水平集方法及其在图像分割中的应用研究
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摘要
在信息社会里,图像已成为人类获取和交换信息的重要途径,而利用计算机进行数字图像处理是为了对图像中的目标进行分析,从而获得目标的客观信息并建立对图像的相关描述。图像分割一直是数字图像处理领域中最为基础和重要的问题,它是对图像进行视觉分析和模式识别的基本前提。所谓图像分割指的是根据灰度、颜色、纹理和形状等特征把图像划分成若干互不交迭的区域,并使这些特征在同一区域内呈现出相似性,而在不同区域间呈现出明显的差异性。近年来,水平集方法已经成为图像分割领域的一个研究热点,并在处理图像分割问题时表现出了良好的性能。相较于传统的图像分割方法,水平集方法有着显著的优点:用隐式表达的演化曲线(面)可以很自然地改变其拓扑结构,因此可以分割图像中具有复杂形状的目标对象;避免了对闭合曲线(面)演化过程的跟踪,将曲线(面)的演化转化成一个纯粹的偏微分方程求解问题;其有着较强的数学背景作为理论支撑,较为容易扩展到高维情况。因此,对其进行研究是非常有必要的。同时,水平集方法仍然处于发展阶段,其理论和应用方面的研究都有待于进一步深化和完善。在此背景下,本论文对水平集方法及其在图像分割中的应用和进一步扩展进行深入的研究,在基于局部信息的混合型水平集模型、基于多层水平集框架的多相图像分割、基于水平集方法的密度聚类框架、基于先验信息的植物叶片图像分割几个方面提出了有效的算法。
本文的主要工作概况如下:
(1)提出了一种新的基于局部信息的Local Chan-Vese(LCV)模型。通过使用局部图像信息,该模型可以在较少的迭代次数内分割灰度不均匀图像。在规则化项中引入能量惩罚项,使得水平集函数在演化过程中很自然地保持为近似的符号距离函数。此外,给出了一个基于演化曲线长度变化的水平集演化终止准则。最后,构造了一个新的扩展型结构张量,将其与LCV模型相结合,可以分割灰度均匀或者不均匀的纹理图像。在一系列人工和真实图像上的实验证明了LCV模型的有效性和鲁棒性。通过与Chan-Vese模型和Local Binary Fitting模型进行实验对比,显示出LCV模型可以在较少的迭代次数内分割灰度均匀或不均匀的普通与纹理图像,并且对于初始轮廓的位置和演化参数的选择不敏感。
(2)通过在水平集方法中引入一种图像层的概念,构建了一种新的多层水平集分割框架。与传统的多水平集分割不同,多层水平集框架仅使用一个水平集函数,并且以一种层级演化的方式来进行多相图像分割。为了保证收敛的速度,提出了一种参数自适应更新方案。此外,定义了单图像层上和全局上的水平集演化终止准则,整个演化过程中无需任何人工干涉。在人工和真实图像上的实验结果表明了多层水平集框架的有效性,与传统的多相Chan-Vese模型相比,多层水平集框架具有较低的计算复杂度和更快的收敛速度。
(3)提出使用水平集演化来逼近聚类中心的思想,并构建了一种基于水平集方法的密度聚类框架,从而成功地将图像分割方法扩展至密度聚类领域。与传统水平集方法不同,借助于数据空间的特性,水平集初始轮廓可被自动创建。演化过程中,不同类型的轮廓会以不同的方式包围各个聚类中心。为了得到包围聚类中心的最优的水平集边界,给出了演化轮廓记录集的动态更新准则。此外,还提出了一种有效的数据空间中的水平集演化终止准则。最后,在水平集边界的基础上设计了一种新的水平集密度,以用于在聚类过程中替代传统的概率密度。在人工和真实数据集上的实验结果表明,所提出的密度聚类框架可以有效地处理聚类中心较为接近的数据集,并进行离群点检测。通过与其它密度聚类算法的实验对比,显示出该聚类框架可以避免过拟合现象,并能解决聚类边界点与噪声或离群点的易混淆问题。
(4)提出了两种有效的基于先验信息的植物叶片图像分割方案。两种方案的共同特点在于,分割过程需要分为预分割和正式分割两步来进行。第一种方案是基于水平集演化方式,使用叶片的近似对称性作为先验信息。第二种分割方案是基于形态学处理中的分水岭算法,使用叶片的形状大小作为先验信息。实验表明,对存在交叠或枝叶干扰情况的真实叶片图像,上述两种方案均能产生正确的分割。
In information society, image has become an important way in which people can acquire and exchange information. So, the purpose of digital image processing on computer is to analyze the existing objects in images and acquire the essential information about the objects and give the related descriptions of image. Image segmentation has always been a most fundamental and important problem in the field of digital image processing. It is also the fundamental premise for the visual analysis and pattern recognition on the images. Generally speaking, image segmentation is to divide one image into some non-overlapping regions according to the intensity, color, texture and shape features. The segmentation result should make these features be homogeneous in the same region and obviously distinct in different regions.
Recently, level set method has become a research hotspot in the field of image segmentation and achieved a good performance while addressing the image segmentation problem. Compared with the traditional image segmentation methods, level set method has some distinct advantages. First, it can segment the object with complicated shape in image since the evolving curve (surface) implicitly represented by the zero level set can naturally change its topological structure. Second, it can avoid the track procedure for the closed evolving curve (surface) and further transform the evolution problem of curve (surface) to the numerical solution to partial differential equation. Finally, it is theoretically supported by some strong mathematical backgrounds and can be easily extended to high dimensional case. Thus, it is very necessary to make a deep study on level set method. However, level set method is still staying in the developing stage, and the investigation of its theory and application should be enhanced and improved. In this thesis, the level set methods with their applications in image segmentation and further extensions have been deeply investigated. Some efficient algorithms have been proposed such as the hybrid level set model based on local information, multi-layer level set framework for multi-phase image segmentation, density-based clustering framework by using level set method, and prior information based plant leaf image segmentation methods.
The main works in this thesis can be summarized as follows:
(1) We proposed a new local Chan-Vese (LCV) model based on local statistical information. By incorporating the local image information into the proposed model, the images with intensity inhomogeneity can be efficiently segmented in few iterations. During the evolution process, the level set function can naturally maintain an approximate signed distance function by introducing a penalizing energy into the regularization term. Moreover, a termination criterion based on the length change of the evolving curve is proposed to ensure that the evolving curve can automatically stop on the true boundaries of objects. Particularly, an extended structure tensor (EST) was constructed for texture image segmentation. Combining the EST with the proposed LCV model, the texture image can be efficiently segmented no matter whether it presents intensity inhomogeneity or not. Finally, the experiments on some synthetic and real images have demonstrated the efficiency and robustness of our model. And the comparisons with the Chan-Vese (CV) model and local binary fitting (LBF) model also show that our LCV model can segment images with few iterations and be less sensitive to the location of initial contour and the selection of governing parameters.
(2) By introducing a conception of image layer into the level set method, we proposed a new multi-layer level set framework. Different from traditional multiple level set segmentation schemes, the proposed multi-layer level set framework employs only one level set function with a hierarchical form to segment the multi-phase images. To keep the convergence speed, an adaptable evolution parameter update scheme was proposed. In addition, we also gave the termination criteria for level set evolution on single image layer and global evolution. It should be emphasized that no manual interventions are needed in the whole evolution process. Finally, the experiments on some synthetic and real images have demonstrated the efficiency of our multi-layer level set framework. And the comparisons with multi-phase Chan-Vese method also show that the proposed framework has a less time-consuming computation and much faster convergence.
(3) We proposed finding the approximations of cluster centers through the level set evolution and constructed a density-based clustering framework by using level set method. Our framework can successfully extend image segmentation method to density-based clustering field. Unlike traditional level set methods, our level set evolution scheme can automatically compute the initial boundaries based on the characteristic of data space. In the evolution process, different types of contours would evolve in different ways to surround each cluster centers. To obtain the optimized level set boundary (LSB) surrounding the corresponding cluster center after the evolution process, the evolving boundary record (EBR) update criterion was defined. In addition, a termination criterion was presented to stop the evolution process when no more cluster centers can be found. Finally, a new level set density (LSD) was computed according to the level set boundary for clustering instead of traditional probability density. The experiments on some synthetic and real datasets show that the proposed framework works well while clustering the dataset with near cluster centers and detecting the outliers. The comparisons with some other density-based clustering methods further show that the proposed framework can successfully avoid the overfitting phenomenon and solve the confusion problem of cluster boundary points and outliers.
(4) We proposed two efficient plant leaf image segmentation schemes based on the prior information. The common feature for two schemes is that the segmentation process can be divided into pre-segmentation procedure and formal segmentation procedure. The first segmentation scheme is based on level set evolution which uses the approximate symmetry of leaf as prior information. The second segmentation scheme is based on watershed algorithm in mathematical morphology which adopts the size of leaf as prior information. The experiments on some real leaf images show that two segmentation schemes can both achieve success while segmenting the leaf images with overlapping phenomenon and interference produced by branches and non-target leaves.
本文的主要工作概况如下:
(1)提出了一种新的基于局部信息的Local Chan-Vese(LCV)模型。通过使用局部图像信息,该模型可以在较少的迭代次数内分割灰度不均匀图像。在规则化项中引入能量惩罚项,使得水平集函数在演化过程中很自然地保持为近似的符号距离函数。此外,给出了一个基于演化曲线长度变化的水平集演化终止准则。最后,构造了一个新的扩展型结构张量,将其与LCV模型相结合,可以分割灰度均匀或者不均匀的纹理图像。在一系列人工和真实图像上的实验证明了LCV模型的有效性和鲁棒性。通过与Chan-Vese模型和Local Binary Fitting模型进行实验对比,显示出LCV模型可以在较少的迭代次数内分割灰度均匀或不均匀的普通与纹理图像,并且对于初始轮廓的位置和演化参数的选择不敏感。
(2)通过在水平集方法中引入一种图像层的概念,构建了一种新的多层水平集分割框架。与传统的多水平集分割不同,多层水平集框架仅使用一个水平集函数,并且以一种层级演化的方式来进行多相图像分割。为了保证收敛的速度,提出了一种参数自适应更新方案。此外,定义了单图像层上和全局上的水平集演化终止准则,整个演化过程中无需任何人工干涉。在人工和真实图像上的实验结果表明了多层水平集框架的有效性,与传统的多相Chan-Vese模型相比,多层水平集框架具有较低的计算复杂度和更快的收敛速度。
(3)提出使用水平集演化来逼近聚类中心的思想,并构建了一种基于水平集方法的密度聚类框架,从而成功地将图像分割方法扩展至密度聚类领域。与传统水平集方法不同,借助于数据空间的特性,水平集初始轮廓可被自动创建。演化过程中,不同类型的轮廓会以不同的方式包围各个聚类中心。为了得到包围聚类中心的最优的水平集边界,给出了演化轮廓记录集的动态更新准则。此外,还提出了一种有效的数据空间中的水平集演化终止准则。最后,在水平集边界的基础上设计了一种新的水平集密度,以用于在聚类过程中替代传统的概率密度。在人工和真实数据集上的实验结果表明,所提出的密度聚类框架可以有效地处理聚类中心较为接近的数据集,并进行离群点检测。通过与其它密度聚类算法的实验对比,显示出该聚类框架可以避免过拟合现象,并能解决聚类边界点与噪声或离群点的易混淆问题。
(4)提出了两种有效的基于先验信息的植物叶片图像分割方案。两种方案的共同特点在于,分割过程需要分为预分割和正式分割两步来进行。第一种方案是基于水平集演化方式,使用叶片的近似对称性作为先验信息。第二种分割方案是基于形态学处理中的分水岭算法,使用叶片的形状大小作为先验信息。实验表明,对存在交叠或枝叶干扰情况的真实叶片图像,上述两种方案均能产生正确的分割。
In information society, image has become an important way in which people can acquire and exchange information. So, the purpose of digital image processing on computer is to analyze the existing objects in images and acquire the essential information about the objects and give the related descriptions of image. Image segmentation has always been a most fundamental and important problem in the field of digital image processing. It is also the fundamental premise for the visual analysis and pattern recognition on the images. Generally speaking, image segmentation is to divide one image into some non-overlapping regions according to the intensity, color, texture and shape features. The segmentation result should make these features be homogeneous in the same region and obviously distinct in different regions.
Recently, level set method has become a research hotspot in the field of image segmentation and achieved a good performance while addressing the image segmentation problem. Compared with the traditional image segmentation methods, level set method has some distinct advantages. First, it can segment the object with complicated shape in image since the evolving curve (surface) implicitly represented by the zero level set can naturally change its topological structure. Second, it can avoid the track procedure for the closed evolving curve (surface) and further transform the evolution problem of curve (surface) to the numerical solution to partial differential equation. Finally, it is theoretically supported by some strong mathematical backgrounds and can be easily extended to high dimensional case. Thus, it is very necessary to make a deep study on level set method. However, level set method is still staying in the developing stage, and the investigation of its theory and application should be enhanced and improved. In this thesis, the level set methods with their applications in image segmentation and further extensions have been deeply investigated. Some efficient algorithms have been proposed such as the hybrid level set model based on local information, multi-layer level set framework for multi-phase image segmentation, density-based clustering framework by using level set method, and prior information based plant leaf image segmentation methods.
The main works in this thesis can be summarized as follows:
(1) We proposed a new local Chan-Vese (LCV) model based on local statistical information. By incorporating the local image information into the proposed model, the images with intensity inhomogeneity can be efficiently segmented in few iterations. During the evolution process, the level set function can naturally maintain an approximate signed distance function by introducing a penalizing energy into the regularization term. Moreover, a termination criterion based on the length change of the evolving curve is proposed to ensure that the evolving curve can automatically stop on the true boundaries of objects. Particularly, an extended structure tensor (EST) was constructed for texture image segmentation. Combining the EST with the proposed LCV model, the texture image can be efficiently segmented no matter whether it presents intensity inhomogeneity or not. Finally, the experiments on some synthetic and real images have demonstrated the efficiency and robustness of our model. And the comparisons with the Chan-Vese (CV) model and local binary fitting (LBF) model also show that our LCV model can segment images with few iterations and be less sensitive to the location of initial contour and the selection of governing parameters.
(2) By introducing a conception of image layer into the level set method, we proposed a new multi-layer level set framework. Different from traditional multiple level set segmentation schemes, the proposed multi-layer level set framework employs only one level set function with a hierarchical form to segment the multi-phase images. To keep the convergence speed, an adaptable evolution parameter update scheme was proposed. In addition, we also gave the termination criteria for level set evolution on single image layer and global evolution. It should be emphasized that no manual interventions are needed in the whole evolution process. Finally, the experiments on some synthetic and real images have demonstrated the efficiency of our multi-layer level set framework. And the comparisons with multi-phase Chan-Vese method also show that the proposed framework has a less time-consuming computation and much faster convergence.
(3) We proposed finding the approximations of cluster centers through the level set evolution and constructed a density-based clustering framework by using level set method. Our framework can successfully extend image segmentation method to density-based clustering field. Unlike traditional level set methods, our level set evolution scheme can automatically compute the initial boundaries based on the characteristic of data space. In the evolution process, different types of contours would evolve in different ways to surround each cluster centers. To obtain the optimized level set boundary (LSB) surrounding the corresponding cluster center after the evolution process, the evolving boundary record (EBR) update criterion was defined. In addition, a termination criterion was presented to stop the evolution process when no more cluster centers can be found. Finally, a new level set density (LSD) was computed according to the level set boundary for clustering instead of traditional probability density. The experiments on some synthetic and real datasets show that the proposed framework works well while clustering the dataset with near cluster centers and detecting the outliers. The comparisons with some other density-based clustering methods further show that the proposed framework can successfully avoid the overfitting phenomenon and solve the confusion problem of cluster boundary points and outliers.
(4) We proposed two efficient plant leaf image segmentation schemes based on the prior information. The common feature for two schemes is that the segmentation process can be divided into pre-segmentation procedure and formal segmentation procedure. The first segmentation scheme is based on level set evolution which uses the approximate symmetry of leaf as prior information. The second segmentation scheme is based on watershed algorithm in mathematical morphology which adopts the size of leaf as prior information. The experiments on some real leaf images show that two segmentation schemes can both achieve success while segmenting the leaf images with overlapping phenomenon and interference produced by branches and non-target leaves.
引文
Adalsteinsson D, Sethian JA. 1995. A fast level set method for propagating interfaces [J]. Journal of Computational Physics, 118:269-277.
Adams R, Bischof L. 1994. Seeded region growing [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 16(6): 641-647.
Aggarwal CC, Yu PS. 2000. Finding generalized projected clusters in high dimensional space [C].In: Proc. ACM SIGMOD Int. Conf. on Management of Data (SIGMOD’00), 70-81.
Aggarwal CC, Yu PS. 2002. Redefining clustering for high-dimensional applications [J]. IEEE Transactions on Knowledge and Data Engineering, 14(2):210-225.
Agarwal G., Belhumeur P, Feiner S, Jacobs D, Kress JW, Ramamoorthi R, Bourg N, Dixit N, Ling H, Mahajan D, Russel Rl, Shirdhonkar S, Sunkavalli K, White S. 2006. First steps toward an electronic field guide for plants [J]. Taxonomy, 55(3):597-610.
Agrawal R, Gehrke J, Gunopulos D, Raghavan P. 1998. Automatic subspace clustering of high dimensional data for data mining applications [C]. In: Proc. International Conference Management of Data (SIGMOD’98), 94-105. Amini A, Weymouth A, Jain R. 1990. Using dynamic programming for solving variational
problem in vision [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(9):855-867.
An J, Rousson M, Xu C. 2007. Gamma-convergence approximation to piecewise smooth medical image segmentation [C]. In: Proc. International Conference on Medical Image Computing and Computer Assisted Intervention, 4792: 495-502.
Ankerst M, Breunig M, Kriegel HP, Sander J. 1999. OPTICS: ordering points to identify the clustering structure [C]. In: Proc. 1999 ACM Special Interest Group on Management of Data (SIGMOD’99), 49-60.
Aubert G, Barlaud M, Faugeras O, Jehan-Besson S. 2002. Image segmentation using active contours: calculus of variations of shape gradients [R]. Research Report, INRIA.
Ayed IB, Mitiche A, Belhadj Z. 2005. Multi region level set partitioning of synthetic aperture radar images [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 27(5): 793-800.
Bigun J, Grandlund GH. 1987. Optimal orientation detection of linear symmetry [C]. In: Proc. IEEE First International Conference on Computer Vision (ICCV’87), 433-438.
Bigun J, Grandlund GH, Wiklund J. 1991. Multidimensional orientation estimation with applications to texture analysis and optical flow [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(8): 775-790.
Boykov Y, Veksler O, Zabih R. 2001. Fast approximate energy minimization via graph cuts [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 23(11):1222-1239.
Brox T, Weickert J. 2004. Level set based image segmentation with multiple regions [C]. In: Proc. 26th DAGM, 415-423.
Brox T, Weickert J, Burgeth B, Mr′azek P. 2006. Nonlinear structure tensors [J]. Image and Vision Computing, 24(1): 41-55.
Brox T, Cremers D. 2007. On the statistical interpretation of the piecewise smooth mumford-shah functional [C]. In: Proc. Scale Space Var. Met. Comp. Vis., 4485:203-213.
Camargo A, Smith JS. 2009. An image-processing based algorithm to automatically identify plant disease visual symptoms [J]. Biosystem Engineering, 102:9-21.
Caselles V, Catte F, Coll T, Dibos F. 1993. A geometric model for active contours [J]. Numerische Mathematik, 66:1-31.
Caselles V, Kimmel R, Sapiro G. 1997. Geodesic active contours [J]. International Journal of Computer Vision, 22(1): 61-79.
Chan T, Vese LA. 2001. Active contours without edges [J]. IEEE Transactions on Image Processing, 10(2):266-277.
Chan T, Zhu W. 2003. Level Set Based Shape Prior Segmentation [R]. UCLA CAM, 3(66).
Cheeseman P, Stutz J. 1996. Bayesian classification (Autoclass): theory and results [M]. In:
Advances in Knowledge Discovery and Data Mining, AAAI Press and MIT Press, Menlo Park, Ca., 153-180.
Chen Y, Tagare H, Thiruvenkadam S, Huang F, Wilson D, Gopinath KS, Briggs RW, Geiser E. 2002. Using shape priors in geometric active contours in a variational framework [J]. International Journal of Computer Vision, 50(3):315–328.
Chop D. 1993. Computing minimal surfaces via level set curvature flow [J]. Journal of Computational Physics, 106:77-91.
Cohen LD. 1991. On active contour models and balloons [J]. Computer Vision, Graphics, Image Processing: image understanding, 53(2):211-218.
Cremers D. Tischhauser F. Weickert J. Schnorr C. 2002. Diffusion snakes: introducing statistical shape knowledge into the Mumford–Shah functional [J]. International Journal of Computer Vision, 50(3): 295-313.
Cremers D, Sochen N, Schn?rr C. 2006. A multiphase dynamic labeling model for variational recognition-driven image segmentation [J]. International Journal of Computer Vision, 66(1): 67-81.
Ding C, Ren XF, Zha H, et al. 2001. Spectral min-max cut for graph partitioning and data clustering [C]. In: Proc. the IEEE International Conference on Data Mining, 2001:107-114.
Droske M, Rumpf M. 2003. A variational approach to nonrigid morphological image registration [J]. SIAM Journal on Applied Mathematics, 64(2):668-687.
Engquist B, Tornberg AK, Tsai R. 2005. Discretization of Dirac delta functions in level set methods [J]. Journal of Computational Physics, 207(1): 28-51.
Enright D, Fedkiw R, Ferziger J, Mitchell I. 2002. A hybrid particle level set method for improved interface capturing [J]. Journal of Computational Physics, 183:83-116.
Esedoglu S, Shen J. 2002. Digital inpainting based on the Mumford-Shah-Euler image model [J]. European Journal of Applied Mathematics, 13: 353-370.
Ester M, Kriegel H, Sander J, Xu X. 1996. A density-based algorithm for discovering clusters in large spatial databases with noise [C]. In: Proc. Int’l Conf. Knowledge Discovery and Data Mining, 226-231.
Feddern C, Weickert J, Burgeth B. 2003. Level-set methods for tensor-valued images [C]. In: Proc. Second IEEE Workshop on Variational, Geometric and Level Set Methods in Computer Vision, 65-72.
Fisher, DH. 1987. Knowledge acquisition via incremental conceptual clustering [J]. Machine Learning, 2:139-172.
Fu H, Chi Z R. 2006. Combined thresholding and neural network approach for vein patternextraction from leaf images [J]. Vision, Image and Signal Processing, 153(6): 881-892.
Fukunaga K. 1990. Introduction to statistical pattern recognition, 2nd ed [M]. Boston Academic Press.
Gdalyahu Y, Weinshall D, Werman M. 2001. Self organization in vision: stochastic clustering for image segmentation, perceptual grouping, and image database organization [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 23(10):1053-1074.
Geraud T, Strub PY, Darbon J. 2001. Color image segmentation based on automatic morphological clustering [C]. In: Proc. IEEE International Conference on Image Processing, 70-73.
Gennari JH, Langley P, Fisher, DH. 1989. Models of incremental concept formation [J]. Artificial Intelligence, 40(1-3):11-61.
Gokcay E, Principe JC. 2002. Information theoretic clustering [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 24(2):158-171.
Goldenberg R, Kimmel R, Rivlin M, Rudzsky M. 2007. Fast geodesic active contour [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 24: 603-619.
Gomes J, Faugeras O. 2000. Reconciling distance functions and level sets [J]. Journal of Visual Communication and Image Representation, l (11):209-22.
Gonzalez RC, Richard EW著,阮秋琦等译. 2002.数字图像处理(第二版)[M].北京:电子工业出版社.
Graham RL, Hell P. 1985. On the history of the minimum spanning tree problem[J]. Annals of the History of Computing, 7(1):43-57.
Gu HB, Causon DM, Mingham CG, Qian L. 2009. A fast-marching semi-Lagrangian level set method for free surface flows [C]. In: Proc. the Nineteenth International Offshore and Polar Engineering Conference, 359-367.
Guha S, Rastogi R, Shim K. 1998. CURE: an efficient clustering algorithm for large databases [C]. In: Proc. ACM SIGMOD International Conference on Management of Data, 73-84.
Han JW, Kamber M. 2006. Data mining concepts and techniques, 2nd ed [M]. The Morgan Kaufmann Series in Data Management Systems, Morgan Kaufmann Publishers.
Harten A, Engquist B, Osher S, Chakravarthy S. 1987. Uniformly high-order accurate essentially non-oscillatory schemes III [J]. Journal of Computational Physics, 71:231-303.
Hinneburg A, Keim DA. 1998. An efficient approach to clustering in large multimedia databases with noise [C]. In: Proc. Int’l Conf. Knowledge Discovery and Data Mining, 58-65.
Hou ZJ. 2006. A review on MR image intensity inhomogeneity correction [J]. International Journal of Biomedical Imaging, 2006:1-11.
Jain AK, Murty MN, Flynn PJ. 1999. Data clustering: a review [J]. ACM Computing Surveys, 31(3): 264-323.
Kapur JN, Sahoo PK, Wong AKC. 1985. A new method for gray-level picture thresholding using the entropy of the histogram [J]. Computer Vision, Graphics, and Image Processing, 29(3): 273-285.
Karantzalos K, Paragios N. 2009. Recognition-driven two-dimensional competing priors toward automatic and accurate building detection [J]. IEEE Transactions on Geosciences and Remote Sending, 47(1):133-144.
Kass M, Witkin A, Terzopoulos D. 1987. Snakes: active contour models [J]. International Journal of Computer Vision, 1: 321–331.
Kichenassamy S, Kumar A, Olver P, Tannenbaum A, Yezzi A. 1995. Gradient flows andgeometric active contour models [C]. In: Proc. IEEE International Conference in Computer Vision, Cambridge, MA, USA, 810-815.
Kimmel R. 2003. Fast edge integration [C]. In Osher S., Paragios N. Geometric Level Set Methods in Imaging, Vision, and Graphics. Springer, 59-78
King B. 1973. Step-wise clustering procedures [J]. Journal of the American Statistical Association, 69: 86-101.
Kittler J, Illingworth J. 1986. Minimum error thresholding [J]. Pattern Recognition, 19(1): 41-47. Kohonen T. 2001. Self-organizing maps, 3rd ed [M]. Berlin: Springer-Vrelag.
Knapp AK, Fay PA, Blair JM, Collins SL, Smith MD, Carlisle JD, Harper CW, Danner BT, Lett MS, McCarron JK. 2002. Rainfall variability, carbon cycling, and plant species diversity in a mesic grassland [J]. Science, 298:2202-2205.
Kunal NC, Ramakrishnan KR. 2007. Stability and convergence of the level set method in computer vision [J]. Pattern Recognition Letters, 28(7):884-893.
Lankton S, Nain D, Yezzi A, Tannenbaum A. 2007. Hybrid geodesic region-based curve evolutions for image segmentation [C]. In: Proc. SPIE:Med. Imag., 6510: 65104U.
Lankton S, Tannenbaum A. 2008. Localizing region-based active contours [J]. IEEE Transactions on Image Processing, 17(11): 2029-2039.
Lee SH, Seo JK. 2006. Level set-based bimodal segmentation with stationary global minimum [J]. IEEE Transactions on Image Processing, 15(9):2843-2852.
Lee SM, Abott AL, Clark NA, Araman P A. 2005. Active contours on statistical manifolds and texture segmentation [C]. In: Proc. IEEE Internat. Conf. on Image Processing (ICIP), 3: 828-831.
Leventon ME, Grimson WEL, Faugeras O. 2000. Statistical shape influence in geodesic active contours [C]. In: Proc. IEEE Conf. Comput. Vis. Pattern Recognit., 1:316–323.
Li CM, Xu CY, Gui CF, Fox MD. 2005. Level set formulation without re-initialization: a new variational formulation [C]. In: Proc. IEEE International Conference on Computer Vision and Pattern Recognition (CVPR’05), 1:430-436.
Li CM, Kao CY, Gore JC, Ding ZH. 2007. Implicit active contours driven by local binary fitting energy [C]. In: Proc. CVPR’07, 1-7.
Li C M, Kao C Y, Gore J C, Ding Z H. 2008. Minimization of region-scalable fitting energy for image segmentation [J]. IEEE Transactions on Image Processing, 17 (10):1940-1949.
Li YF, Zhu QS, Cao YK, Wang CL. 2005. A Leaf vein extraction method based on Snakes technique[C]. In: Proc. IEEE International Conference on Neural Networks and Brain, 2005:885-888.
Lin N, Yu WC, Duncan JS. 2002. Combinative multi-scale level set framework for echocardiographic image segmentation [J]. Medical Image Analysis, 7(4):529-537
Lysaker M, Osher S, Tai XC. 2004. Noise removal using smoothed normals and surface fitting [J]. IEEE Transactions on Image Processing, 13(10):1345-1357.
Liu XD, Osher S, Chan T. 1996. Weighted essentially non-oscillatory schemes [J]. Journal of Computational Physics, 126:202-212.
Luo JZ, Luo Z, Chen LP, Tong LY, Wang MY. 2008. A semi-implicit level set method for structural shape and topology optimization [J]. Journal of Computational Physics, 227(11):5561-5581.
MacQueen J. 1967. Some methods for classification and analysis of multivariate observations [C].In: Proc. 5th Berleley Symposium on Mathematical Statistics and Probability, 1:281-297.
Malladi R, Sethian JA, Vemuri BC. 1995. Shape modeling with front propagation: a level set approach [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17(2):158-175.
Manh AG, Rabatel G, Assemat L, Aldon MJ. 2001. Weed leaf image segmentation by deformable templates [J]. Journal of Agricultural Engineering Research, 80 (2):139-146.
Mansouri AR, Mitiche A, Vázquez C. 2006. Multiregion competition: a level set extension of region competition to multiple region image partitioning [J]. Computer Vision and Image Understanding, 101(3):137-150.
Maroulis DE, Savelonas MA, Iakovidis DK, Karkanis SA, Dimitropoulos N. 2007. Variable background active contour model for computer-aided delineation of nodules in thyroid ultrasound images [J]. IEEE Transactions on Information Technology in Biomedicine, 11(5):537-543.
Meyer F, Beucher S. 1990. Morphology segmentation [J]. Journal of Visual Communication and Image Representation, 1(1):21-26.
Michailovich O, Rathi Y, Tannenbaum A. 2007. Image segmentation using active contours driven by the bhattacharyya gradient flow [J]. IEEE Transactions on Image Processing, 16(11): 2787-2801.
Mumford D, Shah J. 1989. Optimal approximation by piecewise smooth functions and associated variational problems [J]. Communications on Pure and Applied Mathematics, 42: 577-685.
Ng RT, Han J. 2002. CLARANS: a method for clustering objects for spatial data mining [J]. IEEE Transactions on Knowledge and Data Engineering, 14(5):1003-1016.
Osher S, Sethian J A. 1988. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations [J]. Journal of Computational Physics, 79(1):12-49.
Otsu N. 1978. Discriminant and least square threshold selection [C]. In: Proc. the 4th International Journal of Current Pharmaceutical Research, 1978:592-596.
Pan Y, Birdwell JD, Djouadi SM. 2006. Efficient implementation of the Chan-Vese models without solving PDEs [C]. In: Proc. the International Workshop on Multimedia Signal Processing, 350-354.
Paragios N, Deriche R. 2002. Geodesic active regions: a new framework to deal with frame partition problems in computer vision [J]. Journal of Visual Communication and Image Representation, 13(1/2):249-268.
Paragios N, Mellina-Gottardo O, Ramesh V. 2004. Gradient vector flow fast geometric active contours [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 26 (3): 402-407.
Persson M, Astrand B. 2008. Classification of crops and weeds extracted by active shape models [J]. Biosystem Engineering, 100:484-497.
Pham TD. 2001. Image segmentation using probabilistic fuzzy C-Means clustering [C]. In: Proc.
International Conference on Image Processing, 722-725. Pi L, Shen CM, Li F, Fan JS. 2007. A variational formulation for segmenting desired objects in color images [J]. Image and Vision Computing, 25(9):1414-1421.
Piovano J, Rousson M, Papadopoulo T. 2007. Efficient segmentation of piecewise smooth images [C]. In: Proc. Scale Space Var. Met. Comp. Vis., 4485: 709-720.
Pounds JA, Puschendorf R. Ecology: clouded future [J]. Nature, 427:107-109.
Rousson M, Pragios N. 2002. Shape priors for level set representations [C]. In: Eur. Conf. Comput. Vis., 2: 78–92
Rousson M, Brox T, Deriche R. 2003. Active unsupervised texture segmentation on a diffusion based feature space [C]. In: Proc. 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’03), 2: 699-704.
Rouy E, Tourin A. 1992. A viscosity solutions approach to shape from shading [J]. SIAM Journal on Numerical Analysis, 29(3):867-884.
Samson C, Blanc-F′eraud L, Aubert G, Zerubia J. 2000. A level set model for image classification [J]. International Journal of Computer Vision, 40(3):187-197.
Sandberg B, Chan T, Vese L. 2002. A level-set and Gabor-based active contour algorithm for segmenting textured images [R]. Technical Report 39, Math. Dept. UCLA, Los Angeles, USA.
Sander J, Ester M, Kriegel H, Xu X. 1998. Density-based clustering in spatial databases: the algorithm GDBSCAN and its applications [J]. Data Mining and Knowledge Discovery, 2(2): 169-194.
Sethian JA. 1996. Level set methods and fast marching methods [M]. Cambridge University Press.
Sheikholeslami G, Chatterjee S, Zhang A. WaveCluster: a multi-resolution clustering approach for
very large spatial databases [C]. In: Proc. 1998 Conf. Very Large Databases, 428-439.
Shi J, Malik J. 2000. Normalized cuts and image segmentation [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(8): 888-905.
Shi Y, Karl W. 2005. A fast level set method without solving PDES [C]. In: Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP’05), 2:97-100.
Shu CW, Osher S. 1988. Efficient implementation of essentially non-oscillatory shock capturing schemes [J]. Journal of Computational Physics, 77:439-471.
Siddiqi K, Lauziere YB, Tannenbaum A, Zucker SW. 1998. Area and length minimizing flow for shape segmentation [J]. IEEE Transactions on Image Processing, 7: 433-443.
Sifakis E, Garcia C, Tziritas G. 2002. Bayesian Level Sets for Image Segmentation [J]. Journal of Visual Communication and Image Representation, 13(1-2):44-64
Sneath PHA, Sokal RR. 1973. Numerical Taxonomy [M]. Freeman, London, UK. Soille P. 1998. Morphological image analysis [M].Berlin : Springer-Verlag.
Solem JE, Overgaard NC, Heyden A. 2006. Initialization techniques for segmentation with the Chan-Vese model [C]. In: Proc. 18th International Conference on Pattern Recognition (ICPR’06), 2006, 2:171-174.
Sonka M, Hlavac V, Boyle R著,艾海舟等译.数字图像处理、分析和机器视觉(第二版)[M]. 北京:邮电出版社.
Sum K, Cheung P. 2008. Vessel extraction under non-uniform illumination: a level set approach [J]. IEEE Transactions on Biomedical Engineering, 55(1):358-360.
Sussman M, Fatemi E. 1999. An efficient, interface preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow [J]. SIAM Journal on Scientific Computing, 20:1165-1191.
Strain J. 1999. Semi-Lagrangian methods for level set equations [J]. Journal of Computational Physics, 151(2): 498-533.
Tasdizen T, Whitaker, R, Burchard P, Osher S. 2003. Geometric surface processing via normalmaps [J]. ACM Transactions on Graphics, 22(4): 1012-1033.
Towers J. 2007. Two methods for discretizing a delta function supported on a level set [J]. Journal of Computational Physics, 220: 915-931.
Tsai A, Yezzi A, Willsky AS. 2001. Curve evolution implementation of the Mumford–Shah functional for image segmentation, denoising, interpolation, and magnification [J]. IEEE Transactions on Image Processing, 10(8):1169-1186.
Tsai A, Yezzi AJ, Willsky AS. 2003. A shape-based approach to the segmentation of medical imagery using level sets [J]. IEEE Transactions on Medical Imaging, 22(2):137-154.
Tsai YHR. 2002. Rapid and accurate computation of the distance function using grids [J]. Journal of Computational Physics, 178(1): 175-195.
Tsai YHR, Osher, S. 2005. Total variation and level set based methods in image science [J]. Cambridge University Press, Acta Numerica., 2005:1-61.
Tung AKH, Xu X, Ooi CB. 2005. CURLER: finding and visualizing nonlinear correlation clusters [C]. In: Proc. ACM SIGMOD international conference on Management of data, 467-478.
Vese L, Chan T. 2002. A multiphase level set framework for image segmentation using the mumford and shah model [J]. International Journal of Computer Vision, 50:271-293.
Villegas R, Dorn O, Moscoso M, Kindelan M. 2008. Reservoir characterization using stochastic initializations and the level set method [J]. Computers & Mathematics with Applications, 56(3):697-708.
Vincent L, Soille P. 1991. Watersheds in digital spaces: an efficient algorithm based on immersion simulation [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(6):583-598.
Vinod H. 1969. Integer programming and the theory of grouping [J]. Journal of the American Statistical Association, 64:506-517.
Vovk U, Pernu? F, Likar B. 2007. A review of methods for correction of intensity inhomogeneity in MRI [J]. IEEE Transactions on Medical Imaging, 26(3):405-421.
Wang L, Li CM, Suna Q, Xia DS, Kao CY. 2009. Active contours driven by local and global intensity fitting energy with application to brain MR image segmentation [J]. Computerized Medical Imaging and Graphics, 33:520-531.
Wang W, Yang J, Muntz R. 1997. STING: a statistical information grid approach to spatial data mining [C]. In: Proc. 23rd Conf. Very Large Databases, 186-195.
Wang Z, Vemuri B. 2004. Tensor field segmentation using region based active contour model [C]. In: Proc. Eighth European Conf. Computer Vision (ECCV '04), Springer LNCS 3024:304-315.
Weber M, Blake A, Cipolla R. 2003. Initialisation and termination of active contour level-set evolutions [C]. In: Proc. 2nd IEEE workshop on Variational, Geometric and Level Set Methods in Computer Vision, 161-168.
Weickert J, ter Haar Romeny BM, Viergever MA. 1998. Efficient and reliable schemes for nonlinear diffusion filtering [J]. IEEE Transactions on Image Processing, 7(3):398-410.
Wen X. 2009. High order numerical methods to two dimensional delta function integrals in level set methods [J]. Journal of Computational Physics, 228(11):4273-4290
White S, Marino D, Feiner S. 2006. LeafView: A user Interface for automated botanical species identification and data collection [C]. In: Proc. ACM UIST’06, 2006:15-18.
White S, Marino D, Feiner S. 2007. Designing a mobile user interface for automated speciesidentification [C]. In: Proc. ACM CHI’07, 2007:291-294.
Williams DJ, Shah M. 1992. A fast algorithm for active contours and curvature estimation [J]. Computer Vision, Graphics, Image Processing: Image Understanding, 55(1):14-26.
Xia RB, Liu WJ, Zhao JB, Li L. 2007. An optimal initialization technique for improving the segmentation performance of Chan-Vese model [C]. In: Proc. IEEE International Conference on Automation and Logistics. 2007: 411-415.
Xu C, Prince JL. 1998. Snakes, shapes and gradient vector flow [J]. IEEE Transactions on Imaging Processing, 7(3):359-369.
Yang J, Duncan JS. 2004. 3D image segmentation of deformable objects with joint shape-intensity prior models using level sets [J]. Medical Image Analysis, 8(3):285-294
Zhang T, Ramakrishnan R, Livny M. 1996. BIRCH: an efficient data clustering method for very large databases [J]. ACM SIGMOD Record, 25(2):103-114.
Zhao HK, Chan T, Merriman B, Osher S. 1996. A variational level set approach to multiphase motion [J]. Journal of Computational Physics, 127(1):179-195.
Zheng LY, Zhang JT, Wang QY. 2009. Mean-shift-based color segmentation of images containing green vegetation [J]. Computers and Electronics in Agriculture, 65:93–98.
Zhong JM. 2006. Wavelet-based multiscale level-set curve evolution and adaptive statistical analysis for image denoising [J]. Journal of Electronic Imaging, 15(4):043004.
Zhou HY, Yuan Y, Lin FQ, Liu TW. 2008. Level set image segmentation with Bayesian analysis [J]. Neurocomputing, 71(10-12):1994-2000.
Zhu SC, Yuille AL. 1996. Region competition: unifying snakes, region growing, and Bayes/MDL for multiband image segmentation [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 18(9): 884-900.
陈波,赖剑煌. 2007.用于图像分割的活动轮廓模型综述[J].中国图象图形学报, 12(1):11-20.
傅弘,池哲儒,常杰,傅承新. 2004.基于人工神经网络的叶脉信息提取[J].植物学通报, 21(4):429-436.
龚声蓉,刘纯平,王强. 2006.数字图像处理与分析[M].北京:清华大学出版社.
李俊,杨新,施鹏飞. 2002.基于Mumford-Shah模型的快速水平集图像分割方法[J].计算机学报, 11:1175-1183.
刘国才,王耀南,段宣初. 2009.基于知识的多层Mumford-Shah向量值图像分割模型[J].自动化学报, 35(4):356-363.
刘全儒. 2007.植物多样性与人类的关系[R].中国生物多样性保护基金会报告.
刘胜祥,黎维平. 2007.植物学[M].北京:科学出版社.
杨新. 2003.图像偏微分方程的原理与应用[M].上海:上海交通大学出版社.
章毓晋. 2001.图像分割[M].北京:科学出版社.
章毓晋. 2005.中国图像工程[J].中国图象图形学报, 11(5):601-632.
章毓晋. 2006.中国图像工程[J].中国图象图形学报, 12(5):753-775.
章毓晋. 2007.中国图像工程[J].中国图象图形学报, 13(5):825-852.
章毓晋. 2008.中国图像工程[J].中国图象图形学报, 14(5):809-837.
郑小东,王晓洁. 2007.基于图像处理的植物叶特征提取研究现状[J].农机化研究, 8(8):193-195.
朱静,田兴军,陈彬,吕劲紫. 2005.植物叶形的计算机识别系统[J].植物学通报, 22(5):599-604.
Adams R, Bischof L. 1994. Seeded region growing [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 16(6): 641-647.
Aggarwal CC, Yu PS. 2000. Finding generalized projected clusters in high dimensional space [C].In: Proc. ACM SIGMOD Int. Conf. on Management of Data (SIGMOD’00), 70-81.
Aggarwal CC, Yu PS. 2002. Redefining clustering for high-dimensional applications [J]. IEEE Transactions on Knowledge and Data Engineering, 14(2):210-225.
Agarwal G., Belhumeur P, Feiner S, Jacobs D, Kress JW, Ramamoorthi R, Bourg N, Dixit N, Ling H, Mahajan D, Russel Rl, Shirdhonkar S, Sunkavalli K, White S. 2006. First steps toward an electronic field guide for plants [J]. Taxonomy, 55(3):597-610.
Agrawal R, Gehrke J, Gunopulos D, Raghavan P. 1998. Automatic subspace clustering of high dimensional data for data mining applications [C]. In: Proc. International Conference Management of Data (SIGMOD’98), 94-105. Amini A, Weymouth A, Jain R. 1990. Using dynamic programming for solving variational
problem in vision [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(9):855-867.
An J, Rousson M, Xu C. 2007. Gamma-convergence approximation to piecewise smooth medical image segmentation [C]. In: Proc. International Conference on Medical Image Computing and Computer Assisted Intervention, 4792: 495-502.
Ankerst M, Breunig M, Kriegel HP, Sander J. 1999. OPTICS: ordering points to identify the clustering structure [C]. In: Proc. 1999 ACM Special Interest Group on Management of Data (SIGMOD’99), 49-60.
Aubert G, Barlaud M, Faugeras O, Jehan-Besson S. 2002. Image segmentation using active contours: calculus of variations of shape gradients [R]. Research Report, INRIA.
Ayed IB, Mitiche A, Belhadj Z. 2005. Multi region level set partitioning of synthetic aperture radar images [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 27(5): 793-800.
Bigun J, Grandlund GH. 1987. Optimal orientation detection of linear symmetry [C]. In: Proc. IEEE First International Conference on Computer Vision (ICCV’87), 433-438.
Bigun J, Grandlund GH, Wiklund J. 1991. Multidimensional orientation estimation with applications to texture analysis and optical flow [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(8): 775-790.
Boykov Y, Veksler O, Zabih R. 2001. Fast approximate energy minimization via graph cuts [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 23(11):1222-1239.
Brox T, Weickert J. 2004. Level set based image segmentation with multiple regions [C]. In: Proc. 26th DAGM, 415-423.
Brox T, Weickert J, Burgeth B, Mr′azek P. 2006. Nonlinear structure tensors [J]. Image and Vision Computing, 24(1): 41-55.
Brox T, Cremers D. 2007. On the statistical interpretation of the piecewise smooth mumford-shah functional [C]. In: Proc. Scale Space Var. Met. Comp. Vis., 4485:203-213.
Camargo A, Smith JS. 2009. An image-processing based algorithm to automatically identify plant disease visual symptoms [J]. Biosystem Engineering, 102:9-21.
Caselles V, Catte F, Coll T, Dibos F. 1993. A geometric model for active contours [J]. Numerische Mathematik, 66:1-31.
Caselles V, Kimmel R, Sapiro G. 1997. Geodesic active contours [J]. International Journal of Computer Vision, 22(1): 61-79.
Chan T, Vese LA. 2001. Active contours without edges [J]. IEEE Transactions on Image Processing, 10(2):266-277.
Chan T, Zhu W. 2003. Level Set Based Shape Prior Segmentation [R]. UCLA CAM, 3(66).
Cheeseman P, Stutz J. 1996. Bayesian classification (Autoclass): theory and results [M]. In:
Advances in Knowledge Discovery and Data Mining, AAAI Press and MIT Press, Menlo Park, Ca., 153-180.
Chen Y, Tagare H, Thiruvenkadam S, Huang F, Wilson D, Gopinath KS, Briggs RW, Geiser E. 2002. Using shape priors in geometric active contours in a variational framework [J]. International Journal of Computer Vision, 50(3):315–328.
Chop D. 1993. Computing minimal surfaces via level set curvature flow [J]. Journal of Computational Physics, 106:77-91.
Cohen LD. 1991. On active contour models and balloons [J]. Computer Vision, Graphics, Image Processing: image understanding, 53(2):211-218.
Cremers D. Tischhauser F. Weickert J. Schnorr C. 2002. Diffusion snakes: introducing statistical shape knowledge into the Mumford–Shah functional [J]. International Journal of Computer Vision, 50(3): 295-313.
Cremers D, Sochen N, Schn?rr C. 2006. A multiphase dynamic labeling model for variational recognition-driven image segmentation [J]. International Journal of Computer Vision, 66(1): 67-81.
Ding C, Ren XF, Zha H, et al. 2001. Spectral min-max cut for graph partitioning and data clustering [C]. In: Proc. the IEEE International Conference on Data Mining, 2001:107-114.
Droske M, Rumpf M. 2003. A variational approach to nonrigid morphological image registration [J]. SIAM Journal on Applied Mathematics, 64(2):668-687.
Engquist B, Tornberg AK, Tsai R. 2005. Discretization of Dirac delta functions in level set methods [J]. Journal of Computational Physics, 207(1): 28-51.
Enright D, Fedkiw R, Ferziger J, Mitchell I. 2002. A hybrid particle level set method for improved interface capturing [J]. Journal of Computational Physics, 183:83-116.
Esedoglu S, Shen J. 2002. Digital inpainting based on the Mumford-Shah-Euler image model [J]. European Journal of Applied Mathematics, 13: 353-370.
Ester M, Kriegel H, Sander J, Xu X. 1996. A density-based algorithm for discovering clusters in large spatial databases with noise [C]. In: Proc. Int’l Conf. Knowledge Discovery and Data Mining, 226-231.
Feddern C, Weickert J, Burgeth B. 2003. Level-set methods for tensor-valued images [C]. In: Proc. Second IEEE Workshop on Variational, Geometric and Level Set Methods in Computer Vision, 65-72.
Fisher, DH. 1987. Knowledge acquisition via incremental conceptual clustering [J]. Machine Learning, 2:139-172.
Fu H, Chi Z R. 2006. Combined thresholding and neural network approach for vein patternextraction from leaf images [J]. Vision, Image and Signal Processing, 153(6): 881-892.
Fukunaga K. 1990. Introduction to statistical pattern recognition, 2nd ed [M]. Boston Academic Press.
Gdalyahu Y, Weinshall D, Werman M. 2001. Self organization in vision: stochastic clustering for image segmentation, perceptual grouping, and image database organization [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 23(10):1053-1074.
Geraud T, Strub PY, Darbon J. 2001. Color image segmentation based on automatic morphological clustering [C]. In: Proc. IEEE International Conference on Image Processing, 70-73.
Gennari JH, Langley P, Fisher, DH. 1989. Models of incremental concept formation [J]. Artificial Intelligence, 40(1-3):11-61.
Gokcay E, Principe JC. 2002. Information theoretic clustering [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 24(2):158-171.
Goldenberg R, Kimmel R, Rivlin M, Rudzsky M. 2007. Fast geodesic active contour [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 24: 603-619.
Gomes J, Faugeras O. 2000. Reconciling distance functions and level sets [J]. Journal of Visual Communication and Image Representation, l (11):209-22.
Gonzalez RC, Richard EW著,阮秋琦等译. 2002.数字图像处理(第二版)[M].北京:电子工业出版社.
Graham RL, Hell P. 1985. On the history of the minimum spanning tree problem[J]. Annals of the History of Computing, 7(1):43-57.
Gu HB, Causon DM, Mingham CG, Qian L. 2009. A fast-marching semi-Lagrangian level set method for free surface flows [C]. In: Proc. the Nineteenth International Offshore and Polar Engineering Conference, 359-367.
Guha S, Rastogi R, Shim K. 1998. CURE: an efficient clustering algorithm for large databases [C]. In: Proc. ACM SIGMOD International Conference on Management of Data, 73-84.
Han JW, Kamber M. 2006. Data mining concepts and techniques, 2nd ed [M]. The Morgan Kaufmann Series in Data Management Systems, Morgan Kaufmann Publishers.
Harten A, Engquist B, Osher S, Chakravarthy S. 1987. Uniformly high-order accurate essentially non-oscillatory schemes III [J]. Journal of Computational Physics, 71:231-303.
Hinneburg A, Keim DA. 1998. An efficient approach to clustering in large multimedia databases with noise [C]. In: Proc. Int’l Conf. Knowledge Discovery and Data Mining, 58-65.
Hou ZJ. 2006. A review on MR image intensity inhomogeneity correction [J]. International Journal of Biomedical Imaging, 2006:1-11.
Jain AK, Murty MN, Flynn PJ. 1999. Data clustering: a review [J]. ACM Computing Surveys, 31(3): 264-323.
Kapur JN, Sahoo PK, Wong AKC. 1985. A new method for gray-level picture thresholding using the entropy of the histogram [J]. Computer Vision, Graphics, and Image Processing, 29(3): 273-285.
Karantzalos K, Paragios N. 2009. Recognition-driven two-dimensional competing priors toward automatic and accurate building detection [J]. IEEE Transactions on Geosciences and Remote Sending, 47(1):133-144.
Kass M, Witkin A, Terzopoulos D. 1987. Snakes: active contour models [J]. International Journal of Computer Vision, 1: 321–331.
Kichenassamy S, Kumar A, Olver P, Tannenbaum A, Yezzi A. 1995. Gradient flows andgeometric active contour models [C]. In: Proc. IEEE International Conference in Computer Vision, Cambridge, MA, USA, 810-815.
Kimmel R. 2003. Fast edge integration [C]. In Osher S., Paragios N. Geometric Level Set Methods in Imaging, Vision, and Graphics. Springer, 59-78
King B. 1973. Step-wise clustering procedures [J]. Journal of the American Statistical Association, 69: 86-101.
Kittler J, Illingworth J. 1986. Minimum error thresholding [J]. Pattern Recognition, 19(1): 41-47. Kohonen T. 2001. Self-organizing maps, 3rd ed [M]. Berlin: Springer-Vrelag.
Knapp AK, Fay PA, Blair JM, Collins SL, Smith MD, Carlisle JD, Harper CW, Danner BT, Lett MS, McCarron JK. 2002. Rainfall variability, carbon cycling, and plant species diversity in a mesic grassland [J]. Science, 298:2202-2205.
Kunal NC, Ramakrishnan KR. 2007. Stability and convergence of the level set method in computer vision [J]. Pattern Recognition Letters, 28(7):884-893.
Lankton S, Nain D, Yezzi A, Tannenbaum A. 2007. Hybrid geodesic region-based curve evolutions for image segmentation [C]. In: Proc. SPIE:Med. Imag., 6510: 65104U.
Lankton S, Tannenbaum A. 2008. Localizing region-based active contours [J]. IEEE Transactions on Image Processing, 17(11): 2029-2039.
Lee SH, Seo JK. 2006. Level set-based bimodal segmentation with stationary global minimum [J]. IEEE Transactions on Image Processing, 15(9):2843-2852.
Lee SM, Abott AL, Clark NA, Araman P A. 2005. Active contours on statistical manifolds and texture segmentation [C]. In: Proc. IEEE Internat. Conf. on Image Processing (ICIP), 3: 828-831.
Leventon ME, Grimson WEL, Faugeras O. 2000. Statistical shape influence in geodesic active contours [C]. In: Proc. IEEE Conf. Comput. Vis. Pattern Recognit., 1:316–323.
Li CM, Xu CY, Gui CF, Fox MD. 2005. Level set formulation without re-initialization: a new variational formulation [C]. In: Proc. IEEE International Conference on Computer Vision and Pattern Recognition (CVPR’05), 1:430-436.
Li CM, Kao CY, Gore JC, Ding ZH. 2007. Implicit active contours driven by local binary fitting energy [C]. In: Proc. CVPR’07, 1-7.
Li C M, Kao C Y, Gore J C, Ding Z H. 2008. Minimization of region-scalable fitting energy for image segmentation [J]. IEEE Transactions on Image Processing, 17 (10):1940-1949.
Li YF, Zhu QS, Cao YK, Wang CL. 2005. A Leaf vein extraction method based on Snakes technique[C]. In: Proc. IEEE International Conference on Neural Networks and Brain, 2005:885-888.
Lin N, Yu WC, Duncan JS. 2002. Combinative multi-scale level set framework for echocardiographic image segmentation [J]. Medical Image Analysis, 7(4):529-537
Lysaker M, Osher S, Tai XC. 2004. Noise removal using smoothed normals and surface fitting [J]. IEEE Transactions on Image Processing, 13(10):1345-1357.
Liu XD, Osher S, Chan T. 1996. Weighted essentially non-oscillatory schemes [J]. Journal of Computational Physics, 126:202-212.
Luo JZ, Luo Z, Chen LP, Tong LY, Wang MY. 2008. A semi-implicit level set method for structural shape and topology optimization [J]. Journal of Computational Physics, 227(11):5561-5581.
MacQueen J. 1967. Some methods for classification and analysis of multivariate observations [C].In: Proc. 5th Berleley Symposium on Mathematical Statistics and Probability, 1:281-297.
Malladi R, Sethian JA, Vemuri BC. 1995. Shape modeling with front propagation: a level set approach [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17(2):158-175.
Manh AG, Rabatel G, Assemat L, Aldon MJ. 2001. Weed leaf image segmentation by deformable templates [J]. Journal of Agricultural Engineering Research, 80 (2):139-146.
Mansouri AR, Mitiche A, Vázquez C. 2006. Multiregion competition: a level set extension of region competition to multiple region image partitioning [J]. Computer Vision and Image Understanding, 101(3):137-150.
Maroulis DE, Savelonas MA, Iakovidis DK, Karkanis SA, Dimitropoulos N. 2007. Variable background active contour model for computer-aided delineation of nodules in thyroid ultrasound images [J]. IEEE Transactions on Information Technology in Biomedicine, 11(5):537-543.
Meyer F, Beucher S. 1990. Morphology segmentation [J]. Journal of Visual Communication and Image Representation, 1(1):21-26.
Michailovich O, Rathi Y, Tannenbaum A. 2007. Image segmentation using active contours driven by the bhattacharyya gradient flow [J]. IEEE Transactions on Image Processing, 16(11): 2787-2801.
Mumford D, Shah J. 1989. Optimal approximation by piecewise smooth functions and associated variational problems [J]. Communications on Pure and Applied Mathematics, 42: 577-685.
Ng RT, Han J. 2002. CLARANS: a method for clustering objects for spatial data mining [J]. IEEE Transactions on Knowledge and Data Engineering, 14(5):1003-1016.
Osher S, Sethian J A. 1988. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations [J]. Journal of Computational Physics, 79(1):12-49.
Otsu N. 1978. Discriminant and least square threshold selection [C]. In: Proc. the 4th International Journal of Current Pharmaceutical Research, 1978:592-596.
Pan Y, Birdwell JD, Djouadi SM. 2006. Efficient implementation of the Chan-Vese models without solving PDEs [C]. In: Proc. the International Workshop on Multimedia Signal Processing, 350-354.
Paragios N, Deriche R. 2002. Geodesic active regions: a new framework to deal with frame partition problems in computer vision [J]. Journal of Visual Communication and Image Representation, 13(1/2):249-268.
Paragios N, Mellina-Gottardo O, Ramesh V. 2004. Gradient vector flow fast geometric active contours [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 26 (3): 402-407.
Persson M, Astrand B. 2008. Classification of crops and weeds extracted by active shape models [J]. Biosystem Engineering, 100:484-497.
Pham TD. 2001. Image segmentation using probabilistic fuzzy C-Means clustering [C]. In: Proc.
International Conference on Image Processing, 722-725. Pi L, Shen CM, Li F, Fan JS. 2007. A variational formulation for segmenting desired objects in color images [J]. Image and Vision Computing, 25(9):1414-1421.
Piovano J, Rousson M, Papadopoulo T. 2007. Efficient segmentation of piecewise smooth images [C]. In: Proc. Scale Space Var. Met. Comp. Vis., 4485: 709-720.
Pounds JA, Puschendorf R. Ecology: clouded future [J]. Nature, 427:107-109.
Rousson M, Pragios N. 2002. Shape priors for level set representations [C]. In: Eur. Conf. Comput. Vis., 2: 78–92
Rousson M, Brox T, Deriche R. 2003. Active unsupervised texture segmentation on a diffusion based feature space [C]. In: Proc. 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’03), 2: 699-704.
Rouy E, Tourin A. 1992. A viscosity solutions approach to shape from shading [J]. SIAM Journal on Numerical Analysis, 29(3):867-884.
Samson C, Blanc-F′eraud L, Aubert G, Zerubia J. 2000. A level set model for image classification [J]. International Journal of Computer Vision, 40(3):187-197.
Sandberg B, Chan T, Vese L. 2002. A level-set and Gabor-based active contour algorithm for segmenting textured images [R]. Technical Report 39, Math. Dept. UCLA, Los Angeles, USA.
Sander J, Ester M, Kriegel H, Xu X. 1998. Density-based clustering in spatial databases: the algorithm GDBSCAN and its applications [J]. Data Mining and Knowledge Discovery, 2(2): 169-194.
Sethian JA. 1996. Level set methods and fast marching methods [M]. Cambridge University Press.
Sheikholeslami G, Chatterjee S, Zhang A. WaveCluster: a multi-resolution clustering approach for
very large spatial databases [C]. In: Proc. 1998 Conf. Very Large Databases, 428-439.
Shi J, Malik J. 2000. Normalized cuts and image segmentation [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(8): 888-905.
Shi Y, Karl W. 2005. A fast level set method without solving PDES [C]. In: Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP’05), 2:97-100.
Shu CW, Osher S. 1988. Efficient implementation of essentially non-oscillatory shock capturing schemes [J]. Journal of Computational Physics, 77:439-471.
Siddiqi K, Lauziere YB, Tannenbaum A, Zucker SW. 1998. Area and length minimizing flow for shape segmentation [J]. IEEE Transactions on Image Processing, 7: 433-443.
Sifakis E, Garcia C, Tziritas G. 2002. Bayesian Level Sets for Image Segmentation [J]. Journal of Visual Communication and Image Representation, 13(1-2):44-64
Sneath PHA, Sokal RR. 1973. Numerical Taxonomy [M]. Freeman, London, UK. Soille P. 1998. Morphological image analysis [M].Berlin : Springer-Verlag.
Solem JE, Overgaard NC, Heyden A. 2006. Initialization techniques for segmentation with the Chan-Vese model [C]. In: Proc. 18th International Conference on Pattern Recognition (ICPR’06), 2006, 2:171-174.
Sonka M, Hlavac V, Boyle R著,艾海舟等译.数字图像处理、分析和机器视觉(第二版)[M]. 北京:邮电出版社.
Sum K, Cheung P. 2008. Vessel extraction under non-uniform illumination: a level set approach [J]. IEEE Transactions on Biomedical Engineering, 55(1):358-360.
Sussman M, Fatemi E. 1999. An efficient, interface preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow [J]. SIAM Journal on Scientific Computing, 20:1165-1191.
Strain J. 1999. Semi-Lagrangian methods for level set equations [J]. Journal of Computational Physics, 151(2): 498-533.
Tasdizen T, Whitaker, R, Burchard P, Osher S. 2003. Geometric surface processing via normalmaps [J]. ACM Transactions on Graphics, 22(4): 1012-1033.
Towers J. 2007. Two methods for discretizing a delta function supported on a level set [J]. Journal of Computational Physics, 220: 915-931.
Tsai A, Yezzi A, Willsky AS. 2001. Curve evolution implementation of the Mumford–Shah functional for image segmentation, denoising, interpolation, and magnification [J]. IEEE Transactions on Image Processing, 10(8):1169-1186.
Tsai A, Yezzi AJ, Willsky AS. 2003. A shape-based approach to the segmentation of medical imagery using level sets [J]. IEEE Transactions on Medical Imaging, 22(2):137-154.
Tsai YHR. 2002. Rapid and accurate computation of the distance function using grids [J]. Journal of Computational Physics, 178(1): 175-195.
Tsai YHR, Osher, S. 2005. Total variation and level set based methods in image science [J]. Cambridge University Press, Acta Numerica., 2005:1-61.
Tung AKH, Xu X, Ooi CB. 2005. CURLER: finding and visualizing nonlinear correlation clusters [C]. In: Proc. ACM SIGMOD international conference on Management of data, 467-478.
Vese L, Chan T. 2002. A multiphase level set framework for image segmentation using the mumford and shah model [J]. International Journal of Computer Vision, 50:271-293.
Villegas R, Dorn O, Moscoso M, Kindelan M. 2008. Reservoir characterization using stochastic initializations and the level set method [J]. Computers & Mathematics with Applications, 56(3):697-708.
Vincent L, Soille P. 1991. Watersheds in digital spaces: an efficient algorithm based on immersion simulation [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(6):583-598.
Vinod H. 1969. Integer programming and the theory of grouping [J]. Journal of the American Statistical Association, 64:506-517.
Vovk U, Pernu? F, Likar B. 2007. A review of methods for correction of intensity inhomogeneity in MRI [J]. IEEE Transactions on Medical Imaging, 26(3):405-421.
Wang L, Li CM, Suna Q, Xia DS, Kao CY. 2009. Active contours driven by local and global intensity fitting energy with application to brain MR image segmentation [J]. Computerized Medical Imaging and Graphics, 33:520-531.
Wang W, Yang J, Muntz R. 1997. STING: a statistical information grid approach to spatial data mining [C]. In: Proc. 23rd Conf. Very Large Databases, 186-195.
Wang Z, Vemuri B. 2004. Tensor field segmentation using region based active contour model [C]. In: Proc. Eighth European Conf. Computer Vision (ECCV '04), Springer LNCS 3024:304-315.
Weber M, Blake A, Cipolla R. 2003. Initialisation and termination of active contour level-set evolutions [C]. In: Proc. 2nd IEEE workshop on Variational, Geometric and Level Set Methods in Computer Vision, 161-168.
Weickert J, ter Haar Romeny BM, Viergever MA. 1998. Efficient and reliable schemes for nonlinear diffusion filtering [J]. IEEE Transactions on Image Processing, 7(3):398-410.
Wen X. 2009. High order numerical methods to two dimensional delta function integrals in level set methods [J]. Journal of Computational Physics, 228(11):4273-4290
White S, Marino D, Feiner S. 2006. LeafView: A user Interface for automated botanical species identification and data collection [C]. In: Proc. ACM UIST’06, 2006:15-18.
White S, Marino D, Feiner S. 2007. Designing a mobile user interface for automated speciesidentification [C]. In: Proc. ACM CHI’07, 2007:291-294.
Williams DJ, Shah M. 1992. A fast algorithm for active contours and curvature estimation [J]. Computer Vision, Graphics, Image Processing: Image Understanding, 55(1):14-26.
Xia RB, Liu WJ, Zhao JB, Li L. 2007. An optimal initialization technique for improving the segmentation performance of Chan-Vese model [C]. In: Proc. IEEE International Conference on Automation and Logistics. 2007: 411-415.
Xu C, Prince JL. 1998. Snakes, shapes and gradient vector flow [J]. IEEE Transactions on Imaging Processing, 7(3):359-369.
Yang J, Duncan JS. 2004. 3D image segmentation of deformable objects with joint shape-intensity prior models using level sets [J]. Medical Image Analysis, 8(3):285-294
Zhang T, Ramakrishnan R, Livny M. 1996. BIRCH: an efficient data clustering method for very large databases [J]. ACM SIGMOD Record, 25(2):103-114.
Zhao HK, Chan T, Merriman B, Osher S. 1996. A variational level set approach to multiphase motion [J]. Journal of Computational Physics, 127(1):179-195.
Zheng LY, Zhang JT, Wang QY. 2009. Mean-shift-based color segmentation of images containing green vegetation [J]. Computers and Electronics in Agriculture, 65:93–98.
Zhong JM. 2006. Wavelet-based multiscale level-set curve evolution and adaptive statistical analysis for image denoising [J]. Journal of Electronic Imaging, 15(4):043004.
Zhou HY, Yuan Y, Lin FQ, Liu TW. 2008. Level set image segmentation with Bayesian analysis [J]. Neurocomputing, 71(10-12):1994-2000.
Zhu SC, Yuille AL. 1996. Region competition: unifying snakes, region growing, and Bayes/MDL for multiband image segmentation [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 18(9): 884-900.
陈波,赖剑煌. 2007.用于图像分割的活动轮廓模型综述[J].中国图象图形学报, 12(1):11-20.
傅弘,池哲儒,常杰,傅承新. 2004.基于人工神经网络的叶脉信息提取[J].植物学通报, 21(4):429-436.
龚声蓉,刘纯平,王强. 2006.数字图像处理与分析[M].北京:清华大学出版社.
李俊,杨新,施鹏飞. 2002.基于Mumford-Shah模型的快速水平集图像分割方法[J].计算机学报, 11:1175-1183.
刘国才,王耀南,段宣初. 2009.基于知识的多层Mumford-Shah向量值图像分割模型[J].自动化学报, 35(4):356-363.
刘全儒. 2007.植物多样性与人类的关系[R].中国生物多样性保护基金会报告.
刘胜祥,黎维平. 2007.植物学[M].北京:科学出版社.
杨新. 2003.图像偏微分方程的原理与应用[M].上海:上海交通大学出版社.
章毓晋. 2001.图像分割[M].北京:科学出版社.
章毓晋. 2005.中国图像工程[J].中国图象图形学报, 11(5):601-632.
章毓晋. 2006.中国图像工程[J].中国图象图形学报, 12(5):753-775.
章毓晋. 2007.中国图像工程[J].中国图象图形学报, 13(5):825-852.
章毓晋. 2008.中国图像工程[J].中国图象图形学报, 14(5):809-837.
郑小东,王晓洁. 2007.基于图像处理的植物叶特征提取研究现状[J].农机化研究, 8(8):193-195.
朱静,田兴军,陈彬,吕劲紫. 2005.植物叶形的计算机识别系统[J].植物学通报, 22(5):599-604.