脑核磁共振图像分割技术研究
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摘要
核磁共振成像(Magnetic Resonance Imaging, MRI)技术已经成为脑疾病临床诊断的重要辅助手段。准确地分割脑MR图像对脑部解剖、脑疾病诸如阿尔茨海默氏病、帕金森氏病以及精神分裂症的分析与研究等具有重要的指导意义。然而在实际应用中,由于射频场的不均匀性等因素,导致脑MR图像的灰度均匀性变差,其表现为同一组织的像素灰度沿空间呈缓慢平滑的变化,直接导致传统的基于全局灰度值的分割模型分割失败；其次,脑MR图像成像过程中由于受仪器设备等物理原因影响,使得图像中经常含有噪声,影响分割精度。除此之外,图像中存在Partial Volume(PV)效应,即各个软组织之间边界比较模糊,不明确和不连续。这些都给脑MR图像的准确分割造成了很大困难。和成人脑MR图像相比,新生儿脑MR图像分辨率更低,PV效应更加显著；由于新生儿的大脑处在迅速发育中,导致图像中的灰度不均匀性的成因更加复杂；白质／灰质对比度的逆转,使得处在脑脊液和灰质交界处的像素具有和白质相似的灰度,使得分割更加困难。所有这些使得脑MR图像的分割仍然是一个充满挑战的课题。大部分脑MR图像分割方法是基于单个像素的,是离散的,容易受到初始化的影响。为此,本文对成人脑MR图像和新生儿脑MR图像分割进行了深入研究,首先采用连续的方法,提出了一些基于活动轮廓的分割模型来克服脑MR图像中存在的灰度不均匀性；然后,进一步将这些分割模型统一到一个凸优化框架中,同时分割脑MR图像和估计偏移场,特别地,由于采用了凸优化技术,可以很好地克服初始化的影响；最后我们进一步将该凸优化框架模型和活动轮廓模型应用到新生儿脑MR图像分割中,取得了较好的效果。所做的主要工作和研究成果如下：
(1)为了克服灰度不均匀性,提出了一种基于图像局部均值的分割模型。利用多相位水平集方式来拟合局部灰度,并采用一种简单而有效的初始化方法,达到更快更准地分割脑MR图像。由于采用了多相位水平集方法,该模型可以同时得到白质、灰质和脑脊液。另外水平集方法很好地保证了分割结果的光滑性,可以得到光滑的边界／曲面。
(2)为了克服对初始化的敏感性,提出了一种基于局部均值和全局均值的活动轮廓模型。该模型分别定义了一个局部拟合力和全局拟合力。其中,局部拟合力用于驱动曲线向目标靠近并在目标边界处停止,全局拟合力用于驱动远离目标边界的曲线向目标靠拢。在这两个拟合力的作用下,该模型对初始曲线较不敏感同时克服脑MR图像中存在的灰度不均匀性。
(3)提出了一种基于局部高斯概率的活动轮廓分割模型。通过分析每个像素邻域的灰度分布,利用窗口函数定义了一个局部高斯拟合能量。局部高斯概率中的两个参数,局部均值和局部方差是随着空间变化而变化的,因此本文方法可以很好地克服脑图像中存在的灰度不均匀性。值得一提的是,本文方法的局部均值和局部方差不再是显式定义的,而是可以通过变分法原理严格推导出来的。3T和7T的脑MR图像分割实验证明本文方法不仅可以有效地克服灰度不均匀性,还可以克服低对比度。
(4)提出了一种新颖的基于凸优化的脑MR图像分割模型,同时进行图像分割和估计偏移场,因此可以克服灰度不均匀性的影响。特别地,由于该模型关于图像分割变量是凸的,因此对初始化具有很强的鲁棒性。另外该模型也可以克服噪声的影响。和传统的基于梯度下降法求解相比,我们采用Split Bregman方法对该模型进行快速求解,使得对一幅2D的图像处理时间一般不超过1秒,3D的数据处理时间一般不超过100秒。大量的二维和三维实验证明本文方法无论在时间效率上还是准确度上都取得了满意的结果。而且,我们还进一步给出一个基于凸优化的脑MR图像分割框架模型,该框架综合利用了图像的局部统计信息。比较实验也证明了本文提出的框架模型是有效的。
(5)提出基于凸优化和耦合水平集方法的新生儿脑MR图像分割框架。耦合水平集方法综合利用了图像的局部灰度统计信息、基于Atlas的先验信息、大脑皮层的厚度信息。为了克服初始化对分割结果的影响,我们采用凸模型进行分割,然后进行必要的校正,从而为耦合水平集方法提供一个可靠的初始化。该新生儿脑MR图像分割框架已经在10个新生儿数据上取得了满意的结果,和目前流行的新生儿MR图像分割方法相比,本文方法取得了较高的分割精度。
Accurate segmentation of magnetic resonance (MR) images of the brain is undoubtedly of great interest for the study and the treatment of various pathologies such as Alzheimer dis-ease, Parkinson or Parkinson related syndrome. In fact, intensity inhomogeneity often occurs in MR images due to radio frequency (RF) coils or acquisition sequences. The intensity inho-mogeneity in MR images often appears as an intensity variation across the image. Thus the resultant intensities of the same tissue vary with the locations in the image. Although usually hardly noticeable to a human observer, such a bias can cause serious misclassifications when intensity-based segmentation algorithms are used. In addition, images are often corrupted by various noises that challenge the segmentation. Besides these difficulties, the boundaries be-tween tissues are quite fuzzy due to the partial volume (PV) effect. Compared with the adult brain MR images, contrast in neonatal MR images is much lower than that of adult because the majority of white matter is as-yet unmyelinated and has a water content closer to that of gray matter than in adults and adolescents. Besides the image contrast, the intensities of tissues are significantly affected by intensity inhomogeneity due to not only RF inhomogeneity but also biological properties of the developing tissue, which leads to a large overlap in their intensity distributions. The inversion of contrast between GM and WM, compared to adult MRI, is also a difficulty given the limited resolution of neonate MRI. Due to this inverted GM/WM con-trast, many voxels between CSF and GM can be incorrectly classified as WM by conventional intensity-based segmentation approaches. In a word, it remains challenging to segment brain MR images, especially for neonatal brain images. In this paper, we first propose a few segmen-tation methods based on active contour model to deal with the intensity inhomogeneity. These proposed active contour models are then intergraded into a convex framework to simultaneously segment the brain MR images and correct bias fields. The convexity of the framework makes the model robust to initialization. We further extend the convex framework and active con- tour model proposed previously into neonatal brain MR image segmentation. Our work mainly includes the following parts:
(1) To overcome the difficulty caused by intensity inhomogeneity in the segmentation of magnetic resonance (MR) images, this paper presents a new multiphase level set method for segmentation of brain MR images. The proposed model utilizes local image intensities, which enables it to cope with intensity inhomogeneity. With the multiphase level set framework, the model can extract brain white matter (WM), gray matter (GM) and cerebrospinal fluid (CSF) simultaneously and provide a smooth contour/surface. Comparisons of 2D and 3D segmentation prove that the proposed model is effective.
(2) We propose an improved region-based active contour model in a variational level set formulation. We define an energy functional with a local intensity fitting term, which induces a local force to attract the contour and stops it at object boundaries, and an auxiliary global intensity fitting term, which drives the motion of the contour far away from object boundaries. Therefore, the combination of these two forces allows for flexible initialization of the contours. The proposed model is first presented as a two-phase level set formulation and then extended to a multi-phase formulation. The proposed method has been applied to brain MR image segmen-tation with desirable results.
(3) We propose a new region-based active contour model in a variational level set for-mulation for image segmentation. In our model, the local image intensities are described by Gaussian distributions with different means and variances. We define a local Gaussian distri-bution fitting energy with a level set function and local means and variances as variables. The means and variances of local intensities are considered as spatially varying functions to handle intensity inhomogeneities. It is worth noting that the local intensity means and variances, which are two variables of the proposed energy functional, are strictly derived from a variational prin-ciple, instead of being defined empirically. Comparisons with classic methods demonstrate the advantages of the proposed method in terms of accuracy.
(4) We propose a novel method to simultaneously segment the brain MR images and cor-rect the bias fields. The proposed energy is multiphase and convex with respect to its partition variables. Therefore, our method is very robust to the initializations. We also propose a fast and accurate minimization algorithm based on the Split Bregman method for our energy. The flexibility of the method is shown with 2D and 3D segmentation examples of brain MR images. Moreover, we propose a novel convex framework utilizing local image statistical information for simultaneously segmentation of the brain MR images and correction of the bias fields. Many models can be seen as the special cases of the proposed framework. Comparisons also demon-strate the advantages of the proposed convex framework.
(5) We present a novel surface-based method for neonatal brain segmentation. Our method effectively utilizes local image information, atlas prior knowledge, and cortical thickness con-straint for guiding the segmentation, by integrating them into a coupled level set method. We also provide a robust initialization method using convex optimization for this coupled level set method. Our proposed method has been validated on 10 subjects with promising results.
(1)为了克服灰度不均匀性,提出了一种基于图像局部均值的分割模型。利用多相位水平集方式来拟合局部灰度,并采用一种简单而有效的初始化方法,达到更快更准地分割脑MR图像。由于采用了多相位水平集方法,该模型可以同时得到白质、灰质和脑脊液。另外水平集方法很好地保证了分割结果的光滑性,可以得到光滑的边界／曲面。
(2)为了克服对初始化的敏感性,提出了一种基于局部均值和全局均值的活动轮廓模型。该模型分别定义了一个局部拟合力和全局拟合力。其中,局部拟合力用于驱动曲线向目标靠近并在目标边界处停止,全局拟合力用于驱动远离目标边界的曲线向目标靠拢。在这两个拟合力的作用下,该模型对初始曲线较不敏感同时克服脑MR图像中存在的灰度不均匀性。
(3)提出了一种基于局部高斯概率的活动轮廓分割模型。通过分析每个像素邻域的灰度分布,利用窗口函数定义了一个局部高斯拟合能量。局部高斯概率中的两个参数,局部均值和局部方差是随着空间变化而变化的,因此本文方法可以很好地克服脑图像中存在的灰度不均匀性。值得一提的是,本文方法的局部均值和局部方差不再是显式定义的,而是可以通过变分法原理严格推导出来的。3T和7T的脑MR图像分割实验证明本文方法不仅可以有效地克服灰度不均匀性,还可以克服低对比度。
(4)提出了一种新颖的基于凸优化的脑MR图像分割模型,同时进行图像分割和估计偏移场,因此可以克服灰度不均匀性的影响。特别地,由于该模型关于图像分割变量是凸的,因此对初始化具有很强的鲁棒性。另外该模型也可以克服噪声的影响。和传统的基于梯度下降法求解相比,我们采用Split Bregman方法对该模型进行快速求解,使得对一幅2D的图像处理时间一般不超过1秒,3D的数据处理时间一般不超过100秒。大量的二维和三维实验证明本文方法无论在时间效率上还是准确度上都取得了满意的结果。而且,我们还进一步给出一个基于凸优化的脑MR图像分割框架模型,该框架综合利用了图像的局部统计信息。比较实验也证明了本文提出的框架模型是有效的。
(5)提出基于凸优化和耦合水平集方法的新生儿脑MR图像分割框架。耦合水平集方法综合利用了图像的局部灰度统计信息、基于Atlas的先验信息、大脑皮层的厚度信息。为了克服初始化对分割结果的影响,我们采用凸模型进行分割,然后进行必要的校正,从而为耦合水平集方法提供一个可靠的初始化。该新生儿脑MR图像分割框架已经在10个新生儿数据上取得了满意的结果,和目前流行的新生儿MR图像分割方法相比,本文方法取得了较高的分割精度。
Accurate segmentation of magnetic resonance (MR) images of the brain is undoubtedly of great interest for the study and the treatment of various pathologies such as Alzheimer dis-ease, Parkinson or Parkinson related syndrome. In fact, intensity inhomogeneity often occurs in MR images due to radio frequency (RF) coils or acquisition sequences. The intensity inho-mogeneity in MR images often appears as an intensity variation across the image. Thus the resultant intensities of the same tissue vary with the locations in the image. Although usually hardly noticeable to a human observer, such a bias can cause serious misclassifications when intensity-based segmentation algorithms are used. In addition, images are often corrupted by various noises that challenge the segmentation. Besides these difficulties, the boundaries be-tween tissues are quite fuzzy due to the partial volume (PV) effect. Compared with the adult brain MR images, contrast in neonatal MR images is much lower than that of adult because the majority of white matter is as-yet unmyelinated and has a water content closer to that of gray matter than in adults and adolescents. Besides the image contrast, the intensities of tissues are significantly affected by intensity inhomogeneity due to not only RF inhomogeneity but also biological properties of the developing tissue, which leads to a large overlap in their intensity distributions. The inversion of contrast between GM and WM, compared to adult MRI, is also a difficulty given the limited resolution of neonate MRI. Due to this inverted GM/WM con-trast, many voxels between CSF and GM can be incorrectly classified as WM by conventional intensity-based segmentation approaches. In a word, it remains challenging to segment brain MR images, especially for neonatal brain images. In this paper, we first propose a few segmen-tation methods based on active contour model to deal with the intensity inhomogeneity. These proposed active contour models are then intergraded into a convex framework to simultaneously segment the brain MR images and correct bias fields. The convexity of the framework makes the model robust to initialization. We further extend the convex framework and active con- tour model proposed previously into neonatal brain MR image segmentation. Our work mainly includes the following parts:
(1) To overcome the difficulty caused by intensity inhomogeneity in the segmentation of magnetic resonance (MR) images, this paper presents a new multiphase level set method for segmentation of brain MR images. The proposed model utilizes local image intensities, which enables it to cope with intensity inhomogeneity. With the multiphase level set framework, the model can extract brain white matter (WM), gray matter (GM) and cerebrospinal fluid (CSF) simultaneously and provide a smooth contour/surface. Comparisons of 2D and 3D segmentation prove that the proposed model is effective.
(2) We propose an improved region-based active contour model in a variational level set formulation. We define an energy functional with a local intensity fitting term, which induces a local force to attract the contour and stops it at object boundaries, and an auxiliary global intensity fitting term, which drives the motion of the contour far away from object boundaries. Therefore, the combination of these two forces allows for flexible initialization of the contours. The proposed model is first presented as a two-phase level set formulation and then extended to a multi-phase formulation. The proposed method has been applied to brain MR image segmen-tation with desirable results.
(3) We propose a new region-based active contour model in a variational level set for-mulation for image segmentation. In our model, the local image intensities are described by Gaussian distributions with different means and variances. We define a local Gaussian distri-bution fitting energy with a level set function and local means and variances as variables. The means and variances of local intensities are considered as spatially varying functions to handle intensity inhomogeneities. It is worth noting that the local intensity means and variances, which are two variables of the proposed energy functional, are strictly derived from a variational prin-ciple, instead of being defined empirically. Comparisons with classic methods demonstrate the advantages of the proposed method in terms of accuracy.
(4) We propose a novel method to simultaneously segment the brain MR images and cor-rect the bias fields. The proposed energy is multiphase and convex with respect to its partition variables. Therefore, our method is very robust to the initializations. We also propose a fast and accurate minimization algorithm based on the Split Bregman method for our energy. The flexibility of the method is shown with 2D and 3D segmentation examples of brain MR images. Moreover, we propose a novel convex framework utilizing local image statistical information for simultaneously segmentation of the brain MR images and correction of the bias fields. Many models can be seen as the special cases of the proposed framework. Comparisons also demon-strate the advantages of the proposed convex framework.
(5) We present a novel surface-based method for neonatal brain segmentation. Our method effectively utilizes local image information, atlas prior knowledge, and cortical thickness con-straint for guiding the segmentation, by integrating them into a coupled level set method. We also provide a robust initialization method using convex optimization for this coupled level set method. Our proposed method has been validated on 10 subjects with promising results.
引文
[1]Brown E. S, Chan T. F, Bresson X. Convex Formulation and Exact Global Solutions for Multi-phase Piecewise Constant Mumford-Shah Image Segmentation. Technical Report 09-66, UCLA Computational and Applied Mathematics, July 2009
[2]Wang L, Li C, Sun Q, Xia D, Kao C.-Y. Active contours driven by local and global intensity fitting energy with application to brain MR image segmentation. Computerized Medical Imaging and Graphics, October 2009,33(7):520-531
[3]Wells W, Grimson E, Kikinis R, Jolesz F. Adaptive segmentation of MRI data. IEEE Trans Med Imag,1996,15(4):429-442
[4]Leemput V, Maes K, Vandermeulen D, Suetens P. Automated Model-Based Bias Field Correction of MR Images of the Brain. IEEE Trans Med Imag,1999,18(10):885-896
[5]Li C, Huang R, Ding Z, Gatenby C, Metaxas D, Gore J. A Variational Level Set Ap-proach to Segmentation and Bias Correction of Medical Images with Intensity Inhomo-geneity. Proceedings of Medical Image Computing and Computer Aided Intervention, 2008, LNCS 5242, Part Ⅱ:1083-1091
[6]Prastawa M, Gilmore J. H, Lin W, Gerig G. Automatic segmentation of MR images of the developing newborn brain. Medical Image Analysis,2005,9(5):457-466
[7]Shi F, Fan Y, Tang S, Gilmore J. H, Lin W, Shen D. Neonatal brain image segmentation in longitudinal MRI studies. NeuroImage,2010,49(1):391-400
[8]Xue H, Srinivasan L, Jiang S, Rutherford M, Edwards A. D, Rueckert D, Hajnal J. V. Au-tomatic segmentation and reconstruction of the cortex from neonatal MRI. NeuroImage, 2007,38(3):461-477
[9]Kass M, Witkin A, Terzopoulos D. Snakes:active contour models. Int'l J Comp Vis, January 1987,1(4):321-331
[10]Ronfard R. Region-based strategies for active contour models. Int'l J Comp Vis, October 1994,13(2):229-251
[11]Yezzi A, Tsai A, Willsky A. Binary and Ternary Flows for Image Segmentation. ICIP (2),1999:1-5
[12]Samson C, Blanc-Feraud L, Aubert G, Zerubia J. A Variational Model for Image Classi-fication and Restoration. IEEE Trans Patt Anal Mach Intell, May 2000,22(5):460-472
[13]Chan T, Vese L. Active contours without edges. IEEE Trans Imag Proc, February 2001, 10(2):266-277
[14]Tsai A, Yezzi A, Willsky A. S. Curve evolution implementation of the Mumford-Shah Functional for image segmentation, denoising, interpolation, and magnification. IEEE Trans Imag Proc, August 2001,10(8):1169-1186
[15]Paragios N, Deriche R. Geodesic Active Regions and Level Set Methods for Supervised Texture Segmentation. Int'l J Comp Vis, February 2002,46(3):223-247
[16]Vese L, Chan T. A Multiphase Level set framework for Image segmentation Using the Mumford and Shah Model. Int'l J Comp Vis, December 2002,50(3):271-293
[17]Rousson M, Deriche R. A variational framework for active and adaptative segmentation of vector valued images. IEEE Workshop on Motion and Video Computing,2002:52-62
[18]Piovano J, Rousson M, Papadopoulo T. Efficient Segmentation of Piecewise Smooth Images. SSVM,2007:709-720
[19]Li C, Huang R, Ding Z, Gatenby C, Metaxas D, Gore J. A Variational Level Set Ap-proach to Segmentation and Bias Correction of Medical Images with Intensity Inhomo-geneity. Proceedings of Medical Image Computing and Computer Aided Intervention, 2008, LNCS 5242, Part Ⅱ:1083-1091
[20]Wang L, Li C, Sun Q, Xia D, Kao C. Brain MR Image Segmentation Using Local and Global Intensity Fitting Active Contours/Surfaces. Proceedings of Medical Image Computing and Computer Aided Intervention,2008, LNCS 5241, Part I:384-392
[21]Sezgin M, Sankur B. Survey over image thresholding techniques and quantitative perfor-mance evaluation. Journal of Electronic Imaging,2004,13(1):146-165
[22]章毓晋.图像工程,第2版.北京：清华大学出版社,2007
[23]Gonzalez R. C, Woods R. E. Digital Image Processing,2nd Edition. New Jersey:Prentice Hall,2002
[24]MacQueen J. B. Some Methods for classification and Analysis of Multivariate Obser-vations.5-th Berkeley Symposium on Mathematical Statistics and Probability,1967,1: 281-297
[25]Dunn J. C. A Fuzzy Relative of the ISODATA Process and Its Use in Detecting Compact Well-Separated Clusters. Journal of Cybernetics,1973,3:32-57
[26]Dempster A. P, Laird N. M, Rubin D. B. Maximum Likelihood from Incomplete Data via theEM algorithm. Journal of the Royal Statistical Society,1977,39(1):1-38
[27]Ahmed M, Yamany S, Mohamed N, Farag A, Moriarty T. A modified fuzzy c-means algorithm for bias field estimation and segmentation of MRI data. IEEE Trans Med Imaging, March 2002,21(3):193-199
[28]Pham D, Prince J. Adaptive fuzzy segmentation of magnetic resonance images. IEEE Trans Med Imag, September 1999,18(9):737-752
[29]Cohen L, Cohen I. Finite-element methods for active contour models and balloons for 2-D and 3-D images. IEEE Trans Patt Anal Mach Intell, November 1993,15(11):1131-1147
[30]Mcinerney T, Terzopoulos D. Deformable Models in Medical Image Analysis:A Survey. Medical Image Analysis,1996,1:91-108
[31]Xu C, Prince J. Snakes, shapes, and gradient vector flow. IEEE Trans Imag Proc, March 1998,7(3):359-369
[32]Amini A. A, Weymouth T, Jain R. Using Dynamic Programming for Solving Variational Problems in Vision. PAMI, September 1990,12(9):855-867
[33]Williams D, Shah M. A Fast Algorithm for Active Contours and Curvature Estimation. CVGIP, January 1992,55(1):14-26
[34]Wang Y, Teoh E. K. Dynamic B-snake model for complex objects segmentation. Image and Vision Computing,2005,23(12):1029-1040
[35]Caselles V, Catte F, Coll T, Dibos F. A geometric model for active contours in image processing. Numer Math, December 1993,66(1):1-31
[36]Malladi R, Sethian J. A, Vemuri B. C. Shape modeling with front propagation:a level set approach. IEEE Trans Patt Anal Mach Intell, February 1995,17(2):158-175
[37]Osher S, Sethian J. Fronts propagating with curvature-dependent speed:algorithms based on Hamilton-Jacobi formulations. J Comp Phys, November 1988,79(1):12-49
[38]Osher S, Fedkiw R, Level Set Methods and Dynamic Implicit Surfaces. Springer-Verlag, New York,2002
[39]Adalsteinsson D, Sethian J. A fast level set method for propagating interfaces. J Comp Phys, May 1995,118(2):269-277
[40]Li C, Kao C, Gore J, Ding Z. Implicit Active Contours Driven by Local Binary Fitting Energy. CVPR,2007:1-7
[41]陈允杰,张建伟,韦志辉,夏德深,王平安.同时配准-分割脑MR图像的耦合变分模型.计算机辅助设计与图形图像学报,2007，19(5)：215-220
[42]陈志彬,邱天爽,Ruan S.一种基于FCM和Level Set的MRI医学图像分割方法.电子学报,2008,36(9)：1733-1736
[43]Li C. Active contours with local binary fitting energy. IMA Workshop on New Mathe-matics and Algorithms for 3-D Image Analysis, January 2006
[44]An J, Rousson M, Xu C. Γ-Convergence Approximation to Piecewise Smooth Medical Image Segmentation. Proceedings of Medical Image Computing and Computer Aided Intervention,2007:495-502
[45]Lankton S, Nain D, Yezzi A, Tannenbaun A. Hybrid geodesic region-based curve evo-lutions for image segmentation. SPIE Medical Imaging 2007 Symposium, March 2007, 6510
[46]Wang L, He L, Mishra A, Li C. Active Contours Driven by Local Gaussian Distribution Fitting Energy. Signal Processing,2009,89(12):2435-2447
[47]Cootes T. F, Taylor C. J, Cooper D. H, Graham J. Active shape models-their training and application. Computer Vision and Image Understanding,1995,61(1):38-59
[48]Cootes T. F, Edwards G. J, Taylor C. J. Active appearance models. IEEE Transactions on Pattern Analysis and Machine Intelligence,2001,23(6):681-685
[49]Lelieveldt B. P. F, Uzumcu M, van der Geest R. J, Reiber J. H. C, Sonka M. Multi-view active appearance models for consistent segmentation of multiple standard views: application to long and short-axis cardiac MR images. CARS,2003:1141-1146
[50]Kolmogorov V, Zabih R. What Energy Functions Can Be Minimized via Graph Cuts? IEEE Trans Patt Anal Mach Intell,2004,26(2):147-159
[51]Zahn C. T. Graph-Theoretical Methods for Detecting and Describing Gestalt Clusters. IEEE Trans Comput,1971,20(1):68-86
[52]Shi J, Malik J. Normalized cuts and image segmentation. IEEE Trans Patt Anal Mach Intell,2000,22(8):888-905
[53]Felzenszwalb P. F, Huttenlocher D. P. Efficient graph-based image segmentation. Inter-national Journal of Computer Vision,2004,59(2):167-181
[54]闫成新,桑农,张天序.基于图论的图像分割研究进展.计算机工程与应用,2006,42(5)：11-14
[55]Song Z, Tustison N, Avants B, Gee J. C. Integrated Graph Cuts for Brain MRI Segmenta-tion. Proceedings of Medical Image Computing and Computer Aided Intervention,2006: 831-838
[56]Boykov Y, Lee V. S, Rusinek H, Bansal R. Segmentation of dynamic N-D data sets via graph cuts using markov models. In Proc. Medical Image Computing and ComputerAs-sisted Intervention,2001:1058-1066
[57]Vovk U, Pernus F, Likar B. A review of methods for correction of intensity inhomogene-ity in MRI. IEEE Trans Med Imag, March 2007,26(3):405-421
[58]Chen W, Giger L. A fuzzy c-means (FCM) based algorithm for intensity inhomogeneity correction and segmentation of MR images. the 2004 IEEE International Symposium on Biomedical Imaging:From Nano to Macro,2004:1307-1310
[59]Styner M, Brechbuhler C, Szekely G, Gerig G. Parametric estimate of intensity inhomo-geneities applied to MRI. IEEE Trans Med Imag, March 2000,19(3):153-165
[60]王利,陈允杰,汤杨,韦志辉,王平安,夏德深.一种基于遗传算法的脑MR图像去偏移场模型.中国图象图形学报,2008,13(7)：1281-1286
[61]Ashburner J, Friston K. J. Voxel-based morphometry-the methods. IEEE Trans Med Imag, June 2000,11(6):805-821
[62]Salvado O, Hillenbrand C, Wilson D. L. Correction of intensity inhomogeneity in MR images of vascular disease. EMBS'05,2005:4302-4305
[63]Li C, Xu C, Konwar K, Fox M. D. Fast Distance Preserving Level Set Evolution for Medical Image Segmentation. Proceedings of 9th International Conference on Control, Automation, Robotics and Vision,2006:1-7
[64]Li C, Liu J, Fox M. D. Segmentation of Edge Preserving Gradient Vector Flow:An Approach Toward Automatically Initializing and Splitting of Snakes. CVPR,2005,1: 162-167
[65]朱付平,田捷,林瑶,葛行飞.基于Level Set方法的医学图像分割.软件学报,2002,13(9)：1866-1871
[66]Li C, Liu J, Fox M. D. Segmentation of external force field for automatic initialization and splitting of snakes. Pattern Recognition, November 2005,38(11):1947-1960
[67]Li C, Xu C, Gui C, Fox M. D. Distance Regularized Level Set Evolution and Applications to Image Segmentation. IEEE Trans Imag Proc,2009
[68]Mumford D, Shah J. Optimal approximations by piecewise smooth functions and asso-ciated variational problems. Commun Pure Appl Math,1989,42(5):577-685
[69]Zhu S, Yuille A. Region competition:unifying snakes, region growing, and Bayes/MDL for multiband Image segmentation. IEEE Trans Pattern Anal Mach Intell, September 1996,18(9):884-900
[70]Li C, Xu C, Gui C, Fox M. D. Level Set Evolution Without Re-initialization:A New Variational Formulation. CVPR,2005,1:430-436
[71]http://www.bic.mni.mcgill. ca/brainweb/
[72]Jaccard P. The distribution of flora in the alpine zone. New Phytol,1912,11(2):37-50
[73]Cremers D, Rousson M, Deriche R. A Review of Statistical Approaches to Level Set Segmentation:Integrating Color, Texture, Motion and Shape. Int'l J Comp Vis, April 2007,72(2):195-215
[74]Kimmel R, Amir A, Bruckstein A. Finding shortest paths on surfaces using level set propagation. IEEE Trans Patt Anal Mach Intell, June 1995,17(6):635-640
[75]Rousson M, Cremers D. Implicit Active Shape Models for 3D Segmentation in MR Imaging. Proceedings of Medical Image Computing and Computer Aided Intervention, 2004:209-216
[76]Li C, Wang L, Kao C, Ding Z, Gore J. Brain MR Image Segmentation by Minimiz-ing Scalable Neighborhood Intensity Fitting Energy:A Multiphase Level Set Approach. ISMRM'08,2008
[77]Li C, Kao C, Gore J. C, Ding Z. Minimization of Region-Scalable Fitting Energy for Image Segmentation. IEEE Trans Imag Proc, October 2008,17(10):1940-1949
[78]Dice L. Measures of the Amount of Ecologic Association Between Species. Ecology, 1945,26:297-302
[79]李俊,杨新,施鹏飞.基于Mumford-Shah模型的快速水平集图像分割方法.计算机学报,2002,25(11)：1175-1183
[80]Ghanei A, Soltanian-Zadeh H, Windham J. P. Segmentation of Hippocampus from Brain MRI Using Deformable Contours. Computerized Medical Imaging and Graphics,1998, 22(3):203-216
[81]Amini L, Soltanian-Zadeh H, Lucas C, Gity M. Automatic segmentation of thalamus from brain MRI integrating fuzzy clustering and dynamic contours. IEEE Trans Biomed Eng,2004,51(5):800-811
[82]Li S, Fevens T, Krzyzak A, Jin C, Li S. Semi-automatic computer aided lesion detection in dental X-rays using variational level set. Pattern Recognition,2007,40(10):2861-2873
[83]Ayed I. B, Li S, Ross I. Level Set Image Segmentation with a Statistical Overlap Con-straint. Information Processing in Medical Imaging (IPMI),2009, LNCS 5636:589-601
[84]Lankton S, Melonakos J, Malcolm J, Dambreville S, Tannenbaum A. Localized statis-tics for DW-MRI fiber bundle segmentation. Computer Vision and Pattern Recognition Workshops,2008:1-8
[85]Brox T. From pixels to regions:Partial differential equations in image analysis. Ph.D. Thesis, Faculty of Mathematics and Computer Science, Saarland University, Germany, 2005
[86]Rosenhahn B, Brox T, Weickert J. Three-Dimensional Shape Knowledge for Joint Image Segmentation and Pose Tracking. Int'l J Comp Vis, July 2007,73(3):242-262
[87]Brox T, Cremers D. On the Statistical Interpretation of the Piecewise Smooth Mumford-Shah Functional. SSVM07,2007:203-213
[88]Kim J, Fisher J, Yezzi A, Cetin M, Willsky A. Nonparametric methods for image seg-mentation using information theory and curve evolution. IEEE International Conference on Image Processing,2002,3:797-800
[89]Rousson M, Brox T, Deriche R. Active unsupervised texture segmentation on a diffusion based feature space. IEEE Computer Society Conference on Computer Vision and Pattern Recognition,2003:699-704
[90]Li C. Active contours with local binary fitting energy. IMA Workshop on New Mathe-matics and Algorithms for 3-D Image Analysis, January 2006
[91]Aubert G, Kornprobst P. Mathematical Problems in Image Processing:Partial Differen-tial Equations and the Calculus of Variations. New York:Springer,2002
[92]Comaniciu D, Meer P. Mean Shift:A Robust Approach toward Feature Space Analysis. IEEE Trans Patt Anal Mach Intell, May 2002,24(5):603-619
[93]Meer P, Georgescu B. Edge Detection with Embedded Confidence. IEEE Trans Pattern Anal Machine Intell,2001,23:1351-1365
[94]Christoudias C. M, Georgescu B, Meer P, Georgescu C. M. Synergism in Low Level Vision. In International Conference on Pattern Recognition,2002:150-155
[95]Guillemaud R, Brady M. Estimating bias field of MR images. IEEE Trans Med Imag, June 1997,16(3):238-251
[96]Tincher M, Meyer C. R, Gupta R, Williams D. M. Polynomial modeling and reduction of RF body coil spatial inhomogeneity in MRI. IEEE Trans Med Imag,1993,12(2): 361-365
[97]Li C, Xu C, Anderson A. W, Gore J. C. MRI Tissue Classification and Bias Field Esti-mation Based on Coherent Local Intensity Clustering:A Unified Energy Minimization Framework. Information Processing in Medical Imaging (IPMI),2009,5636:288-299
[98]M. Siyal L. Y. An intelligent modified fuzzy c-means based algorithm for bias estimation and segmentation of brain MRI. Pattern Recognition Letters, October 2005,26:2052-2062
[99]Vemuri P, Kholmovski E. G, Parker D. L, Chapman B. E. Coil sensitivity estimation for optimal SNR reconstruction and intensity inhomogeneity correction in phased array MR imaging, the Inf. Process. Med. Imag.:19th Int. Conf. (IPMI 2005),2005:603-614
[100]Milles J, Zhu Y. M, Chen N, Panych L. P, Gimenez G, Guttmann C. R. MRI intensity nonuniformity correction using simultaneously spatial and gray-level histogram infor-mation. Proc. SPIE Med. Imag.2004:Physiol., Function, Structure Med. Images,2004, 5370:734-742
[101]Vovk U, Pernus F, Likar B. MRI intensity inhomogeneity correction by combining in-tensity and spatial information. Phys Med Biol, March 2004,49(3):4119-4133
[102]Hou Z. A Review on MR Image Intensity Inhomogeneity Correction. International Journal of Biomedical Imaging, August 2006,2006
[103]Lewis E, Fox N. Correction of differential intensity inhomogeneity in longitudinal MR images. Neuroimage, SeptemBer 2004,23(1):75-83
[104]Meyer C, Bland P, Pipe J. Retrospective correction of intensity inhomogeneities in MRI. IEEE Trans Med Imag, January 1995,14(1):36-41
[105]Dawant B, Zijdenbos A, Margolin R. Correction of intensity variations in MR images for computer-aided tissues classification. IEEE Trans Med Imag, April 1993,12(4):770-781
[106]Likar B, Viergever M, Pernus F. Retrospective correction of MR intensity inhomogeneity by information minimization. IEEE Trans Med Imag, December 2001,20(12):1398-1410
[107]Sled J, Zijdenbos A, Evans A. A nonparametric method for automatic correction of intensity nonuniformity in MRI data. IEEE Trans Med Imag, January 1998,17(1):87-97
[108]MacDonald D, Kabani N, Avis D, Evans A. C. Automated 3-D Extraction of Inner and Outer Surfaces of Cerebral Cortex from MRI. NeuroImage,2000,12(3):340-356
[109]Boyd S, Vandenberghe L. Convex Optimization. New York, NY, USA:Cambridge University Press,2004
[110]Chan T. F, Esedoglu S, Nikolova M. Algorithms for Finding Global Minimizers of Image Segmentation and Denoising Models. SIAM Journal on Applied Mathematics,2006, 66(5):1632-1648
[111]Fundana K. Variational Segmentation Problems using Prior Knowledge in Imaging and Vision. Ph.D. Thesis, Department of Computer Science, University of Copenhagen, Den-mark,2010
[112]Shattuck D. W, Sandor-Leahy S. R, Schaper K. A, Rottenberg D. A, Leahy R. M. Mag-netic resonance image tissue classification using a partial volume model. Neuroimage, May 2001,13:856-876
[113]Bresson X, Esedogu S, Vandergheynst P, Thiran J.-P, Osher S. Fast Global Minimization of the Active Contour/Snake Model. J Math Imaging Vis,2007,28(2):151-167
[114]Chan T. F, Esedoglu S, Nikolov M. Algorithms for Finding Global Minimizers of Image Segmentation and Denoising Models. SIAM J Appl Math,2006,66(5):1632-1648
[115]Houhou N. Variational methods for texture segmentation. Ph.D. Thesis, STI School of Engineering, IEL Institut de genie electrique et electronique, French,2009
[116]Rudin L. I, Osher S, Fatemi E. Nonlinear Total Variation Based Noise Removal Algo-rithms. Physica,1992,60(1-4):259-268
[117]Chan T, Esedoglu S. Aspects of Total Varation Regularized L1 function Approximation. CAM Report 04-07, UCLA,2004
[118]Mory B, Ardon R. Fuzzy Region Competition:A Convex Two-Phase Segmentation Framework. SSVM07,2007:214-226
[119]Li C, Li F, Kao C.-Y, Xu C. Image Segmentation with Simultaneous Illumination and Reflectance Estimation:An Energy Minimization Approach. Proceedings of the Eighth International Conference on Computer Vision (ICCV),2009
[120]Goldstein T, Bresson X, Osher S. Geometric Applications of the Split Bregman Method: Segmentation and Surface Reconstruction. CAM Report 09-06, UCLA,2009
[121]Bregman L. The Relaxation Method of Finding the Common Points of Convex Sets and Its Application to the Solution of Problems in Convex Programming. USSR Computa-tional Mathematics and Mathematical Physics,1967,7:200-217
[122]Cai J.-F, Osher S, Shen Z. Split Bregman Methods and Frame Based Image Restoration. CAM Report 09-28, UCLA,2009
[123]Wang Y, Yin W, Zhang Y. A Fast Algorithm For Image Deblurring with Total Variation Regularization. CAAM Technical Report TR07-10, Department of Computational and Applied Mathematics,2007
[124]http://www.med. harvard. edu/AANLIB/home.html
[125]Marlow N, Dieter W, Bracewell M, Samara M. Neurologic and developmental disability at six years of age after extremely preterm birth. N Engl J Med,2005,352(1):9-19
[126]McCormick M, Workman-Daniels K, Brooks-Gunn J. The behavioral and emotional well-being of school-age children with different birth weights. Pediatrics,1996,97:18-25
[127]Hack M, Flannery D, Schluchter M, Cartar L, Borawski E, Klein N. Outcomes in young adulthood for very-low-birth-weight infants. N Engl J Med,2002,346(3):149-157
[128]Peterson B, Anderson A, Ehrenkranz R, Staib L, Tageldin M, Colson E, Gore J, Dun-can C, Makuch R, Ment L. Regional brain volumes and their later neurodevelopmental correlates in term and preterm infants. Pediatrics,2003,111:939-948
[129]Isaacs E, Edmonds C, Chong W, Lucas A, Morley R, Gadian D. Brain morphometry and IQ measurements in preterm children. Brain,2004,127:2595-2607
[130]Dubois J, Benders M, Cachia A, Lazeyras F, Ha-vinh R, Sizonenko S. V, Borradori-tolsa C, Mangin J. F. Mapping the Early Cortical Folding Process in the Preterm Newborn Brain. Cerebral Cortex,2008,18:1444-1454
[131]Gerig G, Davis B, Lorenzen P, Xu S, Jomier M, Piven J, Joshi S. Computational Anatomy to Assess Longitudinal Trajectory of Brain Growth.3DPVT'06:Proceedings of the Third International Symposium on 3D Data Processing, Visualization, and Transmission (3DPVT'06),2006:1041-1047
[132]Knickmeyer R, Gouttard S, Kang C, Evans D, Wilber K, Smith J, Hamer R, Lin W, Gerig G, Gilmore J. A structural MRI study of human brain development from birth to 2 years. J Neurosci,2008,28(47):12176-12182
[133]Mewes A. U. J, Huppi P. S, Als H, Rybicki F. J, Inder T. E, McAnulty G. B, Mulkern R. V, Robertson R. L, Rivkin M. J, Warfield S. K. Regional brain development in se-rial magnetic resonance imaging of low-risk preterm infants. Pediatrics,2006,118(1): 23-33
[134]Bazin P. L, Pham D. L. Topology-preserving tissue classification of magnetic resonance brain images. IEEE Trans Med Imag,2007,26(4):487-496
[135]Nishida M, Makris N, Kennedy D. N, Vangel M, Fischl B, Krishnamoorthy K. S, Cavi-ness V. S, Grant P. E. Detailed semiautomated MRI based morphometry of the neonatal brain:preliminary results. NeuroImage,2006,32(3):1041-1049
[136]Song Z, Awate S. P, Licht D. J, Gee J. C. Clinical Neonatal Brain MRI Segmentation Us-ing Adaptive Nonparametric Data Models and Intensity-Based Markov Priors. Proceed-ings of Medical Image Computing and Computer Aided Intervention,2007:883-890
[137]Aljabar P, Heckemann R, Hammers A, Hajnal J, Rueckert D. Multi-atlas based segmen-tation of brain images:Atlas selection and its effect on accuracy. NeuroImage,2009, 46(3):726-738
[138]Warfield S. K, Kaus M, Jolesz F. A, Kikinis R. Adaptive, template moderated, spatially varying statistical classification. Medical Image Analysis,2000,7(4):43-55
[139]Weisenfeld N. I, Warfield S. K. Automatic segmentation of newborn brain MRI. Neu-rolmage,2009,47(2):564-572
[140]Cocosco C. A, Zijdenbos A. P, Evans A. C. A fully automatic and robust brain MRI tissue classification method. Medical Image Analysis,2003,7(4):513-527
[141]Xu C, Pham D. L, Rettmann M. E, Yu D. N, Prince J. L. Reconstruction of the human cerebral cortex from magnetic resonance images. IEEE Trans Med Imag,1999,18(6): 467-480
[142]Zeng X, Staib L, Schultz R, Duncan J. Segmentation and Measurement of the Cortex from 3D MR Images Using Coupled Surfaces Propagation. IEEE Trans Med Imag,1999, 18(10):100-111
[143]Goldenberg R, Kimmel R, Rivlin E, Rudzsky M. Cortex segmentation:a fast variational geometric approach. IEEE Trans Med Imag,2002,21(2):1544-1551
[144]Han X, Pham D. L, Tosun D, Rettmann M. E, Xu C, Prince J. L. CRUISE:Cortical reconstruction using implicit surface evolution. NeuroImage,2004,23(3):997-1012
[145]Dale A, Fischl B, Sereno M. Cortical Surface-Based Analysis:I. Segmentation and Surface Reconstruction. NeuroImage,1999,9(2):179-194
[146]Lorensen W. E, Cline H. E. Marching cubes:A high resolution 3D surface construction algorithm. SIGGRAPH Comput Graph,1987,21(4):163-169
[147]Han X, Xu C, Prince J. A topology preserving level set method for geometric deformable models. IEEE Trans Patt Anal Mach Intell, June 2003,25(6):755-768
[148]Paragios N. A Variational Approach for the Segmentation of the Left Ventricle in MR Cardiac Images. VLSM'01,2001
[149]Sethian J. Level Set Methods and Fast Marching Methods. Cambridge University Press, Cambridge,1999
[2]Wang L, Li C, Sun Q, Xia D, Kao C.-Y. Active contours driven by local and global intensity fitting energy with application to brain MR image segmentation. Computerized Medical Imaging and Graphics, October 2009,33(7):520-531
[3]Wells W, Grimson E, Kikinis R, Jolesz F. Adaptive segmentation of MRI data. IEEE Trans Med Imag,1996,15(4):429-442
[4]Leemput V, Maes K, Vandermeulen D, Suetens P. Automated Model-Based Bias Field Correction of MR Images of the Brain. IEEE Trans Med Imag,1999,18(10):885-896
[5]Li C, Huang R, Ding Z, Gatenby C, Metaxas D, Gore J. A Variational Level Set Ap-proach to Segmentation and Bias Correction of Medical Images with Intensity Inhomo-geneity. Proceedings of Medical Image Computing and Computer Aided Intervention, 2008, LNCS 5242, Part Ⅱ:1083-1091
[6]Prastawa M, Gilmore J. H, Lin W, Gerig G. Automatic segmentation of MR images of the developing newborn brain. Medical Image Analysis,2005,9(5):457-466
[7]Shi F, Fan Y, Tang S, Gilmore J. H, Lin W, Shen D. Neonatal brain image segmentation in longitudinal MRI studies. NeuroImage,2010,49(1):391-400
[8]Xue H, Srinivasan L, Jiang S, Rutherford M, Edwards A. D, Rueckert D, Hajnal J. V. Au-tomatic segmentation and reconstruction of the cortex from neonatal MRI. NeuroImage, 2007,38(3):461-477
[9]Kass M, Witkin A, Terzopoulos D. Snakes:active contour models. Int'l J Comp Vis, January 1987,1(4):321-331
[10]Ronfard R. Region-based strategies for active contour models. Int'l J Comp Vis, October 1994,13(2):229-251
[11]Yezzi A, Tsai A, Willsky A. Binary and Ternary Flows for Image Segmentation. ICIP (2),1999:1-5
[12]Samson C, Blanc-Feraud L, Aubert G, Zerubia J. A Variational Model for Image Classi-fication and Restoration. IEEE Trans Patt Anal Mach Intell, May 2000,22(5):460-472
[13]Chan T, Vese L. Active contours without edges. IEEE Trans Imag Proc, February 2001, 10(2):266-277
[14]Tsai A, Yezzi A, Willsky A. S. Curve evolution implementation of the Mumford-Shah Functional for image segmentation, denoising, interpolation, and magnification. IEEE Trans Imag Proc, August 2001,10(8):1169-1186
[15]Paragios N, Deriche R. Geodesic Active Regions and Level Set Methods for Supervised Texture Segmentation. Int'l J Comp Vis, February 2002,46(3):223-247
[16]Vese L, Chan T. A Multiphase Level set framework for Image segmentation Using the Mumford and Shah Model. Int'l J Comp Vis, December 2002,50(3):271-293
[17]Rousson M, Deriche R. A variational framework for active and adaptative segmentation of vector valued images. IEEE Workshop on Motion and Video Computing,2002:52-62
[18]Piovano J, Rousson M, Papadopoulo T. Efficient Segmentation of Piecewise Smooth Images. SSVM,2007:709-720
[19]Li C, Huang R, Ding Z, Gatenby C, Metaxas D, Gore J. A Variational Level Set Ap-proach to Segmentation and Bias Correction of Medical Images with Intensity Inhomo-geneity. Proceedings of Medical Image Computing and Computer Aided Intervention, 2008, LNCS 5242, Part Ⅱ:1083-1091
[20]Wang L, Li C, Sun Q, Xia D, Kao C. Brain MR Image Segmentation Using Local and Global Intensity Fitting Active Contours/Surfaces. Proceedings of Medical Image Computing and Computer Aided Intervention,2008, LNCS 5241, Part I:384-392
[21]Sezgin M, Sankur B. Survey over image thresholding techniques and quantitative perfor-mance evaluation. Journal of Electronic Imaging,2004,13(1):146-165
[22]章毓晋.图像工程,第2版.北京：清华大学出版社,2007
[23]Gonzalez R. C, Woods R. E. Digital Image Processing,2nd Edition. New Jersey:Prentice Hall,2002
[24]MacQueen J. B. Some Methods for classification and Analysis of Multivariate Obser-vations.5-th Berkeley Symposium on Mathematical Statistics and Probability,1967,1: 281-297
[25]Dunn J. C. A Fuzzy Relative of the ISODATA Process and Its Use in Detecting Compact Well-Separated Clusters. Journal of Cybernetics,1973,3:32-57
[26]Dempster A. P, Laird N. M, Rubin D. B. Maximum Likelihood from Incomplete Data via theEM algorithm. Journal of the Royal Statistical Society,1977,39(1):1-38
[27]Ahmed M, Yamany S, Mohamed N, Farag A, Moriarty T. A modified fuzzy c-means algorithm for bias field estimation and segmentation of MRI data. IEEE Trans Med Imaging, March 2002,21(3):193-199
[28]Pham D, Prince J. Adaptive fuzzy segmentation of magnetic resonance images. IEEE Trans Med Imag, September 1999,18(9):737-752
[29]Cohen L, Cohen I. Finite-element methods for active contour models and balloons for 2-D and 3-D images. IEEE Trans Patt Anal Mach Intell, November 1993,15(11):1131-1147
[30]Mcinerney T, Terzopoulos D. Deformable Models in Medical Image Analysis:A Survey. Medical Image Analysis,1996,1:91-108
[31]Xu C, Prince J. Snakes, shapes, and gradient vector flow. IEEE Trans Imag Proc, March 1998,7(3):359-369
[32]Amini A. A, Weymouth T, Jain R. Using Dynamic Programming for Solving Variational Problems in Vision. PAMI, September 1990,12(9):855-867
[33]Williams D, Shah M. A Fast Algorithm for Active Contours and Curvature Estimation. CVGIP, January 1992,55(1):14-26
[34]Wang Y, Teoh E. K. Dynamic B-snake model for complex objects segmentation. Image and Vision Computing,2005,23(12):1029-1040
[35]Caselles V, Catte F, Coll T, Dibos F. A geometric model for active contours in image processing. Numer Math, December 1993,66(1):1-31
[36]Malladi R, Sethian J. A, Vemuri B. C. Shape modeling with front propagation:a level set approach. IEEE Trans Patt Anal Mach Intell, February 1995,17(2):158-175
[37]Osher S, Sethian J. Fronts propagating with curvature-dependent speed:algorithms based on Hamilton-Jacobi formulations. J Comp Phys, November 1988,79(1):12-49
[38]Osher S, Fedkiw R, Level Set Methods and Dynamic Implicit Surfaces. Springer-Verlag, New York,2002
[39]Adalsteinsson D, Sethian J. A fast level set method for propagating interfaces. J Comp Phys, May 1995,118(2):269-277
[40]Li C, Kao C, Gore J, Ding Z. Implicit Active Contours Driven by Local Binary Fitting Energy. CVPR,2007:1-7
[41]陈允杰,张建伟,韦志辉,夏德深,王平安.同时配准-分割脑MR图像的耦合变分模型.计算机辅助设计与图形图像学报,2007，19(5)：215-220
[42]陈志彬,邱天爽,Ruan S.一种基于FCM和Level Set的MRI医学图像分割方法.电子学报,2008,36(9)：1733-1736
[43]Li C. Active contours with local binary fitting energy. IMA Workshop on New Mathe-matics and Algorithms for 3-D Image Analysis, January 2006
[44]An J, Rousson M, Xu C. Γ-Convergence Approximation to Piecewise Smooth Medical Image Segmentation. Proceedings of Medical Image Computing and Computer Aided Intervention,2007:495-502
[45]Lankton S, Nain D, Yezzi A, Tannenbaun A. Hybrid geodesic region-based curve evo-lutions for image segmentation. SPIE Medical Imaging 2007 Symposium, March 2007, 6510
[46]Wang L, He L, Mishra A, Li C. Active Contours Driven by Local Gaussian Distribution Fitting Energy. Signal Processing,2009,89(12):2435-2447
[47]Cootes T. F, Taylor C. J, Cooper D. H, Graham J. Active shape models-their training and application. Computer Vision and Image Understanding,1995,61(1):38-59
[48]Cootes T. F, Edwards G. J, Taylor C. J. Active appearance models. IEEE Transactions on Pattern Analysis and Machine Intelligence,2001,23(6):681-685
[49]Lelieveldt B. P. F, Uzumcu M, van der Geest R. J, Reiber J. H. C, Sonka M. Multi-view active appearance models for consistent segmentation of multiple standard views: application to long and short-axis cardiac MR images. CARS,2003:1141-1146
[50]Kolmogorov V, Zabih R. What Energy Functions Can Be Minimized via Graph Cuts? IEEE Trans Patt Anal Mach Intell,2004,26(2):147-159
[51]Zahn C. T. Graph-Theoretical Methods for Detecting and Describing Gestalt Clusters. IEEE Trans Comput,1971,20(1):68-86
[52]Shi J, Malik J. Normalized cuts and image segmentation. IEEE Trans Patt Anal Mach Intell,2000,22(8):888-905
[53]Felzenszwalb P. F, Huttenlocher D. P. Efficient graph-based image segmentation. Inter-national Journal of Computer Vision,2004,59(2):167-181
[54]闫成新,桑农,张天序.基于图论的图像分割研究进展.计算机工程与应用,2006,42(5)：11-14
[55]Song Z, Tustison N, Avants B, Gee J. C. Integrated Graph Cuts for Brain MRI Segmenta-tion. Proceedings of Medical Image Computing and Computer Aided Intervention,2006: 831-838
[56]Boykov Y, Lee V. S, Rusinek H, Bansal R. Segmentation of dynamic N-D data sets via graph cuts using markov models. In Proc. Medical Image Computing and ComputerAs-sisted Intervention,2001:1058-1066
[57]Vovk U, Pernus F, Likar B. A review of methods for correction of intensity inhomogene-ity in MRI. IEEE Trans Med Imag, March 2007,26(3):405-421
[58]Chen W, Giger L. A fuzzy c-means (FCM) based algorithm for intensity inhomogeneity correction and segmentation of MR images. the 2004 IEEE International Symposium on Biomedical Imaging:From Nano to Macro,2004:1307-1310
[59]Styner M, Brechbuhler C, Szekely G, Gerig G. Parametric estimate of intensity inhomo-geneities applied to MRI. IEEE Trans Med Imag, March 2000,19(3):153-165
[60]王利,陈允杰,汤杨,韦志辉,王平安,夏德深.一种基于遗传算法的脑MR图像去偏移场模型.中国图象图形学报,2008,13(7)：1281-1286
[61]Ashburner J, Friston K. J. Voxel-based morphometry-the methods. IEEE Trans Med Imag, June 2000,11(6):805-821
[62]Salvado O, Hillenbrand C, Wilson D. L. Correction of intensity inhomogeneity in MR images of vascular disease. EMBS'05,2005:4302-4305
[63]Li C, Xu C, Konwar K, Fox M. D. Fast Distance Preserving Level Set Evolution for Medical Image Segmentation. Proceedings of 9th International Conference on Control, Automation, Robotics and Vision,2006:1-7
[64]Li C, Liu J, Fox M. D. Segmentation of Edge Preserving Gradient Vector Flow:An Approach Toward Automatically Initializing and Splitting of Snakes. CVPR,2005,1: 162-167
[65]朱付平,田捷,林瑶,葛行飞.基于Level Set方法的医学图像分割.软件学报,2002,13(9)：1866-1871
[66]Li C, Liu J, Fox M. D. Segmentation of external force field for automatic initialization and splitting of snakes. Pattern Recognition, November 2005,38(11):1947-1960
[67]Li C, Xu C, Gui C, Fox M. D. Distance Regularized Level Set Evolution and Applications to Image Segmentation. IEEE Trans Imag Proc,2009
[68]Mumford D, Shah J. Optimal approximations by piecewise smooth functions and asso-ciated variational problems. Commun Pure Appl Math,1989,42(5):577-685
[69]Zhu S, Yuille A. Region competition:unifying snakes, region growing, and Bayes/MDL for multiband Image segmentation. IEEE Trans Pattern Anal Mach Intell, September 1996,18(9):884-900
[70]Li C, Xu C, Gui C, Fox M. D. Level Set Evolution Without Re-initialization:A New Variational Formulation. CVPR,2005,1:430-436
[71]http://www.bic.mni.mcgill. ca/brainweb/
[72]Jaccard P. The distribution of flora in the alpine zone. New Phytol,1912,11(2):37-50
[73]Cremers D, Rousson M, Deriche R. A Review of Statistical Approaches to Level Set Segmentation:Integrating Color, Texture, Motion and Shape. Int'l J Comp Vis, April 2007,72(2):195-215
[74]Kimmel R, Amir A, Bruckstein A. Finding shortest paths on surfaces using level set propagation. IEEE Trans Patt Anal Mach Intell, June 1995,17(6):635-640
[75]Rousson M, Cremers D. Implicit Active Shape Models for 3D Segmentation in MR Imaging. Proceedings of Medical Image Computing and Computer Aided Intervention, 2004:209-216
[76]Li C, Wang L, Kao C, Ding Z, Gore J. Brain MR Image Segmentation by Minimiz-ing Scalable Neighborhood Intensity Fitting Energy:A Multiphase Level Set Approach. ISMRM'08,2008
[77]Li C, Kao C, Gore J. C, Ding Z. Minimization of Region-Scalable Fitting Energy for Image Segmentation. IEEE Trans Imag Proc, October 2008,17(10):1940-1949
[78]Dice L. Measures of the Amount of Ecologic Association Between Species. Ecology, 1945,26:297-302
[79]李俊,杨新,施鹏飞.基于Mumford-Shah模型的快速水平集图像分割方法.计算机学报,2002,25(11)：1175-1183
[80]Ghanei A, Soltanian-Zadeh H, Windham J. P. Segmentation of Hippocampus from Brain MRI Using Deformable Contours. Computerized Medical Imaging and Graphics,1998, 22(3):203-216
[81]Amini L, Soltanian-Zadeh H, Lucas C, Gity M. Automatic segmentation of thalamus from brain MRI integrating fuzzy clustering and dynamic contours. IEEE Trans Biomed Eng,2004,51(5):800-811
[82]Li S, Fevens T, Krzyzak A, Jin C, Li S. Semi-automatic computer aided lesion detection in dental X-rays using variational level set. Pattern Recognition,2007,40(10):2861-2873
[83]Ayed I. B, Li S, Ross I. Level Set Image Segmentation with a Statistical Overlap Con-straint. Information Processing in Medical Imaging (IPMI),2009, LNCS 5636:589-601
[84]Lankton S, Melonakos J, Malcolm J, Dambreville S, Tannenbaum A. Localized statis-tics for DW-MRI fiber bundle segmentation. Computer Vision and Pattern Recognition Workshops,2008:1-8
[85]Brox T. From pixels to regions:Partial differential equations in image analysis. Ph.D. Thesis, Faculty of Mathematics and Computer Science, Saarland University, Germany, 2005
[86]Rosenhahn B, Brox T, Weickert J. Three-Dimensional Shape Knowledge for Joint Image Segmentation and Pose Tracking. Int'l J Comp Vis, July 2007,73(3):242-262
[87]Brox T, Cremers D. On the Statistical Interpretation of the Piecewise Smooth Mumford-Shah Functional. SSVM07,2007:203-213
[88]Kim J, Fisher J, Yezzi A, Cetin M, Willsky A. Nonparametric methods for image seg-mentation using information theory and curve evolution. IEEE International Conference on Image Processing,2002,3:797-800
[89]Rousson M, Brox T, Deriche R. Active unsupervised texture segmentation on a diffusion based feature space. IEEE Computer Society Conference on Computer Vision and Pattern Recognition,2003:699-704
[90]Li C. Active contours with local binary fitting energy. IMA Workshop on New Mathe-matics and Algorithms for 3-D Image Analysis, January 2006
[91]Aubert G, Kornprobst P. Mathematical Problems in Image Processing:Partial Differen-tial Equations and the Calculus of Variations. New York:Springer,2002
[92]Comaniciu D, Meer P. Mean Shift:A Robust Approach toward Feature Space Analysis. IEEE Trans Patt Anal Mach Intell, May 2002,24(5):603-619
[93]Meer P, Georgescu B. Edge Detection with Embedded Confidence. IEEE Trans Pattern Anal Machine Intell,2001,23:1351-1365
[94]Christoudias C. M, Georgescu B, Meer P, Georgescu C. M. Synergism in Low Level Vision. In International Conference on Pattern Recognition,2002:150-155
[95]Guillemaud R, Brady M. Estimating bias field of MR images. IEEE Trans Med Imag, June 1997,16(3):238-251
[96]Tincher M, Meyer C. R, Gupta R, Williams D. M. Polynomial modeling and reduction of RF body coil spatial inhomogeneity in MRI. IEEE Trans Med Imag,1993,12(2): 361-365
[97]Li C, Xu C, Anderson A. W, Gore J. C. MRI Tissue Classification and Bias Field Esti-mation Based on Coherent Local Intensity Clustering:A Unified Energy Minimization Framework. Information Processing in Medical Imaging (IPMI),2009,5636:288-299
[98]M. Siyal L. Y. An intelligent modified fuzzy c-means based algorithm for bias estimation and segmentation of brain MRI. Pattern Recognition Letters, October 2005,26:2052-2062
[99]Vemuri P, Kholmovski E. G, Parker D. L, Chapman B. E. Coil sensitivity estimation for optimal SNR reconstruction and intensity inhomogeneity correction in phased array MR imaging, the Inf. Process. Med. Imag.:19th Int. Conf. (IPMI 2005),2005:603-614
[100]Milles J, Zhu Y. M, Chen N, Panych L. P, Gimenez G, Guttmann C. R. MRI intensity nonuniformity correction using simultaneously spatial and gray-level histogram infor-mation. Proc. SPIE Med. Imag.2004:Physiol., Function, Structure Med. Images,2004, 5370:734-742
[101]Vovk U, Pernus F, Likar B. MRI intensity inhomogeneity correction by combining in-tensity and spatial information. Phys Med Biol, March 2004,49(3):4119-4133
[102]Hou Z. A Review on MR Image Intensity Inhomogeneity Correction. International Journal of Biomedical Imaging, August 2006,2006
[103]Lewis E, Fox N. Correction of differential intensity inhomogeneity in longitudinal MR images. Neuroimage, SeptemBer 2004,23(1):75-83
[104]Meyer C, Bland P, Pipe J. Retrospective correction of intensity inhomogeneities in MRI. IEEE Trans Med Imag, January 1995,14(1):36-41
[105]Dawant B, Zijdenbos A, Margolin R. Correction of intensity variations in MR images for computer-aided tissues classification. IEEE Trans Med Imag, April 1993,12(4):770-781
[106]Likar B, Viergever M, Pernus F. Retrospective correction of MR intensity inhomogeneity by information minimization. IEEE Trans Med Imag, December 2001,20(12):1398-1410
[107]Sled J, Zijdenbos A, Evans A. A nonparametric method for automatic correction of intensity nonuniformity in MRI data. IEEE Trans Med Imag, January 1998,17(1):87-97
[108]MacDonald D, Kabani N, Avis D, Evans A. C. Automated 3-D Extraction of Inner and Outer Surfaces of Cerebral Cortex from MRI. NeuroImage,2000,12(3):340-356
[109]Boyd S, Vandenberghe L. Convex Optimization. New York, NY, USA:Cambridge University Press,2004
[110]Chan T. F, Esedoglu S, Nikolova M. Algorithms for Finding Global Minimizers of Image Segmentation and Denoising Models. SIAM Journal on Applied Mathematics,2006, 66(5):1632-1648
[111]Fundana K. Variational Segmentation Problems using Prior Knowledge in Imaging and Vision. Ph.D. Thesis, Department of Computer Science, University of Copenhagen, Den-mark,2010
[112]Shattuck D. W, Sandor-Leahy S. R, Schaper K. A, Rottenberg D. A, Leahy R. M. Mag-netic resonance image tissue classification using a partial volume model. Neuroimage, May 2001,13:856-876
[113]Bresson X, Esedogu S, Vandergheynst P, Thiran J.-P, Osher S. Fast Global Minimization of the Active Contour/Snake Model. J Math Imaging Vis,2007,28(2):151-167
[114]Chan T. F, Esedoglu S, Nikolov M. Algorithms for Finding Global Minimizers of Image Segmentation and Denoising Models. SIAM J Appl Math,2006,66(5):1632-1648
[115]Houhou N. Variational methods for texture segmentation. Ph.D. Thesis, STI School of Engineering, IEL Institut de genie electrique et electronique, French,2009
[116]Rudin L. I, Osher S, Fatemi E. Nonlinear Total Variation Based Noise Removal Algo-rithms. Physica,1992,60(1-4):259-268
[117]Chan T, Esedoglu S. Aspects of Total Varation Regularized L1 function Approximation. CAM Report 04-07, UCLA,2004
[118]Mory B, Ardon R. Fuzzy Region Competition:A Convex Two-Phase Segmentation Framework. SSVM07,2007:214-226
[119]Li C, Li F, Kao C.-Y, Xu C. Image Segmentation with Simultaneous Illumination and Reflectance Estimation:An Energy Minimization Approach. Proceedings of the Eighth International Conference on Computer Vision (ICCV),2009
[120]Goldstein T, Bresson X, Osher S. Geometric Applications of the Split Bregman Method: Segmentation and Surface Reconstruction. CAM Report 09-06, UCLA,2009
[121]Bregman L. The Relaxation Method of Finding the Common Points of Convex Sets and Its Application to the Solution of Problems in Convex Programming. USSR Computa-tional Mathematics and Mathematical Physics,1967,7:200-217
[122]Cai J.-F, Osher S, Shen Z. Split Bregman Methods and Frame Based Image Restoration. CAM Report 09-28, UCLA,2009
[123]Wang Y, Yin W, Zhang Y. A Fast Algorithm For Image Deblurring with Total Variation Regularization. CAAM Technical Report TR07-10, Department of Computational and Applied Mathematics,2007
[124]http://www.med. harvard. edu/AANLIB/home.html
[125]Marlow N, Dieter W, Bracewell M, Samara M. Neurologic and developmental disability at six years of age after extremely preterm birth. N Engl J Med,2005,352(1):9-19
[126]McCormick M, Workman-Daniels K, Brooks-Gunn J. The behavioral and emotional well-being of school-age children with different birth weights. Pediatrics,1996,97:18-25
[127]Hack M, Flannery D, Schluchter M, Cartar L, Borawski E, Klein N. Outcomes in young adulthood for very-low-birth-weight infants. N Engl J Med,2002,346(3):149-157
[128]Peterson B, Anderson A, Ehrenkranz R, Staib L, Tageldin M, Colson E, Gore J, Dun-can C, Makuch R, Ment L. Regional brain volumes and their later neurodevelopmental correlates in term and preterm infants. Pediatrics,2003,111:939-948
[129]Isaacs E, Edmonds C, Chong W, Lucas A, Morley R, Gadian D. Brain morphometry and IQ measurements in preterm children. Brain,2004,127:2595-2607
[130]Dubois J, Benders M, Cachia A, Lazeyras F, Ha-vinh R, Sizonenko S. V, Borradori-tolsa C, Mangin J. F. Mapping the Early Cortical Folding Process in the Preterm Newborn Brain. Cerebral Cortex,2008,18:1444-1454
[131]Gerig G, Davis B, Lorenzen P, Xu S, Jomier M, Piven J, Joshi S. Computational Anatomy to Assess Longitudinal Trajectory of Brain Growth.3DPVT'06:Proceedings of the Third International Symposium on 3D Data Processing, Visualization, and Transmission (3DPVT'06),2006:1041-1047
[132]Knickmeyer R, Gouttard S, Kang C, Evans D, Wilber K, Smith J, Hamer R, Lin W, Gerig G, Gilmore J. A structural MRI study of human brain development from birth to 2 years. J Neurosci,2008,28(47):12176-12182
[133]Mewes A. U. J, Huppi P. S, Als H, Rybicki F. J, Inder T. E, McAnulty G. B, Mulkern R. V, Robertson R. L, Rivkin M. J, Warfield S. K. Regional brain development in se-rial magnetic resonance imaging of low-risk preterm infants. Pediatrics,2006,118(1): 23-33
[134]Bazin P. L, Pham D. L. Topology-preserving tissue classification of magnetic resonance brain images. IEEE Trans Med Imag,2007,26(4):487-496
[135]Nishida M, Makris N, Kennedy D. N, Vangel M, Fischl B, Krishnamoorthy K. S, Cavi-ness V. S, Grant P. E. Detailed semiautomated MRI based morphometry of the neonatal brain:preliminary results. NeuroImage,2006,32(3):1041-1049
[136]Song Z, Awate S. P, Licht D. J, Gee J. C. Clinical Neonatal Brain MRI Segmentation Us-ing Adaptive Nonparametric Data Models and Intensity-Based Markov Priors. Proceed-ings of Medical Image Computing and Computer Aided Intervention,2007:883-890
[137]Aljabar P, Heckemann R, Hammers A, Hajnal J, Rueckert D. Multi-atlas based segmen-tation of brain images:Atlas selection and its effect on accuracy. NeuroImage,2009, 46(3):726-738
[138]Warfield S. K, Kaus M, Jolesz F. A, Kikinis R. Adaptive, template moderated, spatially varying statistical classification. Medical Image Analysis,2000,7(4):43-55
[139]Weisenfeld N. I, Warfield S. K. Automatic segmentation of newborn brain MRI. Neu-rolmage,2009,47(2):564-572
[140]Cocosco C. A, Zijdenbos A. P, Evans A. C. A fully automatic and robust brain MRI tissue classification method. Medical Image Analysis,2003,7(4):513-527
[141]Xu C, Pham D. L, Rettmann M. E, Yu D. N, Prince J. L. Reconstruction of the human cerebral cortex from magnetic resonance images. IEEE Trans Med Imag,1999,18(6): 467-480
[142]Zeng X, Staib L, Schultz R, Duncan J. Segmentation and Measurement of the Cortex from 3D MR Images Using Coupled Surfaces Propagation. IEEE Trans Med Imag,1999, 18(10):100-111
[143]Goldenberg R, Kimmel R, Rivlin E, Rudzsky M. Cortex segmentation:a fast variational geometric approach. IEEE Trans Med Imag,2002,21(2):1544-1551
[144]Han X, Pham D. L, Tosun D, Rettmann M. E, Xu C, Prince J. L. CRUISE:Cortical reconstruction using implicit surface evolution. NeuroImage,2004,23(3):997-1012
[145]Dale A, Fischl B, Sereno M. Cortical Surface-Based Analysis:I. Segmentation and Surface Reconstruction. NeuroImage,1999,9(2):179-194
[146]Lorensen W. E, Cline H. E. Marching cubes:A high resolution 3D surface construction algorithm. SIGGRAPH Comput Graph,1987,21(4):163-169
[147]Han X, Xu C, Prince J. A topology preserving level set method for geometric deformable models. IEEE Trans Patt Anal Mach Intell, June 2003,25(6):755-768
[148]Paragios N. A Variational Approach for the Segmentation of the Left Ventricle in MR Cardiac Images. VLSM'01,2001
[149]Sethian J. Level Set Methods and Fast Marching Methods. Cambridge University Press, Cambridge,1999
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