基于水平集和模糊聚类方法的图像分割技术研究
|
摘要
图像分割是指从图像中提取出感兴趣的区域,是图像分析研究领域一项重要的研究课题,也是目标检测和识别过程中的重要步骤,已经渗透到各行各业,在卫星遥感图像识别、溢油监测、产品检测、指纹识别、光学文字识别、笔记鉴定、雷达图像监测、医学图像诊断、车牌信息提取、印章鉴定等方面有着重要应用。
到目前为止,国内外学者提出数以百计的图像分割方法,但是没有一种方法能适用于所有的图像分割,并且达到满意的分割效果。在提出的这些图像分割方法中,基于水平集和模糊聚类的图像分割方法是图像分割领域里相当重要、应用非常广泛的两类图像分割方法,因此本文重点研究了水平集和模糊聚类这两类图像分割方法,对其发展现状做了深入的探讨、综述,在此基础上所做的工作和取得的成果如下：
水平集分割方法是比较著名的一种图像分割方法,在现有水平集图像分割方法和框架基础上,针对水平集方法分割大型遥感图像效率低下的缺点,提出在低分辨率遥感图像检测出大致边缘,映射到高分辨率遥感图像并形成窄带的快速分割方法；利用虚拟符号距离函数的梯度提出的虚拟距离窄带水平集模型不但具有较强的抗噪声性能,而且具有较快的分割效率,从一定程度上解决了水平集方法演化效率的问题；将此虚拟距离窄带方法运用到LBF模型中,利用图像局部信息来驱动模型的演化,有效地解决了遥感、雷达、医学领域中灰度不均匀图像的分割,具有较高的效率和较强的抗噪声性能；针对水平集方法抗噪声较弱,在零水平集内外均值相近时,容易分割失败,提出基于概率驱动的C-V水平集方法。
模糊聚类方法是另外一种比较著名的、能够运用到图像分割的方法,具有自动分类、无需人工干预、无需确定阈值等优点,但是其运用到图像分割时,算法复杂度高,演化效率低下,为了提高检测大型遥感图像海岸线的效率,研究提出了快速海岸线检测方法；针对普通的模糊聚类方法缺失图像邻域信息,本文运用高斯函数来表达图像中像素的相关性,给出一种比较新颖的相似度度量方法,能比较好地克服模糊聚类方法抗噪声比较弱的特点；为了区分不同特征向量在分类中所起的作用不同,提出的动态加权FCM分类法,能有效的滤除对分类不起作用的特征向量。
在理论研究的基础上,通过理论和实践相结合的方法,实现课题的研究目标,运用水平集和模糊聚类方法在遥感图像海岸线提取、溢油分割、医学图像分割等相关领域的深入研究进行了有益的探索,并取得了良好的效果,其课题的价值在于：从遥感图像中提取海岸线,对于海洋污染监控、沿岸区域监测、海岸线绘图、舰船目标定位、航天器位置和姿态控制、遥感图像配准、巡航导弹制导等活动,均有非常重要的意义；遥感图像溢油分割是溢油识别、溢油面积、溢油漂移速度等计算的基础；医学图像的自动分割有利于医生对疾病的诊断。因此本课题的研究在现实生产和项目中有一定的应用价值。
Image segmentation which is to extract the interesting object from its background in an image is a significant topic in image analysis for many years. It also is an important step in object detection and recognition. Image segmentation, which is playing important roles in remote sensing image segmentation, oil spill monitoring, product testing, fingerprint identification, optical character recognition, note identi-fication, radar image monitoring, medical image diagnosis, license information extraction, seal imprint verification, and watermarking security, has penetrated into different fields now.
So far hundreds of image segmentation methods have been proposed at home and abroad. But no one kind of method can be applied to all image segmentations and achieves satisfactory segmentation result. The level set and the fuzzy clustering for image segmentation are mainly researched in this dissertation, the review focus on the recent studies of level set and fuzzy clustering, the work and the results obtained in this dissertation are as follows:
The level set segmentation method is one of the famous image segmentation methods, the evolution of C-V level set function is also more complex, its main drawback is that the evolution is relatively slow, aiming at this problem, a narrow brand level set method based on region level set without re_initialization is proposed, this optimization method detect the approximate edge in low resolution image, then mapped the edge to the high resolution image, more accurate edges are detected in the narrow brand at the middle of the edge. A novel narrowband level set method is proposed, the gradient of the virtual distance function form a narrow band, where the active contour evolutes by simply adding and simply subtracting, the evolution has the following advantages:simple calculation, high-efficiency segmentation. This virtual distance narrowband level set method is also applied to LBF model, a novel level set model is proposed for the segmentation of the image with gray intensity inhomogeneity. Generally, if the grey means inside and outside the level set are almost equal, segmentation results are poor, so the C-V level set method based on level set and parzen-window probability density is proposed.
Fuzzy clustering method is another one of the most famous methods for image segmentation without human intervention and the threshold, but the efficiency of image segmentation is low, aiming at this problem, a fast coastline detection method based on FCM is proposed. Meanwhile a novel fuzzy c-means image segmentation method is proposed, its effectiveness is due to two mechanisms, the first mechanism is the replacement of the Euclidean distance traditionally used to measure similarity of the image pixels by a novel similarity measure which is considered spatial neighborhoods using Gaussian kernel, and thus our method becomes less sensitive to the noise of the image. Another fuzzy clustering method with dynamic weights based on the kernel method is proposed, this method cluster data with noise features in high feature space mapped by the mercer kernel, not only can overcome the influence of noise feature vector on clustering, but also cluster the line and the non-group data without any experience.
The target of the topic research is realized through combining theory and practice, some research is explored remote sensing image coastline extraction, oil spill segmentation, and medical image segmentation by using the level set and fuzzy clustering method. The coastline extraction of remote sensing image is very important for marine pollution monitoring, coastal region monitoring, coastline drawing, ship target, the spacecraft position and attitude controlling, remote sensing image registration, and cruise missile guidance. The oil spill segmentation of remote sensing image is the basis of oil spill identification, oil spill area computing, and oil spill drift velocity computing. The medical image segmentation is helpful to disease diagnosis for the doctor. And thus the topic research in this dissertation has its application value.
到目前为止,国内外学者提出数以百计的图像分割方法,但是没有一种方法能适用于所有的图像分割,并且达到满意的分割效果。在提出的这些图像分割方法中,基于水平集和模糊聚类的图像分割方法是图像分割领域里相当重要、应用非常广泛的两类图像分割方法,因此本文重点研究了水平集和模糊聚类这两类图像分割方法,对其发展现状做了深入的探讨、综述,在此基础上所做的工作和取得的成果如下：
水平集分割方法是比较著名的一种图像分割方法,在现有水平集图像分割方法和框架基础上,针对水平集方法分割大型遥感图像效率低下的缺点,提出在低分辨率遥感图像检测出大致边缘,映射到高分辨率遥感图像并形成窄带的快速分割方法；利用虚拟符号距离函数的梯度提出的虚拟距离窄带水平集模型不但具有较强的抗噪声性能,而且具有较快的分割效率,从一定程度上解决了水平集方法演化效率的问题；将此虚拟距离窄带方法运用到LBF模型中,利用图像局部信息来驱动模型的演化,有效地解决了遥感、雷达、医学领域中灰度不均匀图像的分割,具有较高的效率和较强的抗噪声性能；针对水平集方法抗噪声较弱,在零水平集内外均值相近时,容易分割失败,提出基于概率驱动的C-V水平集方法。
模糊聚类方法是另外一种比较著名的、能够运用到图像分割的方法,具有自动分类、无需人工干预、无需确定阈值等优点,但是其运用到图像分割时,算法复杂度高,演化效率低下,为了提高检测大型遥感图像海岸线的效率,研究提出了快速海岸线检测方法；针对普通的模糊聚类方法缺失图像邻域信息,本文运用高斯函数来表达图像中像素的相关性,给出一种比较新颖的相似度度量方法,能比较好地克服模糊聚类方法抗噪声比较弱的特点；为了区分不同特征向量在分类中所起的作用不同,提出的动态加权FCM分类法,能有效的滤除对分类不起作用的特征向量。
在理论研究的基础上,通过理论和实践相结合的方法,实现课题的研究目标,运用水平集和模糊聚类方法在遥感图像海岸线提取、溢油分割、医学图像分割等相关领域的深入研究进行了有益的探索,并取得了良好的效果,其课题的价值在于：从遥感图像中提取海岸线,对于海洋污染监控、沿岸区域监测、海岸线绘图、舰船目标定位、航天器位置和姿态控制、遥感图像配准、巡航导弹制导等活动,均有非常重要的意义；遥感图像溢油分割是溢油识别、溢油面积、溢油漂移速度等计算的基础；医学图像的自动分割有利于医生对疾病的诊断。因此本课题的研究在现实生产和项目中有一定的应用价值。
Image segmentation which is to extract the interesting object from its background in an image is a significant topic in image analysis for many years. It also is an important step in object detection and recognition. Image segmentation, which is playing important roles in remote sensing image segmentation, oil spill monitoring, product testing, fingerprint identification, optical character recognition, note identi-fication, radar image monitoring, medical image diagnosis, license information extraction, seal imprint verification, and watermarking security, has penetrated into different fields now.
So far hundreds of image segmentation methods have been proposed at home and abroad. But no one kind of method can be applied to all image segmentations and achieves satisfactory segmentation result. The level set and the fuzzy clustering for image segmentation are mainly researched in this dissertation, the review focus on the recent studies of level set and fuzzy clustering, the work and the results obtained in this dissertation are as follows:
The level set segmentation method is one of the famous image segmentation methods, the evolution of C-V level set function is also more complex, its main drawback is that the evolution is relatively slow, aiming at this problem, a narrow brand level set method based on region level set without re_initialization is proposed, this optimization method detect the approximate edge in low resolution image, then mapped the edge to the high resolution image, more accurate edges are detected in the narrow brand at the middle of the edge. A novel narrowband level set method is proposed, the gradient of the virtual distance function form a narrow band, where the active contour evolutes by simply adding and simply subtracting, the evolution has the following advantages:simple calculation, high-efficiency segmentation. This virtual distance narrowband level set method is also applied to LBF model, a novel level set model is proposed for the segmentation of the image with gray intensity inhomogeneity. Generally, if the grey means inside and outside the level set are almost equal, segmentation results are poor, so the C-V level set method based on level set and parzen-window probability density is proposed.
Fuzzy clustering method is another one of the most famous methods for image segmentation without human intervention and the threshold, but the efficiency of image segmentation is low, aiming at this problem, a fast coastline detection method based on FCM is proposed. Meanwhile a novel fuzzy c-means image segmentation method is proposed, its effectiveness is due to two mechanisms, the first mechanism is the replacement of the Euclidean distance traditionally used to measure similarity of the image pixels by a novel similarity measure which is considered spatial neighborhoods using Gaussian kernel, and thus our method becomes less sensitive to the noise of the image. Another fuzzy clustering method with dynamic weights based on the kernel method is proposed, this method cluster data with noise features in high feature space mapped by the mercer kernel, not only can overcome the influence of noise feature vector on clustering, but also cluster the line and the non-group data without any experience.
The target of the topic research is realized through combining theory and practice, some research is explored remote sensing image coastline extraction, oil spill segmentation, and medical image segmentation by using the level set and fuzzy clustering method. The coastline extraction of remote sensing image is very important for marine pollution monitoring, coastal region monitoring, coastline drawing, ship target, the spacecraft position and attitude controlling, remote sensing image registration, and cruise missile guidance. The oil spill segmentation of remote sensing image is the basis of oil spill identification, oil spill area computing, and oil spill drift velocity computing. The medical image segmentation is helpful to disease diagnosis for the doctor. And thus the topic research in this dissertation has its application value.
引文
[1]章毓晋.图像处理与分析.北京：清华大学出版社,2002.
[2]李弼程,彭天强,彭波.智能图像处理技术.北京：电子工业出版社,2004.
[3]Lee S U, Yoon Chung S, Park R H. A comparative performance study of several global thresholding techniques for segmentation. Computer Vision Graphics and Image Processing,1990, 52(2):171-190.
[4]Doyle W. Operations useful for similarity-invariant pattern recognition. Journal of the ACM (JACM).1962,9 (2):259-267.
[5]Otsu N. A threshold selection method from gray-level histograms. IEEE Trans on System Man and Cybernetics.1979,9 (1):62-66.
[6]Kittler J, Illingworth J. Minimum error thresholding. Pattern Recognition.1986,19 (1):41-47.
[7]Kapur J N, Sahoo P K, Wong A. A new method for gray-level picture thresholding using the entropy of the histogram. Computer Vision Graphicand Image Processing.1985,29 (3):273-285.
[8]Morimoto N, Arita M, Suyama A. Solid phase DNA solution to the Hamiltonian path problem. Proceedings of 3rd Annual DIMACS Meeting for DNA Computers, Philadelphia, PA, USA,1997: 193-206.
[9]Davis L S. A survey of edge detection techniques. Computer Graphics and Image Processing. 1975,4 (3):248-270.
[10]Canny J. A computational approach to edge detection. IEEE Transactions on Pattern Analysis and Machine Intelligence.1986, PAMI-8 (6):679-698.
[11]Marr D, Hildreth E. Theory of edge detection. Proceedings of the Royal Society of London. 1980,207(1167):187-217.
[12]Chassery J M, Garbay C. An iterative segmentation method based on a contextual color and shape criterion. IEEE Transactions on Pattern Analysis and Machine Intelligence.1984, PAMI-6 (6): 794-800.
[13]Horowitz S L, Pavlidis T. Picture segmentation by a tree traversal algorithm. Journal of the ACM (JACM).1976,23 (2):368-388.
[14]Agam G, Armato III S G, Wu C. Vessel tree reconstruction in thoracic CT scans with application to nodule detection. IEEE Transactions on Medical Imaging.2005,24 (4):486-499.
[15]Amini L, Soltanian-Zadeh H, Lucas C et al. Automatic segmentation of thalamus from brain MRI integrating fuzzy clustering and dynamic contours. IEEE Transactions on Biomedical Engineering.2004,51 (5):800-811.
[16]Rodriguez R, Alarcon T E, Pacheco O. A new strategy to obtain robust markers for blood vessels segmentation by using the watersheds method. Computers in Biology and Medicine.2005, 35 (8):665-686.
[17]毛安定.基于小波变换的图像分割技术：(硕士).昆明：昆明理工大学,2009.
[18]Bezdek J C, Ehrlich R, Full W. FCM:the fuzzy c-means clustering algorithm. Computers & Geosciences,1984,10 (3):191-203.
[19]Lie J, Lysaker M, Tai X. A binary level set model and some applications to Mum ford-Shah image segmentation. IEEE Transactions on Image Processing.2006,15 (5):1171-1181.
[20]Tsai A, Yezzi Jr A, Willsky A S. A curve evolution approach to smoothing and segmentation using the Mumford-Shah functional. Proceedings IEEE Conference on Computer Vision and Pattern Recognition, Los Alamitos, CA, USA,2000:119-124.
[21]Shah S, Baza A A, Ross A et al. Automatic tooth segmentation using active contour without edges. Special Session on Research at the Biometric Consortium Conference, Baltimore, MD, United states,2006:1-6.
[22]Tsai A, Yezzi Jr A, Willsky A S. Curve evolution implementation of the Mumford-Shah functional for image segmentation, denoising, interpolation, and magnification. IEEE Transactions on Image Processing.2001,10 (8):1169-1186.
[23]Paragios N. Geodesic active contours and level sets for the detection and tracking of moving objects. IEEE Transactions on Pattern Analysis and Machine Intelligence.2000,22 (3):266-280.
[24]Osher S, Fedkiw R P. Level set methods and dynamic implicit surfaces. Berlin,Germany: Springer Verlag,2003.
[25]Li C, Kao C, Gore J C et al. Minimization of region-scalable fitting energy for image segmentation. IEEE Transactions on Image Processing.2008,17(10):1940-1949.
[26]Mumford D, Shah J. Optimal approximations by piecewise smooth functions and associated variational problems. Communications on Pure and Applied Mathematics.1989,42 (5):577-685.
[27]Kulkarni S, Chatterji B N. Accurate shape modeling with front propagation using adaptive level sets. Pattern Recognition Letters.2002,23 (13):1559-1568.
[28]Zhu G, Zhang S, Zeng Q et al. Boundary-based image segmentation using binary level set method. Optical Engineering.2007,46 (5):50501-50503.
[29]Chunming L, Chiu-Yen K, Gore J C et al. Implicit active contours driven by local binary fitting energy. IEEE Conference on Computer Vision and Pattern Recognition, Piscataway, NJ, USA,2007: 339-445.
[30]Shi Y, Karl W C. Real-time tracking using level sets.2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, San Diego, CA, United states,2005:34-41.
[31]Kass M, Witkin A, Terzopoulos D. Snakes:Active contour models. International Journal of Computer Vision.1988,1 (4):321-331.
[32]Siddiqi K, Lauziere Y B, Tannenbaum A et al. Area and length minimizing flows for shape segmentation. IEEE Transactions on Image Processing.1998,7 (3):433-443.
[33]Cohen L D. On active contour models and balloons. Image Understanding.1991,53 (2): 211-218.
[34]Xu C, Prince J L. Snakes, shapes, and gradient vector flow. IEEE Transactions on Image Processing.1998,7 (3):359-369.
[35]Zeyun Y, Bajaj C. Image segmentation using gradient vector diffusion and region merging. Proceedings of 16th International Conference on Pattern Recognition, Los Alamitos, CA, USA,2002: 941-944.
[36]Adalsteinsson D, Sethian J A. A fast level set method for propagating interfaces. Journal of Computational Physics.1995,118 (2):269-270.
[37]Sussman M, Smereka P, Osher S. A level set approach for computing solutions to incompressible two-phase flow. Journal of Computational Physics.1994,114 (1):146-159.
[38]Peng D, Merriman B, Osher S et al. A PDE-based fast local level set method. Journal of Computational Physics.1999,155 (2):410-438.
[39]Li C, Xu C, Gui C et al. Level set evolution without re-initialization:A new variational formulation.2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Los Alamitos, CA, USA,2005:430-436.
[40]张运平,王美清.边缘强化的无需重新初始化的水平集分割模型.福州大学学报(自然科学版).2009,37(6)：798-802.
[41]王峥,杨新,李俊等.提高水平集方法初始化计算速度的研究.信号处理.2002,18(2)：97-101.
[42]田巧玉,黄水波,何传江.无需重新初始化的自适应快速水平集演化模型.计算机工程与应用.2010,46(18)：174-176,208.
[43]张丽飞,杨鸿波,邹谋炎.一种新的水平截集函数初始化和重新初始化方法——距离函数光滑法.计算机工程与应用.2003,39(10)：26-32.
[44]刘涛,张大龙,周秦武等.一种新颖的快速水平集初始化方法.中国图象图形学报.2010,15(5)：775-781.
[45]周则明,陈强,王平安等.基于窄带水平集的曲线演化与左心室MRI图像分割.计算机工程与应用.2003,(27)：46-48.
[46]周则明,项杰,王洪元等.水平集方法中窄带构造技术.系统工程与电子技术.2007,29(7)：1201-1204.
[47]于洪川,王德军,唐泽圣等.水平集演化中的奇点与改进的窄带算法.软件学报.2003,14(4)：811-817.
[48]李传龙,李颖,兰国新.一种新的窄带快速区域水平集C-V模型图像分割方法.计算机科学.2011,38(12)：17-19,35.
[49]原野,何传江.LBF活动轮廓模型的改进.计算机工程与应用.2009,45(15)：177-179,228.
[50]曹广真,金亚秋.基于水平集方法的多源遥感数据融合及城区道路提取.电子与信息学报.2007,29(6)：1464-1470.
[51]Heydarian M, Noseworthy M D, Kamath M V et al. Optimizing the level set algorithm for detecting object edges in MR and CT images. IEEE Transactions on Nuclear Science.2009,56 (1): 156-166.
[52]Wang Y, Wang C. Genetic algorithm for integral-level set global optimization. Journal of Changsha University of Electric Power (Natural Science Edition).2004,19 (3):8-11.
[53]Wang G, Zhang M, Tian X et al. Unsupervised change detection for remote sensing images using multiscale decomposition and treelet fusion:A level set approach.6th International Conference on Radar, Chengdu, China,2011:1558-1561.
[54]Marques R C P, Medeiros F N, Santos Nobre J. SAR image segmentation based on level set approach and GA model. IEEE Transactions on Pattern Analysis and Machine Intelligence.2012,34 (10):2046-2057.
[55]赵莹,张学东.改进水平集的车辆检测算法.辽宁科技大学学报.2010,33(5)：485-489.
[56]赵璐,于慧敏.基于先验形状信息和水平集方法的车辆检测.浙江大学学报(工学版).2010,44(1)：124-130.
[57]杨剑,田昊,李国辉.多先验形状模型变分水平集建筑物检测.科学技术与工程.2010,10(4)：914-921.
[58]田昊,杨剑,汪彦明等.基于先验形状约束水平集模型的建筑物提取方法.自动化学报.2010,36(11)：1502-1511.
[59]劳丽,吴效明,朱学峰.模糊集理论在图像分割中的应用综述.中国体视学与图像分析.2006,11(3)：200-205.
[60]Moradi G, Shamsi M, Sedaaghi M H et al. Segmentation of pomegranate MR images using spatial fuzzy c-means (SFCM) algorithm. International Conference on Graphic and Image Processing, Cairo, Egypt,2011:22-24.
[61]Ozdemir D, Akarun L. A fuzzy algorithm for color quantization of images. Pattern Recognition. 2002,35(8):1785-1791.
[62]Miin-Shen Y, Kuo-Lung W, Jian Y. A novel fuzzy clustering algorithm.2003 Computational Intelligence in Robotics and Automation, Kobe, Japan,2003:647-652.
[63]Dave R N, Bhaswan K. Adaptive fuzzy c-shells clustering and detection of ellipses. IEEE Transactions on Neural Networks.1992,3 (5):643-662.
[64]Lin J S. Fuzzy clustering using a compensated fuzzy Hopfield network. Neural Processing Letters.1999,10 (1):35-48.
[65]Gustafson D E, Kessel W C. Fuzzy clustering with a fuzzy covariance matrix. Proc IEEE Conf Decis Control Incl Symp Adapt Processes 17th, San Diego, CA, USA,1978:761-766.
[66]Kaymak U, Setnes M. Fuzzy clustering with volume prototypes and adaptive cluster merging. IEEE Transactions on Fuzzy Systems.2002,10 (6):705-712.
[67]Hathaway R J, Bezdek J C, Hu Y. Generalized fuzzy c-means clustering strategies using Lp norm distances. IEEE Transactions on Fuzzy Systems.2000,8 (5):576-582.
[68]Yang M S. On a class of fuzzy classification maximum likelihood procedures. Fuzzy Sets and Systems.1993,57 (3):365-375.
[69]Menard M, Courboulay V, Dardignac P A. Possibilistic and probabilistic fuzzy clustering: Unification within the framework of the non-extensive thermostatistics. Pattern Recognition.2003, 36 (6):1325-1342.
[70]Krishnapuram R, Nasraoui O, Frigui H. The fuzzy c-spherical shells algorithm:A new approach. IEEE Transactions on Neural Networks.1992,3 (5):663-671.
[71]Krishnapuram R, Keller J M. A possibilistic approach to clustering. IEEE Transactions on Fuzzy Systems.1993,1 (2):98-110.
[72]Karayiannis N B. Generalized fuzzy c-means algorithms. Proceedings of the Fifth IEEE International Conference on Fuzzy Systems, New Orleans, LA, USA,1996:1036-1042.
[73]Zhang J S, Leung Y W. Improved possibilistic c-means clustering algorithms. IEEE Transactions on Fuzzy Systems.2004,12 (2):209-217.
[74]Krishnapuram R, Keller J M. The possibilistic c-means algorithm:insights and recommendations. IEEE Transactions on Fuzzy Systems.1996,4 (3):385-393.
[75]Liu S H, Lin J S. Vector quantization in DCT domain using fuzzy possibilistic c-means based on penalized and compensated constraints. Pattern Recognition.2002,35 (10):2201-2211.
[76]Schneider A. Weighted possibilistic c-means clustering algorithms. Ninth IEEE International Conference on Fuzzy Systems, San Antonio, TX, USA,2000:176-180.
[77]劳丽,吴效明,朱学峰.模糊集理论在图像分割中的应用综述.中国体视学与图像分析.2006,11(3)：200-205.
[78]吴林,郭大勇,施克仁等.改进的FCM在人脑MR图像分割中的应用.清华大学学报：自然科学版.2004,44(2)：157-159.
[79]杨勇,黄波,王桥等.结合图像灰度信息和空间信息的有意义区域分割.电子学报.2003,31(2)：252-254.
[80]陈文熙,冯钟葵.基于模糊聚类的遥感图像与现有地形图的变化检测方法.遥感信息.2009,(5)：56-60.
[81]邹刚,孙即祥,敖永红.粒子群模糊聚类方法在病理图像分类中的应用.计算机工程与设计.2009,30(22)：5155-5157,5161.
[82]王雷,叶秀芬,王天.模糊聚类的侧扫声纳图像分割算法.华中科技大学学报(自然科学版).40(9)：25-29.
[83]王曙燕,周明全,耿国华.模糊聚类分析在乳腺癌图像分类中的应用.计算机应用与软件.2006,23(10)：103-104,138.
[84]Osher S, Sethian J A. Fronts propagating with curvature-dependent speed:algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics.1988,79 (1):12-49.
[85]Chan T F, Vese L A. Active contours without edges. IEEE Transactions on Image Processing. 2001,10 (2):266-277.
[86]Mumford D, Shah J. Optimal approximations by piecewise smooth functions and associated variational problems. Communications on Pure and Applied Mathematics.1989,42 (5):577-685.
[87]Caselles V, Kimmel R, Sapiro G. Geodesic active contours. International Journal of Computer Vision.1997,22(1):61-79.
[88]Min L, Li X, Tang Y. Improved C-V model without re-initialization. Guangdian Gongcheng/Opto-Electronic Engineering.2006,33 (9):52-58.
[89]瞿继双,王超,王正志.一种基于多闽值的形态学提取遥感图象海岸线特征方法.中国图象图形学报A辑.2003,8(7)：805-809.
[90]荆浩,陈学佺,顾志伟.一种基于边缘特征的海岸线检测方法.计算机仿真.2006,23(8)：89-93,101.
[91]谢明鸿,张亚飞,付琨.基于种子点增长的SAR图像海岸线提取算法.电脑开发与应用.2006,19(6)：2-3,6.
[92]张永继,闫冬梅,曾峦等.基于邻域相关信息的海岸线提取方法.装备指挥技术学院学报.2005,16(6)：88-92.
[93]Malladi R, Sethian J A, Vemuri B C. Shape modeling with front propagation: a level set approach. IEEE Transactions on Pattern Analysis and Machine Intelligence.1995,17 (2):158-175.
[94]于洪川,王德军,唐泽圣等.水平集演化中的奇点与改进的窄带算法.软件学报.2003,14(4)：811-817.
[95]王岳环,王鼎,周晓玮等.基于Mumford-Shah模型的局部水平集分割窄带算法.华中科技大学学报(自然科学版).2008,36(3)：88-91.
[96]http://ds.rsgs.ac.cn/index.aspx
[97]Adalsteinsson D, Sethian J A. The fast construction of extension velocities in level set methods. Journal of Computational Physics.1999,148 (1):2-22.
[98]Chan T F, Vese L A. Active contours without edges. IEEE Transactions on Image Processing. 2001,10 (2):266-277.
[99]李俊,杨新.图像偏微分方程的原理与应用.上海：上海交通大学出版,2003.
[100]Xu C, Yezzi Jr A, Prince J L. On the relationship between parametric and geometric active contours.34th Asilomar Conference, Pacific Grove, CA, United states,2000:483-489.
[101]Perona P, Malik J. Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence.1990,12 (7):629-639.
[102]肖亮,吴慧中,韦志辉等.图像分割中分段光滑Mumford-Shah模型的水平集算法.计算机研究与发展.2004,41(1)：129-135.
[103]工文杰,封建湖.基于变分Level Set方法的图像分割.计算机工程与应用.2006,42(18)：68-70.
[104]Wang X F, Huang D S, Xu H. An efficient local Chan - Vese model for image segmentation. Pattern Recognition.2010,43 (3):603-618.
[105]王琪,丁辉,张伟等.利用分区处理和水平集算法分割序列三维乳腺MRI.清华大学学报(自然科学版).2009,49(03)：419-423.
[106]Vese L A, Chan T F. A multiphase level set framework for image segmentation using the Mumford and Shah model. International Journal of Computer Vision.2002,50 (3):271-293.
[107]Zhang K, Song H, Zhang L. Active contours driven by local image fitting energy. Pattern Recognition.2010,43 (4):1199-1206.
[108]孙开琼,江少锋,陈震.方向性局部区域活动轮廓血管分割.南昌航空大学学报(自然科学
版).2011,25(4)：9-13,28.
[109]Shi Y, Karl W C. Real-time tracking using level sets.2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, San Diego, CA, United states,2005: 34-41.
[110]李慧芳,沈焕锋,张良培等.一种基于变分Retinex的遥感影像不均匀性校正方法.测绘学报.2010,39(6)：585-591,598.
[111]王斌,高新波.基于水平集接力的图像自动分割方法.软件学报.2009,20(5)：1185-1193.
[112]顾丹丹,汪西莉.结合区域生长和水平集的遥感影像道路提取.计算机应用.2010,30 (2)：433-436,440.
[113]危自福,毕笃彦,马时平.一种改进的快速C-V水平集红外图像分割.数据采集与处理.2010,25(3)：347-352.
[114]徐玲凌,肖进胜,易本顺等.改进的C-V水平集模型图像分割算法.计算机工程.2009,38(10)：209-210.
[115]王明泉,梁君婷,冯晓夏.基于改进水平集的医学图像分割.中国科技论文在线.2011,06(1)：71-75.
[116]王兴梅,印桂生,门志国等.基于水平集改进的水下目标轮廓提取方法.哈尔滨工业大学学报.2010,46(04)：660-664.
[117]Paragios N, Deriche R. Geodesic active regions and level set methods for supervised texture segmentation. International Journal of Computer Vision.2002,46 (3):223-247.
[118]Parzen E. On estimation of a probability density function and mode. The Annals of Mathematical Statistics.1962,33 (3):1065-1076.
[119]Li J, Yang X, Shi P. Fast level set approach to image segmentation based on Mumford-Shah model. Jisuanji Xuebao/Chinese Journal of Computers.2002,25 (11):1175-1183.
[120]Keller J M, Chen S, Crownover R M. Texture description and segmentation through fractal geometry. Computer Vision Graphics and Image Processing.1989,45 (2):150-166.
[121]伍忠东,高新波,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(自然科学版).2004,31(4)：533-537.
[122]张莉,周伟达,焦李成.核聚类算法.计算机学报.2002,25(6)：587-590.
[123]Lzaro J, Arias J, Martn J L et al. Implementation of a modified Fuzzy C-Means clustering algorithm for real-time applications. Microprocessors and Microsystems.2005,29 (8-9):375-380.
[124]Chen S, Zhang D. Robust image segmentation using FCM with spatial constraints based on new kernel-induced distance measure. IEEE Transactions on Systems Man and Cybernetics.2004, 34(4):1907-1916.
[125]Bezdek J C, Hathaway R J, Sabin M J et al. Convergence theory for fuzzy c-means: Counterexamples and repairs. IEEE Transactions on Systems Man and Cybernetics.1987,17 (5): 873-877.
[126]Bezdek J C. Pattern recognition with fuzzy objective function algorithms. Netherlands:Kluwer Academic Publishers,1981.
[127]Lee J S, Jurkevich I. Coastline detection and tracing in SAR images. IEEE Transactions on Geoscience and Remote Sensing.1990,28 (4):662-668.
[128]Lee J S, Jurkevich I. Unsupervised Coastline Detection And Tracing In Sar Images. IGARSS'89-Twelfth Canadian Symposium on Remote Sensing, Vancouver, BC, Can,1989: 2611-2614.
[129]瞿继双,王超,王正志.一种基于多阈值的形态学提取遥感图象海岸线特征方法.中国图象图形学报A辑.2003,8(7)：805-809.
[130]荆浩,陈学佺,顾志伟.一种基于边缘特征的海岸线检测方法.计算机仿真.2006,23(8)：89-93,101.
[131]谢明鸿,张亚飞,付琨.基于种子点增长的SAR图像海岸线自动提取算法.中国科学院研究生院学报.2007,24(1)：93-98.
[132]张永继,闫冬梅,曾峦等.基于邻域相关信息的海岸线提取方法.装备指挥技术学院学报.2005,16(6)：88-92.
[133]欧阳越,种劲松.基于改进水平截集算法的SAR图像海岸线检测.遥感技术与应用.2004,19(6)：456-460.
[134]Yeung D S, Wang X Z. Improving performance of similarity-based clustering by feature weight learning. IEEE Transactions on Pattern Analysis and Machine Intelligence.2002,24 (4): 556-561.
[135]董旭,魏振军.一种加权欧氏距离聚类方法.信息工程大学学报.2005,6(1)：23-25.
[136]李爱国.一种基于属性加权模糊聚类算法.常熟理工学院学报.2007,21(8)：104-107.
[137]陈新泉.特征加权的模糊C聚类算法.计算机工程与设计.2007,28(22)：5329-5333.
[138]Scholkopf B, Mika S, Burges C J C et al. Input space versus feature space in kernel-based methods. IEEE Transactions on Neural Networks.1999,10 (5):1000-1017.
[139]Bezdek J C, Keller J M, Krishnapuram R et al. Will the real iris data please stand up. IEEE Transactions on Fuzzy Systems.1999,7 (3):368-369.
[140]杨晓波.复杂纹理图像的分割：(博士).秦皇岛：燕山大学,2004.
[141]Chaudhuri B B, Sarkar N. Texture segmentation using fractal dimension. IEEE Transactions on Pattern Analysis and Machine Intelligence.1995,17 (1):72-77.
[142]Peleg S, Naor J, Hartley R et al. Multiple resolution texture analysis and classification. IEEE Transactions on Pattern Analysis and Machine Intelligence.1984, PAMI-6 (4):518-523.
[143]Chaudhuri B B, Sarkar N, Kundu P. Improved fractal geometry based texture segmentation technique. IEEE Proceedings:Computers and Digital Techniques, NJ,USA,1993:233-241.
[144]Pentland A P. Fractal-based description of natural scenes. IEEE Transactions on Pattern Analysis and Machine Intelligence.1984, (6):661-674.
[145]Fortin C S, Kumaresan R, Ohley W J et al. Fractal dimension in the analysis of medical images. IEEE Engineering in Medicine and Biology Magazine.1992,11 (2):65-71.
[146]刘明芹,张晓光.差分盒维法在焊缝边缘检测上的应用研究.河北工业科技.2009,26(5)：300-302.
[147]杨词银,许枫.一种抗噪分形维计算方法及其在声纳图像识别中的应用.应用声学.2008,27(2)：95-101.
[148]陈廷,张维龙,吴丽莉.分形维数在原棉异纤图像处理中的应用.测试技术学报.2009,23(3)：248-252.
[149]孙晓妍,董槐林,王备战等.遥感图像中船只目标区域的分割方法.计算机工程.2008,34(10)：196-198.
[150]张小京,孙万蓉,乔静.基于分形维数的白细胞图像特征提取研究.计算机工程与设计.2009,30(4)：941-943.
[151]Yu L, Zhang D, Wang K et al. Coarse iris classification using box-counting to estimate fractal dimensions. Pattern Recognition.2005,38 (11):1791-1798.
[152]张涛,孙林,黄爱民.图像分形维数的差分盒方法的改进研究.电光与控制.2007,14(5)：55-57.
[153]刘松涛.用盒子维评估红外烟幕对舰船目标的遮蔽效果.光电工程.2009,36(2)：34-38.
[154]刘明芹,张晓光.一种计算图像分形维数的有效方法.西安科技大学学报.2009,29(3)：369-373.
[155]Li J, Du Q, Sun C. An improved box-counting method for image fractal dimension estimation. Pattern Recognition.2009,42 (11):2460-2469.
[156]Sarkar N, Chaudhuri B B. An efficient differential box-counting approach to compute fractal dimension of image. IEEE Transactions on Systems Man and Cybernetics.1994,24 (1):115-120.
[157]Sarkar N, Chaudhuri B B. An efficient approach to estimate fractal dimension of textural images. Pattern Recognition.1992,25 (9):1035-1041.
[158]王顺凤,阮晶,王宇.基于改进的LBF模型的图像分割.计算机应用与软件.2011,28(2)：25-27,33.
[159]Rosenberger C, Chehdi K. Unsupervised clustering method with optimal estimation of the number of clusters:Application to image segmentation. Proceedings 15th International Conference on Pattern Recognition, Barcelona, Spain,2000:656-659.
[160]Yuan H, Khorram S, Dai X L. Applications of simulated annealing minimization technique to unsupervised classification of remotely sensed data. IEEE 1999 International Geoscience and Remote Sensing Symposium, Hamburg, Germany,1999:134-136.
[2]李弼程,彭天强,彭波.智能图像处理技术.北京：电子工业出版社,2004.
[3]Lee S U, Yoon Chung S, Park R H. A comparative performance study of several global thresholding techniques for segmentation. Computer Vision Graphics and Image Processing,1990, 52(2):171-190.
[4]Doyle W. Operations useful for similarity-invariant pattern recognition. Journal of the ACM (JACM).1962,9 (2):259-267.
[5]Otsu N. A threshold selection method from gray-level histograms. IEEE Trans on System Man and Cybernetics.1979,9 (1):62-66.
[6]Kittler J, Illingworth J. Minimum error thresholding. Pattern Recognition.1986,19 (1):41-47.
[7]Kapur J N, Sahoo P K, Wong A. A new method for gray-level picture thresholding using the entropy of the histogram. Computer Vision Graphicand Image Processing.1985,29 (3):273-285.
[8]Morimoto N, Arita M, Suyama A. Solid phase DNA solution to the Hamiltonian path problem. Proceedings of 3rd Annual DIMACS Meeting for DNA Computers, Philadelphia, PA, USA,1997: 193-206.
[9]Davis L S. A survey of edge detection techniques. Computer Graphics and Image Processing. 1975,4 (3):248-270.
[10]Canny J. A computational approach to edge detection. IEEE Transactions on Pattern Analysis and Machine Intelligence.1986, PAMI-8 (6):679-698.
[11]Marr D, Hildreth E. Theory of edge detection. Proceedings of the Royal Society of London. 1980,207(1167):187-217.
[12]Chassery J M, Garbay C. An iterative segmentation method based on a contextual color and shape criterion. IEEE Transactions on Pattern Analysis and Machine Intelligence.1984, PAMI-6 (6): 794-800.
[13]Horowitz S L, Pavlidis T. Picture segmentation by a tree traversal algorithm. Journal of the ACM (JACM).1976,23 (2):368-388.
[14]Agam G, Armato III S G, Wu C. Vessel tree reconstruction in thoracic CT scans with application to nodule detection. IEEE Transactions on Medical Imaging.2005,24 (4):486-499.
[15]Amini L, Soltanian-Zadeh H, Lucas C et al. Automatic segmentation of thalamus from brain MRI integrating fuzzy clustering and dynamic contours. IEEE Transactions on Biomedical Engineering.2004,51 (5):800-811.
[16]Rodriguez R, Alarcon T E, Pacheco O. A new strategy to obtain robust markers for blood vessels segmentation by using the watersheds method. Computers in Biology and Medicine.2005, 35 (8):665-686.
[17]毛安定.基于小波变换的图像分割技术：(硕士).昆明：昆明理工大学,2009.
[18]Bezdek J C, Ehrlich R, Full W. FCM:the fuzzy c-means clustering algorithm. Computers & Geosciences,1984,10 (3):191-203.
[19]Lie J, Lysaker M, Tai X. A binary level set model and some applications to Mum ford-Shah image segmentation. IEEE Transactions on Image Processing.2006,15 (5):1171-1181.
[20]Tsai A, Yezzi Jr A, Willsky A S. A curve evolution approach to smoothing and segmentation using the Mumford-Shah functional. Proceedings IEEE Conference on Computer Vision and Pattern Recognition, Los Alamitos, CA, USA,2000:119-124.
[21]Shah S, Baza A A, Ross A et al. Automatic tooth segmentation using active contour without edges. Special Session on Research at the Biometric Consortium Conference, Baltimore, MD, United states,2006:1-6.
[22]Tsai A, Yezzi Jr A, Willsky A S. Curve evolution implementation of the Mumford-Shah functional for image segmentation, denoising, interpolation, and magnification. IEEE Transactions on Image Processing.2001,10 (8):1169-1186.
[23]Paragios N. Geodesic active contours and level sets for the detection and tracking of moving objects. IEEE Transactions on Pattern Analysis and Machine Intelligence.2000,22 (3):266-280.
[24]Osher S, Fedkiw R P. Level set methods and dynamic implicit surfaces. Berlin,Germany: Springer Verlag,2003.
[25]Li C, Kao C, Gore J C et al. Minimization of region-scalable fitting energy for image segmentation. IEEE Transactions on Image Processing.2008,17(10):1940-1949.
[26]Mumford D, Shah J. Optimal approximations by piecewise smooth functions and associated variational problems. Communications on Pure and Applied Mathematics.1989,42 (5):577-685.
[27]Kulkarni S, Chatterji B N. Accurate shape modeling with front propagation using adaptive level sets. Pattern Recognition Letters.2002,23 (13):1559-1568.
[28]Zhu G, Zhang S, Zeng Q et al. Boundary-based image segmentation using binary level set method. Optical Engineering.2007,46 (5):50501-50503.
[29]Chunming L, Chiu-Yen K, Gore J C et al. Implicit active contours driven by local binary fitting energy. IEEE Conference on Computer Vision and Pattern Recognition, Piscataway, NJ, USA,2007: 339-445.
[30]Shi Y, Karl W C. Real-time tracking using level sets.2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, San Diego, CA, United states,2005:34-41.
[31]Kass M, Witkin A, Terzopoulos D. Snakes:Active contour models. International Journal of Computer Vision.1988,1 (4):321-331.
[32]Siddiqi K, Lauziere Y B, Tannenbaum A et al. Area and length minimizing flows for shape segmentation. IEEE Transactions on Image Processing.1998,7 (3):433-443.
[33]Cohen L D. On active contour models and balloons. Image Understanding.1991,53 (2): 211-218.
[34]Xu C, Prince J L. Snakes, shapes, and gradient vector flow. IEEE Transactions on Image Processing.1998,7 (3):359-369.
[35]Zeyun Y, Bajaj C. Image segmentation using gradient vector diffusion and region merging. Proceedings of 16th International Conference on Pattern Recognition, Los Alamitos, CA, USA,2002: 941-944.
[36]Adalsteinsson D, Sethian J A. A fast level set method for propagating interfaces. Journal of Computational Physics.1995,118 (2):269-270.
[37]Sussman M, Smereka P, Osher S. A level set approach for computing solutions to incompressible two-phase flow. Journal of Computational Physics.1994,114 (1):146-159.
[38]Peng D, Merriman B, Osher S et al. A PDE-based fast local level set method. Journal of Computational Physics.1999,155 (2):410-438.
[39]Li C, Xu C, Gui C et al. Level set evolution without re-initialization:A new variational formulation.2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Los Alamitos, CA, USA,2005:430-436.
[40]张运平,王美清.边缘强化的无需重新初始化的水平集分割模型.福州大学学报(自然科学版).2009,37(6)：798-802.
[41]王峥,杨新,李俊等.提高水平集方法初始化计算速度的研究.信号处理.2002,18(2)：97-101.
[42]田巧玉,黄水波,何传江.无需重新初始化的自适应快速水平集演化模型.计算机工程与应用.2010,46(18)：174-176,208.
[43]张丽飞,杨鸿波,邹谋炎.一种新的水平截集函数初始化和重新初始化方法——距离函数光滑法.计算机工程与应用.2003,39(10)：26-32.
[44]刘涛,张大龙,周秦武等.一种新颖的快速水平集初始化方法.中国图象图形学报.2010,15(5)：775-781.
[45]周则明,陈强,王平安等.基于窄带水平集的曲线演化与左心室MRI图像分割.计算机工程与应用.2003,(27)：46-48.
[46]周则明,项杰,王洪元等.水平集方法中窄带构造技术.系统工程与电子技术.2007,29(7)：1201-1204.
[47]于洪川,王德军,唐泽圣等.水平集演化中的奇点与改进的窄带算法.软件学报.2003,14(4)：811-817.
[48]李传龙,李颖,兰国新.一种新的窄带快速区域水平集C-V模型图像分割方法.计算机科学.2011,38(12)：17-19,35.
[49]原野,何传江.LBF活动轮廓模型的改进.计算机工程与应用.2009,45(15)：177-179,228.
[50]曹广真,金亚秋.基于水平集方法的多源遥感数据融合及城区道路提取.电子与信息学报.2007,29(6)：1464-1470.
[51]Heydarian M, Noseworthy M D, Kamath M V et al. Optimizing the level set algorithm for detecting object edges in MR and CT images. IEEE Transactions on Nuclear Science.2009,56 (1): 156-166.
[52]Wang Y, Wang C. Genetic algorithm for integral-level set global optimization. Journal of Changsha University of Electric Power (Natural Science Edition).2004,19 (3):8-11.
[53]Wang G, Zhang M, Tian X et al. Unsupervised change detection for remote sensing images using multiscale decomposition and treelet fusion:A level set approach.6th International Conference on Radar, Chengdu, China,2011:1558-1561.
[54]Marques R C P, Medeiros F N, Santos Nobre J. SAR image segmentation based on level set approach and GA model. IEEE Transactions on Pattern Analysis and Machine Intelligence.2012,34 (10):2046-2057.
[55]赵莹,张学东.改进水平集的车辆检测算法.辽宁科技大学学报.2010,33(5)：485-489.
[56]赵璐,于慧敏.基于先验形状信息和水平集方法的车辆检测.浙江大学学报(工学版).2010,44(1)：124-130.
[57]杨剑,田昊,李国辉.多先验形状模型变分水平集建筑物检测.科学技术与工程.2010,10(4)：914-921.
[58]田昊,杨剑,汪彦明等.基于先验形状约束水平集模型的建筑物提取方法.自动化学报.2010,36(11)：1502-1511.
[59]劳丽,吴效明,朱学峰.模糊集理论在图像分割中的应用综述.中国体视学与图像分析.2006,11(3)：200-205.
[60]Moradi G, Shamsi M, Sedaaghi M H et al. Segmentation of pomegranate MR images using spatial fuzzy c-means (SFCM) algorithm. International Conference on Graphic and Image Processing, Cairo, Egypt,2011:22-24.
[61]Ozdemir D, Akarun L. A fuzzy algorithm for color quantization of images. Pattern Recognition. 2002,35(8):1785-1791.
[62]Miin-Shen Y, Kuo-Lung W, Jian Y. A novel fuzzy clustering algorithm.2003 Computational Intelligence in Robotics and Automation, Kobe, Japan,2003:647-652.
[63]Dave R N, Bhaswan K. Adaptive fuzzy c-shells clustering and detection of ellipses. IEEE Transactions on Neural Networks.1992,3 (5):643-662.
[64]Lin J S. Fuzzy clustering using a compensated fuzzy Hopfield network. Neural Processing Letters.1999,10 (1):35-48.
[65]Gustafson D E, Kessel W C. Fuzzy clustering with a fuzzy covariance matrix. Proc IEEE Conf Decis Control Incl Symp Adapt Processes 17th, San Diego, CA, USA,1978:761-766.
[66]Kaymak U, Setnes M. Fuzzy clustering with volume prototypes and adaptive cluster merging. IEEE Transactions on Fuzzy Systems.2002,10 (6):705-712.
[67]Hathaway R J, Bezdek J C, Hu Y. Generalized fuzzy c-means clustering strategies using Lp norm distances. IEEE Transactions on Fuzzy Systems.2000,8 (5):576-582.
[68]Yang M S. On a class of fuzzy classification maximum likelihood procedures. Fuzzy Sets and Systems.1993,57 (3):365-375.
[69]Menard M, Courboulay V, Dardignac P A. Possibilistic and probabilistic fuzzy clustering: Unification within the framework of the non-extensive thermostatistics. Pattern Recognition.2003, 36 (6):1325-1342.
[70]Krishnapuram R, Nasraoui O, Frigui H. The fuzzy c-spherical shells algorithm:A new approach. IEEE Transactions on Neural Networks.1992,3 (5):663-671.
[71]Krishnapuram R, Keller J M. A possibilistic approach to clustering. IEEE Transactions on Fuzzy Systems.1993,1 (2):98-110.
[72]Karayiannis N B. Generalized fuzzy c-means algorithms. Proceedings of the Fifth IEEE International Conference on Fuzzy Systems, New Orleans, LA, USA,1996:1036-1042.
[73]Zhang J S, Leung Y W. Improved possibilistic c-means clustering algorithms. IEEE Transactions on Fuzzy Systems.2004,12 (2):209-217.
[74]Krishnapuram R, Keller J M. The possibilistic c-means algorithm:insights and recommendations. IEEE Transactions on Fuzzy Systems.1996,4 (3):385-393.
[75]Liu S H, Lin J S. Vector quantization in DCT domain using fuzzy possibilistic c-means based on penalized and compensated constraints. Pattern Recognition.2002,35 (10):2201-2211.
[76]Schneider A. Weighted possibilistic c-means clustering algorithms. Ninth IEEE International Conference on Fuzzy Systems, San Antonio, TX, USA,2000:176-180.
[77]劳丽,吴效明,朱学峰.模糊集理论在图像分割中的应用综述.中国体视学与图像分析.2006,11(3)：200-205.
[78]吴林,郭大勇,施克仁等.改进的FCM在人脑MR图像分割中的应用.清华大学学报：自然科学版.2004,44(2)：157-159.
[79]杨勇,黄波,王桥等.结合图像灰度信息和空间信息的有意义区域分割.电子学报.2003,31(2)：252-254.
[80]陈文熙,冯钟葵.基于模糊聚类的遥感图像与现有地形图的变化检测方法.遥感信息.2009,(5)：56-60.
[81]邹刚,孙即祥,敖永红.粒子群模糊聚类方法在病理图像分类中的应用.计算机工程与设计.2009,30(22)：5155-5157,5161.
[82]王雷,叶秀芬,王天.模糊聚类的侧扫声纳图像分割算法.华中科技大学学报(自然科学版).40(9)：25-29.
[83]王曙燕,周明全,耿国华.模糊聚类分析在乳腺癌图像分类中的应用.计算机应用与软件.2006,23(10)：103-104,138.
[84]Osher S, Sethian J A. Fronts propagating with curvature-dependent speed:algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics.1988,79 (1):12-49.
[85]Chan T F, Vese L A. Active contours without edges. IEEE Transactions on Image Processing. 2001,10 (2):266-277.
[86]Mumford D, Shah J. Optimal approximations by piecewise smooth functions and associated variational problems. Communications on Pure and Applied Mathematics.1989,42 (5):577-685.
[87]Caselles V, Kimmel R, Sapiro G. Geodesic active contours. International Journal of Computer Vision.1997,22(1):61-79.
[88]Min L, Li X, Tang Y. Improved C-V model without re-initialization. Guangdian Gongcheng/Opto-Electronic Engineering.2006,33 (9):52-58.
[89]瞿继双,王超,王正志.一种基于多闽值的形态学提取遥感图象海岸线特征方法.中国图象图形学报A辑.2003,8(7)：805-809.
[90]荆浩,陈学佺,顾志伟.一种基于边缘特征的海岸线检测方法.计算机仿真.2006,23(8)：89-93,101.
[91]谢明鸿,张亚飞,付琨.基于种子点增长的SAR图像海岸线提取算法.电脑开发与应用.2006,19(6)：2-3,6.
[92]张永继,闫冬梅,曾峦等.基于邻域相关信息的海岸线提取方法.装备指挥技术学院学报.2005,16(6)：88-92.
[93]Malladi R, Sethian J A, Vemuri B C. Shape modeling with front propagation: a level set approach. IEEE Transactions on Pattern Analysis and Machine Intelligence.1995,17 (2):158-175.
[94]于洪川,王德军,唐泽圣等.水平集演化中的奇点与改进的窄带算法.软件学报.2003,14(4)：811-817.
[95]王岳环,王鼎,周晓玮等.基于Mumford-Shah模型的局部水平集分割窄带算法.华中科技大学学报(自然科学版).2008,36(3)：88-91.
[96]http://ds.rsgs.ac.cn/index.aspx
[97]Adalsteinsson D, Sethian J A. The fast construction of extension velocities in level set methods. Journal of Computational Physics.1999,148 (1):2-22.
[98]Chan T F, Vese L A. Active contours without edges. IEEE Transactions on Image Processing. 2001,10 (2):266-277.
[99]李俊,杨新.图像偏微分方程的原理与应用.上海：上海交通大学出版,2003.
[100]Xu C, Yezzi Jr A, Prince J L. On the relationship between parametric and geometric active contours.34th Asilomar Conference, Pacific Grove, CA, United states,2000:483-489.
[101]Perona P, Malik J. Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence.1990,12 (7):629-639.
[102]肖亮,吴慧中,韦志辉等.图像分割中分段光滑Mumford-Shah模型的水平集算法.计算机研究与发展.2004,41(1)：129-135.
[103]工文杰,封建湖.基于变分Level Set方法的图像分割.计算机工程与应用.2006,42(18)：68-70.
[104]Wang X F, Huang D S, Xu H. An efficient local Chan - Vese model for image segmentation. Pattern Recognition.2010,43 (3):603-618.
[105]王琪,丁辉,张伟等.利用分区处理和水平集算法分割序列三维乳腺MRI.清华大学学报(自然科学版).2009,49(03)：419-423.
[106]Vese L A, Chan T F. A multiphase level set framework for image segmentation using the Mumford and Shah model. International Journal of Computer Vision.2002,50 (3):271-293.
[107]Zhang K, Song H, Zhang L. Active contours driven by local image fitting energy. Pattern Recognition.2010,43 (4):1199-1206.
[108]孙开琼,江少锋,陈震.方向性局部区域活动轮廓血管分割.南昌航空大学学报(自然科学
版).2011,25(4)：9-13,28.
[109]Shi Y, Karl W C. Real-time tracking using level sets.2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, San Diego, CA, United states,2005: 34-41.
[110]李慧芳,沈焕锋,张良培等.一种基于变分Retinex的遥感影像不均匀性校正方法.测绘学报.2010,39(6)：585-591,598.
[111]王斌,高新波.基于水平集接力的图像自动分割方法.软件学报.2009,20(5)：1185-1193.
[112]顾丹丹,汪西莉.结合区域生长和水平集的遥感影像道路提取.计算机应用.2010,30 (2)：433-436,440.
[113]危自福,毕笃彦,马时平.一种改进的快速C-V水平集红外图像分割.数据采集与处理.2010,25(3)：347-352.
[114]徐玲凌,肖进胜,易本顺等.改进的C-V水平集模型图像分割算法.计算机工程.2009,38(10)：209-210.
[115]王明泉,梁君婷,冯晓夏.基于改进水平集的医学图像分割.中国科技论文在线.2011,06(1)：71-75.
[116]王兴梅,印桂生,门志国等.基于水平集改进的水下目标轮廓提取方法.哈尔滨工业大学学报.2010,46(04)：660-664.
[117]Paragios N, Deriche R. Geodesic active regions and level set methods for supervised texture segmentation. International Journal of Computer Vision.2002,46 (3):223-247.
[118]Parzen E. On estimation of a probability density function and mode. The Annals of Mathematical Statistics.1962,33 (3):1065-1076.
[119]Li J, Yang X, Shi P. Fast level set approach to image segmentation based on Mumford-Shah model. Jisuanji Xuebao/Chinese Journal of Computers.2002,25 (11):1175-1183.
[120]Keller J M, Chen S, Crownover R M. Texture description and segmentation through fractal geometry. Computer Vision Graphics and Image Processing.1989,45 (2):150-166.
[121]伍忠东,高新波,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(自然科学版).2004,31(4)：533-537.
[122]张莉,周伟达,焦李成.核聚类算法.计算机学报.2002,25(6)：587-590.
[123]Lzaro J, Arias J, Martn J L et al. Implementation of a modified Fuzzy C-Means clustering algorithm for real-time applications. Microprocessors and Microsystems.2005,29 (8-9):375-380.
[124]Chen S, Zhang D. Robust image segmentation using FCM with spatial constraints based on new kernel-induced distance measure. IEEE Transactions on Systems Man and Cybernetics.2004, 34(4):1907-1916.
[125]Bezdek J C, Hathaway R J, Sabin M J et al. Convergence theory for fuzzy c-means: Counterexamples and repairs. IEEE Transactions on Systems Man and Cybernetics.1987,17 (5): 873-877.
[126]Bezdek J C. Pattern recognition with fuzzy objective function algorithms. Netherlands:Kluwer Academic Publishers,1981.
[127]Lee J S, Jurkevich I. Coastline detection and tracing in SAR images. IEEE Transactions on Geoscience and Remote Sensing.1990,28 (4):662-668.
[128]Lee J S, Jurkevich I. Unsupervised Coastline Detection And Tracing In Sar Images. IGARSS'89-Twelfth Canadian Symposium on Remote Sensing, Vancouver, BC, Can,1989: 2611-2614.
[129]瞿继双,王超,王正志.一种基于多阈值的形态学提取遥感图象海岸线特征方法.中国图象图形学报A辑.2003,8(7)：805-809.
[130]荆浩,陈学佺,顾志伟.一种基于边缘特征的海岸线检测方法.计算机仿真.2006,23(8)：89-93,101.
[131]谢明鸿,张亚飞,付琨.基于种子点增长的SAR图像海岸线自动提取算法.中国科学院研究生院学报.2007,24(1)：93-98.
[132]张永继,闫冬梅,曾峦等.基于邻域相关信息的海岸线提取方法.装备指挥技术学院学报.2005,16(6)：88-92.
[133]欧阳越,种劲松.基于改进水平截集算法的SAR图像海岸线检测.遥感技术与应用.2004,19(6)：456-460.
[134]Yeung D S, Wang X Z. Improving performance of similarity-based clustering by feature weight learning. IEEE Transactions on Pattern Analysis and Machine Intelligence.2002,24 (4): 556-561.
[135]董旭,魏振军.一种加权欧氏距离聚类方法.信息工程大学学报.2005,6(1)：23-25.
[136]李爱国.一种基于属性加权模糊聚类算法.常熟理工学院学报.2007,21(8)：104-107.
[137]陈新泉.特征加权的模糊C聚类算法.计算机工程与设计.2007,28(22)：5329-5333.
[138]Scholkopf B, Mika S, Burges C J C et al. Input space versus feature space in kernel-based methods. IEEE Transactions on Neural Networks.1999,10 (5):1000-1017.
[139]Bezdek J C, Keller J M, Krishnapuram R et al. Will the real iris data please stand up. IEEE Transactions on Fuzzy Systems.1999,7 (3):368-369.
[140]杨晓波.复杂纹理图像的分割：(博士).秦皇岛：燕山大学,2004.
[141]Chaudhuri B B, Sarkar N. Texture segmentation using fractal dimension. IEEE Transactions on Pattern Analysis and Machine Intelligence.1995,17 (1):72-77.
[142]Peleg S, Naor J, Hartley R et al. Multiple resolution texture analysis and classification. IEEE Transactions on Pattern Analysis and Machine Intelligence.1984, PAMI-6 (4):518-523.
[143]Chaudhuri B B, Sarkar N, Kundu P. Improved fractal geometry based texture segmentation technique. IEEE Proceedings:Computers and Digital Techniques, NJ,USA,1993:233-241.
[144]Pentland A P. Fractal-based description of natural scenes. IEEE Transactions on Pattern Analysis and Machine Intelligence.1984, (6):661-674.
[145]Fortin C S, Kumaresan R, Ohley W J et al. Fractal dimension in the analysis of medical images. IEEE Engineering in Medicine and Biology Magazine.1992,11 (2):65-71.
[146]刘明芹,张晓光.差分盒维法在焊缝边缘检测上的应用研究.河北工业科技.2009,26(5)：300-302.
[147]杨词银,许枫.一种抗噪分形维计算方法及其在声纳图像识别中的应用.应用声学.2008,27(2)：95-101.
[148]陈廷,张维龙,吴丽莉.分形维数在原棉异纤图像处理中的应用.测试技术学报.2009,23(3)：248-252.
[149]孙晓妍,董槐林,王备战等.遥感图像中船只目标区域的分割方法.计算机工程.2008,34(10)：196-198.
[150]张小京,孙万蓉,乔静.基于分形维数的白细胞图像特征提取研究.计算机工程与设计.2009,30(4)：941-943.
[151]Yu L, Zhang D, Wang K et al. Coarse iris classification using box-counting to estimate fractal dimensions. Pattern Recognition.2005,38 (11):1791-1798.
[152]张涛,孙林,黄爱民.图像分形维数的差分盒方法的改进研究.电光与控制.2007,14(5)：55-57.
[153]刘松涛.用盒子维评估红外烟幕对舰船目标的遮蔽效果.光电工程.2009,36(2)：34-38.
[154]刘明芹,张晓光.一种计算图像分形维数的有效方法.西安科技大学学报.2009,29(3)：369-373.
[155]Li J, Du Q, Sun C. An improved box-counting method for image fractal dimension estimation. Pattern Recognition.2009,42 (11):2460-2469.
[156]Sarkar N, Chaudhuri B B. An efficient differential box-counting approach to compute fractal dimension of image. IEEE Transactions on Systems Man and Cybernetics.1994,24 (1):115-120.
[157]Sarkar N, Chaudhuri B B. An efficient approach to estimate fractal dimension of textural images. Pattern Recognition.1992,25 (9):1035-1041.
[158]王顺凤,阮晶,王宇.基于改进的LBF模型的图像分割.计算机应用与软件.2011,28(2)：25-27,33.
[159]Rosenberger C, Chehdi K. Unsupervised clustering method with optimal estimation of the number of clusters:Application to image segmentation. Proceedings 15th International Conference on Pattern Recognition, Barcelona, Spain,2000:656-659.
[160]Yuan H, Khorram S, Dai X L. Applications of simulated annealing minimization technique to unsupervised classification of remotely sensed data. IEEE 1999 International Geoscience and Remote Sensing Symposium, Hamburg, Germany,1999:134-136.