):85-102.
[52]Zhang Yang, Fu-Lai Chung, Wang Shitong. Robust fuzzy clustering-based image segmentation[J]. Applied Soft Computing,2009,9(1):80-84.
[53]Huiyu Zhou, Gerald Schaefer, Chunmei Shi. A mean shift based fuzzy c-means algorithm for image segmentation. In Engineering in Medicine and Biology So-ciety,2008. EMBS 2008.30th Annual International Conference of the IEEE. IEEE,2008,3091-3094.
[54]Zhimin Wang, Qing Song, Yeng Chai Soh, Kang Sim. An adaptive spa-tial information-theoretic fuzzy clustering algorithm for image segmentation[J]. Computer Vision and Image Understanding,2013,117(10):1412-1420.
[55]Naosheng Qiao, Beiji Zou. A segmentation method for noisy photoelectric image[J]. Optik-International Journal for Light and Electron Optics,2013, 124(20):4092-^094.
[56]Raghuram Krishnapuram, James M Keller. A possibilistic approach to cluster-ing[J]. Fuzzy Systems, IEEE Transactions on,1993, 1(2):98-110.
[57]Jianzhong Wang, Jun Kong, Yinghua Lu, Miao Qi, Baoxue Zhang. A modi-fied fcm algorithm for MRI brain image segmentation using both local and non-local spatial constraints[J]. Computerized Medical Imaging and Graphics,2008, 32(8):685-698.
[58]王向阳,王春花.基于特征散度的自适应fcm图像分割算法[J].中国图象图形学报,2008,13(5)：906-910.
[59]李艳灵,沈轶.基于空间邻域信息的fcm图像分割算法[J].华中科技大学学报：自然科学版,2009,(6)：56-59.
[60]于剑.论模糊c均值算法的模糊指标[J].计算机学报,2003,26(8)：968-973.
[61]王丽娟,关守义,王晓龙,王熙照.基于属性权重的fuzzy c mean算法[J].计算机学报,2006,29(10)：1797-1803.
[62]于剑,程乾生.关于FCM算法中的权重指数m的一点注记[J].电子学报,2003,21(3)：478-480.
[63]Jian Yu, Cui-Xia Li. Novel cluster validity index for FCM algorithm[J]. Journal of Computer Science and Technology,2006,21(1):137-140.
[64]Jian Yu, Qiansheng Cheng, Houkuan Huang. Analysis of the weighting expo-nent in the FCM[J]. Systems, Man, and Cybernetics, Part B:Cybernetics, IEEE Transactions on,2004,34(1):634-639.
[65]Weina Wang, Yunjie Zhang. On fuzzy cluster validity indices [J]. Fuzzy sets and systems,2007,158(19):2095-2117.
[66]Richard J Hathaway, James C Bezdek, Yingkang Hu. Generalized fuzzy c-means clustering strategies using 1 p norm distances[J]. Fuzzy Systems, IEEE Transac-tions on,2000,8(5):576-582.
[67]王建英,孙德山,张永.基于马氏距离的FCM图像分割算法[J].计算机工程与应用,2010,46(1)：47-49.
[68]Yong Zhang, Zhuoran Li, Jingying Cai, Jianying Wang. Image segmentation based on FCM with mahalanobis distance. In Information Computing and Ap-plications, Springer,2010,205-212.
[69]SR Kannan, R Devi, S Ramathilagam, K Takezawa. Effective FCM noise cluster-ing algorithms in medical images[J]. Computers in biology and medicine,2013, 43(2):73-83.
[70]AN Benaichouche, Hamouche Oulhadj, Patrick Siarry. Improved spatial fuzzy c-means clustering for image segmentation using pso initialization, mahalanobis distance and post-segmentation correction[J]. Digital Signal Processing,2013, 23(5):1390-1400.
[71]Ajay Singh Raghuvanshi, Sudarshan Tiwari, Rajeev Tripathi, Nand Kishor. Op-timal number of clusters in wireless sensor networks:a FCM approach[J]. Inter-national Journal of Sensor Networks,2012,12(1):16-24.
[72]Haojun Sun, Shengrui Wang, Qingshan Jiang. FCM-based model selection al-gorithms for determining the number of clusters [J]. Pattern recognition,2004, 37(10):2027-2037.
[73]Yaonan Wang, Chunsheng Li, Yi Zuo. A selection model for optimal fuzzy clustering algorithm and number of clusters based on competitive comprehensive fuzzy evaluation[J]. Fuzzy Systems, IEEE Transactions on,2009,17(3):568-577.
[74]Keh-Shih Chuang, Hong-Long Tzeng, Sharon Chen, Jay Wu, Tzong-Jer Chen. Fuzzy c-means clustering with spatial information for image segmentation [J]. computerized medical imaging and graphics,2006,30(1):9-15.
[75]Nikhil R Pal, Sankar K Pal. A review on image segmentation techniques [J]. Pattern recognition,1993,26(9):1277-1294.
[76]Robert M Haralick, Linda G Shapiro. Image segmentation techniques [J]. Com-puter vision, graphics, and image processing,1985,29(1):100-132.
[77]林开颜,吴军辉,徐立鸿,et al.彩色图像分割方法综述田.中国图象图形学报,2005,10(1)：1-10.
[78]Lotfi A Zadeh. Fuzzy sets[J]. Information and control,1965,8(3):338-353.
[79]J Valente de Oliveira, Witold Pedrycz, et al. Advances in fuzzy clustering and its applications[M]. Wiley Online Library,2007.
[80]Milind M Mushrif, Ajoy K Ray. Color image segmentation:Rough-set theoretic approach[J]. Pattern Recognition Letters,2008,29(4):483-493.
[81]Pradipta Maji, Sankar K Pal. RFCM:A hybrid clustering algorithm using rough and fuzzy sets[J]. Fundamenta Informaticae,2007,80(4):475-496.
[82]Pradipta Maji, Sankar K Pal. Rough set based generalized fuzzy c-means al-gorithm and quantitative indices [J]. IEEE Transactions on Systems, Man, and Cybernetics, Part B,2007,37(6):1529-1540.
[83]Yong Zhang, Dan Huang, Min Ji, Fuding Xie. Image segmentation using pso and pcm with mahalanobis distance[J]. Expert Systems with Applications,2011, 38(7):9036-9040.
[84]Chao Xu, Peilin Zhang, Bing Li, Dinghai Wu, Hongbo Fan. Vague c-means clustering algorithm[J]. Pattern Recognition Letters,2013,34(5):505-510.
[85]Dao Q Zhang, Song C Chen. Kernel-based fuzzy and possibilistic c-means clus-tering. In Proceedings of the International Conference Artificial Neural Network. 2003,122-125.
[86]SR Kannan, S Ramathilagam, R Devi, Evor Hines. Strong fuzzy c-means in medical image data analysis[J]. Journal of Systems and Software,2012, 85(11):2425-2438.
[87]Nello Cristianini, John Shawe-Taylor. An introduction to support vector ma-chines and other kernel-based learning methods[M]. Cambridge university press, 2000.
[88]徐海祥,喻莉,朱光喜,张翔,田金文.基于支持向量机的磁共振脑组织图像分割[J].中国图象图形学报,2006,10(10)：1275-1280.
[89]James C Bezdek. Cluster validity with fuzzy sets[M]. Taylor & Francis,1973.
[90]Xuanli Lisa Xie, Gerardo Beni. A validity measure for fuzzy clustering[J]. IEEE Transactions on pattern analysis and machine intelligence,1991,13(8):841-847.
[91]Jianqing Liu, Y-H Yang. Multiresolution color image segmentation[J]. Pattern Analysis and Machine Intelligence, IEEE Transactions on,1994,16(7):689-700.
[92]Witold Pedrycz. Knowledge-based clustering:from data to information gran-ules[M]. John Wiley & Sons,2005.
[93]Daniel Graves, Witold Pedrycz. Kernel-based fuzzy clustering and fuzzy clus-tering:A comparative experimental study [J]. Fuzzy sets and systems,2010, 161(4):522-543.
[94]Khang Siang Tan, Nor Ashidi Mat Isa. Color image segmentation using his-togram thresholding-fuzzy c-means hybrid approach[J]. Pattern Recognition, 2011,44(1):1-15.
[95]Chunming Li, Chiu-Yen Kao, John C Gore, Zhaohua Ding. Minimization of region-scalable fitting energy for image segmentation [J]. Image Processing, IEEE Transactions on,2008,17(10):1940-1949.
[96]Stanley Osher, Ronald P Fedkiw. Level set methods:an overview and some recent results[J]. Journal of Computational physics,2001,169(2):463-502.
[97]Stanley Osher Ronald Fedkiw, S Osher. Level set methods and dynamic implicit surfaces[J]. Surfaces,2002,44:77.
[98]Stanley Osher, James A Sethian. Fronts propagating with curvature-dependent speed:algorithms based on hamilton-jacobi formulations [J]. Journal of compu-tational physics,1988,79(1):12-49.
[99]Vicent Caselles, Francine Catte, Tomeu Coll, Francoise Dibos. A geometric model for active contours in image processing[J]. Numerische mathematik,1993, 66(1):1-31.
[100]Ravi Malladi, James A Sethian, Baba C Vemuri. Shape modeling with front propagation:A level set approach[J]. Pattern Analysis and Machine Intelligence, IEEE Transactions on,1995,17(2):158-175.
[101]David Mumford, Jayant Shah. Optimal approximations by piecewise smooth functions and associated variational problems [J]. Communications on pure and applied mathematics,1989,42(5):577-685.
[102]Chunming Li, Chenyang Xu, Changfeng Gui, Martin D Fox. Distance regu-larized level set evolution and its application to image segmentation [J]. Image Processing, IEEE Transactions on,2010,19(12):3243-3254.
[103]Vicent Caselles, Ron Kimmel, Guillermo Sapiro. Geodesic active contours[J]. International journal of computer vision,1997,22(1):61-79.
[104]Xiang-Yang Wang, Juan Bu. A fast and robust image segmentation using fcm with spatial information [J]. Digital Signal Processing,2010,20(4):1173-1182.
[105]T Esch, M Thiel, M Bock, A Roth, S Dech. Improvement of image segmentation accuracy based on multiscale optimization procedure[J]. Geoscience and Remote Sensing Letters, IEEE,2008,5(3):463-467.
[106]Francisco Varela, Jean-Philippe Lachaux, Eugenio Rodriguez, Jacques Martiner-ie. The brain web:phase synchronization and large-scale integration [J]. Nature reviews neuroscience,2001,2(4):229-239.
[107]Brain Web. Simulated brain database[J]. McConnell Brain Imaging Cen-tre, Montreal Neurological Institute, McGill, http://brainweb. bic. mni. mcgill. ca/brainweb,2004.
[108]D. Martin, C. Fowlkes, D. Tal, J. Malik. A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. In Proc.8th Int'l Conf. Computer Vision.2001, volume 2, 416-423.
[109]Howard Besser. Visual access to visual images:the UC berkeley image database project[J]. Library Trends,1990,38(4):787-798.