基于蛇模型的图像分割与目标轮廓跟踪研究
|
摘要
蛇模型在医学图像分割、视频分析等众多领域有着广泛的应用,尽管已有二十年的历史,在应用中仍然存在一些未解决的问题,本文针对蛇模型分割结果对初始曲线位置过于敏感、难以应用于全自动分割领域以及几何式蛇模型计算效率较低等三个问题进行了研究,取得一些具有理论意义和实用价值的成果。
1.提出一种对初始化曲线位置不敏感的新型蛇模型外力场自适应压力场。首先针对蛇模型初始化问题的原因进行了深入的研究,提出了可以避免初始化问题的力场所应具备的特征:可以自适应的根据其位置的不同而对蛇模型施加不同的压力,即在目标区域内部表现为膨胀力,外部为收缩力。再根据该特征的指导,提出基于邻域和基于梯度两种构造力场的方法,前者计算复杂度较高,但通过调整所用邻域的尺寸,对分割较细的目标有良好的效果,后者计算速度快,适应范围更广。
2.通过将蛇模型外力场与种子区域生长法相结合提出一种高效的全自动分割方法。基于蛇模型的图像分割难以避免人工干预,为此本文对全自动分割进行了研究。根据流场分析理论,向量流场中每个点的性质可以由该点周围向量的方向所反映,通过将这些向量的方向映射为一个标量,得到一个标量场流向标量场,然后以其为辅助图像,用一种改进的种子区域生长法进行初始分割,最后用区域合并得到最终结果。该方法计算速度快,对噪声鲁棒性好,适合快速应用。本文还将其拓展到彩色-纹理图像分割领域。
3.提出一种基于双前沿蛇模型的视频目标轮廓跟踪方法。与参数式蛇模型相比,几何式蛇模型有着更好的特性,然而较大的计算负荷使其难以适应目标跟踪快速化的要求。本文对双前沿活动轮廓模型进行了研究,提出支撑区域限制和拟气球模型两项改进以提高其计算效率,得到了一种新模型Dual-frontsnake with quasi-balloon ,并在此基础上提出了一种快速、灵活的轮廓跟踪方法。该方法保持了几何式蛇模型自适应拓扑结构变化的优点,并能用于背景运动的场景,跟踪运动变化剧烈、变形较大的目标。
Snake model is widely used in the domain of medical image segmentation, videoanalysis and so on. Though being studied for more than 20 years, there are still someproblems to be solved. This dissertation focused on three of the problems: the segmen-tation result of snake is heavily sensitive to the initial contours, the snake model is notappropriate for automatic segmentation, and the low computation velocity of geometricsnake. And three new methods are proposed.
1. A new external force field named adaptive pressure force field which makesthe snake model not sensitive to the position of initial curve is proposed. First, theinitial problem of snake model is studied. Based on the analysis of and comparisonamong the existing external force such as balloon model, gradient vector ?ow and soon, the character of an external force which can avoid the sensitiveness to the positionof initial curve is concluded: the pressure force imposed on the snake model should beable to change adaptively according to its position, namely, it can drive the snake modelto in?ate when the evolution curve locates inside the region of the object and shrinkwhen the curve locates outside. Then, according to the character of adaptive pressureforce field, two method are proposed to construct such force field. One is based on theneighborhood, and the other is based on gradient. The time complexity of the formeris high, but it can get very good result by choosing appropriate size of neighborhood ifthe object to be segmented is thin. The latter can be calculated fast, so it can be widelyused.
2. A fast automatic image segmentation method is proposed by the integrationof the external force field of snake model and seeded region growing method. Theexistence of human interaction makes snake model not appropriate for the domain ofautomatic segmentation. So the automatic segmentation method need to be studied.According to the theory of ?ow field analysis, the characteristic of each point in thefield can be re?ected by the directions of the vectors around it. Thus, an assistant image called ?ow direction scalar field is acquired by mapping the directions of thevectors of each point to be a scalar. Then the scalar field is segmented by using animproved seeded region growing method to get the initial segmentation result. And thefinal result is acquired by a region merging step. The proposed method is very e?cient,robust to noise and fit for the fast application. Besides, it is extended to the domain ofcolor-texture image segmentation.
3. A video object contour tracking method based on dual-front snake model is pro-posed. Comparing with the parametric snake, geometric snake has better performance.But it is di?cult to be used in the domain of object tracking which need a high pro-cessing speed because of its heavy computation load. Two adapt the original dual-frontactive contour to object contour tracking, two improvements called support region re-striction and quasi-balloon model are made, thus a new model named dual-front snakewith quasi-balloon is acquired. Then a fast and ?exible contour tracking method isproposed based on the new model. The method is applicable for tracking fast movingobject and deformable object, and no static background is assumed. In addition, themodel can control the topology change adaptively as other geometric snakes.
1.提出一种对初始化曲线位置不敏感的新型蛇模型外力场自适应压力场。首先针对蛇模型初始化问题的原因进行了深入的研究,提出了可以避免初始化问题的力场所应具备的特征:可以自适应的根据其位置的不同而对蛇模型施加不同的压力,即在目标区域内部表现为膨胀力,外部为收缩力。再根据该特征的指导,提出基于邻域和基于梯度两种构造力场的方法,前者计算复杂度较高,但通过调整所用邻域的尺寸,对分割较细的目标有良好的效果,后者计算速度快,适应范围更广。
2.通过将蛇模型外力场与种子区域生长法相结合提出一种高效的全自动分割方法。基于蛇模型的图像分割难以避免人工干预,为此本文对全自动分割进行了研究。根据流场分析理论,向量流场中每个点的性质可以由该点周围向量的方向所反映,通过将这些向量的方向映射为一个标量,得到一个标量场流向标量场,然后以其为辅助图像,用一种改进的种子区域生长法进行初始分割,最后用区域合并得到最终结果。该方法计算速度快,对噪声鲁棒性好,适合快速应用。本文还将其拓展到彩色-纹理图像分割领域。
3.提出一种基于双前沿蛇模型的视频目标轮廓跟踪方法。与参数式蛇模型相比,几何式蛇模型有着更好的特性,然而较大的计算负荷使其难以适应目标跟踪快速化的要求。本文对双前沿活动轮廓模型进行了研究,提出支撑区域限制和拟气球模型两项改进以提高其计算效率,得到了一种新模型Dual-frontsnake with quasi-balloon ,并在此基础上提出了一种快速、灵活的轮廓跟踪方法。该方法保持了几何式蛇模型自适应拓扑结构变化的优点,并能用于背景运动的场景,跟踪运动变化剧烈、变形较大的目标。
Snake model is widely used in the domain of medical image segmentation, videoanalysis and so on. Though being studied for more than 20 years, there are still someproblems to be solved. This dissertation focused on three of the problems: the segmen-tation result of snake is heavily sensitive to the initial contours, the snake model is notappropriate for automatic segmentation, and the low computation velocity of geometricsnake. And three new methods are proposed.
1. A new external force field named adaptive pressure force field which makesthe snake model not sensitive to the position of initial curve is proposed. First, theinitial problem of snake model is studied. Based on the analysis of and comparisonamong the existing external force such as balloon model, gradient vector ?ow and soon, the character of an external force which can avoid the sensitiveness to the positionof initial curve is concluded: the pressure force imposed on the snake model should beable to change adaptively according to its position, namely, it can drive the snake modelto in?ate when the evolution curve locates inside the region of the object and shrinkwhen the curve locates outside. Then, according to the character of adaptive pressureforce field, two method are proposed to construct such force field. One is based on theneighborhood, and the other is based on gradient. The time complexity of the formeris high, but it can get very good result by choosing appropriate size of neighborhood ifthe object to be segmented is thin. The latter can be calculated fast, so it can be widelyused.
2. A fast automatic image segmentation method is proposed by the integrationof the external force field of snake model and seeded region growing method. Theexistence of human interaction makes snake model not appropriate for the domain ofautomatic segmentation. So the automatic segmentation method need to be studied.According to the theory of ?ow field analysis, the characteristic of each point in thefield can be re?ected by the directions of the vectors around it. Thus, an assistant image called ?ow direction scalar field is acquired by mapping the directions of thevectors of each point to be a scalar. Then the scalar field is segmented by using animproved seeded region growing method to get the initial segmentation result. And thefinal result is acquired by a region merging step. The proposed method is very e?cient,robust to noise and fit for the fast application. Besides, it is extended to the domain ofcolor-texture image segmentation.
3. A video object contour tracking method based on dual-front snake model is pro-posed. Comparing with the parametric snake, geometric snake has better performance.But it is di?cult to be used in the domain of object tracking which need a high pro-cessing speed because of its heavy computation load. Two adapt the original dual-frontactive contour to object contour tracking, two improvements called support region re-striction and quasi-balloon model are made, thus a new model named dual-front snakewith quasi-balloon is acquired. Then a fast and ?exible contour tracking method isproposed based on the new model. The method is applicable for tracking fast movingobject and deformable object, and no static background is assumed. In addition, themodel can control the topology change adaptively as other geometric snakes.
引文
[1]吴立德.计算机视觉.上海:复旦大学出版社, 1993.
[2]马颂德,张正友.计算机视觉.北京:科学出版社, 1998.
[3]高文,陈熙霖.计算机视觉.北京:清华大学出版社, 1999.
[4] Sonka M, Hlavac V, Boyle R. Image processing, analysis, and machine vision. Beijing:Peoples Posts and Telecommunications Publishing House, 2002.
[5] Forsyth D A, Pone J. Computer vision: a modern approach. English reprint ed., Beijing:Pearson education Asia limited and Tsinghua University Press, 2004.
[6] Marr D. Vision: a computational investigation into the human representation and processingof visual information. U.S.A: W. H. Freeman, 1982.
[7] Castleman K R,朱志刚等译.数字图像处理.北京:电子工业出版社, 1998.
[8]阮秋琦.数字图像处理学.北京:电子工业出版社, 2001.
[9] Gonzalez R C, Woods R E. Digital Image Processing. 2nd ed., Beijing: Publishing houseof Electronics industry, 2002.
[10]章毓晋.图像工程(上册)图像处理. 2nd ed.,北京:清华大学出版社, 2006.
[11]章毓晋.图像工程(中册)图像分析. 2nd ed.,北京:清华大学出版社, 2006.
[12]章毓晋.图像工程(下册)图像理解. 2nd ed.,北京:清华大学出版社, 2007.
[13] Nagy G. Twenty years of document image analysis in PAMI. IEEE Transactions on PatternAnalysis and Machine Intelligence, 2000, 20(1):38–62.
[14] Shah M. Guest introduction: the changing shape of computer vision in the twenty-firstcentury. International Jounal of Computer Vision, 2002, 50(2):103–110.
[15] Kass M, Witkin A, Terzopoulos D. Snakes: active contour models. Proceedings of Interna-tional Conference on Computer Vision, 1987. 259– 268.
[16] K.S.Fu , J.K.Mui . A survey on image segmentation. Pattern Recognition, 1981, 13(1):3–16.
[17] Haralick R M, Shapiro L G. Survey: Image segmentation techniques. Computer Vision,Graphics, and Image Processing, 1985, 29(1):100–132.
[18] Pal N R, Pal S K. A review on image segmentation techniques. Pattern Recognition, 1993,26(9):1277–1294.
[19]罗希平,田捷.图像分割方法综述.模式识别与人工智能, 1999, 12(3):300–312.
[20]章毓晋.图像分割.北京:科学出版社, 2001.
[21] Zhang Y J. A survey on evaluation methods for image segmentation. Pattern Recognition,1996, 29(8):1335–1346.
[22] Canny J F. A computational approach to edge detection. IEEE Transactions on PatternAnalysis and Machine Intelligence, 1986, 8(6):679–698.
[23] Adams R, Bischof L. Seeded region growing. IEEE Transactions on Pattern Analysis andMachine Intelligence, 1994, 16(6):641–647.
[24] Chung R H, Yung N H, Cheung P Y. An e?cient parameterless quadrilateral-based imagesegmentation method. IEEE Transactions on Pattern Analysis and Machine Intelligence,2005, 27(9):1446–1457.
[25] Munoz X, Freixenet J, CufíX, et al. Strategies for image segmentation combining regionand boundary information. Pattern Recognition Letters, 2003, 24(1-3):375–392.
[26] Zhang T, Boult T E, Johnson R C. Two thresholds are better than one. Proceedings of IEEEConf. Computer Vision and Pattern Recognition, 2007. 1-8.
[27] Otsu N. A threshold selection method from gray-level histogram. IEEE Transactions onSystems, Man, and Cybernetics, 1979, 9(1):62–66.
[28] Comaniciu D, Meer P. Mean shift: a robust approach toward feature space analysis. IEEETransactions on Pattern Analysis and Machine Intelligence, 2002, 24(5):603–619.
[29] Geman S, Geman D. Stochastic relaxation, Gibbs distribution and the Bayesian restora-tion of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1984,6(6):721–741.
[30] Li S Z. Markov random field modeling in image analysis. Tokyo: Springer-Verlag, 2001.
[31]崔屹.图像处理与分析――数学形态学方法及应用.北京:科学出版社, 2000.
[32] Roerdink J B, Meijster A. The watershed transform: definitions, algorithms and paralleliza-tion strategies. Fundamenta Informaticae, 2001, 41:187–228.
[33] Vincent L, Soille P. Watersheds in digital spaces: an e?cient algorithm based on immer-sion simulations. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1991,13(6):583–598.
[34] Wang D. A multiscale gradient algorithm for image segmentation using watershelds. PatternRecognition, 1997, 30(12):2043–2052.
[35] Bleau A, Leon L J. Watershed-based segmentation and region merging. Computer Visionand Image Understanding, 2000, 77(3):317–370.
[36] Chien S Y, Huang Y W, Chen L G. Predictive watershed: a fast watershed algorithm forvideo segmentation. IEEE Transactions on Circuits and Systems for Video Technology,2003, 13(5):453–461.
[37] Beare R. A locally constrained watershed transform. IEEE Transactions on Pattern Analysisand Machine Intelligence, 2006, 28(7):1063–1074.
[38] Osma-Ruiz V, Godino-Llorente J I, Sáenz-Lechón N, et al. An improved watershed al-gorithm based on e?cient computation of shortest paths. Pattern Recognition, 2007,40(3):1078–1090.
[39] Levner I, Zhang H. Classification-driven watershed segmentation. IEEE Transactions onImage Processing, 2007, 16(5):1437–1445.
[40] Aubert G, Kornprobst P. Mathematical problems in image processing: partial di?erentialequations and the calculus of variations. New York: Springer-Verlag, 2002.
[41] Sapiro G. Geometric partial di?erential equations and image analysis.世界图书出版公司, 2003.
[42]杨新.图像偏微分方程的原理与应用.上海:上海交通大学出版社, 2003.
[43] Tek H, Kimia B B. Image segmentation by reaction-di?usion bubbles. Proceedings of 5thInternational Conference on Computer Vision, 1995. 156–162.
[44] Chen Y, Vemuri B C, Wang L. Image denoising and segmentation via nonlinear di?usion.Computers & Mathematics with Applications, 2000, 39(5):131–149.
[45] Sofou A, Maragos P. PDE-based modeling of image segmentation using volumic ?ooding.Proceedings of International Conference on Image Processing, 2003. 14–17.
[46] Chan T F, Vese L A. Active contours without edges. IEEE Transactions on Image Process-ing, 2001, 10(2):266–277.
[47] Tsai A, Anthony Yezzi J, Willsky A S. Curve evolution implementation of the Mumford-Shah functional for image segmentation, denoising, interpolation, and magnification. IEEETransactions on Image Processing, 2001, 10(8):1169–1186.
[48] Gao S, Bui T D. Image segmentation and selective smoothing by using Mumford-Shahmodel. IEEE Transactions on Image Processing, 2005, 14(10):1537–1549.
[49] Kolmogorov V, Zabih R. What energy functions can be minimized via graph cuts. IEEETransactions on Pattern Analysis and Machine Intelligence, 2004, 26(2):147–159.
[50] Boykov Y, Jolly M P. Interactive graph cuts for optimal boundary and region segmentationof objects in N-D images. Proceedings of International Conference on Computer Vision,2001. 105–112.
[51] Boykov Y, Kolmogorov V. An experimental comparison of min-cut/max- ?ow algorithmsfor energy minimization in vision.pdf. IEEE Transactions on Patttern Analysis and MachineIntelligence, 2004, 26(9):1124–1137.
[52] Lombaert H, Sun Y, Grady L, et al. A multilevel banded graph cuts method for fast imagesegmentation. Proceedings of International Conference on Computer Vision, 2005. 259–265.
[53] Juan O, Boykov Y. Active graph cuts. Proceedings of IEEE Conference on Computer Visionand Pattern Recognition, 2006. 1023-1029 1023-1029 1023–1029.
[54]林瑶,田捷.医学图像分割方法综述.模式识别与人工智能, 2002, 15(2):192–204.
[55] Zhang D, Lu G. Segmentation of moving objects in image sequence: a review. Circuits,Systems, and Signal Processing, 2001, 20(2):143–183.
[56] Blake A. Visual tracking: a very short research roadmap. IEE Electronics Letters, 2006,42(5):254– 256.
[57]侯志强,韩崇昭.视觉跟踪技术综述.自动化学报, 2006, 32(4):603–617.
[58] Lee D S. E?ective Gaussian mixture learning for video background subtraction. IEEETransactions on Pattern Analysis and Machine Intelligence, 2005, 27(5):827–832.
[59] Song X, Nevatia R. A model-based vehicle segmentation method for tracking. Proceedingsof International Conference on Computer Vision, Beijing, 2005. 1124–1131.
[60] Cootes T F, Taylor C J, Cooper D H, et al. Active shape models—Their training andapplication. Computer Vision and Image Understanding, 1995, 61(1):38–59.
[61] Kim W, Lee J J. Object tracking based on the modular active shape model. Mechatronics,2005, 15(3):371–402.
[62] Cremers D. Dynamical statistical shape priors for level set-based tracking. IEEE Transac-tions on Pattern Analysis and Machine Intelligence, 2006, 28(8):1262–1273.
[63] Comaniciu D, Ramesh V, Meer P. Kernel-based object tracking. IEEE Transactions onPattern Analysis and Machine Intelligence, 2003, 25(5):564– 577.
[64] Collins R T. Mean-shift blob tracking through scale space. Proceedings of IEEE Conferenceof Computer Vision and Pattern Recognition, 2003. 234–240.
[65] Blake A, Isard M. Active contours: the application of techniqures from graphics, vision,control theory and statistics to visual tracking of shapes in motion. London: Springer-Verlag, 1998.
[66] Nguyen H T, Worring M, Boomgaard R, et al. Tracking Nonparameterized Object Contoursin Video. IEEE Transactions on Image Processing, 2002, 11(9):1081– 1091.
[67] Terzopoulos D, Szeliski R. Tracking with Kalman snakes. In: Blake A, Yullie A, (eds.).Proceedings of Active vision. U.S.A: MIT Press, 1992: 3– 20.
[68] Paragios N, Deriche R. Geodesic active contours and level sets for the detection and trackingof moving objects. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2000,22(3):266– 280.
[69] Paragios N, Deriche R. Geodesic active regions and level set methods for motion estimationand tracking. Computer Vision and Image Understanding, 2005, 97(3):259– 282.
[70] Peterfreund N. Robust tracking of position and velocity with Kalman snakes. IEEE Trans-actions on Pattern Analysis and Machine Intelligence, 1999, 21(6):564–569.
[71] Doucet A, Freitas N, Gordon N, (eds.). Sequential Monte Carlo methods in practice (statis-tics for engineering and information science). Springer–Verlag, 2001.
[72] Djuric P, Kotecha J, Zhang J, et al. Particle filtering. IEEE Signal Processing Magazine,2003, 20(5):19–38.
[73] Isard M, Blake A. CONDENSATION—conditional density propagation for visual track-ing. International Journal of Computer Vision, 1998, 29(1):5– 28.
[74] Isard M, Blake A. Contour tracking by stochastic propagation of conditional density. Pro-ceedings of European Conference on Computer Vision, 1996. 343–356.
[75] Li P, Zhang T, Pece A E. Visual contour tracking based on particle filters. Image and VisionComputing, 2003, 21(1):111–123.
[76] Koller-Meier E B, Ade F. Tracking multiple objects using the Condensation algorithm.Robotics and Automation Systems, 2001, 34(2-3):93–105.
[77] Zhou S K, Chellappa R, Moghaddam B. Visual tracking and recognition using appearance-adaptive models in particle filters. IEEE Transactions on Image Processing, 2004,13(11):1491–1506.
[78] Caselles V, Coll B. Snakes in movement. SIAM Journal on Numerical Analysis, 1996,33(6):2445–2456.
[79] Paragios N, Deriche R. A PDE-based level set approach for detection and tracking ofmoving object. Technical report 3173, INRIA, 1997.
[80] Bertalmio M, Sapiro G, Randall G. Morphing active contours. IEEE Transactions on PatternAnalysis and Machine Intelligence, 2000, 22(7):733–737.
[81] Jehan-Besson S, Barlaud M. DREAM2S: deformable regions driven by an Eulerian accurateminimization method for image and video segmentation. International Journal of ComputerVision, 2003, 53(1):45– 70.
[82] Freedman D, Zhang T. Active contours for tracking distributions. IEEE Transactions onImage Processing, 2004, 13(4):418–526.
[83] Zhang T, Freedman D. Improving performance of distribution tracking through back-ground mismatch. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2005,27(2):282–287.
[84] Zhang T, Freedman D. Tracking objects using density matching and shape priors. Proceed-ings of International Conference on Computer Vision, 2003. 1079–1085.
[85] Yilmaz A, Li X, Shah M. Contour-based object tracking with occlusion handling in videoacquired using mobile cameras. IEEE Transactions on Pattern Analysis and Machine Intel-ligence, 2004, 26(11):1531–1536.
[86] Rathi Y, Vaswani N, Tannenbaum A, et al. Particle filtering for geometric active contourswith application to tracking moving and deforming objects. Proceedings of IEEE ComputerSociety Conference on Computer Vision and Pattern Recognition, 2005. 2–9.
[87] Rathi Y, Tannenbaum N V A, Yezzi A. Tracking deforming objects using particle filter-ing for geometric active contours. IEEE Transactions on Pattern Analysis and MachineIntelligence, 2007, 29(8):1470–1475.
[88] Yu Z, Bajaj C. Normalized gradient vector di?usion and image segmentation. Proceedingsof European Conference on Computer Vision, 2002. 517–530.
[89] He Y, Luo Y, Hu D. Semi-automatic initialization of gradient vector ?ow snakes. Journalof Electronic Imaging, 2006, 15(4):043006.
[90] Chuang C, Lie W. A downstream algorithm based on extended gradient vector ?ow field forobject segmentation. IEEE Transactions on Image Processing, 2004, 13(10):1379–1392.
[91] Kass M, Witkin A, Terzopoulos D. Snakes: active contour models. International Journal ofComputer Vision, 1988, 1(4):321–331.
[92] Ranganath S. Contour extraction from cardiac MRI studies using snakes. IEEE Transactionson Medical Imaging, 1995, 14(2):328– 338.
[93] Székely G, Kelemen A, Brechbühler C, et al. Segmentation of 2-D and 3-D objects fromMRI volume data using constrained elastic deformations of ?exible Fourier contour andsurface models. Medical Image Analysis, 1996, 1(1):19– 34.
[94] Yezzi J, Kichenassamy S, Kumar A, et al. A geometric snake model for segmentation ofmedical imagery. IEEE Transactions on Medical Imaging, 1997, 16(2):199– 209.
[95] Atkins M, Mackiewich B. Fully automatic segmentation of the brain in MRI. IEEE Trans-actions on Medical Imaging, 1998, 17(1):98– 107.
[96] Canero C, Vilarino F, Mauri J, et al. Predictive (un)distortion model and 3-D reconstructionby biplane snakes. IEEE Transactions on Medical Imaging, 2002, 21(9):1188– 1201.
[97] Pardo X M, Radeva P, Cabello D. Discriminant snakes for 3D reconstruction of anatomicalorgans. Medical Image Analysis, 2003, 7(3):293–310.
[98] Chiou G I, Hwang J N. Image sequence classification using a neural network based activecontour model and a hidden Markov model. Proceedings of IEEE International Conferenceon Image Processing, 1994. 926– 930.
[99]李培华,张田文.主动轮廓线模型(蛇模型)综述.软件学报, 2000, 11(6):751– 757.
[100]陈波,赖剑煌.用于图像分割的活动轮廓模型综述.中国图象图形学报, 2007, 12(1):11– 20.
[101] Xu C, Yezzi J, Prince J. On the relationship between parametric and geometric activecontours. Proceedings of the Thirty-Fourth Asilomar Conference on Signals, Systems andComputers, 2000. 483–489.
[102] Xu N, Ahuja N, Bansal R. Object segmentation using graph cuts based active contours.Computer Vision and Image Understanding, 2007, 107(3):210–224.
[103] Li H, Yezzi A. Local or global minima: ?exible dual-front active contours. IEEE Transac-tions on Pattern Analysis and Machine Intelligence, 2006, 29(1):1–14.
[104] Caselles V, CattéF, Coll T, et al. A geometric model for active contours in image processing.Numerische Mathematik, 1993, 66(1):1–31.
[105] Malladi R, Sethian J A, Vemuri B C. Shape modeling with front propagation: a level set ap-proach. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1995, 17(2):158–175.
[106] Osher S, Sethian J. Fronts propagating with curvature dependent speed: algorithms basedon the Hamilton-Jacobi formulation. Journal of Computational Physics, 1988, 79(1):12–49.
[107] Sethian J A. Level set method and fast marching method. U. K.: Cambridge Universitypress, 1999.
[108] Osher S, Fedkiw R. Level set nethods and dynamic implicit surfaces. New York: Springer-Verlag, 2003.
[109] Chopp D L. Computing minimal surfaces via level set curvature ?ow. Journal of Computa-tional Physics, 1993, 106(1):77–91.
[110] Adalsteinsson D, Sethian J A. A fast level set method for propagating interfaces. Journalof Computational Physics, 1995, 118(2):269–277.
[111] Sethian J A. A fast marching level set method for monotonically advancing fronts. AppliedMathematics, 1996, 93(4):1591–1593.
[112] Sethian J A. Evolution, implementation, and application of level set and fast marchingmethods for advancing fronts. Journal of Computational Physics, 2001, 169(2):503–555.
[113] Zhao H. Fast sweeping method for Eikonal equations. Mathematics of Computation, 2005,74(250):603–627.
[114] Borgefors G. Distance transformations in digital images. Computer Vision, Graphics, andImage Processing, 1986, 34(3):344–371.
[115] Peng D, Merriman B, Osher S, et al. A PDE-based fast local level set method. Journal ofComputational Physics, 1999, 155(2):410–438.
[116] Li C, Xu C, Gui C, et al. Level set evolution without re-initialization: a new variationalformulation. Proceedings of Computer Vision and Pattern Recognition, 2005. 430–436.
[117] Caselles V, Kimmel R, Sapiro G. Geodesic active contours. Proceedings of Fifth Interna-tional Conference on Computer Vision, 1995. 694–699.
[118] Caselles V, Kimmel R, Sapiro G. Geodesic active contour. International Journal of Com-puter Vision, 1997, 22(1):61–79.
[119] Cohen L D. On active contour models and balloons. CVGIP: Image Understanding, 1991,53(2):211–218.
[120] Cohen L D, Cohen I. Finite-element methods for active contour models and balloons for2-D and 3-D images. IEEE Transactions on Pattern Analysis and Machine Intelligence,1993, 15(11):1131–1147.
[121] Xu C, Prince J L. Gradient vector ?ow: a new external force for snakes. Proceedings ofIEEE Conference of Computer Vision and Pattern Recognition, 1997. 66–71.
[122] Xu C, Prince J L. Snakes, shapes, and gradient vector ?ow. IEEE Transactions on ImageProcessing, 1998, 7(3):359–369.
[123]王元全,贾云得.梯度矢量流Snake模型临界点剖析.软件学报, 2006, 17(9):1915–1921.
[124] Paragios N, Mellina-Gottardo O, Ramesh V. Gradient vector ?ow fast geometric active con-tours. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2004, 26(3):402–407.
[125] Xu C, Prince J L. Generalized gradient vector ?ow external forces for active contours.Signal Processing, 1998, 71(2):131–139.
[126] Ray N, Acton S T. Motion gradient vector ?ow: An external force for tracking rollingleukocytes with shape and size constrained active contours. IEEE Transactions on MedicalImaging, 2004, 23(12):1466–1478.
[127] Cheng J, Foo S W. Dynamic directional gradient vector ?ow for snakes. IEEE Transactionson Image Processing, 2006, 15(6):1563–1571.
[128] Park H K, Chung M J. External force of snake: virtual electric field. Electronics Letters,2002, 38(24):1500–1502.
[129] Yuan D, Lu S. Simulated static electric field (SSEF) snake for deformable models. Pro-ceedings of International Conference on Pattern Recognition, 2002. 83–86.
[130] Li B, Acton S T. Active contour external force using vector field convolution for imagesegmentation. IEEE Transactions on Image Processing, 2007, 16(8):2096–2106.
[131] Li B, Acton S T. Vector field convolution for image segmentation using snakes. Proceedingsof International Conference of Image Processing, 2006. 1637–1640.
[132] Mumford D, Shah J. Optimal Approximations by piecewise smooth functions and asso-ciated variational problems. Communications on Pure and Applied Mathematics, 1989,42(4):577–685.
[133] Morel J M, Solimini S. Variational models for image segmentation: with seven imageprocessing experiments (progress in nonlinear di?erential equations and their applications).Birkhauser, 1994.
[134] Zhu S, Yuille A. Region competition: unifying snakes, region growing, and Bayes/MDLfor multiband image segmentation. IEEE Transactions on Pattern Analysis and MachineIntelligence, 1996, 18(9):884–900.
[135] Paragios N, Deriche R. Geodesic active regions: a new framework to deal with framepartition problems in computer vision. Journal of Visual Communication and Image Rep-resentation, 2002, 13(1-2):249–268.
[136] Paragios N, Deriche R. Geodesic active regions for texture segmentation. Technical report3440, INRIA, 1998.
[137] Chan T F, Vese L A. An active contour model without edges. Proceedings of Scale-SpaceTheories in Computer Vision, 1999.
[138] Vese L A, Chan T F. A multiple level set framework for image segmentation using theMumford and Shah model. International Journal of Computer Vision, 2002, 50(3):271–293.
[139] Nguyen H T, Worring M, Boomgaard R. Watersnakes: energy-driven watershed segmen-tation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2003, 25(3):330–342.
[140] Xie X, Mirmehdi M. RAGS: region-aided geometric snake. IEEE Transactions on ImageProcessing, 2004, 13(5):640–652.
[141] Ayed I B, Hennane N, Mitiche A. Unsupervised variational image segmenta-tion/classification using a Weibull observation model. IEEE Transactions on Image Pro-cessing, 2006, 15(11):34313439.
[142] Kim J, John W. Fisher I, Yezzi A, et al. A nonparametric statistical method for imagesegmentation using information theory and curve evolution. IEEE Transactions on ImageProcessing, 2005, 14(10):1486–1502.
[143] Cremers D, Rousson M, Deriche R. A review of statistical approaches to level set seg-mentation: integrating color, texture, motion and shape. International Journal of ComputerVision, 2007, 72(2):195–215.
[144] Trier O D, Taxt T. Evaluation of binarization methods for document images. IEEE Trans-actions on Pattern Analysis and Machine Intelligence, 1995, 17(3):312–315.
[145] Trier O, Jain A. Goal-directed evaluation of binarization methods. IEEE Transactions onPattern Analysis and Machine Intelligence, 1995, 17(12):1191–1201 1191–1201.
[146] Yanowitz S D, Bruckstein A M. A new method for image segmentation. Computer Vision,Graphics and Image Processing, 1989, 46:82–95.
[147] Liu F, Luo Y, Hu D. Active surface model-based adaptive thresholding algorithm by repul-sive external force. Journal of Electronic Imaging, 2003, 12(2):299–306.
[148]刘飞.图象分割的理论研究与应用[D].清华大学, 2003.
[149] Liang J, Doermann D, Li H. Camera-based analysis of text and document: a survey. Inter-national Journal on Document Analysis and Recognition, 2005, 7(2-3):84–104.
[150] Liang J, DeMenthon D, Doermann D. Geometric rectification of camera-captured documentimages. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2008, 30(4):591–605.
[151] Smeulders A W M, Worring M, Santini S, et al. Content -based image retrievel at the endof the early years. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2000,22(12):1349–1380.
[152] Fan J, Zeng G, Body M, et al. Seeded region growing: an extensive and comparative study.Pattern Recognition Letters, 2005, 26(8):1139–1156.
[153] Shih F Y, Cheng S. Automatic seeded region growing for color image segmentation. Imageand Vision Computing, 2005, 23(10):877–886.
[154] Deng Y, Manjunath B S. Unsupervised segmentation of color-texture regions in images andvideo. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2001, 23(8):800–810.
[155] Yu Z, Bajaj C. Image segmentation using gradient vector di?usion and region merging.Proceedings of 16th International Conference on Pattern Recognition, 2002. 941–944.
[156] Ray N, Acton S T, Altes T, et al. Merging parametric active contours within homogeneousimage regions for MRI-based lung segmentation. IEEE Transactions on Medical Imaging,2003, 22(2):189–199.
[157] He Y, Luo Y, Hu D. Automatic seeded region growing based on gradient vector ?ow forcolor image segmentation. Optical Engineering, 2007, 46(4):047003.
[158] Cheng H, Jiang X, Sun Y, et al. Color image segmentation: advances and prospects. PatternRecognition, 2001, 34(12):2259–2281.
[159] Ma Y, Manjunath B S. EdgeFlow: a technique for boundary detection and image segmen-tation. IEEE Transactions on Image Processing, 2000, 9(8):1375–1388.
[160] Nock R, Nielsen F. Statistical region merging. IEEE Transations on Pattern Analysis andMachine Intelligence, 2004, 26(11):1452–1458.
[161] Geusebroek J, Boomgaard R, Smeulders A W, et al. Color invariance. IEEE Transactionson Pattern Analysis and Machine Intelligence, 2001, 23(12):1338–1350.
[162] Koschan A, Abidi M. Detection and classification of edges in color images. IEEE SignalProcessing Magzine, 2005, 22(1):64–73.
[163] Manjunath B S, Ma W Y. Texture features for browsing and retrievel of image data. IEEETransactions on Pattern Analysis and Machine Intelligence, 1996, 18(8):837–842.
[164] Sagiv C, Sochen N A, Zeevi Y Y. Integrated active contours for texture segmentation. IEEETransactions on Image Processing, 2006, 15(6):1633–1646.
[165] Randen T, Husoy J H. Filtering for texture classification: a comparative study. IEEETransactions on Pattern Analysis and Machine Intelligence, 1999, 21(4):291–310.
[166] Ng I, Tan T, Kittler J. On local linear transform and Gabor filter representation of texture.Proceedings of International Conference on. Pattern Recognition, 1992. 627–631.
[167] Vincent L. Morphological grayscale reconstruction in image analysis: applications ande?cient algorithms. IEEE Transactions on Image Processing, 1993, 2(2):176–201.
[168] Beucher S, Meyer F. The morphological approach to segmentation: the watershed trans-formation. In: R.Dougherty E, (eds.). Proceedings of Mathematical Morphology in ImageProcessing, chapter 12, 433–481. New York: Marcel Dekker, Inc., 1993: 433–481.
[169] Haris K, Efstratiadis S N, Maglaveras N, et al. Hybrid image segmentation using watershedsand fast region merging. IEEE Transactions on Image Processing, 1998, 7(12):1684–1699.
[170] Trémeau A, Colantoni P. Regions adjacency graph applied to color image segmentation.IEEE Transactions on Image Processing, 2000, 9(4):735–744.
[171] Martin D, Fowlkes C, Tal D, et al. A database of human segmented natural images andits application to evaluating segmentation algorithms and measuring ecological statistics.Proceedings of 8th International Conference on Computer Vision, 2001. 416–423.
[172] Han X, Xu C, Prince J L. Fast numerical scheme for gradient vector ?ow computation usinga multigrid method. IET Image Processing, 2007, 1(1):48–55.
[173] Pavlovic V L, Sharma R, Huang T S. Visual interpretation of hand gestures for human-computer interaction: a review. IEEE Transactions on Pattern Analysis and Machine Intel-ligence, 1997, 19(7):677–695.
[174] Moelich M, Chan T. Tracking objects with the Chan-Vese algorithm. Technical ReportCam03-14, Mathematics Department, UCLA, 2003.
[175] Xu N, Bansal R, Ahuja N. Object segmentation using graph cuts based active contours.Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, 2003. 46–53.
[176] Xu N, Ahuja N. Object contour tracking using graph cuts based active contours. Proceed-ings of International Conference on Image Processing, 2002. 277–280.
[177] Li H, Elmoataz A, Fadili J, et al. A multi-label front propagation approach for objectsegmentation. Proceedings of International Conference on Pattern Recognition, 2004. 600–603.
[178] Li H, Elmoataz A, Fadili J, et al. Dual front evolution model and Its application in medicalimaging. Proceedings of MICCAI 2004, LNCS 3216, 2004. 103–110.
[179] Gunn S R, Nixon M S. A robust snake implementation: a dual active contour. IEEETransactions on Pattern Analysis and Machine Intelligence, 1997, 19(19):63–68.
[180] Sifakis E, Tziritas G. Moving object localisation using a muti-label fast marching algorithm.Signal Processing: Image Communication, 2001, 16(10):963–976.
[181] Cohen L D. Global minimum for active contour models: a minimal path approach. Inter-national Journal of Computer Vision, 1997, 24(1):57–78.
[2]马颂德,张正友.计算机视觉.北京:科学出版社, 1998.
[3]高文,陈熙霖.计算机视觉.北京:清华大学出版社, 1999.
[4] Sonka M, Hlavac V, Boyle R. Image processing, analysis, and machine vision. Beijing:Peoples Posts and Telecommunications Publishing House, 2002.
[5] Forsyth D A, Pone J. Computer vision: a modern approach. English reprint ed., Beijing:Pearson education Asia limited and Tsinghua University Press, 2004.
[6] Marr D. Vision: a computational investigation into the human representation and processingof visual information. U.S.A: W. H. Freeman, 1982.
[7] Castleman K R,朱志刚等译.数字图像处理.北京:电子工业出版社, 1998.
[8]阮秋琦.数字图像处理学.北京:电子工业出版社, 2001.
[9] Gonzalez R C, Woods R E. Digital Image Processing. 2nd ed., Beijing: Publishing houseof Electronics industry, 2002.
[10]章毓晋.图像工程(上册)图像处理. 2nd ed.,北京:清华大学出版社, 2006.
[11]章毓晋.图像工程(中册)图像分析. 2nd ed.,北京:清华大学出版社, 2006.
[12]章毓晋.图像工程(下册)图像理解. 2nd ed.,北京:清华大学出版社, 2007.
[13] Nagy G. Twenty years of document image analysis in PAMI. IEEE Transactions on PatternAnalysis and Machine Intelligence, 2000, 20(1):38–62.
[14] Shah M. Guest introduction: the changing shape of computer vision in the twenty-firstcentury. International Jounal of Computer Vision, 2002, 50(2):103–110.
[15] Kass M, Witkin A, Terzopoulos D. Snakes: active contour models. Proceedings of Interna-tional Conference on Computer Vision, 1987. 259– 268.
[16] K.S.Fu , J.K.Mui . A survey on image segmentation. Pattern Recognition, 1981, 13(1):3–16.
[17] Haralick R M, Shapiro L G. Survey: Image segmentation techniques. Computer Vision,Graphics, and Image Processing, 1985, 29(1):100–132.
[18] Pal N R, Pal S K. A review on image segmentation techniques. Pattern Recognition, 1993,26(9):1277–1294.
[19]罗希平,田捷.图像分割方法综述.模式识别与人工智能, 1999, 12(3):300–312.
[20]章毓晋.图像分割.北京:科学出版社, 2001.
[21] Zhang Y J. A survey on evaluation methods for image segmentation. Pattern Recognition,1996, 29(8):1335–1346.
[22] Canny J F. A computational approach to edge detection. IEEE Transactions on PatternAnalysis and Machine Intelligence, 1986, 8(6):679–698.
[23] Adams R, Bischof L. Seeded region growing. IEEE Transactions on Pattern Analysis andMachine Intelligence, 1994, 16(6):641–647.
[24] Chung R H, Yung N H, Cheung P Y. An e?cient parameterless quadrilateral-based imagesegmentation method. IEEE Transactions on Pattern Analysis and Machine Intelligence,2005, 27(9):1446–1457.
[25] Munoz X, Freixenet J, CufíX, et al. Strategies for image segmentation combining regionand boundary information. Pattern Recognition Letters, 2003, 24(1-3):375–392.
[26] Zhang T, Boult T E, Johnson R C. Two thresholds are better than one. Proceedings of IEEEConf. Computer Vision and Pattern Recognition, 2007. 1-8.
[27] Otsu N. A threshold selection method from gray-level histogram. IEEE Transactions onSystems, Man, and Cybernetics, 1979, 9(1):62–66.
[28] Comaniciu D, Meer P. Mean shift: a robust approach toward feature space analysis. IEEETransactions on Pattern Analysis and Machine Intelligence, 2002, 24(5):603–619.
[29] Geman S, Geman D. Stochastic relaxation, Gibbs distribution and the Bayesian restora-tion of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1984,6(6):721–741.
[30] Li S Z. Markov random field modeling in image analysis. Tokyo: Springer-Verlag, 2001.
[31]崔屹.图像处理与分析――数学形态学方法及应用.北京:科学出版社, 2000.
[32] Roerdink J B, Meijster A. The watershed transform: definitions, algorithms and paralleliza-tion strategies. Fundamenta Informaticae, 2001, 41:187–228.
[33] Vincent L, Soille P. Watersheds in digital spaces: an e?cient algorithm based on immer-sion simulations. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1991,13(6):583–598.
[34] Wang D. A multiscale gradient algorithm for image segmentation using watershelds. PatternRecognition, 1997, 30(12):2043–2052.
[35] Bleau A, Leon L J. Watershed-based segmentation and region merging. Computer Visionand Image Understanding, 2000, 77(3):317–370.
[36] Chien S Y, Huang Y W, Chen L G. Predictive watershed: a fast watershed algorithm forvideo segmentation. IEEE Transactions on Circuits and Systems for Video Technology,2003, 13(5):453–461.
[37] Beare R. A locally constrained watershed transform. IEEE Transactions on Pattern Analysisand Machine Intelligence, 2006, 28(7):1063–1074.
[38] Osma-Ruiz V, Godino-Llorente J I, Sáenz-Lechón N, et al. An improved watershed al-gorithm based on e?cient computation of shortest paths. Pattern Recognition, 2007,40(3):1078–1090.
[39] Levner I, Zhang H. Classification-driven watershed segmentation. IEEE Transactions onImage Processing, 2007, 16(5):1437–1445.
[40] Aubert G, Kornprobst P. Mathematical problems in image processing: partial di?erentialequations and the calculus of variations. New York: Springer-Verlag, 2002.
[41] Sapiro G. Geometric partial di?erential equations and image analysis.世界图书出版公司, 2003.
[42]杨新.图像偏微分方程的原理与应用.上海:上海交通大学出版社, 2003.
[43] Tek H, Kimia B B. Image segmentation by reaction-di?usion bubbles. Proceedings of 5thInternational Conference on Computer Vision, 1995. 156–162.
[44] Chen Y, Vemuri B C, Wang L. Image denoising and segmentation via nonlinear di?usion.Computers & Mathematics with Applications, 2000, 39(5):131–149.
[45] Sofou A, Maragos P. PDE-based modeling of image segmentation using volumic ?ooding.Proceedings of International Conference on Image Processing, 2003. 14–17.
[46] Chan T F, Vese L A. Active contours without edges. IEEE Transactions on Image Process-ing, 2001, 10(2):266–277.
[47] Tsai A, Anthony Yezzi J, Willsky A S. Curve evolution implementation of the Mumford-Shah functional for image segmentation, denoising, interpolation, and magnification. IEEETransactions on Image Processing, 2001, 10(8):1169–1186.
[48] Gao S, Bui T D. Image segmentation and selective smoothing by using Mumford-Shahmodel. IEEE Transactions on Image Processing, 2005, 14(10):1537–1549.
[49] Kolmogorov V, Zabih R. What energy functions can be minimized via graph cuts. IEEETransactions on Pattern Analysis and Machine Intelligence, 2004, 26(2):147–159.
[50] Boykov Y, Jolly M P. Interactive graph cuts for optimal boundary and region segmentationof objects in N-D images. Proceedings of International Conference on Computer Vision,2001. 105–112.
[51] Boykov Y, Kolmogorov V. An experimental comparison of min-cut/max- ?ow algorithmsfor energy minimization in vision.pdf. IEEE Transactions on Patttern Analysis and MachineIntelligence, 2004, 26(9):1124–1137.
[52] Lombaert H, Sun Y, Grady L, et al. A multilevel banded graph cuts method for fast imagesegmentation. Proceedings of International Conference on Computer Vision, 2005. 259–265.
[53] Juan O, Boykov Y. Active graph cuts. Proceedings of IEEE Conference on Computer Visionand Pattern Recognition, 2006. 1023-1029 1023-1029 1023–1029.
[54]林瑶,田捷.医学图像分割方法综述.模式识别与人工智能, 2002, 15(2):192–204.
[55] Zhang D, Lu G. Segmentation of moving objects in image sequence: a review. Circuits,Systems, and Signal Processing, 2001, 20(2):143–183.
[56] Blake A. Visual tracking: a very short research roadmap. IEE Electronics Letters, 2006,42(5):254– 256.
[57]侯志强,韩崇昭.视觉跟踪技术综述.自动化学报, 2006, 32(4):603–617.
[58] Lee D S. E?ective Gaussian mixture learning for video background subtraction. IEEETransactions on Pattern Analysis and Machine Intelligence, 2005, 27(5):827–832.
[59] Song X, Nevatia R. A model-based vehicle segmentation method for tracking. Proceedingsof International Conference on Computer Vision, Beijing, 2005. 1124–1131.
[60] Cootes T F, Taylor C J, Cooper D H, et al. Active shape models—Their training andapplication. Computer Vision and Image Understanding, 1995, 61(1):38–59.
[61] Kim W, Lee J J. Object tracking based on the modular active shape model. Mechatronics,2005, 15(3):371–402.
[62] Cremers D. Dynamical statistical shape priors for level set-based tracking. IEEE Transac-tions on Pattern Analysis and Machine Intelligence, 2006, 28(8):1262–1273.
[63] Comaniciu D, Ramesh V, Meer P. Kernel-based object tracking. IEEE Transactions onPattern Analysis and Machine Intelligence, 2003, 25(5):564– 577.
[64] Collins R T. Mean-shift blob tracking through scale space. Proceedings of IEEE Conferenceof Computer Vision and Pattern Recognition, 2003. 234–240.
[65] Blake A, Isard M. Active contours: the application of techniqures from graphics, vision,control theory and statistics to visual tracking of shapes in motion. London: Springer-Verlag, 1998.
[66] Nguyen H T, Worring M, Boomgaard R, et al. Tracking Nonparameterized Object Contoursin Video. IEEE Transactions on Image Processing, 2002, 11(9):1081– 1091.
[67] Terzopoulos D, Szeliski R. Tracking with Kalman snakes. In: Blake A, Yullie A, (eds.).Proceedings of Active vision. U.S.A: MIT Press, 1992: 3– 20.
[68] Paragios N, Deriche R. Geodesic active contours and level sets for the detection and trackingof moving objects. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2000,22(3):266– 280.
[69] Paragios N, Deriche R. Geodesic active regions and level set methods for motion estimationand tracking. Computer Vision and Image Understanding, 2005, 97(3):259– 282.
[70] Peterfreund N. Robust tracking of position and velocity with Kalman snakes. IEEE Trans-actions on Pattern Analysis and Machine Intelligence, 1999, 21(6):564–569.
[71] Doucet A, Freitas N, Gordon N, (eds.). Sequential Monte Carlo methods in practice (statis-tics for engineering and information science). Springer–Verlag, 2001.
[72] Djuric P, Kotecha J, Zhang J, et al. Particle filtering. IEEE Signal Processing Magazine,2003, 20(5):19–38.
[73] Isard M, Blake A. CONDENSATION—conditional density propagation for visual track-ing. International Journal of Computer Vision, 1998, 29(1):5– 28.
[74] Isard M, Blake A. Contour tracking by stochastic propagation of conditional density. Pro-ceedings of European Conference on Computer Vision, 1996. 343–356.
[75] Li P, Zhang T, Pece A E. Visual contour tracking based on particle filters. Image and VisionComputing, 2003, 21(1):111–123.
[76] Koller-Meier E B, Ade F. Tracking multiple objects using the Condensation algorithm.Robotics and Automation Systems, 2001, 34(2-3):93–105.
[77] Zhou S K, Chellappa R, Moghaddam B. Visual tracking and recognition using appearance-adaptive models in particle filters. IEEE Transactions on Image Processing, 2004,13(11):1491–1506.
[78] Caselles V, Coll B. Snakes in movement. SIAM Journal on Numerical Analysis, 1996,33(6):2445–2456.
[79] Paragios N, Deriche R. A PDE-based level set approach for detection and tracking ofmoving object. Technical report 3173, INRIA, 1997.
[80] Bertalmio M, Sapiro G, Randall G. Morphing active contours. IEEE Transactions on PatternAnalysis and Machine Intelligence, 2000, 22(7):733–737.
[81] Jehan-Besson S, Barlaud M. DREAM2S: deformable regions driven by an Eulerian accurateminimization method for image and video segmentation. International Journal of ComputerVision, 2003, 53(1):45– 70.
[82] Freedman D, Zhang T. Active contours for tracking distributions. IEEE Transactions onImage Processing, 2004, 13(4):418–526.
[83] Zhang T, Freedman D. Improving performance of distribution tracking through back-ground mismatch. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2005,27(2):282–287.
[84] Zhang T, Freedman D. Tracking objects using density matching and shape priors. Proceed-ings of International Conference on Computer Vision, 2003. 1079–1085.
[85] Yilmaz A, Li X, Shah M. Contour-based object tracking with occlusion handling in videoacquired using mobile cameras. IEEE Transactions on Pattern Analysis and Machine Intel-ligence, 2004, 26(11):1531–1536.
[86] Rathi Y, Vaswani N, Tannenbaum A, et al. Particle filtering for geometric active contourswith application to tracking moving and deforming objects. Proceedings of IEEE ComputerSociety Conference on Computer Vision and Pattern Recognition, 2005. 2–9.
[87] Rathi Y, Tannenbaum N V A, Yezzi A. Tracking deforming objects using particle filter-ing for geometric active contours. IEEE Transactions on Pattern Analysis and MachineIntelligence, 2007, 29(8):1470–1475.
[88] Yu Z, Bajaj C. Normalized gradient vector di?usion and image segmentation. Proceedingsof European Conference on Computer Vision, 2002. 517–530.
[89] He Y, Luo Y, Hu D. Semi-automatic initialization of gradient vector ?ow snakes. Journalof Electronic Imaging, 2006, 15(4):043006.
[90] Chuang C, Lie W. A downstream algorithm based on extended gradient vector ?ow field forobject segmentation. IEEE Transactions on Image Processing, 2004, 13(10):1379–1392.
[91] Kass M, Witkin A, Terzopoulos D. Snakes: active contour models. International Journal ofComputer Vision, 1988, 1(4):321–331.
[92] Ranganath S. Contour extraction from cardiac MRI studies using snakes. IEEE Transactionson Medical Imaging, 1995, 14(2):328– 338.
[93] Székely G, Kelemen A, Brechbühler C, et al. Segmentation of 2-D and 3-D objects fromMRI volume data using constrained elastic deformations of ?exible Fourier contour andsurface models. Medical Image Analysis, 1996, 1(1):19– 34.
[94] Yezzi J, Kichenassamy S, Kumar A, et al. A geometric snake model for segmentation ofmedical imagery. IEEE Transactions on Medical Imaging, 1997, 16(2):199– 209.
[95] Atkins M, Mackiewich B. Fully automatic segmentation of the brain in MRI. IEEE Trans-actions on Medical Imaging, 1998, 17(1):98– 107.
[96] Canero C, Vilarino F, Mauri J, et al. Predictive (un)distortion model and 3-D reconstructionby biplane snakes. IEEE Transactions on Medical Imaging, 2002, 21(9):1188– 1201.
[97] Pardo X M, Radeva P, Cabello D. Discriminant snakes for 3D reconstruction of anatomicalorgans. Medical Image Analysis, 2003, 7(3):293–310.
[98] Chiou G I, Hwang J N. Image sequence classification using a neural network based activecontour model and a hidden Markov model. Proceedings of IEEE International Conferenceon Image Processing, 1994. 926– 930.
[99]李培华,张田文.主动轮廓线模型(蛇模型)综述.软件学报, 2000, 11(6):751– 757.
[100]陈波,赖剑煌.用于图像分割的活动轮廓模型综述.中国图象图形学报, 2007, 12(1):11– 20.
[101] Xu C, Yezzi J, Prince J. On the relationship between parametric and geometric activecontours. Proceedings of the Thirty-Fourth Asilomar Conference on Signals, Systems andComputers, 2000. 483–489.
[102] Xu N, Ahuja N, Bansal R. Object segmentation using graph cuts based active contours.Computer Vision and Image Understanding, 2007, 107(3):210–224.
[103] Li H, Yezzi A. Local or global minima: ?exible dual-front active contours. IEEE Transac-tions on Pattern Analysis and Machine Intelligence, 2006, 29(1):1–14.
[104] Caselles V, CattéF, Coll T, et al. A geometric model for active contours in image processing.Numerische Mathematik, 1993, 66(1):1–31.
[105] Malladi R, Sethian J A, Vemuri B C. Shape modeling with front propagation: a level set ap-proach. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1995, 17(2):158–175.
[106] Osher S, Sethian J. Fronts propagating with curvature dependent speed: algorithms basedon the Hamilton-Jacobi formulation. Journal of Computational Physics, 1988, 79(1):12–49.
[107] Sethian J A. Level set method and fast marching method. U. K.: Cambridge Universitypress, 1999.
[108] Osher S, Fedkiw R. Level set nethods and dynamic implicit surfaces. New York: Springer-Verlag, 2003.
[109] Chopp D L. Computing minimal surfaces via level set curvature ?ow. Journal of Computa-tional Physics, 1993, 106(1):77–91.
[110] Adalsteinsson D, Sethian J A. A fast level set method for propagating interfaces. Journalof Computational Physics, 1995, 118(2):269–277.
[111] Sethian J A. A fast marching level set method for monotonically advancing fronts. AppliedMathematics, 1996, 93(4):1591–1593.
[112] Sethian J A. Evolution, implementation, and application of level set and fast marchingmethods for advancing fronts. Journal of Computational Physics, 2001, 169(2):503–555.
[113] Zhao H. Fast sweeping method for Eikonal equations. Mathematics of Computation, 2005,74(250):603–627.
[114] Borgefors G. Distance transformations in digital images. Computer Vision, Graphics, andImage Processing, 1986, 34(3):344–371.
[115] Peng D, Merriman B, Osher S, et al. A PDE-based fast local level set method. Journal ofComputational Physics, 1999, 155(2):410–438.
[116] Li C, Xu C, Gui C, et al. Level set evolution without re-initialization: a new variationalformulation. Proceedings of Computer Vision and Pattern Recognition, 2005. 430–436.
[117] Caselles V, Kimmel R, Sapiro G. Geodesic active contours. Proceedings of Fifth Interna-tional Conference on Computer Vision, 1995. 694–699.
[118] Caselles V, Kimmel R, Sapiro G. Geodesic active contour. International Journal of Com-puter Vision, 1997, 22(1):61–79.
[119] Cohen L D. On active contour models and balloons. CVGIP: Image Understanding, 1991,53(2):211–218.
[120] Cohen L D, Cohen I. Finite-element methods for active contour models and balloons for2-D and 3-D images. IEEE Transactions on Pattern Analysis and Machine Intelligence,1993, 15(11):1131–1147.
[121] Xu C, Prince J L. Gradient vector ?ow: a new external force for snakes. Proceedings ofIEEE Conference of Computer Vision and Pattern Recognition, 1997. 66–71.
[122] Xu C, Prince J L. Snakes, shapes, and gradient vector ?ow. IEEE Transactions on ImageProcessing, 1998, 7(3):359–369.
[123]王元全,贾云得.梯度矢量流Snake模型临界点剖析.软件学报, 2006, 17(9):1915–1921.
[124] Paragios N, Mellina-Gottardo O, Ramesh V. Gradient vector ?ow fast geometric active con-tours. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2004, 26(3):402–407.
[125] Xu C, Prince J L. Generalized gradient vector ?ow external forces for active contours.Signal Processing, 1998, 71(2):131–139.
[126] Ray N, Acton S T. Motion gradient vector ?ow: An external force for tracking rollingleukocytes with shape and size constrained active contours. IEEE Transactions on MedicalImaging, 2004, 23(12):1466–1478.
[127] Cheng J, Foo S W. Dynamic directional gradient vector ?ow for snakes. IEEE Transactionson Image Processing, 2006, 15(6):1563–1571.
[128] Park H K, Chung M J. External force of snake: virtual electric field. Electronics Letters,2002, 38(24):1500–1502.
[129] Yuan D, Lu S. Simulated static electric field (SSEF) snake for deformable models. Pro-ceedings of International Conference on Pattern Recognition, 2002. 83–86.
[130] Li B, Acton S T. Active contour external force using vector field convolution for imagesegmentation. IEEE Transactions on Image Processing, 2007, 16(8):2096–2106.
[131] Li B, Acton S T. Vector field convolution for image segmentation using snakes. Proceedingsof International Conference of Image Processing, 2006. 1637–1640.
[132] Mumford D, Shah J. Optimal Approximations by piecewise smooth functions and asso-ciated variational problems. Communications on Pure and Applied Mathematics, 1989,42(4):577–685.
[133] Morel J M, Solimini S. Variational models for image segmentation: with seven imageprocessing experiments (progress in nonlinear di?erential equations and their applications).Birkhauser, 1994.
[134] Zhu S, Yuille A. Region competition: unifying snakes, region growing, and Bayes/MDLfor multiband image segmentation. IEEE Transactions on Pattern Analysis and MachineIntelligence, 1996, 18(9):884–900.
[135] Paragios N, Deriche R. Geodesic active regions: a new framework to deal with framepartition problems in computer vision. Journal of Visual Communication and Image Rep-resentation, 2002, 13(1-2):249–268.
[136] Paragios N, Deriche R. Geodesic active regions for texture segmentation. Technical report3440, INRIA, 1998.
[137] Chan T F, Vese L A. An active contour model without edges. Proceedings of Scale-SpaceTheories in Computer Vision, 1999.
[138] Vese L A, Chan T F. A multiple level set framework for image segmentation using theMumford and Shah model. International Journal of Computer Vision, 2002, 50(3):271–293.
[139] Nguyen H T, Worring M, Boomgaard R. Watersnakes: energy-driven watershed segmen-tation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2003, 25(3):330–342.
[140] Xie X, Mirmehdi M. RAGS: region-aided geometric snake. IEEE Transactions on ImageProcessing, 2004, 13(5):640–652.
[141] Ayed I B, Hennane N, Mitiche A. Unsupervised variational image segmenta-tion/classification using a Weibull observation model. IEEE Transactions on Image Pro-cessing, 2006, 15(11):34313439.
[142] Kim J, John W. Fisher I, Yezzi A, et al. A nonparametric statistical method for imagesegmentation using information theory and curve evolution. IEEE Transactions on ImageProcessing, 2005, 14(10):1486–1502.
[143] Cremers D, Rousson M, Deriche R. A review of statistical approaches to level set seg-mentation: integrating color, texture, motion and shape. International Journal of ComputerVision, 2007, 72(2):195–215.
[144] Trier O D, Taxt T. Evaluation of binarization methods for document images. IEEE Trans-actions on Pattern Analysis and Machine Intelligence, 1995, 17(3):312–315.
[145] Trier O, Jain A. Goal-directed evaluation of binarization methods. IEEE Transactions onPattern Analysis and Machine Intelligence, 1995, 17(12):1191–1201 1191–1201.
[146] Yanowitz S D, Bruckstein A M. A new method for image segmentation. Computer Vision,Graphics and Image Processing, 1989, 46:82–95.
[147] Liu F, Luo Y, Hu D. Active surface model-based adaptive thresholding algorithm by repul-sive external force. Journal of Electronic Imaging, 2003, 12(2):299–306.
[148]刘飞.图象分割的理论研究与应用[D].清华大学, 2003.
[149] Liang J, Doermann D, Li H. Camera-based analysis of text and document: a survey. Inter-national Journal on Document Analysis and Recognition, 2005, 7(2-3):84–104.
[150] Liang J, DeMenthon D, Doermann D. Geometric rectification of camera-captured documentimages. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2008, 30(4):591–605.
[151] Smeulders A W M, Worring M, Santini S, et al. Content -based image retrievel at the endof the early years. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2000,22(12):1349–1380.
[152] Fan J, Zeng G, Body M, et al. Seeded region growing: an extensive and comparative study.Pattern Recognition Letters, 2005, 26(8):1139–1156.
[153] Shih F Y, Cheng S. Automatic seeded region growing for color image segmentation. Imageand Vision Computing, 2005, 23(10):877–886.
[154] Deng Y, Manjunath B S. Unsupervised segmentation of color-texture regions in images andvideo. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2001, 23(8):800–810.
[155] Yu Z, Bajaj C. Image segmentation using gradient vector di?usion and region merging.Proceedings of 16th International Conference on Pattern Recognition, 2002. 941–944.
[156] Ray N, Acton S T, Altes T, et al. Merging parametric active contours within homogeneousimage regions for MRI-based lung segmentation. IEEE Transactions on Medical Imaging,2003, 22(2):189–199.
[157] He Y, Luo Y, Hu D. Automatic seeded region growing based on gradient vector ?ow forcolor image segmentation. Optical Engineering, 2007, 46(4):047003.
[158] Cheng H, Jiang X, Sun Y, et al. Color image segmentation: advances and prospects. PatternRecognition, 2001, 34(12):2259–2281.
[159] Ma Y, Manjunath B S. EdgeFlow: a technique for boundary detection and image segmen-tation. IEEE Transactions on Image Processing, 2000, 9(8):1375–1388.
[160] Nock R, Nielsen F. Statistical region merging. IEEE Transations on Pattern Analysis andMachine Intelligence, 2004, 26(11):1452–1458.
[161] Geusebroek J, Boomgaard R, Smeulders A W, et al. Color invariance. IEEE Transactionson Pattern Analysis and Machine Intelligence, 2001, 23(12):1338–1350.
[162] Koschan A, Abidi M. Detection and classification of edges in color images. IEEE SignalProcessing Magzine, 2005, 22(1):64–73.
[163] Manjunath B S, Ma W Y. Texture features for browsing and retrievel of image data. IEEETransactions on Pattern Analysis and Machine Intelligence, 1996, 18(8):837–842.
[164] Sagiv C, Sochen N A, Zeevi Y Y. Integrated active contours for texture segmentation. IEEETransactions on Image Processing, 2006, 15(6):1633–1646.
[165] Randen T, Husoy J H. Filtering for texture classification: a comparative study. IEEETransactions on Pattern Analysis and Machine Intelligence, 1999, 21(4):291–310.
[166] Ng I, Tan T, Kittler J. On local linear transform and Gabor filter representation of texture.Proceedings of International Conference on. Pattern Recognition, 1992. 627–631.
[167] Vincent L. Morphological grayscale reconstruction in image analysis: applications ande?cient algorithms. IEEE Transactions on Image Processing, 1993, 2(2):176–201.
[168] Beucher S, Meyer F. The morphological approach to segmentation: the watershed trans-formation. In: R.Dougherty E, (eds.). Proceedings of Mathematical Morphology in ImageProcessing, chapter 12, 433–481. New York: Marcel Dekker, Inc., 1993: 433–481.
[169] Haris K, Efstratiadis S N, Maglaveras N, et al. Hybrid image segmentation using watershedsand fast region merging. IEEE Transactions on Image Processing, 1998, 7(12):1684–1699.
[170] Trémeau A, Colantoni P. Regions adjacency graph applied to color image segmentation.IEEE Transactions on Image Processing, 2000, 9(4):735–744.
[171] Martin D, Fowlkes C, Tal D, et al. A database of human segmented natural images andits application to evaluating segmentation algorithms and measuring ecological statistics.Proceedings of 8th International Conference on Computer Vision, 2001. 416–423.
[172] Han X, Xu C, Prince J L. Fast numerical scheme for gradient vector ?ow computation usinga multigrid method. IET Image Processing, 2007, 1(1):48–55.
[173] Pavlovic V L, Sharma R, Huang T S. Visual interpretation of hand gestures for human-computer interaction: a review. IEEE Transactions on Pattern Analysis and Machine Intel-ligence, 1997, 19(7):677–695.
[174] Moelich M, Chan T. Tracking objects with the Chan-Vese algorithm. Technical ReportCam03-14, Mathematics Department, UCLA, 2003.
[175] Xu N, Bansal R, Ahuja N. Object segmentation using graph cuts based active contours.Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, 2003. 46–53.
[176] Xu N, Ahuja N. Object contour tracking using graph cuts based active contours. Proceed-ings of International Conference on Image Processing, 2002. 277–280.
[177] Li H, Elmoataz A, Fadili J, et al. A multi-label front propagation approach for objectsegmentation. Proceedings of International Conference on Pattern Recognition, 2004. 600–603.
[178] Li H, Elmoataz A, Fadili J, et al. Dual front evolution model and Its application in medicalimaging. Proceedings of MICCAI 2004, LNCS 3216, 2004. 103–110.
[179] Gunn S R, Nixon M S. A robust snake implementation: a dual active contour. IEEETransactions on Pattern Analysis and Machine Intelligence, 1997, 19(19):63–68.
[180] Sifakis E, Tziritas G. Moving object localisation using a muti-label fast marching algorithm.Signal Processing: Image Communication, 2001, 16(10):963–976.
[181] Cohen L D. Global minimum for active contour models: a minimal path approach. Inter-national Journal of Computer Vision, 1997, 24(1):57–78.