非参数变形模型结合模糊技术的MRI图像分割
|
摘要
本论文的目标是开发自动分割算法,将脑MRI图像分割成不同的组织,即脑白质、脑灰质和脑脊液,为脑发育与人的衰老、有关脑疾病的诊断和治疗、脑外科手术规划和导航等应用提供定量脑测度信息。在本论文中,提出了几个非参数化变形模型和统计信息或模糊信息相结合的算法,从不同模态的MRI图像中分割出白质、灰质、脑脊液等脑组织。对提出的算法采用实验的方法进行验证和评估,实验图像包括T1-加权、T2-加权和PD-加权的仿真和真实的脑MRI图像。
论文首先提出了一个基于直方图分析的非参数变形模型算法。算法中,用混合高斯模型(mixture Gaussian Model, MGM)来对图像的灰度直方图进行建模,利用期望最大化(Expectation Maximization, EM)算法来估计混合高斯模型中各分量的参数。获得的参数用于产生新的约束项,以指导水平集曲线的进化,并最终完成脑MRI图像的组织分割。用仿真和真实的MRI图像对算法进行了评估,论文中提供了MRI图像的分割结果,并对分割结果进行了定量评价。
其次,对基于区域的几何活动轮廓(Region-based Geometric Active Contour, RGAC)模型进行了研究。在稳定性分析基础上,采用新的区域压力项对RGAC算法进行了改进。新算法解决了原算法存在的稳定性问题。与原算法相比,改进算法的迭代次数明显减少,分割结果对参数的敏感度较低,因而有更好的韧性。算法能够从T1-加权、T2-加权和PD-加权等不同模态的MRI图像中分割白质、灰质、脑脊液等脑组织。用10个MRI仿真图像和5个真实MRI数据集对新算法进行评估,并与其它算法的分割结果进行了比较,验证了算法改进的可行性和有效性。算法中采用的模糊区域指示子函数被推广应用到模糊自适应水平集算法中,它是几何轮廓模型的一个改进算法。在曲线进化过程中,算法能够自适应地调整曲线进化的方向,达到快速收敛的目的。同时也克服了经典活动轮廓模型算法对图像的梯度信息过度依赖和因高斯平滑造成的边界定位精度下降的问题。文中通过仿真和真实的MRI图像对算法进行了评估。
论文最后提出了一个模糊C-均值和水平集方法相结合的多类算法。算法由一组常微分方程组成,一个组织类别由一个水平集函数表示。算法由各向异性扩散滤波、模糊聚类分析以及水平集分割方法等三个主要阶段组成。算法用人工合成图像、20幅仿真MRI图像和10个真实MRI图像集进行了评估。与多相算法相比,多类算法降低了计算复杂度,能够以更快的速度收敛。与其它算法相比,多类算法有更好的分割性能和噪声鲁棒性。
算法中采用的模糊逻辑,考虑了MRI图像中脑组织的模糊性和不确定性,与硬分割算法性比,能够包含更丰富的信息。与水平集方法相结合,有利于提高算法的性能和韧性。
The research goal in this dissertation is to develop an automatic segmentation method to segment brain MRI images into different tissue classes (gray matter, white matter, and cerebrospinal fluid), to provide quantitative brain measurements to the study of brain development and human aging, disease diagnosis and treatment, surgical planning and navigation, and other applications. In this dissertation, we develop several algorithms which integrate the non-parametric deformable models with statistical information or fuzzy information of images to segment the brain MRI images. These algorithms are assessed and validated with the experiments on multi-modalities of MRI images:T1-weighted, T2-weighted and PD-weighted.
We firstly present a histogram-analysis based non-parametric deformable model, where the intensity histogram of the MRI image is modeled via the mixture Gaussian model (MGM). The parameters of each component in MGM are estimated via the Expectation Maximization (EM) algorithm. Then the estimated parameters are used to generate the constraint term to guide the evolution of the level set curves to achieve the brain tissues segmentation. The algorithm is evaluated with the simulated and real MRI images. The segmentation results and quantitative analyses are provided.
We then explore the region-based geometric active contour (RGAC) of Suri. Based on the stability analysis, we propose the improved algorithm of the RGAC with new regional force terms. The new algorithm solves the underlying stability problem associated with the original algorithm. Compared with the original algorithm, the improved algorithm achieves convergence with less iteration number, and its segmentation results are less sensitive to some parameters. The algorithm can segment brain tissues into gray matter (GM), white matter (WM) and cerebrospinal fluid (CSF) classes from different modalities of MRI images (T1-weighted, T2-weighted, and PD-weighted). The algorithm is evaluated with ten simulated MRI images and five real MRI datasets, and compared quantitatively with other algorithms. The proposed fuzzy region indicator is used in an adaptive level set method. The method adaptively adjusts the directions of fronts during the curves evolution and achieves the final segmentation with fast convergence rate. The algorithm overcomes the limitations, associated with geometric active contour, of overly relying on the gradient information of images and reducing in accuracy of boundary locating caused by Gaussian smoothing. The algorithm is evaluated with the experiments on simulated and real MRI images.
Finally, we present a multiclass algorithm by integrating fuzzy clustering analysis with the level set methods. The algorithm uses a set of ordinary differential equations; each of them represents a class to be segmented. The algorithm consists of the anisotropic diffusion filtering, fuzzy clustering analysis and the level set refining segmentation steps. The algorithm is also evaluated with synthetic images,20 simulated MRI images and 10 real MRI datasets. Compared with the multiphase algorithm, the multiclass algorithm reduces the computational complexity, can achieve faster convergence. The comparison with other algorithms indicates the better segmentation performance and good robustness to noises.
The adopted fuzzy logic framework in the proposed algorithms allows for the ambiguity and uncertainty of the brain tissues in MRI images, can retain more information than the crisp approaches. The combination of fuzzy C-means (FCM) with level set methods allows to improve the segmentation performance and robustness of the algorithms.
论文首先提出了一个基于直方图分析的非参数变形模型算法。算法中,用混合高斯模型(mixture Gaussian Model, MGM)来对图像的灰度直方图进行建模,利用期望最大化(Expectation Maximization, EM)算法来估计混合高斯模型中各分量的参数。获得的参数用于产生新的约束项,以指导水平集曲线的进化,并最终完成脑MRI图像的组织分割。用仿真和真实的MRI图像对算法进行了评估,论文中提供了MRI图像的分割结果,并对分割结果进行了定量评价。
其次,对基于区域的几何活动轮廓(Region-based Geometric Active Contour, RGAC)模型进行了研究。在稳定性分析基础上,采用新的区域压力项对RGAC算法进行了改进。新算法解决了原算法存在的稳定性问题。与原算法相比,改进算法的迭代次数明显减少,分割结果对参数的敏感度较低,因而有更好的韧性。算法能够从T1-加权、T2-加权和PD-加权等不同模态的MRI图像中分割白质、灰质、脑脊液等脑组织。用10个MRI仿真图像和5个真实MRI数据集对新算法进行评估,并与其它算法的分割结果进行了比较,验证了算法改进的可行性和有效性。算法中采用的模糊区域指示子函数被推广应用到模糊自适应水平集算法中,它是几何轮廓模型的一个改进算法。在曲线进化过程中,算法能够自适应地调整曲线进化的方向,达到快速收敛的目的。同时也克服了经典活动轮廓模型算法对图像的梯度信息过度依赖和因高斯平滑造成的边界定位精度下降的问题。文中通过仿真和真实的MRI图像对算法进行了评估。
论文最后提出了一个模糊C-均值和水平集方法相结合的多类算法。算法由一组常微分方程组成,一个组织类别由一个水平集函数表示。算法由各向异性扩散滤波、模糊聚类分析以及水平集分割方法等三个主要阶段组成。算法用人工合成图像、20幅仿真MRI图像和10个真实MRI图像集进行了评估。与多相算法相比,多类算法降低了计算复杂度,能够以更快的速度收敛。与其它算法相比,多类算法有更好的分割性能和噪声鲁棒性。
算法中采用的模糊逻辑,考虑了MRI图像中脑组织的模糊性和不确定性,与硬分割算法性比,能够包含更丰富的信息。与水平集方法相结合,有利于提高算法的性能和韧性。
The research goal in this dissertation is to develop an automatic segmentation method to segment brain MRI images into different tissue classes (gray matter, white matter, and cerebrospinal fluid), to provide quantitative brain measurements to the study of brain development and human aging, disease diagnosis and treatment, surgical planning and navigation, and other applications. In this dissertation, we develop several algorithms which integrate the non-parametric deformable models with statistical information or fuzzy information of images to segment the brain MRI images. These algorithms are assessed and validated with the experiments on multi-modalities of MRI images:T1-weighted, T2-weighted and PD-weighted.
We firstly present a histogram-analysis based non-parametric deformable model, where the intensity histogram of the MRI image is modeled via the mixture Gaussian model (MGM). The parameters of each component in MGM are estimated via the Expectation Maximization (EM) algorithm. Then the estimated parameters are used to generate the constraint term to guide the evolution of the level set curves to achieve the brain tissues segmentation. The algorithm is evaluated with the simulated and real MRI images. The segmentation results and quantitative analyses are provided.
We then explore the region-based geometric active contour (RGAC) of Suri. Based on the stability analysis, we propose the improved algorithm of the RGAC with new regional force terms. The new algorithm solves the underlying stability problem associated with the original algorithm. Compared with the original algorithm, the improved algorithm achieves convergence with less iteration number, and its segmentation results are less sensitive to some parameters. The algorithm can segment brain tissues into gray matter (GM), white matter (WM) and cerebrospinal fluid (CSF) classes from different modalities of MRI images (T1-weighted, T2-weighted, and PD-weighted). The algorithm is evaluated with ten simulated MRI images and five real MRI datasets, and compared quantitatively with other algorithms. The proposed fuzzy region indicator is used in an adaptive level set method. The method adaptively adjusts the directions of fronts during the curves evolution and achieves the final segmentation with fast convergence rate. The algorithm overcomes the limitations, associated with geometric active contour, of overly relying on the gradient information of images and reducing in accuracy of boundary locating caused by Gaussian smoothing. The algorithm is evaluated with the experiments on simulated and real MRI images.
Finally, we present a multiclass algorithm by integrating fuzzy clustering analysis with the level set methods. The algorithm uses a set of ordinary differential equations; each of them represents a class to be segmented. The algorithm consists of the anisotropic diffusion filtering, fuzzy clustering analysis and the level set refining segmentation steps. The algorithm is also evaluated with synthetic images,20 simulated MRI images and 10 real MRI datasets. Compared with the multiphase algorithm, the multiclass algorithm reduces the computational complexity, can achieve faster convergence. The comparison with other algorithms indicates the better segmentation performance and good robustness to noises.
The adopted fuzzy logic framework in the proposed algorithms allows for the ambiguity and uncertainty of the brain tissues in MRI images, can retain more information than the crisp approaches. The combination of fuzzy C-means (FCM) with level set methods allows to improve the segmentation performance and robustness of the algorithms.
引文
[1]Gonzalez R F, Woods R E. Digital Image Processing (Second Edition), Prentice Hall.阮秋琦,阮宇智译.北京：电子工业出版社,2003.
[2]Brummer M E, Merseerau R M, Eisner R L et al. Automatic detection of brain contours in MRI data sets. IEEE T. Med. Imag.,1993,12:153-166.
[3]Sandor S, Leahy R. Surface-based labeling of cortical anatomy using a deformable atlas. IEEE T. Med. Imag.,16:41-54,1997.
[4]Kapur T, Grimson E,, Wells W et al. Segmentation of brain tissue from magnetic resonance images. Medical Image. Analysis,1996, 1(2):109-127.
[5]Atkins M S, Mackiewich B T. Fully automatic segmentation of the brain in MRI. IEEE T. Med. Imag., 17:98-109,1998.
[6]Aboutanos G B, Dawant B M. Automatic brain segmentation and validation:image-based versus atlas-based deformable models. In Medical Imaging, SPIE Proc.,1997,3034:299-310.
[7]Momenan R, Hommer D, Rawlings R et al. Intensity-adaptive segmentation of single-echo T1-weighted magnetic resonance images. Human Brain Mapping,1997,5:194-205.
[8]Rajapakse J C, Giedd J N, Rapoport J L. Statistical approach to segmentation of single-channel cerebral MR images. IEEE T. Med. Imag.,1997,16:176-186.
[9]Wang Y, Adah T, Kung S et al. Quantification and segmentation of brain tissues from MR images:a probabilistic neural network approach. IEEE T. Image. Process.,1998,7:1165-1181.
[10]Liang Z, MacFall J R, Harrington D P. Parameter estimation and tissue segmentation from multispectral MR images. IEEE T. Med. Imag.,1994,13:441-449.
[11]Kaufhold J, Schneider M, Willsky A S et al. A statistical method for efficient segmentation of MR imagery. Int. J. Patt. Rec. Art. Intel.,1997,11:1213-1231.
[12]Tsai C, Manjunath B S, Jagadeesan R. Automated segmentation of brain MR images. Pattern.Recognition,1995,28:1825-1837.
[13]Reddick W E, Glass J O, Cook E N et al. Automated segmentation and classification of multispectral magnetic resonance images of brain using artificial neural networks. IEEE T. Med. Imag.,1997,16(6): 911-918.
[14]Santago P, Gage H D. Statistical models of partial volume effect. IEEE T. Image Process.,1995, 4:1531-1540.
[15]Bullmore E, Brammer M, Rouleau G et al. Computerized brain tissue classification of magnetic resonance images:a new approach to the problem of partial volume artifact. Neuroimage,1995, 2:133-147.
[16]Johnston B, Atkins M S, Mackiewich B et al. Segmentation of multiple sclerosis lesions in intensity corrected multispectral MRI. IEEE T. Med. Imag.,1996,15:154-169.
[17]Laidlaw D H, Fleischer K W, Barr A H. Partial-volume bayesian classification of material mixtures in MR volume data using voxel histograms. IEEE T. Med. Imag.,1998,17:98-107.
[18]Clark M C, Hall L O, Goldgof D B et al. MRI segmentation using fuzzy clustering techniques. IEEE Eng. Med. Biol.,1994,13(5):730-742.
[19]Brandt M E, Bohan T P, Kramer L A et al. Estimation of CSF, white and gray matter volumes in hydrocephalic children using fuzzy clustering of MR images. Computerized Medical Imaging and Graphics,1994,18:25-34.
[20]Reiss A L, Hennessey J G, Rubin M et al. Reliability and validity of an algorithm for fuzzy tissue segmentation of MRI. J. Comp. Assist. Tom.,1998,22:471-479.
[21]Pham D L, Prince J L. An adaptive fuzzy c-means algorithm for image segmentation in the presence of intensity inhomogeneities. Pattern Recognition Letters,1999,20(1):57-68.
[22]Soltanian-Zadeh H, Windham J P, Peck D J. Optimal linear transformation for MRI features extraction. IEEE T. Med. Imag.,1996,15:749-767.
[23]Ge Y, Fitzpatrick J M, Dawant B M et al. Accurate localization of cortical convolutions in MR brain images. IEEE T. Med. Imag.,1996,15:418^428.
[24]Davatzikos C, Bryan R N. Using a deformable surface model to obtain a shape representation of the cortex. IEEE T. Med. Imag.,1996,15:785-795.
[25]McInerney T, Terzopoulos D. Medical image segmentation using topologically adaptable surfaces. Lecture Notes in Computer Science,1997,1205:23-22.
[26]Xu C, Pham D L, Prince J L et al. Reconstruction of the central layer of the human cerebral cortex from MR images. In Proc.1st Int. Conf. Med. Im. Comput. Comp. Assist.Intervent.,1998:482-488.
[27]McAuliffe M J, Eberly D, Fritsch D S et al. Scale-space boundary evolution initialized by cores. Lecture Notes in Computer Science,1996,1131:173-172.
[28]Wang Y, Staib L H. Boundary finding with correspondence using statistical shape models. In Proc. IEEE Conf. Comp. Vis. Patt. Rec.,1998:338-345.
[29]Davatzikos C, Vaillant M, Resnick S et al. A computerized method for morphological analysis of the corpus callosum. J. Comp. Assist. Tom.,1996,20:88-97.
[30]Ashton E A, Berg M J, Parker K J et al. Segmentation and feature extraction techniques, with applications to MRI head studies. Mag. Res. Med.,1995,33:670-677.
[31]Ghanei A, Soltanian-Zadeh H, Windham J P. A 3D deformable surface model for segmentation of objects from volumetric data in medical images. Computers in Biology and Medicine,1998, 28:239-253.
[32]Szekely G, Kelemen A, Brechbuhler C, Gerig G. Segmentation of 2-D and 3-D objects from MRI volume data using constrained elastic deformations of flexible Fourier contour and surface models. Med. Im. Anal.,1996,1:19-34.
[33]Vemuri B C, Guo Y, Leonard C M et al. Fast numerical algorithms for fitting multiresolution hybrid shape models to brain MRI. Medical Image. Analysis,1997,1:343-362.
[34]Tek H, Kimia B B. Volumetric segmentation of medical images by three-dimensional bubbles. Comp. Vis. Im. Understand.,1997,65:246-258.
[35]Arata L K, Dhawan A P, Broderick J P et al. Threedimensional anatomical model-based segmentation of MR brain images through principal axes registration. IEEE T. Biomed. Eng.,1995.,42:1069-1078
[36]Pien H H, Desai M, Shah J. Segmentation of MR images using curve evolution and prior information. Int. J. Patt. Rec. Art. Intell.,1997,11:1233-1245.
[37]Joshi S C, Miller M I, Grenander U. On the geometry and shape of brain sub-manifolds. Int. J. Patt. Rec. Art. Intell.,1997,11:1317-1343.
[38]Zhu Y, Yan H. Computerized tumor boundary detection using a hopfield neural network. IEEE T. Med. Imag.,1997,16:55-67.
[39]Kamber M, Shinghal R, Collins D L, et al. Model-based 3-D segmentation of multiple sclerosis lesions in magnetic resonance brain images. IEEE T. Med. Imag.,1995.,14:442-453
[40]Clark M C, Hall L O, Goldgof D B et al. Automatic tumor segmentation using knowledge based techniques. IEEE T. Med. Imag.,1998,17 (2):187-201.
[41]Vaidynathan M, Clarke L P, Heidtman C et al. Normal brain-volume measurements using multispectral MRI segmentation. Magnetic Resonance Imaging,1997,15(1):87-97.
[42]Cocosco C A, Kollokian V, Kwan R K S et al. Brainweb:online interface to a 3D MRI simulated brain database [DB]. http://www.bic.mni.mcgill.ca/brainweb,2006-06-12/2006-10-21.
[43]Statistical Parametric Mapping, www.fil.ion.ucl.ac.uk/spm/software/spm5/
[44]谢逢,罗立民,田雪芹,胡刚.基于知识的人脑三维医学图像自动分析显示系统.自动化学报,1997,23(4)：496-501
[45]林亚忠.基于Gibbs随机场模型的医学图像分割算法研究(博士论文).第一军医大学,2004.
[46]聂生东,章鲁,顾顺德,陈瑛.磁共振图像分割.国外医学生物医学工程分册,1999,22(6)：348-355.
[47]Lundervold A, Storvik G. Segmentation of brain parenchyma and cerbrospinal fluid in multispectral magnetic resonance images. IEEE.T. Med. Imag.,1995,14 (2):339-349.
[48]Kunt M. Edge detection:a tutorial review. IEEE ICASSP,1982,7:1172-1175.
[49]Canny J. A computational approach to edge detection. IEEE T. PAMI,1988,8(6):679-698.
[50]Staib L H, Duncan J S. Boundary finding with parametrically deformable models. IEEE T. PAMI, 2002,14(11):1061-1075.
[51]Kass M, Witkin A, Terzopoulos D. Snakes:Active contour models. Int. J. Computer Vision,1988,1 (4):321-331.
[52]Luo S, Li R, Ourselin S. A new deformable model using dynamic gradient vector flow and adaptive balloon forces. In Lovell B. eidtor, APRS Workshop on Digital Images Computing, Brisbane, Australia,2003:232-238.
[53]Xu C. Prince J L. Snakes, shapes and gradient flow. IEEE T. Image Process.,1998,7(3):359-369.
[54]Jiang C Y, Zhang X H, Huang W J et al. Segmentation quantification of brain tumor. In IEEE Symposium on Virtual Environments, Human-Computer Interfaces and Measurement Systems. Boston, MA, USA,2004:61-66.
[55]Ganser K A, Dickhaus H, Metzner R, et al. A deformable digital brain atlas system according to Talairach and Tournoux. Medical Image Analysis,2004,8:3-22.
[56]Shan Z Y, Yue G H, Liu J Z. Automated histogram-based brain segmentation in Tl-weighted three-dimensional magnetic resonance head images. NeuroImage,2002,17:1587-1598.
[57]Jack C R, O'Brien P C, Rettman D W et al. FLAIR histogram segmentation for measurement of leukoaraiosis volume. Journal of Magnetic Resonance Imaging,2001,14:668-676.
[58]Xue J H, Zhang Y J, Lin X G. Threshold selection using cross-entropy and fuzzy divergence. Proc. of SPIE,1998,3561:152-162.
[59]Chang Y L, Li X B. Adaptive image region-growing. IEEE T. Image Process.,1994,3(6):868-872.
[60]Adams R, Bischof L. Seeded region growing. IEEE T. PAMI,1994,16(6):641-647.
[61]Heinonen T, Dastidar P, Eskola H et al. Applicability of semi-automatic segmentation for volumetric analysis of brain lesions. Journal of Medical Engineering and Technology,1998,22:173-178.
[62]Tamez-Pena J G, Totterman S, Parker K. Unsupervised statistical segmentation of multispectral volumetric MR images. Proc. of SPIE,1999,3661:300-311.
[63]Pohle R, Toennies K D. Segmentation of medical images using adaptive region growing. Proc. of SPIE, 2001,4322:1337-1346.
[64]Manousakas I N, Undrill P E, Cameron G et al. Split-and Merge segmentation of magnetic resonance medical images:performance evaluation and extension to three dimensions. Computers and Biomedical Research,1998,31:393-412.
[65]Yung-Chieh L, Yu-Pao T, Yi-Ping H et al. Comparison between immersion-based and toboggan-based watershed image segmentation. IEEE T. Image Process.,2006,15(3):632-640.
[66]Meyer F. An overview of morphological segmentation. Int. J. Patt. Rec. Art. Intell.,2001, 15(7):1089-1118.
[67]Sijber F, Scheunders P, Verhoye M et al. Watershed based segmentation of 3D MR data for volume quantization. Journal of Magnetic Resonance Imaging,1997,15:679-688.
[68]Bueno G, Musse O, Heitz F et al.3D Watershed-based segmentation of internal structures within MR brain Images. Proc. of SPIE,2000,3979:284-293.
[69]Grau V, Mewes O, Alcaniz M et al. Improved watershed transform for medical image segmentation using prior information. IEEE T. Med. Imag.,2004,23(4):447-459.
[70]Geman D, Geman S. Stochastic relaxation, Gibbs distribution and Bayesian restoration of images. IEEE T. PAMI,1984,6(6):721-741.
[71]Clifford P. Markov random fields in statistics. In Grimmett, G. R., Welsh, D. J. A. Disorder in Physical Systems:A Volume in Honour of John M. Hammersley. Oxford University Press,1990.
[72]Wells W M, Grimson W E L, Kinkins R et al. Adaptive segmentation of MRI data. IEEE T. Image Process.,1996,15:429-442.
[73]Held K, Kops E P, Krause B J et al. Markov random field segmentation of brain MR images. IEEE T. Med. Imag.,1997,16(6):878-886.
[74]Leemput K V. Probabilistic Brain Atlas Encoding Using Bayesian Inference. Medical Image Computing and Computer-Assisted Intervention,2006, (1):704-711.
[75]Desco M, Gispert J D, Reig S et al. Statistical segmentation of multidimensional brain datasets. Proc. of SPIE,2001,4322:184-193.
[76]Zhang Y, Brady M, Smith S. Segmentation of brain MR images through a hidden Markoc random field model and the expectation maximization algorithm. IEEE T. Med. Imag.,2001,20(1):45-57.
[77]Solomon J, Butman J A, Sood A. Segmentation of brain tumors in 4D MR images using the Hidden Markov model. Computer Methods and Programs in Biomedcine,2006,84:76-85.
[78]边肇祺,张学工等.模式识别(第二版).北京：清华大学出版社,2000.
[79]Dunn J C. A Fuzzy Relative of The ISODATA Process and Its Use in Detecting Compact Well Separated Cluster. J. Cybernet,1974,3:32-57.
[80]Bezdek J C. Pattern Recognition with Fuzzy Objective Function Algorithms.New York:Plenum Press, 1981.
[81]Bezdek J C. A Convergence Theorem for the Fuzzy ISODATA Clustering Algorithm. IEEE T. PAMI,
1980, 1(2):1-8.
[82]Rosenberger C, Chehdi K. Unsupervised Clustering Method with Optimal Estimation of the Number of Clusters:Application to Image Segmentation. In Proceedings of 15th Int. Conf. on Pattern Recognition. Barcelona Spain,2000,1:656-659
[83]王培珍,陈维南.基于模糊聚类和二维阈值的图像分割.东南大学学报,1998,6：74-78
[84]丁震,胡钟山,杨静宇.一种基于模糊聚类的图像分割方法.计算机研究与发展,1997,7：536-541.
[85]Hui Yuan, Khorram S, Dai X L. Applications of Simulated Annealing Minimization Technique to Unsupervised Classification of Remotely Sensed Data.In:IGARSS'99 Proc. of IEEE Int. Conf. on Geoscience and Remote Sensing Symposium. Hamburg Germany.1999,1:134-136.
[86]Selim S Z, Alsultan K. A Simulated Annealing Algorithm for the Clustering Problem. Pattern Recognition,1991,24(10):1003-1008.
[87]Chaudhuri D, Chaudhuri B B. A Novel Multiseed Nonhierarchical Data Clustering Technique. IEEE SMC,1997,27(5):871-877.
[88]Postaire J G, Zhuang R D, Lecocq-Botte C. Cluster Analysis by Binary Morphology. IEEE T. PAMI, 1993,15(2):170-180.
[89]Pham D L. Spatial models for fuzzy clustering. Computer Vision and Image Understanding,2001,84: 285-97.
[90]Ahmed M N, Yamany S M, Mohamed N et al. A modified fuzzy c-means algorithm for bias field estimation and segmentation of MRI data. IEEE T. Med. Imag.,2002; 21(3):193-199.
[91]Shen S, Sandham W, Granat M et al. MRI fuzzy segmentation of brain tissue using neighborhood attraction with neural-network optimization. IEEE Trans, on Information Technology in Biomedicine, 2005,9(3):459-67.
[92]Boskovitz V, Guterman H. An adaptive Neuro-Fuzzy System for automatic Image Segmentation and Edge Detection. IEEE Trans, on Fuzzy Systems,2002,10(2):247-262.
[93]Masulli F, Schenone A. A fuzzy clustering based segmentation system as support to diagnosis in medical imaging. Artificial Intelligence in Medicine,1999, (16):129-147.
[94]Yang A M, Zhou Y M, Li X G et al. A Region-based Image Segmentation Method with Kernel FCM. Fuzzy Information and Engineering,2007,40:902-910.
[95]Chen S, Zhang D Q. Robust Image Segmentation using FCM with Spatial Constraints based on New kernel-induced Distance Measure. IEEE Trans. System, Man, and Cybernetics-part B:Cybernetics, 2004,34(4):1907-1916.
[96]Zhang D, Chen C. A novel kernelized fuzzy c-means algorithm with application in medical image segmentation. Artificial Intelligence in Medicine,2004,32:37-50.
[97]Buades A, Morel J M. A non-local algorithm for image denoising. In Proc. of Int. Conf. on Computer Vision and Pattern Recognition,2005, pp.60-65.
[98]Wang J Z, Kong J, Lu Y H et al. A modified FCM algorithm for MRI brain image segmentation using both local and non-local spatial constraints. Computerized Medical Imaging and Graphics,2008,32: 685-698.
[99]Hou Z, Qian W, Huang S et al. Regularized fuzzy cmeans method for brain tissue clustering. Pattern Recognition Letters,2007,28:88-94.
[100]Xue J H, Pizurica A, Philips W et al. An integrated method of adaptive enhancement for unsupervised segmentation of MRI brain images. Patter Recognition Letters,2003,24:2549-2560.
[101]Cai W, Chen S. Zhang D. Fast and robust fuzzy c-means clustering algorithms incorporating local information for image segmentation. Pattern Recognition,2007,40:825-838.
[102]Karmakar G C, Dooley L. A Generic Fuzzy Rule Based Technique for Image Segmentation. In: Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing. Salt Lake City, UT USA.2001,3:1577-1580.
[103]Udupa J K, Wei L, Samarasekera S et al. Fuzzy Connectedness and Object Definition:Theory, Algorithms and Applications in Image Segmentation. Graphical Models and Image Processing,1996, 58(3):246-261.
[104]Udupa J K, Saha P K, Lotufo R A. Fuzzy Connected Object Definition in Images with Respect to Co-Objects. In Proc. Int'l Soc. for Optical Eng-(SPIE) Conf. Medical Imaging,1999,3661:236-235.
[105]Udupa J K, Punam K, Saha P K et al. Relative Fuzzy Connectedness and Object Definition:Theory, Algorithms, and Applications in Image segmentation. IEEE T. PAMI,2003,24(11):1485-1500
[106]Liew A W C, Leung S H, Lau W H. Fuzzy Image Clustering Incorporating Spatial Continuity. IEE Proc-Vis. Image Signal Process,2000,147(2):185-192
[107]Liew A W C, Yan H. Adaptive Spatial Constraint fuzzy clustering for image segmentation. IEEE International Fuzzy System Conference,2001,801-804.
[108]Liew A W, Yan H. An adaptive spatial fuzzy clustering algorithm for 3-D MR image segmentation. IEEE T. Med. Imag.,2003,22(9):1063-1075.
[109]Dempster A P, Laird N M, Rubin D B. Maximum likelihood from incomplete data via the EM algorithm. J. Royal Statiseal Soc., Ser. B,1977,39(1):1-38.
[110]Jiang C. The use of mixture models to detect effects of major genes on quantitative characteristics in a plant-breeding experiment. Genetics,1994,36(1):383-394.
[111]Redner R, Walker H F. Mixture densities, maximum-likelihood estimation and the EM algorithm (review). SIAM Rev.,1984,26(2):195-237.
[112]Little R, Rubin D. On jointly estimating parameters and missing data by maximizing the complete-data likelihood. Am. Statistn.,1983,37(3):218-200.
[113]Kapur T, Grimson W E L, Kikinis R et al. Enhanced spatial priors for segmentation of magnetic resonance imagery. In:Wells, W M, Colchester, A C F, Delp S. (Eds.), Medical Image Computing and Computer-Assisted Intervention-MICCAI'98. Lecture Notes in Computer Science. Springer, Berlin,1998:457-468.
[114]Shattuck D W, Leahy R M. BrainSuite:An automated cortical surface identification tool. Medical Image Analysis,2002,6:129-142.
[115]Hashimoto A, Kudo H. Ordered-subsets EM algorithm for image segmentation with application to brain MRI. In IEEE Nuclear Science Symposium, Lyon, France,2000.
[116]Osher S, Sethian J A. Fronts propagating with curvature dependent speed:algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics,1988,79(1):12-49.
[117]Osher S, Shu C W. High-order essentially non oscillatory schemes for Hamilton-Jacobi equation. SIAM Journal of Numerical Analysis,1991,28(4):907-922.
[118]Osher S, Fedkiw R. Level Set Methods and Dynamic Implicit Surfaces. New York:Springer-Verlag, 2003.
[119]GigaY. Surface Evolution Equation--A Level Set Method. Lipchitz Lecture Notes 44, Germany: University of Bonn,2002:56-85.
[120]Richard T Y H, Osher S. Total Variation and Level Set Based Methods in Image Science. Los Angles:University of Cambridge,2005.
[121]Malladi R, Sethian J A, Vemuri B.Shape modeling with front propagation:A level set approach. IEEET.PAMI,1995,17(2):158-174.
[122]Caselles V, CaRe T, Coil T et al. A geometric model for active contours in image processing. Numeric Math,1993,66(1):1-31.
[123]Caselles V, Kimmel K, Sapim G. On geodesic active contour. Int. J. of Computer Vision,1997, 22(1):61-79.
[124]Mumford D, Shah J. Optimal approximation by piecewise-smooth functions and associated variational problems. Communications on Pure and Applied Mathematics,1989,42(6):577-685.
[125]Chan T, Vese L. Active contours without edges. IEEE T. Image Process.,2001,10(2):266-277.
[126]Vese L A, Chan T F. A multiphase level set framework for image segmentation using the Mumford and Shah model. Int. J. of Computer Vision,2002,50(3):271-293.
[127]Zhao H K, Chan T, Merriman B et al. A variational level set approach to muhiphase motion. International Journal of Computer Physics,1996,127(12):179-195.
[128]Baillard C. Barillot C, Bouthemy P. Robust Adaptive Segmentation of 3D Medical Images with Level Sets. Research Report, INRIA, Rennes, France, Nov.2000.
[129]Zeng X, Staib L H, Schultz RT et al. Segmentation and measurement of the cortex from 3-D MR images using coupled-surfaces propagation. IEEE T. Med. Imag.,1999,18(10):927-937.
[130]Yang J, Duncan J S.3D Image segmentation of deformable objects with shapeappearance joint prior models. MICCAI, Montreal, Canada,2003:573-580.
[131]Goldenberg R, Kimmel R, Rivlin E et al. Cortex segmentation-a fast variational geometric approach. IEEE T. Med. Imag.,2001,10(10):1467-1475
[132]Ballester M A G, Zisserman A, Brady M. Segmentation and measurement of brain structures in MRI including confidence bounds. Medical Image Analysis,2000,4:189-200.
[133]Shen D, Herskovits E H, Davatzikos C. An adaptive-focus statistical shape model for segmentation and shape modeling of 3-D brain structures. IEEE T. Med. Imag.,2001,20:257-270.
[134]Suri J S. Two-dimensional fast magnetic resonance brain segmentation. IEEE Engineering in Medicine and Biology Magazine,2001,20(4):84-95.
[135]Christensen G E, Hoshi S C, Miller M I. Volumetric Transformation of Brain Anatomy. IEEE Trans. Med. Imag.,1997,16:864-877.
[136]Amartur S C, Piraino D, Takefuji Y. Optimization neural networks for the segmentation of magnetic resonance images. IEEE T. Med. Imag.,1992,11 (2):215-220.
[137]Cohen L D, Cohen I. Finite-element methods for active contour models and balloons for 2D and 3D images, IEEE T. PAMI,1993,15(11):1131-1147
[138]McInerney T, Terzopoulos D. T-Snakes:topology adaptive snakes, Medical Image Analysis,2000, 4:73-91
[139]Xu C Y, Prince J.L. Gradient vector flow:A new external force for snakes. In Proc. of IEEE Conf. On Comp.Vis. Patt. Recog,1997:66-71
[140]Caselles V, Kimmel R, Sapiro G. Geodesic active contours. Int. J. of Computer Vision,1997,22(1): 61-79.
[141]Yezzi A, Kichenassamy S, Kumar A et al. A geometric snake model for segmentation of medical imagery. IEEE T. Med. Imag.,1997,16(2):199-209
[142]Siddiqi K, Lauriere Y B, Tannenbaum A et al. Area and length miniming flows for shape segmentation. IEEE T. Image Process.,1998,7:433-443.
[143]Lobregt S, Viergeber M A. A Discrete Dynamic Contour Model. IEEE T. Med. Imag.,1995,14(1): 12-24.
[144]陈明.医学图像融合中配准方法的研究.学位论文,第一军医大学,1997年7月：23-30.
[145]Ranganath S. Contour Extraetion from Cardiac MRI Studies Using Snakes. IEEE T. Med. Imag., 1995,14(2):328-338.
[146]Xu C Y, Prince J L. Generalized Gradient Vector Flow Extemal Forces for Active Contours. Signal Proceessing,1998,71 (2):121-139.
[147]MacDonald D. Avis D, Evans A.C. Proximity Constraints in Deformable Models for Cortical Surfaee Identification. Int. Conf. on Medical Image Computing and Compter-Assisted Intervention, 1998:650-659.
[148]MacDonald D, Kabani N, Avis D et al. Automated 3D Extraction of Inner and outer Surfaees of Cerebral Cortex from MRI. Neurolmage,2000,12(3):340-356.
[149]Durikovie R, Kaneda K, Yamashita H. Dynamie Contour:A Texture Approachand Contour operations; The Visual Computer,1995,11:277-289.
[150]Sethian J A. A Fast Marching Level Set Method for Monotonacily Advanceing Fronts. Proc. of the National Acadamy of Science,1996,4:1591-1595.
[151]Suri J S, Liu K, Laxminarayan S N et al. Shaper Recovery Algorithms Using Level Set in 2D/3D Mdeical Imagery:A State of-the-Art Review. IEEE Trans, on Information Technology in Biomedicine,2002,6(1):8-28.
[152]Suri J S. Computer Vision, pattern Recognition, and Image Processing in Left Ventriele Segmentation:Last 50 Years. J. Pattern Anal. Applicat.,2000,3:209-242.
[153]Leventon M E, Grimson W, Eric L et al. Statistical Shape Influenee in Geodesic Active Contours. Proceedings of Computer Vision Pattern Recognition (CVPR),2000,1:316-323.
[154]Kichenassamy S, Kumar A, Olver P et al. Conformal Curvatures Rows:From Phase Transitiors to Active Vision. Arch. Rational Meth. Anal.,1996,134 (3):275-301.
[155]Siddiqi K, Tannenbaum A, Zueker S W. Hyperbolic Smoothing of Shapes. In Proc.6th Int. Conf. Comput. Vision (ICCV), Bombay, India,1:215-221,1998.
[156]Malladi R, Sethian J A. An O(NlogN) Algorithm for Shape Modeling. Appl. Math. Proc. Nat. Academy Sci.,1996,93 (18):9389-9392.
[157]Sethian J A. Level Set Methods and Fast Marching Methods:Evolving Interfaces in Computational Geometry, Fluid Mechanics. Computer Vision and Materials Science. Cambridge University Press, 1999.
[158]Sussman M, Smeraka P, Osher S. A Level Set Approach for Computing Solution to Incompressible Tw-Phase Flow. J. Comput. Phys.,1994,114:146-159.
[159]Zhang Y J, Gerbrands J. Objective and quantitative segmentation evaluation and comparison. Signal Processing,1994,39(1-2):43-54.
[160]Hoover A, Jean-Baptiste G, Jiang X at al. An experimental comparison of range image segmentation algorithms. IEEE T. PAMI,1996,18(7):673-689.
[161]Sonka M, Hlavac V, Boyle R. Image Processing, Analysis and Machine Vision (Second Edition). USA:Brooks/Cole, Thomson Asia PteLed,1999:123-133.
[162]Yezzi A, Tsai A, Willsky A. A Statistical Approach to snakes for Bimodal and Trimodal Imagery. In Proc. of IEEE Int. Conf. on Computer Vision. KerKyra, Greece,1999:898-903.
[163]David W, David J R. Maximum likelihood estimates of the parameters of a mixture of two regression lines. Communications in Statisties,1974,3(10):995-1005.
[164]Frank R J, Grabowski T J, Damasio H. Voxelwise percentage tissue segmentation of human brain MRI. Soc. Neurosci. Abstr.,1995,21:694-699.
[165]Savitzky A, Golay M J E. Smoothing and differentiation of data by simplified least squares procedures. Analytical Chemistry,1964,36:1627-1639.
[166]Aitnouri E, Wang S R, Ziou D et al. Estimation of Multi-Modal Histogram's PDF using a Mixture Model. Journal of Neural, Parallel & Scientific Computation,1999,7(1):103-118.
[167]Kulkarni S, Chatterji B N. Accurate shape modeling with front propagating using adaptive level sets. Pattern Recognition Letters,2002,23:1559-1568.
[168]Abd-Almageed W, Smith C E. Mixture models for dynamic statistical pressure snakes. In IEEE Int. Conf. on Pattern Recognition. Quebec, Canada,2002:721-724.
[169]Zhou J, Chan K L, Chong V F H et al. Extraction of brain tumor from MR images using one-class support vector machine. In Proc. of IEEE Engineering in Medicine and Biology Conference (EMBC), Shanghai, China, pp.6411-6414,2005.
[170]Autti T, Raininko R, Vanhanen S L et al. MRI of the normal brain from early childhood to middle age, Neuroradiology,1994,36(8):644-648.
[171]Rusinek H, De Leon M J, George A E et al., Alzheimer disease:measuring loss of cerebral gray matter with MR imaging. Radiology,1991,178:109-114.
[172]Pham D L, Prince J L. An adaptive fuzzy segmentation algorithm for three-dimensional magnetic resonance images. Information Processing in Medical Imaging, Springer-Verlag, London,1999: 140-153.
[173]Awate S P, Zhang H, Gee J C. A fuzzy nonparametric segmentation framework for DTI and MRI analysis:with applications to DTI-tract extraction. IEEE T. Med. Imag.,2007,26(11):1525-1536.
[174]Leemput K V, Maes F, Vandermeulen Det al. Automated model-based tissue classification of MR images of the brain. IEEE T. Med. Imag.,1999,18(10):897-908.
[175]Leemput K V; Maes F, Vandermeulen Det al. A unifying framework for partial volume segmentation of brain MR images. IEEE T. Med. Imag.,2003,22(1):105-119.
[176]Cho W H, Park S C, Lee M E et al. Segmentation for medical image using a statistical initial process and a level set method. Medical Imaging and Augmented Reality, Springer Berlin/Heidelberg, pp. 380-388,2006.
[177]Poon C S, Brain M. Image segmentation by a deformable contour model incorporating region analysis. Physics in Medicine and Biology,1997,42(9):1833-1841.
[178]Suri J S. White Matter/Gray Matter boundary segmentation using geometric snakes:a fuzzy deformable model. In Proc. of Second Int. Conf. on Advances in Pattern Recognition (ICAPR), Rio de Janeiro, Brazil,2001:331-338.
[179]Bezdek J C, Hall L 0, Clarke L P. Review of MR image segmentation techniques using pattern recognition, Medical Physics,1993,20(4):1033-1048.
[180]Internet Brain Segmentation Repository, http://www.cms.mgh.harvard.edu/ibsr/.
[181]Zijdenbos A P, Dawant B M, Margolin R A et al. Morphometric analysis of white matter lesions in MR images:method and validation, IEEE T. Med. Imag.,1994,13(4):716-724,.
[182]BrainSuite. http://www.loni.ucla.edu/Software/BrainSuite/.
[183]Chaudhury K N, Ramakrishnan K R. Stability and convergence of the level set method in computer vision. Pattern Recognition Letters,2007,28(7):884-893.
[184]Amadieu O, Debreuve E, Barlaud M et al. Inward and outward curve evolution using level set method. In Proc. of IEEE Int. Conf. in Image Processing (ICIP), KOBE, JAPAN,1999,3:188-192.
[185]Yezzi Y, Tsai A, Willsky A. Binary and ternary flows for image segmentation. In Proc. of IEEE Int. Conf. in Image Processing (ICIP), KOBE, JAPAN,1999,2:1-5.
[186]Jalba A C, Wilkinson M H F, Roerdink J B T M. CPM:a deformable model for shape recovery and segmentation based on charged particles, IEEE T. PAMI,2004,26(10):1320-1335.
[187]Saini S. Radiologic measurement of tumor size in clinical trials:Past, present, and future. American Roentgen Ray Society,2001,.176(2):333-334.
[188]Auttib T, Raininko R, Vanhanen S Let al. MRI of the normal brain from early children to middle age. Neuroradiology,1994.36,644-648.
[189]Xue H, Ruan S, Moretti B et al. Fuzzy modeling of knowledge for MRI brain structure segmentation. In:Proc. of Int. Conf. on Image Processing (ICIP2000),2000:617-620.
[190]Koepfler G, Lopez C, Morel J M A multiscale algorithm for image segmentation by variational method. SIAM Journal of Numerical Analysis,1994,31(1):282-299.
[191]Chan T F, Esedoglu S. A multiscale algorithm for Mumford-Shah image segmentation. UCLA Tech. Rep. CAM03-77,2003.
[192]Chan T, Vese L. Image segmentation using level sets and piecewise constant Mumford-Shah model. UCLA Tech. Rep. CAM00-14,2000.
[193]Gibou F, Fedkiw R. A fast hybrid k-means level set algorithm for segmentation. In Proc. of Int. Conf. on Statistics and Mathematics,2005:281-291.
[194]Perona P, Malik J. Scale-space and edge detection using anisotropic diffusion. IEEE T. PAMI,1990, 12(1):629-639.
[195]Song B, Chan T. A fast algorithm for level set based optimization. UCLA CAM Report 02-68,2002.
[196]Lie J, Lysaker M, Tai X C. A binary Level set method and some applications to Mumford-Shah Image Segmentation. IEEE T. Image Process.,2006,15(5):1171-1181.
[197]Lysaker M, Tai X C. A variant of the level set method and applications to image segmentation. Mathematics of Computation,2006,75(25):1155-1174.
[198]Shi Y G, Karl W C. A fast level set method without solving PDES. In:Proc. of IEEE Int. Conf. on Acoustics, Speech, and Signal Processing (ICASSP 2005),2005:97-100.
[199]Esedoglu S, Tsai R. Threshold dynamics for the piecewise constant Mumford-Shah functional. UCLA. CAM Report 04-63,2004.
[200]Smereka P. Semi-implicit level set methods for curvature and surface diffusion motion. Journal of Scientific Computing,2003,19(1-3):439-456.
[201]Samson C, Blanc-Feraud L, Aubert G et al. A level set model for image classification. Int. J. of Computer Vision,2000,40(3):187-197.
[202]Paragios N, Deriche R. Coupled geodesic active contour regions for image segmentation:A level set approach. In:Proc. of 6th European Conference on Computer Vision,2000,2:224-240.
[203]Brox T, Weickert J. Level set segmentation with multiple regions. IEEE T. Image Process.,2006, 15(10),3213-3218.
[204]Brox T, Weickert J. Level set based image segmentation with multiple regions. Pattern Recognition, Springer LNCS,2004,3175:415-213.
[205]Mansouri A, Mitiche A, Feghali U. Spatio-temporal motion segmentation via level sets partial differential equations. In:IEEE Southwest Symposium on Image Analysis and Interpretation,2002: 243-247.
[206]Catte F, Lions P L, Morel J M et al. Image selective smoothing and edge detection by nonlinear diffusion, SIAM Journal on Numerical Analysis,1992,29 (1):1895-1909.
[207]Weickert J, Romeny B, Viergever M. Efficient and reliable scheme for nonlinear diffusion filtering. IEEE T. Image Process.,1998,7(3):398-410.
[208]You Y L, Xu W Y, Tannenbaum A et al. Behavioral analysis of anisotropic diffusion in image processing. IEEE T. PAMI,1990,12:629-639.
[209]Dou W, Ren Y, Wu Q et al. Fuzzy kappa for the agreement measure of fuzzy classifications. Neurocomputing,2007,70:726-734.
[210]Lukin A. A multiresolution approach for improving quality of image denoising algorithm. In Proc. of IEEE Int. Conf. on Acoustics, Speech, and Signal Processing (ICASSP-2006),2006,2:857-860.
[211]Buades A, Coll B, Morel J M. On image denoising methods. CMLA Tech. Rep.2004-15,2004.
[2]Brummer M E, Merseerau R M, Eisner R L et al. Automatic detection of brain contours in MRI data sets. IEEE T. Med. Imag.,1993,12:153-166.
[3]Sandor S, Leahy R. Surface-based labeling of cortical anatomy using a deformable atlas. IEEE T. Med. Imag.,16:41-54,1997.
[4]Kapur T, Grimson E,, Wells W et al. Segmentation of brain tissue from magnetic resonance images. Medical Image. Analysis,1996, 1(2):109-127.
[5]Atkins M S, Mackiewich B T. Fully automatic segmentation of the brain in MRI. IEEE T. Med. Imag., 17:98-109,1998.
[6]Aboutanos G B, Dawant B M. Automatic brain segmentation and validation:image-based versus atlas-based deformable models. In Medical Imaging, SPIE Proc.,1997,3034:299-310.
[7]Momenan R, Hommer D, Rawlings R et al. Intensity-adaptive segmentation of single-echo T1-weighted magnetic resonance images. Human Brain Mapping,1997,5:194-205.
[8]Rajapakse J C, Giedd J N, Rapoport J L. Statistical approach to segmentation of single-channel cerebral MR images. IEEE T. Med. Imag.,1997,16:176-186.
[9]Wang Y, Adah T, Kung S et al. Quantification and segmentation of brain tissues from MR images:a probabilistic neural network approach. IEEE T. Image. Process.,1998,7:1165-1181.
[10]Liang Z, MacFall J R, Harrington D P. Parameter estimation and tissue segmentation from multispectral MR images. IEEE T. Med. Imag.,1994,13:441-449.
[11]Kaufhold J, Schneider M, Willsky A S et al. A statistical method for efficient segmentation of MR imagery. Int. J. Patt. Rec. Art. Intel.,1997,11:1213-1231.
[12]Tsai C, Manjunath B S, Jagadeesan R. Automated segmentation of brain MR images. Pattern.Recognition,1995,28:1825-1837.
[13]Reddick W E, Glass J O, Cook E N et al. Automated segmentation and classification of multispectral magnetic resonance images of brain using artificial neural networks. IEEE T. Med. Imag.,1997,16(6): 911-918.
[14]Santago P, Gage H D. Statistical models of partial volume effect. IEEE T. Image Process.,1995, 4:1531-1540.
[15]Bullmore E, Brammer M, Rouleau G et al. Computerized brain tissue classification of magnetic resonance images:a new approach to the problem of partial volume artifact. Neuroimage,1995, 2:133-147.
[16]Johnston B, Atkins M S, Mackiewich B et al. Segmentation of multiple sclerosis lesions in intensity corrected multispectral MRI. IEEE T. Med. Imag.,1996,15:154-169.
[17]Laidlaw D H, Fleischer K W, Barr A H. Partial-volume bayesian classification of material mixtures in MR volume data using voxel histograms. IEEE T. Med. Imag.,1998,17:98-107.
[18]Clark M C, Hall L O, Goldgof D B et al. MRI segmentation using fuzzy clustering techniques. IEEE Eng. Med. Biol.,1994,13(5):730-742.
[19]Brandt M E, Bohan T P, Kramer L A et al. Estimation of CSF, white and gray matter volumes in hydrocephalic children using fuzzy clustering of MR images. Computerized Medical Imaging and Graphics,1994,18:25-34.
[20]Reiss A L, Hennessey J G, Rubin M et al. Reliability and validity of an algorithm for fuzzy tissue segmentation of MRI. J. Comp. Assist. Tom.,1998,22:471-479.
[21]Pham D L, Prince J L. An adaptive fuzzy c-means algorithm for image segmentation in the presence of intensity inhomogeneities. Pattern Recognition Letters,1999,20(1):57-68.
[22]Soltanian-Zadeh H, Windham J P, Peck D J. Optimal linear transformation for MRI features extraction. IEEE T. Med. Imag.,1996,15:749-767.
[23]Ge Y, Fitzpatrick J M, Dawant B M et al. Accurate localization of cortical convolutions in MR brain images. IEEE T. Med. Imag.,1996,15:418^428.
[24]Davatzikos C, Bryan R N. Using a deformable surface model to obtain a shape representation of the cortex. IEEE T. Med. Imag.,1996,15:785-795.
[25]McInerney T, Terzopoulos D. Medical image segmentation using topologically adaptable surfaces. Lecture Notes in Computer Science,1997,1205:23-22.
[26]Xu C, Pham D L, Prince J L et al. Reconstruction of the central layer of the human cerebral cortex from MR images. In Proc.1st Int. Conf. Med. Im. Comput. Comp. Assist.Intervent.,1998:482-488.
[27]McAuliffe M J, Eberly D, Fritsch D S et al. Scale-space boundary evolution initialized by cores. Lecture Notes in Computer Science,1996,1131:173-172.
[28]Wang Y, Staib L H. Boundary finding with correspondence using statistical shape models. In Proc. IEEE Conf. Comp. Vis. Patt. Rec.,1998:338-345.
[29]Davatzikos C, Vaillant M, Resnick S et al. A computerized method for morphological analysis of the corpus callosum. J. Comp. Assist. Tom.,1996,20:88-97.
[30]Ashton E A, Berg M J, Parker K J et al. Segmentation and feature extraction techniques, with applications to MRI head studies. Mag. Res. Med.,1995,33:670-677.
[31]Ghanei A, Soltanian-Zadeh H, Windham J P. A 3D deformable surface model for segmentation of objects from volumetric data in medical images. Computers in Biology and Medicine,1998, 28:239-253.
[32]Szekely G, Kelemen A, Brechbuhler C, Gerig G. Segmentation of 2-D and 3-D objects from MRI volume data using constrained elastic deformations of flexible Fourier contour and surface models. Med. Im. Anal.,1996,1:19-34.
[33]Vemuri B C, Guo Y, Leonard C M et al. Fast numerical algorithms for fitting multiresolution hybrid shape models to brain MRI. Medical Image. Analysis,1997,1:343-362.
[34]Tek H, Kimia B B. Volumetric segmentation of medical images by three-dimensional bubbles. Comp. Vis. Im. Understand.,1997,65:246-258.
[35]Arata L K, Dhawan A P, Broderick J P et al. Threedimensional anatomical model-based segmentation of MR brain images through principal axes registration. IEEE T. Biomed. Eng.,1995.,42:1069-1078
[36]Pien H H, Desai M, Shah J. Segmentation of MR images using curve evolution and prior information. Int. J. Patt. Rec. Art. Intell.,1997,11:1233-1245.
[37]Joshi S C, Miller M I, Grenander U. On the geometry and shape of brain sub-manifolds. Int. J. Patt. Rec. Art. Intell.,1997,11:1317-1343.
[38]Zhu Y, Yan H. Computerized tumor boundary detection using a hopfield neural network. IEEE T. Med. Imag.,1997,16:55-67.
[39]Kamber M, Shinghal R, Collins D L, et al. Model-based 3-D segmentation of multiple sclerosis lesions in magnetic resonance brain images. IEEE T. Med. Imag.,1995.,14:442-453
[40]Clark M C, Hall L O, Goldgof D B et al. Automatic tumor segmentation using knowledge based techniques. IEEE T. Med. Imag.,1998,17 (2):187-201.
[41]Vaidynathan M, Clarke L P, Heidtman C et al. Normal brain-volume measurements using multispectral MRI segmentation. Magnetic Resonance Imaging,1997,15(1):87-97.
[42]Cocosco C A, Kollokian V, Kwan R K S et al. Brainweb:online interface to a 3D MRI simulated brain database [DB]. http://www.bic.mni.mcgill.ca/brainweb,2006-06-12/2006-10-21.
[43]Statistical Parametric Mapping, www.fil.ion.ucl.ac.uk/spm/software/spm5/
[44]谢逢,罗立民,田雪芹,胡刚.基于知识的人脑三维医学图像自动分析显示系统.自动化学报,1997,23(4)：496-501
[45]林亚忠.基于Gibbs随机场模型的医学图像分割算法研究(博士论文).第一军医大学,2004.
[46]聂生东,章鲁,顾顺德,陈瑛.磁共振图像分割.国外医学生物医学工程分册,1999,22(6)：348-355.
[47]Lundervold A, Storvik G. Segmentation of brain parenchyma and cerbrospinal fluid in multispectral magnetic resonance images. IEEE.T. Med. Imag.,1995,14 (2):339-349.
[48]Kunt M. Edge detection:a tutorial review. IEEE ICASSP,1982,7:1172-1175.
[49]Canny J. A computational approach to edge detection. IEEE T. PAMI,1988,8(6):679-698.
[50]Staib L H, Duncan J S. Boundary finding with parametrically deformable models. IEEE T. PAMI, 2002,14(11):1061-1075.
[51]Kass M, Witkin A, Terzopoulos D. Snakes:Active contour models. Int. J. Computer Vision,1988,1 (4):321-331.
[52]Luo S, Li R, Ourselin S. A new deformable model using dynamic gradient vector flow and adaptive balloon forces. In Lovell B. eidtor, APRS Workshop on Digital Images Computing, Brisbane, Australia,2003:232-238.
[53]Xu C. Prince J L. Snakes, shapes and gradient flow. IEEE T. Image Process.,1998,7(3):359-369.
[54]Jiang C Y, Zhang X H, Huang W J et al. Segmentation quantification of brain tumor. In IEEE Symposium on Virtual Environments, Human-Computer Interfaces and Measurement Systems. Boston, MA, USA,2004:61-66.
[55]Ganser K A, Dickhaus H, Metzner R, et al. A deformable digital brain atlas system according to Talairach and Tournoux. Medical Image Analysis,2004,8:3-22.
[56]Shan Z Y, Yue G H, Liu J Z. Automated histogram-based brain segmentation in Tl-weighted three-dimensional magnetic resonance head images. NeuroImage,2002,17:1587-1598.
[57]Jack C R, O'Brien P C, Rettman D W et al. FLAIR histogram segmentation for measurement of leukoaraiosis volume. Journal of Magnetic Resonance Imaging,2001,14:668-676.
[58]Xue J H, Zhang Y J, Lin X G. Threshold selection using cross-entropy and fuzzy divergence. Proc. of SPIE,1998,3561:152-162.
[59]Chang Y L, Li X B. Adaptive image region-growing. IEEE T. Image Process.,1994,3(6):868-872.
[60]Adams R, Bischof L. Seeded region growing. IEEE T. PAMI,1994,16(6):641-647.
[61]Heinonen T, Dastidar P, Eskola H et al. Applicability of semi-automatic segmentation for volumetric analysis of brain lesions. Journal of Medical Engineering and Technology,1998,22:173-178.
[62]Tamez-Pena J G, Totterman S, Parker K. Unsupervised statistical segmentation of multispectral volumetric MR images. Proc. of SPIE,1999,3661:300-311.
[63]Pohle R, Toennies K D. Segmentation of medical images using adaptive region growing. Proc. of SPIE, 2001,4322:1337-1346.
[64]Manousakas I N, Undrill P E, Cameron G et al. Split-and Merge segmentation of magnetic resonance medical images:performance evaluation and extension to three dimensions. Computers and Biomedical Research,1998,31:393-412.
[65]Yung-Chieh L, Yu-Pao T, Yi-Ping H et al. Comparison between immersion-based and toboggan-based watershed image segmentation. IEEE T. Image Process.,2006,15(3):632-640.
[66]Meyer F. An overview of morphological segmentation. Int. J. Patt. Rec. Art. Intell.,2001, 15(7):1089-1118.
[67]Sijber F, Scheunders P, Verhoye M et al. Watershed based segmentation of 3D MR data for volume quantization. Journal of Magnetic Resonance Imaging,1997,15:679-688.
[68]Bueno G, Musse O, Heitz F et al.3D Watershed-based segmentation of internal structures within MR brain Images. Proc. of SPIE,2000,3979:284-293.
[69]Grau V, Mewes O, Alcaniz M et al. Improved watershed transform for medical image segmentation using prior information. IEEE T. Med. Imag.,2004,23(4):447-459.
[70]Geman D, Geman S. Stochastic relaxation, Gibbs distribution and Bayesian restoration of images. IEEE T. PAMI,1984,6(6):721-741.
[71]Clifford P. Markov random fields in statistics. In Grimmett, G. R., Welsh, D. J. A. Disorder in Physical Systems:A Volume in Honour of John M. Hammersley. Oxford University Press,1990.
[72]Wells W M, Grimson W E L, Kinkins R et al. Adaptive segmentation of MRI data. IEEE T. Image Process.,1996,15:429-442.
[73]Held K, Kops E P, Krause B J et al. Markov random field segmentation of brain MR images. IEEE T. Med. Imag.,1997,16(6):878-886.
[74]Leemput K V. Probabilistic Brain Atlas Encoding Using Bayesian Inference. Medical Image Computing and Computer-Assisted Intervention,2006, (1):704-711.
[75]Desco M, Gispert J D, Reig S et al. Statistical segmentation of multidimensional brain datasets. Proc. of SPIE,2001,4322:184-193.
[76]Zhang Y, Brady M, Smith S. Segmentation of brain MR images through a hidden Markoc random field model and the expectation maximization algorithm. IEEE T. Med. Imag.,2001,20(1):45-57.
[77]Solomon J, Butman J A, Sood A. Segmentation of brain tumors in 4D MR images using the Hidden Markov model. Computer Methods and Programs in Biomedcine,2006,84:76-85.
[78]边肇祺,张学工等.模式识别(第二版).北京：清华大学出版社,2000.
[79]Dunn J C. A Fuzzy Relative of The ISODATA Process and Its Use in Detecting Compact Well Separated Cluster. J. Cybernet,1974,3:32-57.
[80]Bezdek J C. Pattern Recognition with Fuzzy Objective Function Algorithms.New York:Plenum Press, 1981.
[81]Bezdek J C. A Convergence Theorem for the Fuzzy ISODATA Clustering Algorithm. IEEE T. PAMI,
1980, 1(2):1-8.
[82]Rosenberger C, Chehdi K. Unsupervised Clustering Method with Optimal Estimation of the Number of Clusters:Application to Image Segmentation. In Proceedings of 15th Int. Conf. on Pattern Recognition. Barcelona Spain,2000,1:656-659
[83]王培珍,陈维南.基于模糊聚类和二维阈值的图像分割.东南大学学报,1998,6：74-78
[84]丁震,胡钟山,杨静宇.一种基于模糊聚类的图像分割方法.计算机研究与发展,1997,7：536-541.
[85]Hui Yuan, Khorram S, Dai X L. Applications of Simulated Annealing Minimization Technique to Unsupervised Classification of Remotely Sensed Data.In:IGARSS'99 Proc. of IEEE Int. Conf. on Geoscience and Remote Sensing Symposium. Hamburg Germany.1999,1:134-136.
[86]Selim S Z, Alsultan K. A Simulated Annealing Algorithm for the Clustering Problem. Pattern Recognition,1991,24(10):1003-1008.
[87]Chaudhuri D, Chaudhuri B B. A Novel Multiseed Nonhierarchical Data Clustering Technique. IEEE SMC,1997,27(5):871-877.
[88]Postaire J G, Zhuang R D, Lecocq-Botte C. Cluster Analysis by Binary Morphology. IEEE T. PAMI, 1993,15(2):170-180.
[89]Pham D L. Spatial models for fuzzy clustering. Computer Vision and Image Understanding,2001,84: 285-97.
[90]Ahmed M N, Yamany S M, Mohamed N et al. A modified fuzzy c-means algorithm for bias field estimation and segmentation of MRI data. IEEE T. Med. Imag.,2002; 21(3):193-199.
[91]Shen S, Sandham W, Granat M et al. MRI fuzzy segmentation of brain tissue using neighborhood attraction with neural-network optimization. IEEE Trans, on Information Technology in Biomedicine, 2005,9(3):459-67.
[92]Boskovitz V, Guterman H. An adaptive Neuro-Fuzzy System for automatic Image Segmentation and Edge Detection. IEEE Trans, on Fuzzy Systems,2002,10(2):247-262.
[93]Masulli F, Schenone A. A fuzzy clustering based segmentation system as support to diagnosis in medical imaging. Artificial Intelligence in Medicine,1999, (16):129-147.
[94]Yang A M, Zhou Y M, Li X G et al. A Region-based Image Segmentation Method with Kernel FCM. Fuzzy Information and Engineering,2007,40:902-910.
[95]Chen S, Zhang D Q. Robust Image Segmentation using FCM with Spatial Constraints based on New kernel-induced Distance Measure. IEEE Trans. System, Man, and Cybernetics-part B:Cybernetics, 2004,34(4):1907-1916.
[96]Zhang D, Chen C. A novel kernelized fuzzy c-means algorithm with application in medical image segmentation. Artificial Intelligence in Medicine,2004,32:37-50.
[97]Buades A, Morel J M. A non-local algorithm for image denoising. In Proc. of Int. Conf. on Computer Vision and Pattern Recognition,2005, pp.60-65.
[98]Wang J Z, Kong J, Lu Y H et al. A modified FCM algorithm for MRI brain image segmentation using both local and non-local spatial constraints. Computerized Medical Imaging and Graphics,2008,32: 685-698.
[99]Hou Z, Qian W, Huang S et al. Regularized fuzzy cmeans method for brain tissue clustering. Pattern Recognition Letters,2007,28:88-94.
[100]Xue J H, Pizurica A, Philips W et al. An integrated method of adaptive enhancement for unsupervised segmentation of MRI brain images. Patter Recognition Letters,2003,24:2549-2560.
[101]Cai W, Chen S. Zhang D. Fast and robust fuzzy c-means clustering algorithms incorporating local information for image segmentation. Pattern Recognition,2007,40:825-838.
[102]Karmakar G C, Dooley L. A Generic Fuzzy Rule Based Technique for Image Segmentation. In: Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing. Salt Lake City, UT USA.2001,3:1577-1580.
[103]Udupa J K, Wei L, Samarasekera S et al. Fuzzy Connectedness and Object Definition:Theory, Algorithms and Applications in Image Segmentation. Graphical Models and Image Processing,1996, 58(3):246-261.
[104]Udupa J K, Saha P K, Lotufo R A. Fuzzy Connected Object Definition in Images with Respect to Co-Objects. In Proc. Int'l Soc. for Optical Eng-(SPIE) Conf. Medical Imaging,1999,3661:236-235.
[105]Udupa J K, Punam K, Saha P K et al. Relative Fuzzy Connectedness and Object Definition:Theory, Algorithms, and Applications in Image segmentation. IEEE T. PAMI,2003,24(11):1485-1500
[106]Liew A W C, Leung S H, Lau W H. Fuzzy Image Clustering Incorporating Spatial Continuity. IEE Proc-Vis. Image Signal Process,2000,147(2):185-192
[107]Liew A W C, Yan H. Adaptive Spatial Constraint fuzzy clustering for image segmentation. IEEE International Fuzzy System Conference,2001,801-804.
[108]Liew A W, Yan H. An adaptive spatial fuzzy clustering algorithm for 3-D MR image segmentation. IEEE T. Med. Imag.,2003,22(9):1063-1075.
[109]Dempster A P, Laird N M, Rubin D B. Maximum likelihood from incomplete data via the EM algorithm. J. Royal Statiseal Soc., Ser. B,1977,39(1):1-38.
[110]Jiang C. The use of mixture models to detect effects of major genes on quantitative characteristics in a plant-breeding experiment. Genetics,1994,36(1):383-394.
[111]Redner R, Walker H F. Mixture densities, maximum-likelihood estimation and the EM algorithm (review). SIAM Rev.,1984,26(2):195-237.
[112]Little R, Rubin D. On jointly estimating parameters and missing data by maximizing the complete-data likelihood. Am. Statistn.,1983,37(3):218-200.
[113]Kapur T, Grimson W E L, Kikinis R et al. Enhanced spatial priors for segmentation of magnetic resonance imagery. In:Wells, W M, Colchester, A C F, Delp S. (Eds.), Medical Image Computing and Computer-Assisted Intervention-MICCAI'98. Lecture Notes in Computer Science. Springer, Berlin,1998:457-468.
[114]Shattuck D W, Leahy R M. BrainSuite:An automated cortical surface identification tool. Medical Image Analysis,2002,6:129-142.
[115]Hashimoto A, Kudo H. Ordered-subsets EM algorithm for image segmentation with application to brain MRI. In IEEE Nuclear Science Symposium, Lyon, France,2000.
[116]Osher S, Sethian J A. Fronts propagating with curvature dependent speed:algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics,1988,79(1):12-49.
[117]Osher S, Shu C W. High-order essentially non oscillatory schemes for Hamilton-Jacobi equation. SIAM Journal of Numerical Analysis,1991,28(4):907-922.
[118]Osher S, Fedkiw R. Level Set Methods and Dynamic Implicit Surfaces. New York:Springer-Verlag, 2003.
[119]GigaY. Surface Evolution Equation--A Level Set Method. Lipchitz Lecture Notes 44, Germany: University of Bonn,2002:56-85.
[120]Richard T Y H, Osher S. Total Variation and Level Set Based Methods in Image Science. Los Angles:University of Cambridge,2005.
[121]Malladi R, Sethian J A, Vemuri B.Shape modeling with front propagation:A level set approach. IEEET.PAMI,1995,17(2):158-174.
[122]Caselles V, CaRe T, Coil T et al. A geometric model for active contours in image processing. Numeric Math,1993,66(1):1-31.
[123]Caselles V, Kimmel K, Sapim G. On geodesic active contour. Int. J. of Computer Vision,1997, 22(1):61-79.
[124]Mumford D, Shah J. Optimal approximation by piecewise-smooth functions and associated variational problems. Communications on Pure and Applied Mathematics,1989,42(6):577-685.
[125]Chan T, Vese L. Active contours without edges. IEEE T. Image Process.,2001,10(2):266-277.
[126]Vese L A, Chan T F. A multiphase level set framework for image segmentation using the Mumford and Shah model. Int. J. of Computer Vision,2002,50(3):271-293.
[127]Zhao H K, Chan T, Merriman B et al. A variational level set approach to muhiphase motion. International Journal of Computer Physics,1996,127(12):179-195.
[128]Baillard C. Barillot C, Bouthemy P. Robust Adaptive Segmentation of 3D Medical Images with Level Sets. Research Report, INRIA, Rennes, France, Nov.2000.
[129]Zeng X, Staib L H, Schultz RT et al. Segmentation and measurement of the cortex from 3-D MR images using coupled-surfaces propagation. IEEE T. Med. Imag.,1999,18(10):927-937.
[130]Yang J, Duncan J S.3D Image segmentation of deformable objects with shapeappearance joint prior models. MICCAI, Montreal, Canada,2003:573-580.
[131]Goldenberg R, Kimmel R, Rivlin E et al. Cortex segmentation-a fast variational geometric approach. IEEE T. Med. Imag.,2001,10(10):1467-1475
[132]Ballester M A G, Zisserman A, Brady M. Segmentation and measurement of brain structures in MRI including confidence bounds. Medical Image Analysis,2000,4:189-200.
[133]Shen D, Herskovits E H, Davatzikos C. An adaptive-focus statistical shape model for segmentation and shape modeling of 3-D brain structures. IEEE T. Med. Imag.,2001,20:257-270.
[134]Suri J S. Two-dimensional fast magnetic resonance brain segmentation. IEEE Engineering in Medicine and Biology Magazine,2001,20(4):84-95.
[135]Christensen G E, Hoshi S C, Miller M I. Volumetric Transformation of Brain Anatomy. IEEE Trans. Med. Imag.,1997,16:864-877.
[136]Amartur S C, Piraino D, Takefuji Y. Optimization neural networks for the segmentation of magnetic resonance images. IEEE T. Med. Imag.,1992,11 (2):215-220.
[137]Cohen L D, Cohen I. Finite-element methods for active contour models and balloons for 2D and 3D images, IEEE T. PAMI,1993,15(11):1131-1147
[138]McInerney T, Terzopoulos D. T-Snakes:topology adaptive snakes, Medical Image Analysis,2000, 4:73-91
[139]Xu C Y, Prince J.L. Gradient vector flow:A new external force for snakes. In Proc. of IEEE Conf. On Comp.Vis. Patt. Recog,1997:66-71
[140]Caselles V, Kimmel R, Sapiro G. Geodesic active contours. Int. J. of Computer Vision,1997,22(1): 61-79.
[141]Yezzi A, Kichenassamy S, Kumar A et al. A geometric snake model for segmentation of medical imagery. IEEE T. Med. Imag.,1997,16(2):199-209
[142]Siddiqi K, Lauriere Y B, Tannenbaum A et al. Area and length miniming flows for shape segmentation. IEEE T. Image Process.,1998,7:433-443.
[143]Lobregt S, Viergeber M A. A Discrete Dynamic Contour Model. IEEE T. Med. Imag.,1995,14(1): 12-24.
[144]陈明.医学图像融合中配准方法的研究.学位论文,第一军医大学,1997年7月：23-30.
[145]Ranganath S. Contour Extraetion from Cardiac MRI Studies Using Snakes. IEEE T. Med. Imag., 1995,14(2):328-338.
[146]Xu C Y, Prince J L. Generalized Gradient Vector Flow Extemal Forces for Active Contours. Signal Proceessing,1998,71 (2):121-139.
[147]MacDonald D. Avis D, Evans A.C. Proximity Constraints in Deformable Models for Cortical Surfaee Identification. Int. Conf. on Medical Image Computing and Compter-Assisted Intervention, 1998:650-659.
[148]MacDonald D, Kabani N, Avis D et al. Automated 3D Extraction of Inner and outer Surfaees of Cerebral Cortex from MRI. Neurolmage,2000,12(3):340-356.
[149]Durikovie R, Kaneda K, Yamashita H. Dynamie Contour:A Texture Approachand Contour operations; The Visual Computer,1995,11:277-289.
[150]Sethian J A. A Fast Marching Level Set Method for Monotonacily Advanceing Fronts. Proc. of the National Acadamy of Science,1996,4:1591-1595.
[151]Suri J S, Liu K, Laxminarayan S N et al. Shaper Recovery Algorithms Using Level Set in 2D/3D Mdeical Imagery:A State of-the-Art Review. IEEE Trans, on Information Technology in Biomedicine,2002,6(1):8-28.
[152]Suri J S. Computer Vision, pattern Recognition, and Image Processing in Left Ventriele Segmentation:Last 50 Years. J. Pattern Anal. Applicat.,2000,3:209-242.
[153]Leventon M E, Grimson W, Eric L et al. Statistical Shape Influenee in Geodesic Active Contours. Proceedings of Computer Vision Pattern Recognition (CVPR),2000,1:316-323.
[154]Kichenassamy S, Kumar A, Olver P et al. Conformal Curvatures Rows:From Phase Transitiors to Active Vision. Arch. Rational Meth. Anal.,1996,134 (3):275-301.
[155]Siddiqi K, Tannenbaum A, Zueker S W. Hyperbolic Smoothing of Shapes. In Proc.6th Int. Conf. Comput. Vision (ICCV), Bombay, India,1:215-221,1998.
[156]Malladi R, Sethian J A. An O(NlogN) Algorithm for Shape Modeling. Appl. Math. Proc. Nat. Academy Sci.,1996,93 (18):9389-9392.
[157]Sethian J A. Level Set Methods and Fast Marching Methods:Evolving Interfaces in Computational Geometry, Fluid Mechanics. Computer Vision and Materials Science. Cambridge University Press, 1999.
[158]Sussman M, Smeraka P, Osher S. A Level Set Approach for Computing Solution to Incompressible Tw-Phase Flow. J. Comput. Phys.,1994,114:146-159.
[159]Zhang Y J, Gerbrands J. Objective and quantitative segmentation evaluation and comparison. Signal Processing,1994,39(1-2):43-54.
[160]Hoover A, Jean-Baptiste G, Jiang X at al. An experimental comparison of range image segmentation algorithms. IEEE T. PAMI,1996,18(7):673-689.
[161]Sonka M, Hlavac V, Boyle R. Image Processing, Analysis and Machine Vision (Second Edition). USA:Brooks/Cole, Thomson Asia PteLed,1999:123-133.
[162]Yezzi A, Tsai A, Willsky A. A Statistical Approach to snakes for Bimodal and Trimodal Imagery. In Proc. of IEEE Int. Conf. on Computer Vision. KerKyra, Greece,1999:898-903.
[163]David W, David J R. Maximum likelihood estimates of the parameters of a mixture of two regression lines. Communications in Statisties,1974,3(10):995-1005.
[164]Frank R J, Grabowski T J, Damasio H. Voxelwise percentage tissue segmentation of human brain MRI. Soc. Neurosci. Abstr.,1995,21:694-699.
[165]Savitzky A, Golay M J E. Smoothing and differentiation of data by simplified least squares procedures. Analytical Chemistry,1964,36:1627-1639.
[166]Aitnouri E, Wang S R, Ziou D et al. Estimation of Multi-Modal Histogram's PDF using a Mixture Model. Journal of Neural, Parallel & Scientific Computation,1999,7(1):103-118.
[167]Kulkarni S, Chatterji B N. Accurate shape modeling with front propagating using adaptive level sets. Pattern Recognition Letters,2002,23:1559-1568.
[168]Abd-Almageed W, Smith C E. Mixture models for dynamic statistical pressure snakes. In IEEE Int. Conf. on Pattern Recognition. Quebec, Canada,2002:721-724.
[169]Zhou J, Chan K L, Chong V F H et al. Extraction of brain tumor from MR images using one-class support vector machine. In Proc. of IEEE Engineering in Medicine and Biology Conference (EMBC), Shanghai, China, pp.6411-6414,2005.
[170]Autti T, Raininko R, Vanhanen S L et al. MRI of the normal brain from early childhood to middle age, Neuroradiology,1994,36(8):644-648.
[171]Rusinek H, De Leon M J, George A E et al., Alzheimer disease:measuring loss of cerebral gray matter with MR imaging. Radiology,1991,178:109-114.
[172]Pham D L, Prince J L. An adaptive fuzzy segmentation algorithm for three-dimensional magnetic resonance images. Information Processing in Medical Imaging, Springer-Verlag, London,1999: 140-153.
[173]Awate S P, Zhang H, Gee J C. A fuzzy nonparametric segmentation framework for DTI and MRI analysis:with applications to DTI-tract extraction. IEEE T. Med. Imag.,2007,26(11):1525-1536.
[174]Leemput K V, Maes F, Vandermeulen Det al. Automated model-based tissue classification of MR images of the brain. IEEE T. Med. Imag.,1999,18(10):897-908.
[175]Leemput K V; Maes F, Vandermeulen Det al. A unifying framework for partial volume segmentation of brain MR images. IEEE T. Med. Imag.,2003,22(1):105-119.
[176]Cho W H, Park S C, Lee M E et al. Segmentation for medical image using a statistical initial process and a level set method. Medical Imaging and Augmented Reality, Springer Berlin/Heidelberg, pp. 380-388,2006.
[177]Poon C S, Brain M. Image segmentation by a deformable contour model incorporating region analysis. Physics in Medicine and Biology,1997,42(9):1833-1841.
[178]Suri J S. White Matter/Gray Matter boundary segmentation using geometric snakes:a fuzzy deformable model. In Proc. of Second Int. Conf. on Advances in Pattern Recognition (ICAPR), Rio de Janeiro, Brazil,2001:331-338.
[179]Bezdek J C, Hall L 0, Clarke L P. Review of MR image segmentation techniques using pattern recognition, Medical Physics,1993,20(4):1033-1048.
[180]Internet Brain Segmentation Repository, http://www.cms.mgh.harvard.edu/ibsr/.
[181]Zijdenbos A P, Dawant B M, Margolin R A et al. Morphometric analysis of white matter lesions in MR images:method and validation, IEEE T. Med. Imag.,1994,13(4):716-724,.
[182]BrainSuite. http://www.loni.ucla.edu/Software/BrainSuite/.
[183]Chaudhury K N, Ramakrishnan K R. Stability and convergence of the level set method in computer vision. Pattern Recognition Letters,2007,28(7):884-893.
[184]Amadieu O, Debreuve E, Barlaud M et al. Inward and outward curve evolution using level set method. In Proc. of IEEE Int. Conf. in Image Processing (ICIP), KOBE, JAPAN,1999,3:188-192.
[185]Yezzi Y, Tsai A, Willsky A. Binary and ternary flows for image segmentation. In Proc. of IEEE Int. Conf. in Image Processing (ICIP), KOBE, JAPAN,1999,2:1-5.
[186]Jalba A C, Wilkinson M H F, Roerdink J B T M. CPM:a deformable model for shape recovery and segmentation based on charged particles, IEEE T. PAMI,2004,26(10):1320-1335.
[187]Saini S. Radiologic measurement of tumor size in clinical trials:Past, present, and future. American Roentgen Ray Society,2001,.176(2):333-334.
[188]Auttib T, Raininko R, Vanhanen S Let al. MRI of the normal brain from early children to middle age. Neuroradiology,1994.36,644-648.
[189]Xue H, Ruan S, Moretti B et al. Fuzzy modeling of knowledge for MRI brain structure segmentation. In:Proc. of Int. Conf. on Image Processing (ICIP2000),2000:617-620.
[190]Koepfler G, Lopez C, Morel J M A multiscale algorithm for image segmentation by variational method. SIAM Journal of Numerical Analysis,1994,31(1):282-299.
[191]Chan T F, Esedoglu S. A multiscale algorithm for Mumford-Shah image segmentation. UCLA Tech. Rep. CAM03-77,2003.
[192]Chan T, Vese L. Image segmentation using level sets and piecewise constant Mumford-Shah model. UCLA Tech. Rep. CAM00-14,2000.
[193]Gibou F, Fedkiw R. A fast hybrid k-means level set algorithm for segmentation. In Proc. of Int. Conf. on Statistics and Mathematics,2005:281-291.
[194]Perona P, Malik J. Scale-space and edge detection using anisotropic diffusion. IEEE T. PAMI,1990, 12(1):629-639.
[195]Song B, Chan T. A fast algorithm for level set based optimization. UCLA CAM Report 02-68,2002.
[196]Lie J, Lysaker M, Tai X C. A binary Level set method and some applications to Mumford-Shah Image Segmentation. IEEE T. Image Process.,2006,15(5):1171-1181.
[197]Lysaker M, Tai X C. A variant of the level set method and applications to image segmentation. Mathematics of Computation,2006,75(25):1155-1174.
[198]Shi Y G, Karl W C. A fast level set method without solving PDES. In:Proc. of IEEE Int. Conf. on Acoustics, Speech, and Signal Processing (ICASSP 2005),2005:97-100.
[199]Esedoglu S, Tsai R. Threshold dynamics for the piecewise constant Mumford-Shah functional. UCLA. CAM Report 04-63,2004.
[200]Smereka P. Semi-implicit level set methods for curvature and surface diffusion motion. Journal of Scientific Computing,2003,19(1-3):439-456.
[201]Samson C, Blanc-Feraud L, Aubert G et al. A level set model for image classification. Int. J. of Computer Vision,2000,40(3):187-197.
[202]Paragios N, Deriche R. Coupled geodesic active contour regions for image segmentation:A level set approach. In:Proc. of 6th European Conference on Computer Vision,2000,2:224-240.
[203]Brox T, Weickert J. Level set segmentation with multiple regions. IEEE T. Image Process.,2006, 15(10),3213-3218.
[204]Brox T, Weickert J. Level set based image segmentation with multiple regions. Pattern Recognition, Springer LNCS,2004,3175:415-213.
[205]Mansouri A, Mitiche A, Feghali U. Spatio-temporal motion segmentation via level sets partial differential equations. In:IEEE Southwest Symposium on Image Analysis and Interpretation,2002: 243-247.
[206]Catte F, Lions P L, Morel J M et al. Image selective smoothing and edge detection by nonlinear diffusion, SIAM Journal on Numerical Analysis,1992,29 (1):1895-1909.
[207]Weickert J, Romeny B, Viergever M. Efficient and reliable scheme for nonlinear diffusion filtering. IEEE T. Image Process.,1998,7(3):398-410.
[208]You Y L, Xu W Y, Tannenbaum A et al. Behavioral analysis of anisotropic diffusion in image processing. IEEE T. PAMI,1990,12:629-639.
[209]Dou W, Ren Y, Wu Q et al. Fuzzy kappa for the agreement measure of fuzzy classifications. Neurocomputing,2007,70:726-734.
[210]Lukin A. A multiresolution approach for improving quality of image denoising algorithm. In Proc. of IEEE Int. Conf. on Acoustics, Speech, and Signal Processing (ICASSP-2006),2006,2:857-860.
[211]Buades A, Coll B, Morel J M. On image denoising methods. CMLA Tech. Rep.2004-15,2004.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |