基于Snake模型的纤维图像分割的研究与应用
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摘要
纤维图像分割是纤维图像自动识别系统中的一个重要步骤,是纤维特征提取以及纤维识别的基础。在纤维图像采集过程中,由于纤维包埋和切片技术、图像采集系统中的环境、设备及人为等因素的限制,采集到的图像存在光斑、扭曲变形、光照不均等噪声,这给纤维图像分割带来困难。
本文在深入分析现有的图像分割方法的基础上,为解决传统图像分割方法用于纤维图像分割存在双边缘、伪边缘和轮廓不连续的问题,将Snake模型引入到纤维图像分割中,提出了一种基于Snake模型的纤维图像分割算法。
本文在研究了Snake模型的基础上,为解决传统Snake模型对初始轮廓线位置敏感和不能分割凹陷区域等问题,重点研究了GVFSnake模型在纤维图像分割领域中的应用.虽然GVF Snake模型有效解决了传统Snake模型的缺点,但运用到纤维图像分割中也存在着很多难点,比如时间效率、初始轮廓线的有效区域等问题。针对这些难点,本文首先结合GVF Snake模型的特点和纤维图像自有的特性,研究了适用于GVF Snake模型的纤维图像平滑去噪、去除光照不均的预处理方法；其次,提出融合聚类分割算法和GVF Snake模型的纤维图像分割方法,选取K-means聚类分割结果作为GVF Snake模型的初始轮廓线,充分发挥二者的优点,有效地解决了传统纤维图像分割存在的诸多问题；最后,由于纤维图像本身的特点,上一步的分割结果中可能存在毛刺,本文在轮廓跟踪方法的基础上找到毛刺并将其去除,得到完整、连续且单像素的纤维分割结果。
大量实验数据表明,利用本文算法分割纤维图像,有效解决了传统图像分割方法分割结果的双边缘、伪边缘或者轮廓不连续等问题,得到的结果准确、完整,实现了准确分割各类较复杂的纤维图像的目的,而且有效缩短了纤维图像的分割时间。
Fiber image segmentation is an indispensable step in the automatic fiber recognition system, and it is the base of the processes of feature exaction, classification recognition. So to segment a complete, continuous and single pixel fiber is the critical task. With the limits of fiber embedding and sectioning technology and illuminated with point light source techniques in making fiber cross-sectional samples, the fiber images sometimes have problems such as distorting and uneven illumination. This situation brings fiber image segmentation many difficulties.
Based on the research of classic image segmentation methods, for the limits of traditional segmentation algorithms such as false edge, double edge or discontinuous contour, Snake model is used in fiber image segmentation.
The paper illuminates the foundation of Snake model, because Snake model cannot solve boundary concavities better and the original contour must be placed close to the real boundary of object, we introduce GVF (Gradient Vector Flow) Snake model. It can solve these problems better than Snake model. But there are also many difficulties in the fiber image segmentation, such as time efficiency or effective original contour. For these difficulties, the GVF Snake model is applied in the segmentation of fiber image, we analyzes and researches the pre-segmentation processing first, and then a new fiber image segmentation algorithm based on clustering segmentation and GVF Snake model is proposed. The clustering segmentation is used to obtain the original coarse contour of fiber; and next GVF Snake algorithm is applied to calculate the accurate fiber contour. At last due to the noise of fiber micrographic image, some fiber contours have burrs, which can be removed by contour tracing method.
The experimental result shows that this algorithm is effectively and accurately, which can not only solve the problems such as false edge, double edge or discontinuous contour of the traditional segmentation algorithms, extract the complete and continuous fiber contour, but also depress the noise of fiber image.
本文在深入分析现有的图像分割方法的基础上,为解决传统图像分割方法用于纤维图像分割存在双边缘、伪边缘和轮廓不连续的问题,将Snake模型引入到纤维图像分割中,提出了一种基于Snake模型的纤维图像分割算法。
本文在研究了Snake模型的基础上,为解决传统Snake模型对初始轮廓线位置敏感和不能分割凹陷区域等问题,重点研究了GVFSnake模型在纤维图像分割领域中的应用.虽然GVF Snake模型有效解决了传统Snake模型的缺点,但运用到纤维图像分割中也存在着很多难点,比如时间效率、初始轮廓线的有效区域等问题。针对这些难点,本文首先结合GVF Snake模型的特点和纤维图像自有的特性,研究了适用于GVF Snake模型的纤维图像平滑去噪、去除光照不均的预处理方法；其次,提出融合聚类分割算法和GVF Snake模型的纤维图像分割方法,选取K-means聚类分割结果作为GVF Snake模型的初始轮廓线,充分发挥二者的优点,有效地解决了传统纤维图像分割存在的诸多问题；最后,由于纤维图像本身的特点,上一步的分割结果中可能存在毛刺,本文在轮廓跟踪方法的基础上找到毛刺并将其去除,得到完整、连续且单像素的纤维分割结果。
大量实验数据表明,利用本文算法分割纤维图像,有效解决了传统图像分割方法分割结果的双边缘、伪边缘或者轮廓不连续等问题,得到的结果准确、完整,实现了准确分割各类较复杂的纤维图像的目的,而且有效缩短了纤维图像的分割时间。
Fiber image segmentation is an indispensable step in the automatic fiber recognition system, and it is the base of the processes of feature exaction, classification recognition. So to segment a complete, continuous and single pixel fiber is the critical task. With the limits of fiber embedding and sectioning technology and illuminated with point light source techniques in making fiber cross-sectional samples, the fiber images sometimes have problems such as distorting and uneven illumination. This situation brings fiber image segmentation many difficulties.
Based on the research of classic image segmentation methods, for the limits of traditional segmentation algorithms such as false edge, double edge or discontinuous contour, Snake model is used in fiber image segmentation.
The paper illuminates the foundation of Snake model, because Snake model cannot solve boundary concavities better and the original contour must be placed close to the real boundary of object, we introduce GVF (Gradient Vector Flow) Snake model. It can solve these problems better than Snake model. But there are also many difficulties in the fiber image segmentation, such as time efficiency or effective original contour. For these difficulties, the GVF Snake model is applied in the segmentation of fiber image, we analyzes and researches the pre-segmentation processing first, and then a new fiber image segmentation algorithm based on clustering segmentation and GVF Snake model is proposed. The clustering segmentation is used to obtain the original coarse contour of fiber; and next GVF Snake algorithm is applied to calculate the accurate fiber contour. At last due to the noise of fiber micrographic image, some fiber contours have burrs, which can be removed by contour tracing method.
The experimental result shows that this algorithm is effectively and accurately, which can not only solve the problems such as false edge, double edge or discontinuous contour of the traditional segmentation algorithms, extract the complete and continuous fiber contour, but also depress the noise of fiber image.
引文
[1]张军英,崔瑞芳.涤／麻混纺沙性能与混纺比的关系.四川纺织科技,2003(4)：18-20
[2]来红林.大麻与其它纤维混纺布工艺初探.现代纺织技术,2004,12(2)：13-15
[3]吴宏仁,纺织纤维的结构和性能.北京：纺织工业出版社,1985
[4]姚重焘.计算机辅助测定麻棉混合比.中国纤维,1994(6)：21-22
[5]FZ/T01070.2-1999.麻棉混纺物纤维含量的测定方法-吸附等温线法
[6]FZ/T01070.1-1999.麻棉混纺物纤维含量的测定方法-数值逼近法
[7]王玉琦,李宣蔚.棉纤维中含糖量的制定方法.纤维标准与检验,1991(4)：7-8
[8]SN/T 0756-1999,进出口麻／棉混纺产品定量分析方法显微投影仪法.中华人民共和国国家出入境检验检疫局
[9]曹锡生.麻棉混纺布混纺比的测定.棉纺织技术,1989,17(11)：39-40
[10]Mak K L and Peng P, An automated inspection system for textile fabrics based on Gabor filters. Robotics Computer-Integrated Manufacturing,2007,02
[11]许国柱,杨晓琴.麻棉产品混纺比的测定.贺龙将纺织,1997(1)：20-21
[12]狄炜,徐伯俊.数字图像处理在纺织中的应用及发展.上海纺织科技,2002,30(3)：61-62
[13]Tae Jin Kang. Automatic Recognition of Fabric Weave Patterns by Digital Image Analysis.Textile-Res,1999.69(2):77-83
[14]Ohta, K., Nonaka, Y., Lshii, T., Okada, M. Automatic Analyzing of a Fabric Design with Frequency Components. Part 1:Automatic Analyzing of a Wearing Design. Textile Mach.Soc.Jpn,1998,49(9):61-68
[15]辛斌杰,余序芬,吴兆平.机织物经纬密度测量的图像处理技术.中国纺织大学学报,1999.3
[16]余序芬,吴兆平.数学形态学边缘检测法及其对棉麻自动识别的应用.东华大学学报,1996,22(5)：67-72
[17]余序芬,吴兆平.棉麻混纺比图像处理测试系统的开发研究.东华大学学报,1998,24(1)：41-45
[18]Thibodeaux D.P., Evans J.P. Cotton Fiber Maturity by Image Analysis. Textile Research Journal, 1986,56(2):130-139
[19]Thibodeaux D.P., Price J.B. Reference Method for Determination of the Maturity of Cotton Fiber. Melliand Textilberichte,1988,70(4):243-246
[20]Thibodeaux D.P., Rajasekaran K. Development of New Reference Standards for Cotton Fiber Maturity. Journal of Cotton Science,1999,3(4):188-193
[21]XU B. Fiber Cross-Sectional Shape Analysis Using Image Processing Techniques. Textile Research Journal,1993,63(12):717-730
[22]XU B., Ting Y. L. Fiber-image Analysis Part Ⅰ:Fiber Enchantment. Textile Research Journal, UK, 1995,87(2):274-283
[23]XU B., Wang S., Su J. Fiber Image Analysis Part III:Autonomous Separation of Fiber Cross Sections. Journal of Textile Institute,1999,90(3):588-297
[24]Huang Y., XU B. Image Analysis for Cotton Fibers, Part I:Longitudinal Measurements. Textile Research Journal,2002,72(8):713-720
[25]XU B., Characterizing Fiber Crimp by Image Analysis:Definitions, Algorithms and Techniques, Textile Research Journal,1992,62(2):73-80
[26]张乐.基于距离变换的剥离算法在纤维识别中的研究与应用.硕士学位论文,东华大学,2008.9
[27]董辛酉.纤维图像光照不均修正算法的研究.硕士学位论文,东华大学,2007.9
[28]Nello C. and Shawe-Taylor J., An Introduction to Support Vector Machines and Other Kernel-based Learning Methods,2003,7(12):23-25
[29]陆辉.基于核函数学习算法的研究及其在图像识别中的应用.硕士学位论文.东华大学.2009.9
[30]章毓晋.图像分割.北京：科学出版社,2001
[31]张强,活动轮廓线模型在足迹图像分割中的应用.硕士学位论文,东北大学,2006.9
[32]季虎,孙即祥,邵晓芳,毛玲.图像边缘提取方法及展望.计算机工程与应用,2004,14：70-73
[33]禹素萍,曾培峰,陈建平.基于棉纤维截面图像的改进型Canny边缘检测.计算机工程与应用.2008,44(10)：176-178
[34]KENNETH R, CASTLEMAN. Digital Image Processing 影印版.北京:清华大学出版 社,2002:474-482
[35]杨绍清,贾传莹.基于模糊判决的图像边缘连接.光学技术,2002,28(2)：108-112
[36]贺赛先,唐艳.一种基于人类感知的边缘连接方法.红外技术,2005,27(4)：338-342
[37]王靖,田捷.改进的多尺度顺序边缘连接检测法及其在医学图像中的应用.计算机学报2001,24(8)：525-529
[38]Torre V, Poggio T A. On Edge Detection. IEEE Trans on PAMI,1986,8(2):142-163
[39]Marr D and Hildreth E C. Theory of edge detection. Proc. Royal Soc. of London, 1980,207:187-217
[40]Clark J. Authenticating edges Produced by zero-crossing algorithm. IEEE Trans on PAMI, 1998,11(1):43-57
[41]罗希平,田捷,诸葛婴等.图像分割方法综述.模式识别与人工智能.1999,12(3)：300-312
[42]Staib L H,Duncan J S.Boundary Finding with Parametrically Deformable Models. IEEE Trans on Pattern Analysis and Machine Intelligence,1992,14(11):1061-1075
[43]Gashtasby A.Design and Recovery of 2-D and 3-D Shapes Using Retional Gaussian Curves and Surfaces. International Journal of Computer Vision,1993,10(3):233-256
[44]Legault R,Suen C Y.Optimal Local Weighted Averaging Methods in Contour Smoothing. IEEE Trans on Pattern Analysis and Machine Intelligence,1997,19(9):801-817
[45]袁华,滕奇志,边缘检测及其在医学图像中的应用,生物医学工程学杂志,2001,18(1)：149-153
[46]J. P. Wang. Stochastic relaxation on partitions with connected components and its application to image segmentation, IEEE Trans.PAMI,1998, PAMI-20(8):619-636
[47]Otsu N., A threshold selection method from gray-level histogram. IEEE Transactions on Systems, Man and Cybernetics,1979,9:62-66
[48]J. Bernsen, Dynamic thresholding of grey-level images, Proc. Eighth Int'l Conf. Pattern Recognition, pp.1251-1255, Paris,1986
[49]Abutaleb A S, Automatic thresholding of gray-level pictures using two-dimensional entropy. Computer Vision, Graphics, and Image Processing,1989,47(1):22-32
[50]Kittler J, Illingworth J, Minimum error thresholding. Pattern Recognition,1986,19(1):41-47
[51]Coleman G B, Andrews H C. Image Segmentation by Clustering. Proc.IEEE,1979,5(67):773-785
[52]李艳灵.基于聚类的图像分割算法研究.博士学位论文.华中科技大学.2009.12
[53]朱嵬鹏,基于聚类算法的图像分割.硕士学位论文,江南大学,2009.9
[54]T. Kohnllen. Self-organized information of to Pologically correct feature maps.Biological Cybernetics,1992(43):59-69
[55]Chanda B, Kundu M K K, Padmaha V Y. A Multi-scale Morphologic Edge Detetor. Pattern Recognition,1998,31 (10):1469-1478
[56]Atkins M S, Mackiwich R T. Fully Automatic Segmentation of the Brain in MRL. IEEE Trans on Medical Imaging,1998,17(1):98-107
[57]Vincent L, Soille P. Watersheds in Digital Spaces:An Efficient Algorithm Based on Immersion Simulations. IEEE Trans on Pattern Analysis and Machine Intelligence,1991,13(6):583-598
[58]Stan Z Li. Markov Random Field Modeling in Image Analysis. Tokyo Japan:Springer,2001
[59]高新波,裴继红,谢维信.模糊c均值聚类算法中加权指数m的研究.电子学报,2000,28(4)：80-83
[60]KASS M, WITKIN A, TERZOPOULOS D. Snakes:Active Contour Models. International Journal of Computer Vision,1987,1(4):321-331
[61]Frederic F. Leymarie.Tracking and Describing DeformableObjects Using Active Contour Models.1986
[62]李培华,张田文.主动轮廓线(蛇模型)综述.软件学报,2000,11(6)：751-757
[63]Cohen L D. Note:On active contour models and balloons. CVGIP:Image Understanding,1991,53(2):211-218
[64]Williams D J, Shah M. A fast algorithm for active contours and curvature estimation. 1992,55(1):14-26
[65]Cohen L D, Cohen I. Finite-element Methods for Active Contour Models and Balloons for 2D and 3D images. IEEE Trans. Pallern Anal. Intell.1993,15(11):1131-1147
[66]Eviatar H, Somorjai R L. A Fast Simple Contour Algorithm for Biomedical Images. Pattern Recognition Letters.1996,17:969-974
[67]XU C, PRINCE JL. Snakes, Shapes, and Gradient Vector Flow. IEEE Transactions on Image Processing,1998,7(3):359-369
[68]刘彩霞,范延滨,杨厚俊.GVF Snake模型中一种新的初始轮廓线设置方法.计算机应用,2006,26(7)：1614-1616
[69]肖助明,冯月亮,李涛.一种新型自适应中值滤波算法.湘潭师范学院学报(自然科学版),2006,28(2)：28-32
[70]Keren D. Using Symbolic Computation to Find Algebraic Invariants. IEEE Transactions on Pattern Analysis and Machine Intelligence,2003,16(11):1143-1149
[71]朱虹,钱学明,冯春来,等.掺气水流图象检测中的一种气泡区域提取方法.中国图象图形学报,2003,8(11)：1254-1260
[72]简林莎,张田昊.喷雾液滴图像亮度不均的校正方法.计算机工程,2006,32(7)：180-181
[73]董辛酉,姚砺,万燕等.纤维图像光照不均迭代修正算法,东华大学学报(自然科学版),2008,34(5)：594-618
[74]ZHANG B, HSU M. K-Harmonic Means-A Data Clustering Algorithm [R]. Hewlett-Packard Labs Technical Report, HPL-1999-124,1999(10):1-25
[75]王蓓,张立明.利用图像先验知识与Snake结合对心脏序列图像的分割.复旦学报,2003,42(1)：81-86
[76]王立功,于甬华等.基于Snake模型的图像目标轮廓自动跟踪方法.东南大学学报,2003,(3)
[77]杨勇,黄波等.一种基于内容表示的图像序列运动分割算法.通信学报.2001,(6)
[78]罗渝兰,王景熙等.基于Snake模型的B超心脏图像的腔体分割及算法研究.四川师范大学学报,2002(1)
[79]张伟伟,赵歆波,张涛等.基于改进的GVF Snake模型CT图像轮廓提取技术.计算机工程与应用,2008,44(5)：206-208
[80]刘彩霞.虚拟手术系统中彩色图像的边缘检测算法研究.硕士学位论文.青岛大学.2007.9
[81]范延滨,刘彩霞,贾世宇等.GVF Snake模型中初始轮廓线设置算法的研究.中国图象图形学报.2008,13(1)：58-63
[82]孙俊,李春雷,刘洲峰等.基于小波变换及GVF模型的SAR图像轮廓提取算法.河南大学学报(自然科学版),2008,38(4)：414-417
[83]李丽勤,高焕文,周兴祥.Snake模型初始轮廓选取的研究.计算机工程与应用.2004,11：43-45
[84]田丽丽.基于GVF Snake模型的轮廓提取方法研究.硕士学位论文.陕西师范大学.2009.5
[85]陆宗骐.C/C++图像处理编程.北京：清华大学出版社,2005：286-289
[86]陆宗骐,童韬.链码和在边界形状分析中的应用.中国图像图形学报.2002,7(12)：1323-1328
[87]张秋花.纤维图像掩码提取算法的研究.[硕士学位论文].东华大学.2007.9
[2]来红林.大麻与其它纤维混纺布工艺初探.现代纺织技术,2004,12(2)：13-15
[3]吴宏仁,纺织纤维的结构和性能.北京：纺织工业出版社,1985
[4]姚重焘.计算机辅助测定麻棉混合比.中国纤维,1994(6)：21-22
[5]FZ/T01070.2-1999.麻棉混纺物纤维含量的测定方法-吸附等温线法
[6]FZ/T01070.1-1999.麻棉混纺物纤维含量的测定方法-数值逼近法
[7]王玉琦,李宣蔚.棉纤维中含糖量的制定方法.纤维标准与检验,1991(4)：7-8
[8]SN/T 0756-1999,进出口麻／棉混纺产品定量分析方法显微投影仪法.中华人民共和国国家出入境检验检疫局
[9]曹锡生.麻棉混纺布混纺比的测定.棉纺织技术,1989,17(11)：39-40
[10]Mak K L and Peng P, An automated inspection system for textile fabrics based on Gabor filters. Robotics Computer-Integrated Manufacturing,2007,02
[11]许国柱,杨晓琴.麻棉产品混纺比的测定.贺龙将纺织,1997(1)：20-21
[12]狄炜,徐伯俊.数字图像处理在纺织中的应用及发展.上海纺织科技,2002,30(3)：61-62
[13]Tae Jin Kang. Automatic Recognition of Fabric Weave Patterns by Digital Image Analysis.Textile-Res,1999.69(2):77-83
[14]Ohta, K., Nonaka, Y., Lshii, T., Okada, M. Automatic Analyzing of a Fabric Design with Frequency Components. Part 1:Automatic Analyzing of a Wearing Design. Textile Mach.Soc.Jpn,1998,49(9):61-68
[15]辛斌杰,余序芬,吴兆平.机织物经纬密度测量的图像处理技术.中国纺织大学学报,1999.3
[16]余序芬,吴兆平.数学形态学边缘检测法及其对棉麻自动识别的应用.东华大学学报,1996,22(5)：67-72
[17]余序芬,吴兆平.棉麻混纺比图像处理测试系统的开发研究.东华大学学报,1998,24(1)：41-45
[18]Thibodeaux D.P., Evans J.P. Cotton Fiber Maturity by Image Analysis. Textile Research Journal, 1986,56(2):130-139
[19]Thibodeaux D.P., Price J.B. Reference Method for Determination of the Maturity of Cotton Fiber. Melliand Textilberichte,1988,70(4):243-246
[20]Thibodeaux D.P., Rajasekaran K. Development of New Reference Standards for Cotton Fiber Maturity. Journal of Cotton Science,1999,3(4):188-193
[21]XU B. Fiber Cross-Sectional Shape Analysis Using Image Processing Techniques. Textile Research Journal,1993,63(12):717-730
[22]XU B., Ting Y. L. Fiber-image Analysis Part Ⅰ:Fiber Enchantment. Textile Research Journal, UK, 1995,87(2):274-283
[23]XU B., Wang S., Su J. Fiber Image Analysis Part III:Autonomous Separation of Fiber Cross Sections. Journal of Textile Institute,1999,90(3):588-297
[24]Huang Y., XU B. Image Analysis for Cotton Fibers, Part I:Longitudinal Measurements. Textile Research Journal,2002,72(8):713-720
[25]XU B., Characterizing Fiber Crimp by Image Analysis:Definitions, Algorithms and Techniques, Textile Research Journal,1992,62(2):73-80
[26]张乐.基于距离变换的剥离算法在纤维识别中的研究与应用.硕士学位论文,东华大学,2008.9
[27]董辛酉.纤维图像光照不均修正算法的研究.硕士学位论文,东华大学,2007.9
[28]Nello C. and Shawe-Taylor J., An Introduction to Support Vector Machines and Other Kernel-based Learning Methods,2003,7(12):23-25
[29]陆辉.基于核函数学习算法的研究及其在图像识别中的应用.硕士学位论文.东华大学.2009.9
[30]章毓晋.图像分割.北京：科学出版社,2001
[31]张强,活动轮廓线模型在足迹图像分割中的应用.硕士学位论文,东北大学,2006.9
[32]季虎,孙即祥,邵晓芳,毛玲.图像边缘提取方法及展望.计算机工程与应用,2004,14：70-73
[33]禹素萍,曾培峰,陈建平.基于棉纤维截面图像的改进型Canny边缘检测.计算机工程与应用.2008,44(10)：176-178
[34]KENNETH R, CASTLEMAN. Digital Image Processing 影印版.北京:清华大学出版 社,2002:474-482
[35]杨绍清,贾传莹.基于模糊判决的图像边缘连接.光学技术,2002,28(2)：108-112
[36]贺赛先,唐艳.一种基于人类感知的边缘连接方法.红外技术,2005,27(4)：338-342
[37]王靖,田捷.改进的多尺度顺序边缘连接检测法及其在医学图像中的应用.计算机学报2001,24(8)：525-529
[38]Torre V, Poggio T A. On Edge Detection. IEEE Trans on PAMI,1986,8(2):142-163
[39]Marr D and Hildreth E C. Theory of edge detection. Proc. Royal Soc. of London, 1980,207:187-217
[40]Clark J. Authenticating edges Produced by zero-crossing algorithm. IEEE Trans on PAMI, 1998,11(1):43-57
[41]罗希平,田捷,诸葛婴等.图像分割方法综述.模式识别与人工智能.1999,12(3)：300-312
[42]Staib L H,Duncan J S.Boundary Finding with Parametrically Deformable Models. IEEE Trans on Pattern Analysis and Machine Intelligence,1992,14(11):1061-1075
[43]Gashtasby A.Design and Recovery of 2-D and 3-D Shapes Using Retional Gaussian Curves and Surfaces. International Journal of Computer Vision,1993,10(3):233-256
[44]Legault R,Suen C Y.Optimal Local Weighted Averaging Methods in Contour Smoothing. IEEE Trans on Pattern Analysis and Machine Intelligence,1997,19(9):801-817
[45]袁华,滕奇志,边缘检测及其在医学图像中的应用,生物医学工程学杂志,2001,18(1)：149-153
[46]J. P. Wang. Stochastic relaxation on partitions with connected components and its application to image segmentation, IEEE Trans.PAMI,1998, PAMI-20(8):619-636
[47]Otsu N., A threshold selection method from gray-level histogram. IEEE Transactions on Systems, Man and Cybernetics,1979,9:62-66
[48]J. Bernsen, Dynamic thresholding of grey-level images, Proc. Eighth Int'l Conf. Pattern Recognition, pp.1251-1255, Paris,1986
[49]Abutaleb A S, Automatic thresholding of gray-level pictures using two-dimensional entropy. Computer Vision, Graphics, and Image Processing,1989,47(1):22-32
[50]Kittler J, Illingworth J, Minimum error thresholding. Pattern Recognition,1986,19(1):41-47
[51]Coleman G B, Andrews H C. Image Segmentation by Clustering. Proc.IEEE,1979,5(67):773-785
[52]李艳灵.基于聚类的图像分割算法研究.博士学位论文.华中科技大学.2009.12
[53]朱嵬鹏,基于聚类算法的图像分割.硕士学位论文,江南大学,2009.9
[54]T. Kohnllen. Self-organized information of to Pologically correct feature maps.Biological Cybernetics,1992(43):59-69
[55]Chanda B, Kundu M K K, Padmaha V Y. A Multi-scale Morphologic Edge Detetor. Pattern Recognition,1998,31 (10):1469-1478
[56]Atkins M S, Mackiwich R T. Fully Automatic Segmentation of the Brain in MRL. IEEE Trans on Medical Imaging,1998,17(1):98-107
[57]Vincent L, Soille P. Watersheds in Digital Spaces:An Efficient Algorithm Based on Immersion Simulations. IEEE Trans on Pattern Analysis and Machine Intelligence,1991,13(6):583-598
[58]Stan Z Li. Markov Random Field Modeling in Image Analysis. Tokyo Japan:Springer,2001
[59]高新波,裴继红,谢维信.模糊c均值聚类算法中加权指数m的研究.电子学报,2000,28(4)：80-83
[60]KASS M, WITKIN A, TERZOPOULOS D. Snakes:Active Contour Models. International Journal of Computer Vision,1987,1(4):321-331
[61]Frederic F. Leymarie.Tracking and Describing DeformableObjects Using Active Contour Models.1986
[62]李培华,张田文.主动轮廓线(蛇模型)综述.软件学报,2000,11(6)：751-757
[63]Cohen L D. Note:On active contour models and balloons. CVGIP:Image Understanding,1991,53(2):211-218
[64]Williams D J, Shah M. A fast algorithm for active contours and curvature estimation. 1992,55(1):14-26
[65]Cohen L D, Cohen I. Finite-element Methods for Active Contour Models and Balloons for 2D and 3D images. IEEE Trans. Pallern Anal. Intell.1993,15(11):1131-1147
[66]Eviatar H, Somorjai R L. A Fast Simple Contour Algorithm for Biomedical Images. Pattern Recognition Letters.1996,17:969-974
[67]XU C, PRINCE JL. Snakes, Shapes, and Gradient Vector Flow. IEEE Transactions on Image Processing,1998,7(3):359-369
[68]刘彩霞,范延滨,杨厚俊.GVF Snake模型中一种新的初始轮廓线设置方法.计算机应用,2006,26(7)：1614-1616
[69]肖助明,冯月亮,李涛.一种新型自适应中值滤波算法.湘潭师范学院学报(自然科学版),2006,28(2)：28-32
[70]Keren D. Using Symbolic Computation to Find Algebraic Invariants. IEEE Transactions on Pattern Analysis and Machine Intelligence,2003,16(11):1143-1149
[71]朱虹,钱学明,冯春来,等.掺气水流图象检测中的一种气泡区域提取方法.中国图象图形学报,2003,8(11)：1254-1260
[72]简林莎,张田昊.喷雾液滴图像亮度不均的校正方法.计算机工程,2006,32(7)：180-181
[73]董辛酉,姚砺,万燕等.纤维图像光照不均迭代修正算法,东华大学学报(自然科学版),2008,34(5)：594-618
[74]ZHANG B, HSU M. K-Harmonic Means-A Data Clustering Algorithm [R]. Hewlett-Packard Labs Technical Report, HPL-1999-124,1999(10):1-25
[75]王蓓,张立明.利用图像先验知识与Snake结合对心脏序列图像的分割.复旦学报,2003,42(1)：81-86
[76]王立功,于甬华等.基于Snake模型的图像目标轮廓自动跟踪方法.东南大学学报,2003,(3)
[77]杨勇,黄波等.一种基于内容表示的图像序列运动分割算法.通信学报.2001,(6)
[78]罗渝兰,王景熙等.基于Snake模型的B超心脏图像的腔体分割及算法研究.四川师范大学学报,2002(1)
[79]张伟伟,赵歆波,张涛等.基于改进的GVF Snake模型CT图像轮廓提取技术.计算机工程与应用,2008,44(5)：206-208
[80]刘彩霞.虚拟手术系统中彩色图像的边缘检测算法研究.硕士学位论文.青岛大学.2007.9
[81]范延滨,刘彩霞,贾世宇等.GVF Snake模型中初始轮廓线设置算法的研究.中国图象图形学报.2008,13(1)：58-63
[82]孙俊,李春雷,刘洲峰等.基于小波变换及GVF模型的SAR图像轮廓提取算法.河南大学学报(自然科学版),2008,38(4)：414-417
[83]李丽勤,高焕文,周兴祥.Snake模型初始轮廓选取的研究.计算机工程与应用.2004,11：43-45
[84]田丽丽.基于GVF Snake模型的轮廓提取方法研究.硕士学位论文.陕西师范大学.2009.5
[85]陆宗骐.C/C++图像处理编程.北京：清华大学出版社,2005：286-289
[86]陆宗骐,童韬.链码和在边界形状分析中的应用.中国图像图形学报.2002,7(12)：1323-1328
[87]张秋花.纤维图像掩码提取算法的研究.[硕士学位论文].东华大学.2007.9