基于局部统计和结构的活动轮廓分割模型
|
摘要
图像分割是将原始图像划分为一系列彼此互补交叠的匀质区域从而提取图像中感兴趣的区域(region of interest, ROI)。核磁共振成像(magnetic resonance image, MRI)技术在医学疾病诊断和治疗等领域中的作用日益重要。对于MR图像分割是器官解剖、组织量化测量、病理成因分析、病症发展追踪等医疗手段必不可少的研究准备和基础。然而由于拍摄过程中光频振动的不确定和杂质的存在,会分别引起图像缓慢的灰度不均匀性(即属于同一目标的灰度随空间的变化而不同)和一定程度的噪声。因此基于全局灰度统计信息的分割模型在处理含灰度不均匀性和噪声的图像时会产生错误的分割结果。同时,由于医学图像中的局部容积效应(Partial Volume Effects),即目标边界呈现出对比度较低和不连续的现象会严重影响组织器官的分割提取,尤其是脑和血管的MR图像。另一方面,由于医学图像中纹理、不规则变化的灰度不均匀性、噪声等,以及目标边界的结构可能较为复杂,因此,对医学图像中的目标实现智能提取和识别是目前极具实用价值的一项科研任务,进一步增加了分割的难度和挑战。
针对医学图像分割的需求及难点,本文利用活动轮廓模型对医学图像进行分割进行了深入研究。本文的主要工作和研究成果如下：
(1)针对同时含噪声、灰度不均匀性及多个待分割目标的图像,提出一种基于改进的模糊聚类(fuzzy c-means clustering, FCM)算法的Chan-Vese(CV)模型。本文基于直方图统计灰度种类、并利用邻域内计算的空间信息修正隶属度函数以此克服灰度不均匀性和噪声的影响,将改进后的FCM算法应用到CV模型的区域检测项,可准确的对像素点归类,成为曲线的演化依据。在演化时采用一种各向异性的模板来控制轮廓线的及时分裂,在较短时间内分割出更多目标。
(2)针对图像中光滑和纹理这两种不同组成成份,提出一种能同时考虑光滑部分和纹理部分的分割模型。首先在局部块中分别检测图像卡通部分的灰度统计特征以及纹理部分的特征信息用以计算区别不同纹理之间的Kullback-Leibler (KL)距离,并且该局部块能够根据图像的梯度信息自动调整其大小。进一步采用Split Bregman方法对模型进行快速求解,在医学和纹理图像的实验上验证了该本文模型能够明显的提高准确性和时效性。
(3)提出一种结合了图像结构信息、并基于灰度和梯度模两种统计特征新型活动轮廓模型。灰度不均匀性理论上是空间不规则变化的,且分布并不单一,提取水平集曲线邻域内灰度和梯度模的统计特征检测不同区域的灰度差异和灰度不均匀性。特别的,针对传统活动轮廓模型中全变差形式的正则项保持边缘不足,将结构张量通过水平集函数的对偶变量嵌入关于水平集函数的正则项,使得水平集曲线高效率的逼近图像的目标边界而避免产生过度平滑,进而利用改进的Chambolle对偶算法对整个模型进行快速求解。与其他同类的经典方法相比本文算法不论对初始条件的鲁棒性、分割时效和精度均有明显提高。
(4)针对图像中深凸的拓扑结构以及灰度不均匀性和噪声的同时存在的情况,提出一种鲁棒型基于非局部分片局部块统计方法的活动轮廓模型。由于灰度不均匀性随空间变化且分布并不规则,因此可以将灰度不均匀性和噪声一样看做一种灰度不规则变化的情况。利用一种分片局部块统计信息的区域项计算像素点的归属度,作为驱动曲线演化的力之一。灰度不规则变化影响水平集曲线演化到目标边界的效率,因此通过加上一个灰度惩罚项来控制当遇到灰度不规则变化时的水平集曲线的演化。同时利用图像梯度信息作为权值用于计算关于水平集函数的正则项,进一步增强水平集曲线的形状与目标边界拟合。应用于医学图像和自然图像上的实验证明该算法能够明显抑制强噪声和灰度不均匀性的影响,取得高效率和高准确性的分割结果。
(5)局部容积效应、噪声、灰度不均匀性的共同作用增加了MR图像中血管、组织末梢等具有细长拓扑结构的分割难度。针对这些问题,从两个方面将图像的结构信息与活动轮廓模型相结合。一方面,利用基于图像的结构信息改进的梯度流方程训练关于水平集函数的对偶变量以增强扑捉深凹型的目标结构；另一方面,根据图像边界的结构变化自适应的计算全局和局部的灰度统计信息,不仅克服了灰度不均匀性,同时进一步提高了曲线演化的效率。局部统计信息可以正确指导曲线克服灰度不均匀性,尤其是在临近边界处的灰度不均匀性,从而捕捉到正确的目标边界。而在远离边界处根据全局灰度统计信息演化,能够加快曲线演化到图像的目标边界。根据基于边界和基于区域的活动轮廓模型的特点,利用基于结构信息改进的梯度流方程(Gradient Vector Flow, GVF)计算用于表示活动轮廓曲线的水平集函数的对偶变量,通过对偶变量的内迭代使水平集曲线在演化中进一步与图像中狭长的边界结构保持一致。
Image segmantation is a process that partition the image into different non-overlapping regions, which are called region of interest (ROI). The magnetic resonance image (MRI) technique has played more and more important role in the medical diagnosis and treatment. Segmentation for MRI is the basis for organ diagnosis, tissue quantization, pathalogy factor analysis, and disease developement tracking, etc. However, as the result of the instability of radio frequency and the existence of the imprurity, the intensity inhomogeneity and noise is induced during the process of imaging. The intensity inhomogeneity is the phenomenon that the intensity in the same ROI varies spatially. And for the intensity inhomogeneity in MRI, the intensity varies slowly. The segmentation models assuming that the image intensity is homogeneous may obtain the inaccurate results when the images are intensity inhomogeneity. Besides that, there is usually partial volume effects in the medical MR images. The partial volume effects leads to the low-contrast and uncontinuous boundaries in brain and vessel MR images, which are difficult to extract. The components of the medical images including the textures, the noise, the irregular intensity inhomogeneity, and the complex topology structures of the edges brings about difficulties for image segmentation.
In this paper, we focus on the research of image segmentation for medical MR images to solve the problems given above. The primary work and the remarks are as follows
(1) For the images with multiple objects, intensity inhomogeneity, and noise, a multiphase Chan-Vese model based on an improved fuzzy c-means algorithm is proposed. First, the classes of the intensity are calculated based on the histogram statistics, and the spatial information computed in the neighborhood revise the grade of membership. The improved FCM algorithm applied with the region fitting term of CV model, working as the reliance of evolving the level-set curve. Anisotropic local template is then used to handle the different objects so as to control the split-up of the contour accurately and segment more objects in less time.
(2) For the components of the cartoon part and the texture in images, a segmentation model is proposed for both the two kinds of the components. Two kinds of region data terms are designed for detecting cartoon and texture parts respectively. The local statistic information is extracted in the adaptive patch to solve the over-segmentation induced by the intensity inhomogeneities. And the texture feature information calculated in the adaptive patch is utilized to compute the Kullback-Leibler distance for detecting the texture part. The proposed model is solved by the split Bregman method for efficiency. Experiments are carried on both medical and texture images to compare our approach with some competitors, demonstrating the precision and efficiency of the proposed model.
(3) A novel active contour model with image structure information and multiple statistical information for image segmentation. The intensity inhomogeneity varies spatially. To solve this problem, this model utilizes an improved region fitting term to partition the regions of interests in images depending on the local statistics regarding the intensity and the magnitude of gradient in the neighborhood of a contour. In particular, integrated with the duality theory and the anisotropic diffusion process based on structure tensor, a new regularization term is defined through the duality formulation to penalize the length of active contour. By this new regularization term, the structure information of images is utilized to improve the ability of capturing the geometric features such as corners and cusps. From a numerical point of view, we minimize the energy function of the proposed model by an efficient dual algorithm, which avoids the instability and the non-differentiability of traditional numerical solutions, e.g. the gradient descent method. Experiments on medical and nature images demonstrate the advantages of the proposed model over other segmentation models in terms of both efficiency and accuracy.
(4) For the images with noise, intensity inhomogeneity and the concave structures, a robust patch-statistical active contour model is proposed. The intensity inhomogeneity and noise are both considered as the irregular intensity variation. The patch-statistical region fitting term computes the local statistical information by Nadaraya-Watson operator in each patch as the basis for driving the curve accurately with resist to the intensity inhomogeneity and the weak boundaries. And the regularization term coupling with the gradient information improves the ability of capturing the boundaries with cusps and narrow topology structures. Furthermore, an intensity variation penalization term is proposed to overcome the negative effectiveness of the irregular intensity variation. Experiments on medical and nature images show that the proposed model is more robust than the popular active contour models for images with noise and intensity inhomogeneity.
(5) It is a challenge to extract the vessels and the ends of the tissues in the MR images because of the partial volume effects, noise and the intensity inhomogeneity. Consequently, the active contour models based on the structure information of images are proposed. Coupling with the duality theory and a structural gradient vector flow (SGVF) method, we formulate a new regularization term of the level set function via a duality formulation to penalize the length of active contour. By this new regularization term, the structural information of images is utilized to improve the ability of preserving the elongated structures in the MR images. The experiments on brain and vessel MR images demonstrates that this model incorprates the advantages of both edge-based and region-based active contour models and preserves the enlongated structures in MR images.
针对医学图像分割的需求及难点,本文利用活动轮廓模型对医学图像进行分割进行了深入研究。本文的主要工作和研究成果如下：
(1)针对同时含噪声、灰度不均匀性及多个待分割目标的图像,提出一种基于改进的模糊聚类(fuzzy c-means clustering, FCM)算法的Chan-Vese(CV)模型。本文基于直方图统计灰度种类、并利用邻域内计算的空间信息修正隶属度函数以此克服灰度不均匀性和噪声的影响,将改进后的FCM算法应用到CV模型的区域检测项,可准确的对像素点归类,成为曲线的演化依据。在演化时采用一种各向异性的模板来控制轮廓线的及时分裂,在较短时间内分割出更多目标。
(2)针对图像中光滑和纹理这两种不同组成成份,提出一种能同时考虑光滑部分和纹理部分的分割模型。首先在局部块中分别检测图像卡通部分的灰度统计特征以及纹理部分的特征信息用以计算区别不同纹理之间的Kullback-Leibler (KL)距离,并且该局部块能够根据图像的梯度信息自动调整其大小。进一步采用Split Bregman方法对模型进行快速求解,在医学和纹理图像的实验上验证了该本文模型能够明显的提高准确性和时效性。
(3)提出一种结合了图像结构信息、并基于灰度和梯度模两种统计特征新型活动轮廓模型。灰度不均匀性理论上是空间不规则变化的,且分布并不单一,提取水平集曲线邻域内灰度和梯度模的统计特征检测不同区域的灰度差异和灰度不均匀性。特别的,针对传统活动轮廓模型中全变差形式的正则项保持边缘不足,将结构张量通过水平集函数的对偶变量嵌入关于水平集函数的正则项,使得水平集曲线高效率的逼近图像的目标边界而避免产生过度平滑,进而利用改进的Chambolle对偶算法对整个模型进行快速求解。与其他同类的经典方法相比本文算法不论对初始条件的鲁棒性、分割时效和精度均有明显提高。
(4)针对图像中深凸的拓扑结构以及灰度不均匀性和噪声的同时存在的情况,提出一种鲁棒型基于非局部分片局部块统计方法的活动轮廓模型。由于灰度不均匀性随空间变化且分布并不规则,因此可以将灰度不均匀性和噪声一样看做一种灰度不规则变化的情况。利用一种分片局部块统计信息的区域项计算像素点的归属度,作为驱动曲线演化的力之一。灰度不规则变化影响水平集曲线演化到目标边界的效率,因此通过加上一个灰度惩罚项来控制当遇到灰度不规则变化时的水平集曲线的演化。同时利用图像梯度信息作为权值用于计算关于水平集函数的正则项,进一步增强水平集曲线的形状与目标边界拟合。应用于医学图像和自然图像上的实验证明该算法能够明显抑制强噪声和灰度不均匀性的影响,取得高效率和高准确性的分割结果。
(5)局部容积效应、噪声、灰度不均匀性的共同作用增加了MR图像中血管、组织末梢等具有细长拓扑结构的分割难度。针对这些问题,从两个方面将图像的结构信息与活动轮廓模型相结合。一方面,利用基于图像的结构信息改进的梯度流方程训练关于水平集函数的对偶变量以增强扑捉深凹型的目标结构；另一方面,根据图像边界的结构变化自适应的计算全局和局部的灰度统计信息,不仅克服了灰度不均匀性,同时进一步提高了曲线演化的效率。局部统计信息可以正确指导曲线克服灰度不均匀性,尤其是在临近边界处的灰度不均匀性,从而捕捉到正确的目标边界。而在远离边界处根据全局灰度统计信息演化,能够加快曲线演化到图像的目标边界。根据基于边界和基于区域的活动轮廓模型的特点,利用基于结构信息改进的梯度流方程(Gradient Vector Flow, GVF)计算用于表示活动轮廓曲线的水平集函数的对偶变量,通过对偶变量的内迭代使水平集曲线在演化中进一步与图像中狭长的边界结构保持一致。
Image segmantation is a process that partition the image into different non-overlapping regions, which are called region of interest (ROI). The magnetic resonance image (MRI) technique has played more and more important role in the medical diagnosis and treatment. Segmentation for MRI is the basis for organ diagnosis, tissue quantization, pathalogy factor analysis, and disease developement tracking, etc. However, as the result of the instability of radio frequency and the existence of the imprurity, the intensity inhomogeneity and noise is induced during the process of imaging. The intensity inhomogeneity is the phenomenon that the intensity in the same ROI varies spatially. And for the intensity inhomogeneity in MRI, the intensity varies slowly. The segmentation models assuming that the image intensity is homogeneous may obtain the inaccurate results when the images are intensity inhomogeneity. Besides that, there is usually partial volume effects in the medical MR images. The partial volume effects leads to the low-contrast and uncontinuous boundaries in brain and vessel MR images, which are difficult to extract. The components of the medical images including the textures, the noise, the irregular intensity inhomogeneity, and the complex topology structures of the edges brings about difficulties for image segmentation.
In this paper, we focus on the research of image segmentation for medical MR images to solve the problems given above. The primary work and the remarks are as follows
(1) For the images with multiple objects, intensity inhomogeneity, and noise, a multiphase Chan-Vese model based on an improved fuzzy c-means algorithm is proposed. First, the classes of the intensity are calculated based on the histogram statistics, and the spatial information computed in the neighborhood revise the grade of membership. The improved FCM algorithm applied with the region fitting term of CV model, working as the reliance of evolving the level-set curve. Anisotropic local template is then used to handle the different objects so as to control the split-up of the contour accurately and segment more objects in less time.
(2) For the components of the cartoon part and the texture in images, a segmentation model is proposed for both the two kinds of the components. Two kinds of region data terms are designed for detecting cartoon and texture parts respectively. The local statistic information is extracted in the adaptive patch to solve the over-segmentation induced by the intensity inhomogeneities. And the texture feature information calculated in the adaptive patch is utilized to compute the Kullback-Leibler distance for detecting the texture part. The proposed model is solved by the split Bregman method for efficiency. Experiments are carried on both medical and texture images to compare our approach with some competitors, demonstrating the precision and efficiency of the proposed model.
(3) A novel active contour model with image structure information and multiple statistical information for image segmentation. The intensity inhomogeneity varies spatially. To solve this problem, this model utilizes an improved region fitting term to partition the regions of interests in images depending on the local statistics regarding the intensity and the magnitude of gradient in the neighborhood of a contour. In particular, integrated with the duality theory and the anisotropic diffusion process based on structure tensor, a new regularization term is defined through the duality formulation to penalize the length of active contour. By this new regularization term, the structure information of images is utilized to improve the ability of capturing the geometric features such as corners and cusps. From a numerical point of view, we minimize the energy function of the proposed model by an efficient dual algorithm, which avoids the instability and the non-differentiability of traditional numerical solutions, e.g. the gradient descent method. Experiments on medical and nature images demonstrate the advantages of the proposed model over other segmentation models in terms of both efficiency and accuracy.
(4) For the images with noise, intensity inhomogeneity and the concave structures, a robust patch-statistical active contour model is proposed. The intensity inhomogeneity and noise are both considered as the irregular intensity variation. The patch-statistical region fitting term computes the local statistical information by Nadaraya-Watson operator in each patch as the basis for driving the curve accurately with resist to the intensity inhomogeneity and the weak boundaries. And the regularization term coupling with the gradient information improves the ability of capturing the boundaries with cusps and narrow topology structures. Furthermore, an intensity variation penalization term is proposed to overcome the negative effectiveness of the irregular intensity variation. Experiments on medical and nature images show that the proposed model is more robust than the popular active contour models for images with noise and intensity inhomogeneity.
(5) It is a challenge to extract the vessels and the ends of the tissues in the MR images because of the partial volume effects, noise and the intensity inhomogeneity. Consequently, the active contour models based on the structure information of images are proposed. Coupling with the duality theory and a structural gradient vector flow (SGVF) method, we formulate a new regularization term of the level set function via a duality formulation to penalize the length of active contour. By this new regularization term, the structural information of images is utilized to improve the ability of preserving the elongated structures in the MR images. The experiments on brain and vessel MR images demonstrates that this model incorprates the advantages of both edge-based and region-based active contour models and preserves the enlongated structures in MR images.
引文
[1]田捷,包尚联,周明全,医学影像处理与分析,电子工业出版社。2003.9
[2]Lee A. B, Pedersen K. S, Mumford D. The Nonlinear Statistics of High-Contrast Patches in Natural Images, Int'1 J.Comp. Vis.,2003,54(8):83-103.
[3]Yang A.Y, Wright, Ma J Y, Sastry S. Unsupervised segmentation of natural images via lossy data compression. Computer Vision and Image Understanding,2007,110: 212-225.
[4]Sudderth E. B, Jordan M. I. Shared Segmentation of Natural Scenes Using Dependent Pitman-Yor Processes. Advances in Neural Information Processing Systems,2009, 21:98-107.
[5]Ashburner J, Friston K. J. Voxel-based morphometry-the methods. IEEE Trans Med Imag, June 2000,11(6):805-821.
[6]Levin A, Weiss Y. Learning to combine Bottom-up and Top-down Segmentation, Int'1 J.Comp. Vis.,2009,81(1):105-118.
[7]Osher S, Sethian J. A. Fronts propagating with curvature dependent speed:algorithms based on the Hamilton-Jacobi formulation. Journal of Computational Physics, 1988,79(1):12-49.
[8]Kass M, Witkin A., Terzopoulos D. Snake:active contour models. Int'1 J.Comp. Vis. 1988,1(4):321-331.
[9]Terzopoulos D, Fleischer K. Deformable models. The Visual Computer,1988, 4(6):306-331.
[10]Terzopoulos D, Witkin A, Kass M. Constraints on deformable models:recovering 3D shape and nonrigid motion. Artificial Intelligence,1988,36(1):91-123.
[11]Wong A. K. C, Sahoo P. K. A gray-level threshold selection method based on maximum entropy principle. IEEE Transactions on Systems, Man and Cybernetics. 1989,19(4):866-871.
[12]Otsy N. A threshold selection method from gray-level histograms. Automatcia,1975, 11:285-296.
[13]Kapur JN., Sahoo P.K., Wong AKC. A new method for gray-level picture thresholding using the entropy of histogram.Computer Vision graphics, and image processing,1985, 29(3):273-285.
[14]Tsai W H, Moment-preserving thresholding:a new approach[J]. Computer Vision, Graphics, and Image Processing,1985,29(3):377-393.
[15]Rafeal C Gonzalez, Richard E Woods. Digital Image Processing(Second Edition). Beijing:Publishing House of Electronics Industry,2003.612-616.
[16]戴剑彬,张大力,图像分析中的松弛标记法.中国图象图形学报,1998,3(2)：97-99.
[17]Yu Q, Clausi A. IRGS:Image Segmentation using edge penalties and region growing. IEEE transaction on pattern analysis and Machine Intelligence,2008,30(12): 2126-2139.
[18]Forgy E, Cluster analysis of multivariate data:efficiency vs. interpretablity of classifications. Biometrics,1965,21(3):768-780.
[19]Bezdek J, Ehrilich C. R, FCM:The fuzzy c-means clustering algorithm. Computers & Geosciences,1984,10(2-3):191-203.
[20]李明,李云松.改进的快速模糊C均值聚类的图像分割方法.兰州理工大学学报,2007,33(3)：95-99.
[21]Brand M, Huang K. A unifying threorem for spectral embedding and clustering.9th International Coference on Artificial Intelligence and Statistics, Key West, Florida, 2002.
[22]Zhuang X, Huang Y, Palaniappan K, Zhao Y. Gausian mixture density modeling, decomposition, and applications IEEE Trans. Image Process,1996,5(9):1293-1302.
[23]于林森,张田文.用于图像分割的滤波EM算法.计算机学报,2006,29(6)：928-935.
[24]李明,李云松.改进的快速模糊C均值聚类的图像分割方法[J].兰州理工大学学报,2007,33(3)：95-99.
[25]叶吉祥,陈香华,谭冠政.利用小波和分层聚类进行彩色图像分割.计算机与数字工程,2006,34(1)：1-4.
[26]Oliver N, Pentland A.P, Berard F. LAFTER: Lips and face real time tracker. Computer Vision and Pattern Recongnition, IEEE Computer Society, Los Alamitos, CA. 1997,123-129.
[27]Harvey R, Matthews I, Bangham J. A, Cox S. Lip reading from scale-space measure-ments. Computer Vision and Pattern Recognition, IEEE Computer Society, Los Alamtios, CA.1997,582-587.
[28]Brand M, Oliver N. Pentland A. P. Coupled hidden Markov models for complex action recognition. Computer Vision and Pattern Recognition, IEEE Computer Society, Los Alamitos, CA.1997,994-999.
[29]Gross G, Jain A, Markov random field texture models. IEEE Transactions on Pattern Analysis and Machine Intelligence,1983,5(1):25-39.
[30]Elfadel I. M, Picard R. W. Gibbs random fields, cooccurrences, and texture modeding, IEEE Transactions on Pattern Analysis and Machine Intelligence,16(1):24-37,1994.
[31]申小阳,姜伯军.多个数字仪表字符串区域的定位和识别研究.苏州科技学院学报(自然科学版),2005,22(4)：42-49.
[32]Pemmaraju S, Mitra S, Shieh Y, Roberson G.H. Multiresolution Wavelet Decomposition and Fuzzy Clustering for Segmentation of Radiographic Images. CBMS,1995.142-149.
[33]Li H, Qian W, Clarkel P. Wavelet Transform for Directional Feature Extraction in Medical Imaging. Proceedings of IEEE International Conference on Image Processing,1997,3(3):500-5.
[34]陈武凡.小波分析及其在图像处理中的应用.北京：科学出版社,2002.
[35]宋军,邵谦明,周耀华.小波变换尺度过零点表征及在医学超声图像分割中的应用.复旦学报(自然科学版),2001,40(1)：40-43
[36]Xu C, Prince J., Snakes, shapes, and gradient vector flow, IEEE Transactions on Image Processing,1998,7(3):359-369.
[37]Xu C, Prince J, Generalized gradient vector flow external forces for active contours, Signal Processing,1998,71 (2):131-139.
[38]Caselles V, Kimmel R, Sapiro G. Geodesic active contours. Int. J. Comp. Vis., 1997,22(1):61-79.
[39]Chan T, Vese L, Active contours without edges. IEEE Transactions on Image Processing.2001,10(2):266-277.
[40]Vese L, Chan T. A multiphase level set framework for image segmentation using the mumford and shah model. Int. J. Comp. Vis.,2002,50:271-293.
[41]Chan T, Vese L. An efficient variational multiphase motion for the Mumford-Shah model. In:Proceedings of the 34'th Asilomar Conference on Signals, Systems and Computers,2000,1:490-494.
[42]Tsai A., Yezzi A., Willsky A., Curve evolution implementation of the Mumford-Shah functional for image segmentation, denoising, interpolation, and magnification, IEEE Transaction on Image Processing,2001,10(8):1169-1186.
[43]Li C, Kao C, Gore J, Ding Z. Implicit Active Contours Driven by Local Binary Fitting Energy, In IEEE Conference on Computer Vision and Pattern Recognotion(CVPR), 2007,1-7.
[44]Li C, Kao C, Gore J, Ding Z. Minimization of region-scalable fitting energy for image segmentation, IEEE Transactions on Image Processing,2008,17(10),1940-1949.
[45]Li C, Xu C, Gui C, Fox M. D. Level set evolution without re-initialization:A new variational. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2005,1:430-436.
[46]Li C, Xu C, Gui C, Fox M. D. Distance Regularized Level Set Evolution and its Application to Image Segmentation, IEEE Trans. Image Processing,2010,19 (12), 3243-3254.
[47]Malladi R, Sethian J.A. Shape modeling with front propagating:a level set approach. IEEE Transaction on Pattern Analysis and Machine Intelligence,1995,17(2):158-175.
[48]Xu G, Segawa E, Tsuji S. Robust active contours with incentive parmenters. Pattern Recoginetion.1994,27(7):879-884.
[49]Jundong L, David C., Charles S, Hima C., Automatic Subcortical Structure Segmentation using Local Likelihood-based Active Contour,3D Segmentation in The Clinic:A Grand Challenge,2007,91-98.
[50]Goldstein T., Bresson X. Geometric Application of the Split Bregman Method: Segmentation and Surface Reconstruction. Technical Report09-06, UCLA, Computational and Applied Mathematic,2009.
[51]Bresson X, Esedoglu S. Fast Global Minimization of the Active Contour/Snake Model. J Math Imaging Vis.2007,28(2):151-167.
[52]Bresson X, Chan T. Non-Local Unsupervised Variational Image Segmentation Models. Technical Report 08-67, UCLA, Computational and Applied Mathematic, 2008.
[53]Cohen L D. On Active Contour Models and Balloons. CVGIP:Image Understanding, 1991,53(2):211-218.
[54]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)：1722-1736.
[55]Mumford D, Shah J. Boundary detection by minimizing functionals,Image Understanding,1988,19-43.
[56]Mumford D, Shah J, Optimal approximations by piece wise smooth functions and associated variational problems.Communications on Pure and Applied Mathematics, 1989,42(5):577-685.
[57]Ambrosio L, Tortorelli V. On the approximation of functionals depending on jumps by elliptic functionals via γ-convergence. Communication on Pure and Applied Mathematics,1990,43(8):999-1036.
[58]Ambrosio L., Tortorelli V. On the approximation of free discontinuity problems. Boll. Un. Mat. Ital.,19927(6-B):105-123.
[59]Chan T., Esedoglu S., Nikolova M., Algorithms for finding global minimizers of image segmentation and denoising models, SIAM Journal on Applied Mathematics, 2006,66:1632-1648.
[60]Piovana J, Rousson M, Papadopoulo T. Efficient Segmentation of Piecewise Smooth Images. SSVM,2007:709-720.
[61]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.
[62]Lankton S, Melonakos J, Malcolm J, Dambreville S, Tannenbaum A. Localized statistics for DW-MRI fiber bundle segmentation. Computer Vision and Pattern Recognition Workshops,2008:1-8.
[63]Goldstein T, Osher S. The Split Bregman Algorithm for L1 Regularized Problems, Technical Report 08-29, UCLA, Computatial and Applied Mathematic,2008.
[64]Giusti E, Mimimal surfaces and functions of bounded variation, Australian National University, Canberra,1977.
[65]Chambolle A, An algorithm for total variation minimization and applications. J. Math.Imaging Vis.2004,20(1-2):89-97.
[66]Boykov Y, Jolly M. P. Interactive graph cuts for optimal boundary and region segmentation of objects in N-D images, Proc. International Conference on Computer Vision,2001,105-112.
[67]Boykov Y, Kolmogorov V, An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision, EEE Trans Patt Anal Mach Intell,2004, 26:1124-1137.
[68]Boykov Y, Funka-Lea G, Graph cuts and efficient N-D image segmentation, International Journal of Computer Vision,2006,70:109-131.
[69]Kolmogorov V, Zabih R. What Energy Functions Can Be Minimized via Graph Cuts? IEEE Trans Patt Anal Mach Intell,2004,26(2):147-159.
[70]Shi J, Malik J. Normalized cuts and image segmentation. IEEE Trans Patt Anal Mach Intell,2000,22(8):888-905.
[71]Egil B, Xue C. T, Efficient Global Optimization For The Multiphase Chan-Vese Model Of Image Segmentation by Graph Cuts. Technical Report 09-53, UCLA, Computational and Applied Mathematic,2009.
[72]Xue C T, Duan P Y. Domain Decomposition Methods With Graph cuts Algorithms For Image Segmentions. Technical Report,09-54, UCLA, Computational and Applied Mathematic,2009.
[73]Wenbing T, Xue C T. Multiple Piecewise Constant Active Contours for Image Segmentation using Graph Cuts Optimization. Technical Report,09-13, UCLA, Computinal and Applied Mathematic,2009.
[74]Kichenesamy S, Kumar A, Olver P, Tannenbaum A, A. Yezzi Conformal curvature flows:from phase transitions to active vision, in Archive for Rational Mechanics and Analysis.1996,134:275-301.
[75]Adalsteinsson D, Sethian J A. A Fast Level Set Method for Propagation Interfaces. Journal of Computational Physics,1995,118(2):269-277
[76]Adalsteinsson D, Sethian J A. The fast construction of extension velocities in level set methods. J. Comput. Phys.1999,148(1):2-22.
[77]Sethian J. A, An analysis of flame propagation, Ph.D Thesis, Dept. of Mathematics, University of California, Berkeley, CA,1982.
[78]Sethian J A. A Review of the Theory, Algorithms, and Applications of Level Set Methods for Propagating Interfaces. Acta Numerica, Cambridge University Press, 1996.
[79]Chopp D L. Computing Minimal Surfaces Via Level Set Curvature Flow. J.Comp. Phys,1993,106:77-91.
[80]Paragios, N. and R. Deriche, Geodesic active regions and level set methods for supervised texture segmentation. International Journal of Computer Vision, 2002,46(3):223-247.
[81]Soatto S, Yezzi A. J:Deformation:Deforming motion, shape average and the joint registration and segmentation of images. In:European Conference on Computer Vision, Graz,2002,32-57.
[82]Kim, J, C-etin, M., Willsky, A.S. Nonparametric shape priors for active contour-based image segmentation,Signal Processing,2007,87(12):3021-3044
[83]Chan T, Zhu. W, Level set based shape prior segmentation, Computer Vision and Pattern Recognition,2005. CVPR 2005. IEEE Computer Society Conference on,2005, 2:1164-1170
[84]Cremers, D, Osher, S.J, Soatto S. Kernel density estimation and intrinsic alignment for shape priors in level set segmentation, International Journal of Computer Vision,2006, 69(3):335-351
[85]Li H, Tai X. C. Piecewise constant level set methods for multiphase motion, International Journal of Numerical Analysis and Modeling,4(2):291-305
[86]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 information. Proc. SPIE Med. Imag. Physiol, Function, Strucuture Med. Images,2004, 5370:734-742.
[87]Siyal MY, Yu L. An intelligient modified fuzzy c-means based algorithm for bias estimation and segmentation of brain MRI. Pattern Recognition Letters, October 2005, 26:2052-2062
[88]Zhenping Xie Shitong Wang. A New Level Set Method for Image Segmentation Integrated with FCM, in Proceedings of the Fourth International Conference on Fuzzy Systems and Knowledge Discovery, Haikou, China,2007,4:699-703
[89]Lankton S, Tannenbaum A, localizing region-based active contours, IEEE Transactions on Image Processing,2008,17:2029-2039
[90]吴林,郭大勇等.改进的FCM在人脑MR图像分割中的应用.清华大学学报(自然科学版),2004,44(2)：157-159
[91]龚永义,罗笑南,廖国钧,张余,基于单水平集的多目标轮廓提取.计算机学报,2007,30(1)：95-99.
[92]Cohen F. S, Fan Z, Patel M. A. Classification of rotated and scaled textured images using Gaussian Markov Random Field models, IEEE Transactions on Pattern Analysis and Machine Intelligence,1991,13(2):192-202
[93]Zhu S, Wu Y, Mumford D. Filters, random field and maximum entropy:towards a unified theory for texture modeling. International Journal of Computer Vision,1998. 27(2):1-20
[94]Derin H, Elliott H. Model and segmentation of noisy and textured images using Gibbs random fields, IEEE Transaction on Pattern Analysis and Machine Intelligence,1987, 9:39-55
[95]Duda R.O, Hart P. E., Stock D. G, Pattern Classification (2nd Edit), John Wiley, New York,2001
[96]Dunn D, Higgins W.E. Optimal Gabor filters for texture segmentation. IEEE transactions on image processing,1995,4(7):947-964
[97]Unser M, Local linear transforms for texture, measurements. Signal Processing,1986, 11(1):61-79
[98]Arivazhagan S., Ganesan L, Texture segmentation using wavelet transform. Pattern Recognition Letters,2003,24(16):3197-3203
[99]Laine A., Fan J. Texture classification by wavelet packet signatures. IEEE Transactions on Pattern Analysis and Machine Intelligence,1993,15(11):1186-1191
[100]HouHou N, Philippe J. Fast Texture Segmentation Based on Semi-Local Region Descriptor and Active Contour. Numerical Mathematics:Theory, Methods and Applications.2009,2(4):445-468
[101]HouHou N, Thiran J.P, Bresson X. Fast Texture Segmentation Model based on the Shape Operator and Active Contour. In IEEE Conference on Computer Vision and Pattern Recognition, Anchorage, U. S., IEEE,2008:1-8
[102]Ni K, Bresson X, Chan T, Esedoglu S. Local histogram based segmentation using the Wasserstein distance, International journal of computer vision.2009,84(1):97-111
[103]Sochen N, Kimmel R, Malladi R. A General Framework For Low Level Vision. IEEE. Transactions on Image Processing,1998,7(3):310-318
[104]Kreyszing E., Differential Geometry. New York:Dover,1991
[105]张建伟,夏德深,基于双水平集的图像分割模型.计算机研究与发展,2006,43(1)：120-125.
[106]Rother C, Kolmogorov V, Blake A. Grabcut-Interactive Foreground Extraction using Iterative Graph Cuts, in ACM Transactions on Graphics (TOG). ACM,2004,23: 309-314.
[107]Zhang K, Song H, Zhang L. Active contours driven by local image fitting energy. Pattern Recognition,2010,43 (4):1199-1206.
[108]Tian Y, Zhou M, Wu Z, Wang X. A region-based Active Contour model for Image Segmentation, in IEEE,International Conference on Computational Intelligence and Security.2009,376-380.
[109]Markus G, Frank L, Anisotropic Total Variation Filtering. Appl. Math. Optim 62 2010,62(3):323-339.
[110]Buades A, Coll B. A Review of image denoising algorithms, with a new one. SIAM Multiscale Modeling and Simulation (MMS),2005,4(2):490-530
[111]Rudin L, Osher S, Fatemi E. Nonlinear total variation based noise removal algorithms, Physica D,1992,60(1-1):259-268
[112]Weickert J. Coherence-enhancing diffusion filtering. International Journal of Computer Vision,1999,31(2-3):111-127.
[113]Weikert J. Anisotropic diffusion in image processing, ECMI series, Teubner-Verlog, Stuttgart, Germany,1998.
[114]Weickert J. Scale-space properties of nonlinear diffusion filtering with a diffusion tensor. Technical Report, Laboratory of Technomathematics, University of Kaiserslautern, Germany,1994.
[115]Aujol J. F, Gilboa G, Chan T, Osher S. Structure-Texture Image Decomposition Modeling, algorithms, and Parameter Selection. Int'1 J.Comp. Vis.,2006,67(1): 111-136,
[116]Chan T, Esedo(?)lu S. Aspects of total variation regularized L1 function approximation. SIAM Journal on Applied Mathematics,2005,1817--1837
[117]Wang X. F., Huang D. S., Xu, H., An efficient local Chan-Vese model for image segmentation, Pattern Recognition,2010,43(3):603-618.
[118]Perona P, Malik J. Scale space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell,1990,12(7):629-639.
[119]Catte F, Lions P L. Morel J M, Coll T. Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. Numer. Anal.,1992,29:182-193
[120]Giusti E. Mimimal surfaces and functions of bounded variation, Australian National University, Canberra,1977.
[121]Meyer Y. Oscillating patterns in image processing and nonlinear evolution equation. Am. Math. Soc,2001.
[122]Rogowska J. Overview, fundamentals of medical image segmentation. Handbook of Medical Imageing Processing and Analysis, Academic Press,2000,69-86.
[123]Ginneken B, Alejandro F Frangi, Joes J. Active shape model segmentation with optimal features. IEEE Transactions on Medical Imaging,2002,21(8):924-933
[124]Pham L, Chengyang Xu, Prince L. A survey of current methods in medical image segmentation. Annual Review of Biomedical Engineering,2000,2:315-317
[125]Ourselin S. Overview on computer-assisted medical image segmentation, World Congress on Medical Physics and Biomedical Engineering, Sydney, Australia, August 24-292003, Invited speaker
[126]Gonzalez R. C, Woods R. E. Digital Image Processing,2nd Edition. New Jersey: Prentice Hall,2002.
[127]Siyal M. Y, Yu L. An intelligient modified fuzzy c-means based algorithm for bias estimation and segmentation of brain MRI. Pattern Recognition Letters, October 2005, 26:2052-2062
[128]Giger L. A fuzzy c-means (FCM) based algorithm for intensity inhomogeneity correction and segmentation of MR images. in IEEE International Symposium on Biomedical Imaging:From Nano to Macro,2004:1307-1310
[129]Ahmed M, Yamany S, Mohamed N, Frag 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
[130]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 information. Proc. SPIE Med. Imag.2004:Physiol., Function, Strucuture Med. Images, 2004,5370:734-742.
[131]Wells W, Grimson E, Kikinis R, Jolesz F. Adaptive segmentation of MRI data. IEEE Trans Med Image,1996,15(4):429-442.
[132]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.
[133]Pham D, Prince J. Adaptive fuzzy segmentation of magnetic resonance images. IEEE. Trans Medi Imag, September 1999,18(9):737-752
[134]Li C, Xu C, Anderson A. W, Gore J. C. MRI Tissue Classification and Bias Field Estimation Based on Coherent Local Intensity Clustering:A Unified Energy Minimization Framework. Information Processing in Medical Imaging (IPMI),2009, 5636:288-299.
[135]Li, C, Huang R, Ding Z, Gatenby C, Metaxas D, Gore J,. A Varaitional Level set approach to segmentation and bias correction of medical images with intensity inhomogeneity, MICCAI.2008,1083-1091.
[136]Li C. Active contours with local binary fitting energy. IMA workshop on New Mathematics and Algorithms for 3-D Image Analysis, January 2006.
[137]Vovk U, Pernus F, Likar B. A review of methods for correction of intensity inhomogeneity in MRI. IEEE Trans Med Imag, March 2007,26(3):405-421.
[138]Hou Z. A Review on MR Image Intensity Inhomogeneity Correction. International Journal of Biomedical Imaging, August 2006
[139]Shattuck D. W, Sandor-Leahy S. R, Schaper K. A, Rottenberg D. A, Leahy R. M. Magnetic resonance image tissur classification using a partial volumn model. Neuroimage, May 2001,13:856-876.
[140]Salvado O, Hillenbrand C, Wilson D. L. Correction of intensity inhomogeneity in MR images of vascular disease. EMBS'05,2005:4302-4305.
[141]Ben S.M., Ben A. I., Mitiche A. Active curve recovery of region boundary patterns, 2012,34(5):834-850,
[142]Brox, T., Cremers, D.,2010. On the statistical interpretation of the piecewise smooth Mumford-Shah functional, Scale Space and Variational methods in Computer Vision, 203-213.
[143]Nadaraya, E. A.1964. On estimating regression, Theory Probabil. Appl.,141-142.
[144]Shattuck, D.W., Sandor-Leahy, S.R., Schaper, K.A., Rottenberg, D.A., Leahy, R.M. Magnetic resonance image tissue classification using a partial volume model. NeuroImage,2001,13(5),856-876.
[145]Ourselin S. Overview on computer-assisted medical image segmentation, World Congress on Medical Physics and Biomedical Engineering, Sydney, Australia, Augest 24-29.
[146]Bezdek J C, Hall L O, Clarke L P. Review of MR image segmentation techniques using pattern recognition. Med. Phys.1993,20:1033-1048
[147]Wang Y, Audli T, Kung. Quantification and segmentation of brain tissues from MR images. IEEE Transactions on Image Processing,1998,7(8):1165-1181
[148]Wang Y, Audli T, Xuan. Magnetic resonance image analysis by information theoretic criteria and stochastic site models. IEEE Transactions on Imag Processing,2001, 5(2):150-158
[149]Kiknis R, Shenton M, Jolesz F. A, et al. Quantitative analysis of brain and cerebrospinal fliud spaces with MR imaging, J. Magn. Res. Imag.,1992:619-629.
[150]Miki'c I, Krucinski S, Thomas J. D. Segmentation and tracking in echocardiographic sequences:Active contours guided by optical flow estimates. IEEE Transcations on Medical Imaging,1998,17(2):274-283
[151]Yongye Zhang, Brady M, Smith S. Segmentation of brain MR images through a hidden markov random field model and the expectation-maximization algorithm. IEEE Transactions on Image Processing,2000,20(1):45-57
[152]Melnerney T, Terzopoulos D. Deformable models in medical image analysis. Proceedings of the workshop on methematical methods in biomedical image analysis, San Francisco, CAUSA,21-22 June 1996,171-180
[153]Knickmeyer R, Gousttard S, Kang C, Evans D, Wilber K, Smith J, Hamer R, Lin W, Gerig G, Gilmore J. A structural MRI study of human brain developement from birth to 2 years. J Neurosci,2008,28(47):121176-12182
[154]Isaacs E, Edmonds C, Chong W, Lucas A, Morley R, Gadian D. Brain morphometry and IQ measurements in preterm children, Brain,2004,127(12):2595-2607
[155]Goldenberg R, Kimmel R, Rivlin E, Rudzsky M. Cotex segmentation: fast variational geometric approach. IEEE Trans Med Imag,2002,21(2):1544-1551.
[156]Dale A, Fischl B, Sereno M. Cortical Surface-Based Analysis: Ⅰ. Segmentation and Surface Reconstruction. NeuroImage,1999,9(2):179-194.
[157]B. P. F. Lelieveldt, et al. Multi-views active appearance models for consistent segmentation of multiple standard views:application to long- and short-axis cardiac MR images. in Proceedings of the 17th International Congress and Exhibition.2003. London, United Kingdom.
[158]Bazin P. L, Pham D. L. Topology-preserving tissue classification of magenetic resonance brain images. IEEE Trans Med Imag,2007,26(4):487-496
[159]Sethian J. A. Algorithms for tracking interfaces in CFD and material science. Annu. Rev. Comput. Fluid Mechanics,1995.
[160]Wollschleger H, Tenspiel RW et al. Reliable automatic frame-by-frame contour detection of digitized LV cine-angiograms. IEEE Computers in Cardiology, 1998:353-356
[161]Nishida M, Makris N, Kennedy D. N, Vangel M, Fischl B, Krishnamoorthy K. S, Caviness V. S, Grant P. E. Detailed semiautomated MRI based morphometry of the neonatal brain:preliminary results. Nero Image,2006,32(3):1041-1049
[162]Miki'c I, Krucinski S, Thomas J. D. Segmentation and tracking in echocardiographic sequences:Active contours guided by optical flow estimates. IEEE Transcations on Medical Imaging,1998,17(2):274-283
[163]Yongye Zhang, Brady M, Smith S. Segmentation of brain MR images through a hidden markov random field model and the expectation-maximization algorithm. IEEE Transactions on Image Processing,2000,20(1):45-57
[164]Melnerney T, Terzopoulos D. Deformable models in medical image analysis. Proceedings of the workshop on methematical methods in biomedical image analysis, San Francisco, CA USA,21-22 June 1996,171-180
[165]Knickmeyer R, Gousttard S, Kang C, Evans D, Wilber K, Smith J, Hamer R, Lin W, Gerig G, Gilmore J. A structural MRI study of human brain developement from birth to 2 years. J Neurosci,2008,28(47):121176-12182
[166]Song Z, Awate S. P, Licht D, J, Gee J. C. Clinical Neonatal Brain MRI Segmentation Using Adaptive Nonparametric Data Models and Intensity-Based Makov Priors. Proceedings of Medical Image Computing and Computer Aided Intervention, 2007:883-890
[167]Aljabar P, Heckemann R, Hammers A, Hajnal J, Rueckert D. Multi-atlas based segmentation of brain images:Atlas selection and its effect on accuracy. NeroImage, 2009,46(3):726-738
[168]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.
[169]Zeng X, Staib L, Schultz R, Duncan J. Segmentation and Measurement of the Cotex from 3D MR Images Using Coupled Surfaces Propagation. IEEE Trans Med Imag, 1999,18(10):100-111.
[170]Guillemaud R, Brady M. Esitmating bias field of MR images. IEEE Trans Med Imag, June 1997,16(3):238-251.
[171]Ahmed M, Yamany S, Mohamed N, Frag 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
[172]Pham D, Prince J. Adaptive fuzzy segmentation of magnetic resonance images. IEEE Trans Med Imag, September 1999,18(9):737-752.
[173]Li C. Active contours with local binary fitting energy. IMA workshop on New Mathematics and Algorithms for 3-D Image Analysis, January 2006.
[174]N. Paragios and R. Deriche, Geodesic active regions:A new paradigm to deal with frame partition problems in computer vision. Joournal of Visual Communication and Image Representation,2002,13(1-2):249-268.
[175]Y. Q. Wang, W. F. Chen, T. L. Yu, Y. T Zhang, Hessian Based Image Structure Adaptive Gradient Vector Flow For Parametric Active Contours, Proceeding of 2010 IEEE 17th International Conference on Image Processing, HongKong,2010,649-652.
[2]Lee A. B, Pedersen K. S, Mumford D. The Nonlinear Statistics of High-Contrast Patches in Natural Images, Int'1 J.Comp. Vis.,2003,54(8):83-103.
[3]Yang A.Y, Wright, Ma J Y, Sastry S. Unsupervised segmentation of natural images via lossy data compression. Computer Vision and Image Understanding,2007,110: 212-225.
[4]Sudderth E. B, Jordan M. I. Shared Segmentation of Natural Scenes Using Dependent Pitman-Yor Processes. Advances in Neural Information Processing Systems,2009, 21:98-107.
[5]Ashburner J, Friston K. J. Voxel-based morphometry-the methods. IEEE Trans Med Imag, June 2000,11(6):805-821.
[6]Levin A, Weiss Y. Learning to combine Bottom-up and Top-down Segmentation, Int'1 J.Comp. Vis.,2009,81(1):105-118.
[7]Osher S, Sethian J. A. Fronts propagating with curvature dependent speed:algorithms based on the Hamilton-Jacobi formulation. Journal of Computational Physics, 1988,79(1):12-49.
[8]Kass M, Witkin A., Terzopoulos D. Snake:active contour models. Int'1 J.Comp. Vis. 1988,1(4):321-331.
[9]Terzopoulos D, Fleischer K. Deformable models. The Visual Computer,1988, 4(6):306-331.
[10]Terzopoulos D, Witkin A, Kass M. Constraints on deformable models:recovering 3D shape and nonrigid motion. Artificial Intelligence,1988,36(1):91-123.
[11]Wong A. K. C, Sahoo P. K. A gray-level threshold selection method based on maximum entropy principle. IEEE Transactions on Systems, Man and Cybernetics. 1989,19(4):866-871.
[12]Otsy N. A threshold selection method from gray-level histograms. Automatcia,1975, 11:285-296.
[13]Kapur JN., Sahoo P.K., Wong AKC. A new method for gray-level picture thresholding using the entropy of histogram.Computer Vision graphics, and image processing,1985, 29(3):273-285.
[14]Tsai W H, Moment-preserving thresholding:a new approach[J]. Computer Vision, Graphics, and Image Processing,1985,29(3):377-393.
[15]Rafeal C Gonzalez, Richard E Woods. Digital Image Processing(Second Edition). Beijing:Publishing House of Electronics Industry,2003.612-616.
[16]戴剑彬,张大力,图像分析中的松弛标记法.中国图象图形学报,1998,3(2)：97-99.
[17]Yu Q, Clausi A. IRGS:Image Segmentation using edge penalties and region growing. IEEE transaction on pattern analysis and Machine Intelligence,2008,30(12): 2126-2139.
[18]Forgy E, Cluster analysis of multivariate data:efficiency vs. interpretablity of classifications. Biometrics,1965,21(3):768-780.
[19]Bezdek J, Ehrilich C. R, FCM:The fuzzy c-means clustering algorithm. Computers & Geosciences,1984,10(2-3):191-203.
[20]李明,李云松.改进的快速模糊C均值聚类的图像分割方法.兰州理工大学学报,2007,33(3)：95-99.
[21]Brand M, Huang K. A unifying threorem for spectral embedding and clustering.9th International Coference on Artificial Intelligence and Statistics, Key West, Florida, 2002.
[22]Zhuang X, Huang Y, Palaniappan K, Zhao Y. Gausian mixture density modeling, decomposition, and applications IEEE Trans. Image Process,1996,5(9):1293-1302.
[23]于林森,张田文.用于图像分割的滤波EM算法.计算机学报,2006,29(6)：928-935.
[24]李明,李云松.改进的快速模糊C均值聚类的图像分割方法[J].兰州理工大学学报,2007,33(3)：95-99.
[25]叶吉祥,陈香华,谭冠政.利用小波和分层聚类进行彩色图像分割.计算机与数字工程,2006,34(1)：1-4.
[26]Oliver N, Pentland A.P, Berard F. LAFTER: Lips and face real time tracker. Computer Vision and Pattern Recongnition, IEEE Computer Society, Los Alamitos, CA. 1997,123-129.
[27]Harvey R, Matthews I, Bangham J. A, Cox S. Lip reading from scale-space measure-ments. Computer Vision and Pattern Recognition, IEEE Computer Society, Los Alamtios, CA.1997,582-587.
[28]Brand M, Oliver N. Pentland A. P. Coupled hidden Markov models for complex action recognition. Computer Vision and Pattern Recognition, IEEE Computer Society, Los Alamitos, CA.1997,994-999.
[29]Gross G, Jain A, Markov random field texture models. IEEE Transactions on Pattern Analysis and Machine Intelligence,1983,5(1):25-39.
[30]Elfadel I. M, Picard R. W. Gibbs random fields, cooccurrences, and texture modeding, IEEE Transactions on Pattern Analysis and Machine Intelligence,16(1):24-37,1994.
[31]申小阳,姜伯军.多个数字仪表字符串区域的定位和识别研究.苏州科技学院学报(自然科学版),2005,22(4)：42-49.
[32]Pemmaraju S, Mitra S, Shieh Y, Roberson G.H. Multiresolution Wavelet Decomposition and Fuzzy Clustering for Segmentation of Radiographic Images. CBMS,1995.142-149.
[33]Li H, Qian W, Clarkel P. Wavelet Transform for Directional Feature Extraction in Medical Imaging. Proceedings of IEEE International Conference on Image Processing,1997,3(3):500-5.
[34]陈武凡.小波分析及其在图像处理中的应用.北京：科学出版社,2002.
[35]宋军,邵谦明,周耀华.小波变换尺度过零点表征及在医学超声图像分割中的应用.复旦学报(自然科学版),2001,40(1)：40-43
[36]Xu C, Prince J., Snakes, shapes, and gradient vector flow, IEEE Transactions on Image Processing,1998,7(3):359-369.
[37]Xu C, Prince J, Generalized gradient vector flow external forces for active contours, Signal Processing,1998,71 (2):131-139.
[38]Caselles V, Kimmel R, Sapiro G. Geodesic active contours. Int. J. Comp. Vis., 1997,22(1):61-79.
[39]Chan T, Vese L, Active contours without edges. IEEE Transactions on Image Processing.2001,10(2):266-277.
[40]Vese L, Chan T. A multiphase level set framework for image segmentation using the mumford and shah model. Int. J. Comp. Vis.,2002,50:271-293.
[41]Chan T, Vese L. An efficient variational multiphase motion for the Mumford-Shah model. In:Proceedings of the 34'th Asilomar Conference on Signals, Systems and Computers,2000,1:490-494.
[42]Tsai A., Yezzi A., Willsky A., Curve evolution implementation of the Mumford-Shah functional for image segmentation, denoising, interpolation, and magnification, IEEE Transaction on Image Processing,2001,10(8):1169-1186.
[43]Li C, Kao C, Gore J, Ding Z. Implicit Active Contours Driven by Local Binary Fitting Energy, In IEEE Conference on Computer Vision and Pattern Recognotion(CVPR), 2007,1-7.
[44]Li C, Kao C, Gore J, Ding Z. Minimization of region-scalable fitting energy for image segmentation, IEEE Transactions on Image Processing,2008,17(10),1940-1949.
[45]Li C, Xu C, Gui C, Fox M. D. Level set evolution without re-initialization:A new variational. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2005,1:430-436.
[46]Li C, Xu C, Gui C, Fox M. D. Distance Regularized Level Set Evolution and its Application to Image Segmentation, IEEE Trans. Image Processing,2010,19 (12), 3243-3254.
[47]Malladi R, Sethian J.A. Shape modeling with front propagating:a level set approach. IEEE Transaction on Pattern Analysis and Machine Intelligence,1995,17(2):158-175.
[48]Xu G, Segawa E, Tsuji S. Robust active contours with incentive parmenters. Pattern Recoginetion.1994,27(7):879-884.
[49]Jundong L, David C., Charles S, Hima C., Automatic Subcortical Structure Segmentation using Local Likelihood-based Active Contour,3D Segmentation in The Clinic:A Grand Challenge,2007,91-98.
[50]Goldstein T., Bresson X. Geometric Application of the Split Bregman Method: Segmentation and Surface Reconstruction. Technical Report09-06, UCLA, Computational and Applied Mathematic,2009.
[51]Bresson X, Esedoglu S. Fast Global Minimization of the Active Contour/Snake Model. J Math Imaging Vis.2007,28(2):151-167.
[52]Bresson X, Chan T. Non-Local Unsupervised Variational Image Segmentation Models. Technical Report 08-67, UCLA, Computational and Applied Mathematic, 2008.
[53]Cohen L D. On Active Contour Models and Balloons. CVGIP:Image Understanding, 1991,53(2):211-218.
[54]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)：1722-1736.
[55]Mumford D, Shah J. Boundary detection by minimizing functionals,Image Understanding,1988,19-43.
[56]Mumford D, Shah J, Optimal approximations by piece wise smooth functions and associated variational problems.Communications on Pure and Applied Mathematics, 1989,42(5):577-685.
[57]Ambrosio L, Tortorelli V. On the approximation of functionals depending on jumps by elliptic functionals via γ-convergence. Communication on Pure and Applied Mathematics,1990,43(8):999-1036.
[58]Ambrosio L., Tortorelli V. On the approximation of free discontinuity problems. Boll. Un. Mat. Ital.,19927(6-B):105-123.
[59]Chan T., Esedoglu S., Nikolova M., Algorithms for finding global minimizers of image segmentation and denoising models, SIAM Journal on Applied Mathematics, 2006,66:1632-1648.
[60]Piovana J, Rousson M, Papadopoulo T. Efficient Segmentation of Piecewise Smooth Images. SSVM,2007:709-720.
[61]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.
[62]Lankton S, Melonakos J, Malcolm J, Dambreville S, Tannenbaum A. Localized statistics for DW-MRI fiber bundle segmentation. Computer Vision and Pattern Recognition Workshops,2008:1-8.
[63]Goldstein T, Osher S. The Split Bregman Algorithm for L1 Regularized Problems, Technical Report 08-29, UCLA, Computatial and Applied Mathematic,2008.
[64]Giusti E, Mimimal surfaces and functions of bounded variation, Australian National University, Canberra,1977.
[65]Chambolle A, An algorithm for total variation minimization and applications. J. Math.Imaging Vis.2004,20(1-2):89-97.
[66]Boykov Y, Jolly M. P. Interactive graph cuts for optimal boundary and region segmentation of objects in N-D images, Proc. International Conference on Computer Vision,2001,105-112.
[67]Boykov Y, Kolmogorov V, An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision, EEE Trans Patt Anal Mach Intell,2004, 26:1124-1137.
[68]Boykov Y, Funka-Lea G, Graph cuts and efficient N-D image segmentation, International Journal of Computer Vision,2006,70:109-131.
[69]Kolmogorov V, Zabih R. What Energy Functions Can Be Minimized via Graph Cuts? IEEE Trans Patt Anal Mach Intell,2004,26(2):147-159.
[70]Shi J, Malik J. Normalized cuts and image segmentation. IEEE Trans Patt Anal Mach Intell,2000,22(8):888-905.
[71]Egil B, Xue C. T, Efficient Global Optimization For The Multiphase Chan-Vese Model Of Image Segmentation by Graph Cuts. Technical Report 09-53, UCLA, Computational and Applied Mathematic,2009.
[72]Xue C T, Duan P Y. Domain Decomposition Methods With Graph cuts Algorithms For Image Segmentions. Technical Report,09-54, UCLA, Computational and Applied Mathematic,2009.
[73]Wenbing T, Xue C T. Multiple Piecewise Constant Active Contours for Image Segmentation using Graph Cuts Optimization. Technical Report,09-13, UCLA, Computinal and Applied Mathematic,2009.
[74]Kichenesamy S, Kumar A, Olver P, Tannenbaum A, A. Yezzi Conformal curvature flows:from phase transitions to active vision, in Archive for Rational Mechanics and Analysis.1996,134:275-301.
[75]Adalsteinsson D, Sethian J A. A Fast Level Set Method for Propagation Interfaces. Journal of Computational Physics,1995,118(2):269-277
[76]Adalsteinsson D, Sethian J A. The fast construction of extension velocities in level set methods. J. Comput. Phys.1999,148(1):2-22.
[77]Sethian J. A, An analysis of flame propagation, Ph.D Thesis, Dept. of Mathematics, University of California, Berkeley, CA,1982.
[78]Sethian J A. A Review of the Theory, Algorithms, and Applications of Level Set Methods for Propagating Interfaces. Acta Numerica, Cambridge University Press, 1996.
[79]Chopp D L. Computing Minimal Surfaces Via Level Set Curvature Flow. J.Comp. Phys,1993,106:77-91.
[80]Paragios, N. and R. Deriche, Geodesic active regions and level set methods for supervised texture segmentation. International Journal of Computer Vision, 2002,46(3):223-247.
[81]Soatto S, Yezzi A. J:Deformation:Deforming motion, shape average and the joint registration and segmentation of images. In:European Conference on Computer Vision, Graz,2002,32-57.
[82]Kim, J, C-etin, M., Willsky, A.S. Nonparametric shape priors for active contour-based image segmentation,Signal Processing,2007,87(12):3021-3044
[83]Chan T, Zhu. W, Level set based shape prior segmentation, Computer Vision and Pattern Recognition,2005. CVPR 2005. IEEE Computer Society Conference on,2005, 2:1164-1170
[84]Cremers, D, Osher, S.J, Soatto S. Kernel density estimation and intrinsic alignment for shape priors in level set segmentation, International Journal of Computer Vision,2006, 69(3):335-351
[85]Li H, Tai X. C. Piecewise constant level set methods for multiphase motion, International Journal of Numerical Analysis and Modeling,4(2):291-305
[86]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 information. Proc. SPIE Med. Imag. Physiol, Function, Strucuture Med. Images,2004, 5370:734-742.
[87]Siyal MY, Yu L. An intelligient modified fuzzy c-means based algorithm for bias estimation and segmentation of brain MRI. Pattern Recognition Letters, October 2005, 26:2052-2062
[88]Zhenping Xie Shitong Wang. A New Level Set Method for Image Segmentation Integrated with FCM, in Proceedings of the Fourth International Conference on Fuzzy Systems and Knowledge Discovery, Haikou, China,2007,4:699-703
[89]Lankton S, Tannenbaum A, localizing region-based active contours, IEEE Transactions on Image Processing,2008,17:2029-2039
[90]吴林,郭大勇等.改进的FCM在人脑MR图像分割中的应用.清华大学学报(自然科学版),2004,44(2)：157-159
[91]龚永义,罗笑南,廖国钧,张余,基于单水平集的多目标轮廓提取.计算机学报,2007,30(1)：95-99.
[92]Cohen F. S, Fan Z, Patel M. A. Classification of rotated and scaled textured images using Gaussian Markov Random Field models, IEEE Transactions on Pattern Analysis and Machine Intelligence,1991,13(2):192-202
[93]Zhu S, Wu Y, Mumford D. Filters, random field and maximum entropy:towards a unified theory for texture modeling. International Journal of Computer Vision,1998. 27(2):1-20
[94]Derin H, Elliott H. Model and segmentation of noisy and textured images using Gibbs random fields, IEEE Transaction on Pattern Analysis and Machine Intelligence,1987, 9:39-55
[95]Duda R.O, Hart P. E., Stock D. G, Pattern Classification (2nd Edit), John Wiley, New York,2001
[96]Dunn D, Higgins W.E. Optimal Gabor filters for texture segmentation. IEEE transactions on image processing,1995,4(7):947-964
[97]Unser M, Local linear transforms for texture, measurements. Signal Processing,1986, 11(1):61-79
[98]Arivazhagan S., Ganesan L, Texture segmentation using wavelet transform. Pattern Recognition Letters,2003,24(16):3197-3203
[99]Laine A., Fan J. Texture classification by wavelet packet signatures. IEEE Transactions on Pattern Analysis and Machine Intelligence,1993,15(11):1186-1191
[100]HouHou N, Philippe J. Fast Texture Segmentation Based on Semi-Local Region Descriptor and Active Contour. Numerical Mathematics:Theory, Methods and Applications.2009,2(4):445-468
[101]HouHou N, Thiran J.P, Bresson X. Fast Texture Segmentation Model based on the Shape Operator and Active Contour. In IEEE Conference on Computer Vision and Pattern Recognition, Anchorage, U. S., IEEE,2008:1-8
[102]Ni K, Bresson X, Chan T, Esedoglu S. Local histogram based segmentation using the Wasserstein distance, International journal of computer vision.2009,84(1):97-111
[103]Sochen N, Kimmel R, Malladi R. A General Framework For Low Level Vision. IEEE. Transactions on Image Processing,1998,7(3):310-318
[104]Kreyszing E., Differential Geometry. New York:Dover,1991
[105]张建伟,夏德深,基于双水平集的图像分割模型.计算机研究与发展,2006,43(1)：120-125.
[106]Rother C, Kolmogorov V, Blake A. Grabcut-Interactive Foreground Extraction using Iterative Graph Cuts, in ACM Transactions on Graphics (TOG). ACM,2004,23: 309-314.
[107]Zhang K, Song H, Zhang L. Active contours driven by local image fitting energy. Pattern Recognition,2010,43 (4):1199-1206.
[108]Tian Y, Zhou M, Wu Z, Wang X. A region-based Active Contour model for Image Segmentation, in IEEE,International Conference on Computational Intelligence and Security.2009,376-380.
[109]Markus G, Frank L, Anisotropic Total Variation Filtering. Appl. Math. Optim 62 2010,62(3):323-339.
[110]Buades A, Coll B. A Review of image denoising algorithms, with a new one. SIAM Multiscale Modeling and Simulation (MMS),2005,4(2):490-530
[111]Rudin L, Osher S, Fatemi E. Nonlinear total variation based noise removal algorithms, Physica D,1992,60(1-1):259-268
[112]Weickert J. Coherence-enhancing diffusion filtering. International Journal of Computer Vision,1999,31(2-3):111-127.
[113]Weikert J. Anisotropic diffusion in image processing, ECMI series, Teubner-Verlog, Stuttgart, Germany,1998.
[114]Weickert J. Scale-space properties of nonlinear diffusion filtering with a diffusion tensor. Technical Report, Laboratory of Technomathematics, University of Kaiserslautern, Germany,1994.
[115]Aujol J. F, Gilboa G, Chan T, Osher S. Structure-Texture Image Decomposition Modeling, algorithms, and Parameter Selection. Int'1 J.Comp. Vis.,2006,67(1): 111-136,
[116]Chan T, Esedo(?)lu S. Aspects of total variation regularized L1 function approximation. SIAM Journal on Applied Mathematics,2005,1817--1837
[117]Wang X. F., Huang D. S., Xu, H., An efficient local Chan-Vese model for image segmentation, Pattern Recognition,2010,43(3):603-618.
[118]Perona P, Malik J. Scale space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell,1990,12(7):629-639.
[119]Catte F, Lions P L. Morel J M, Coll T. Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. Numer. Anal.,1992,29:182-193
[120]Giusti E. Mimimal surfaces and functions of bounded variation, Australian National University, Canberra,1977.
[121]Meyer Y. Oscillating patterns in image processing and nonlinear evolution equation. Am. Math. Soc,2001.
[122]Rogowska J. Overview, fundamentals of medical image segmentation. Handbook of Medical Imageing Processing and Analysis, Academic Press,2000,69-86.
[123]Ginneken B, Alejandro F Frangi, Joes J. Active shape model segmentation with optimal features. IEEE Transactions on Medical Imaging,2002,21(8):924-933
[124]Pham L, Chengyang Xu, Prince L. A survey of current methods in medical image segmentation. Annual Review of Biomedical Engineering,2000,2:315-317
[125]Ourselin S. Overview on computer-assisted medical image segmentation, World Congress on Medical Physics and Biomedical Engineering, Sydney, Australia, August 24-292003, Invited speaker
[126]Gonzalez R. C, Woods R. E. Digital Image Processing,2nd Edition. New Jersey: Prentice Hall,2002.
[127]Siyal M. Y, Yu L. An intelligient modified fuzzy c-means based algorithm for bias estimation and segmentation of brain MRI. Pattern Recognition Letters, October 2005, 26:2052-2062
[128]Giger L. A fuzzy c-means (FCM) based algorithm for intensity inhomogeneity correction and segmentation of MR images. in IEEE International Symposium on Biomedical Imaging:From Nano to Macro,2004:1307-1310
[129]Ahmed M, Yamany S, Mohamed N, Frag 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
[130]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 information. Proc. SPIE Med. Imag.2004:Physiol., Function, Strucuture Med. Images, 2004,5370:734-742.
[131]Wells W, Grimson E, Kikinis R, Jolesz F. Adaptive segmentation of MRI data. IEEE Trans Med Image,1996,15(4):429-442.
[132]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.
[133]Pham D, Prince J. Adaptive fuzzy segmentation of magnetic resonance images. IEEE. Trans Medi Imag, September 1999,18(9):737-752
[134]Li C, Xu C, Anderson A. W, Gore J. C. MRI Tissue Classification and Bias Field Estimation Based on Coherent Local Intensity Clustering:A Unified Energy Minimization Framework. Information Processing in Medical Imaging (IPMI),2009, 5636:288-299.
[135]Li, C, Huang R, Ding Z, Gatenby C, Metaxas D, Gore J,. A Varaitional Level set approach to segmentation and bias correction of medical images with intensity inhomogeneity, MICCAI.2008,1083-1091.
[136]Li C. Active contours with local binary fitting energy. IMA workshop on New Mathematics and Algorithms for 3-D Image Analysis, January 2006.
[137]Vovk U, Pernus F, Likar B. A review of methods for correction of intensity inhomogeneity in MRI. IEEE Trans Med Imag, March 2007,26(3):405-421.
[138]Hou Z. A Review on MR Image Intensity Inhomogeneity Correction. International Journal of Biomedical Imaging, August 2006
[139]Shattuck D. W, Sandor-Leahy S. R, Schaper K. A, Rottenberg D. A, Leahy R. M. Magnetic resonance image tissur classification using a partial volumn model. Neuroimage, May 2001,13:856-876.
[140]Salvado O, Hillenbrand C, Wilson D. L. Correction of intensity inhomogeneity in MR images of vascular disease. EMBS'05,2005:4302-4305.
[141]Ben S.M., Ben A. I., Mitiche A. Active curve recovery of region boundary patterns, 2012,34(5):834-850,
[142]Brox, T., Cremers, D.,2010. On the statistical interpretation of the piecewise smooth Mumford-Shah functional, Scale Space and Variational methods in Computer Vision, 203-213.
[143]Nadaraya, E. A.1964. On estimating regression, Theory Probabil. Appl.,141-142.
[144]Shattuck, D.W., Sandor-Leahy, S.R., Schaper, K.A., Rottenberg, D.A., Leahy, R.M. Magnetic resonance image tissue classification using a partial volume model. NeuroImage,2001,13(5),856-876.
[145]Ourselin S. Overview on computer-assisted medical image segmentation, World Congress on Medical Physics and Biomedical Engineering, Sydney, Australia, Augest 24-29.
[146]Bezdek J C, Hall L O, Clarke L P. Review of MR image segmentation techniques using pattern recognition. Med. Phys.1993,20:1033-1048
[147]Wang Y, Audli T, Kung. Quantification and segmentation of brain tissues from MR images. IEEE Transactions on Image Processing,1998,7(8):1165-1181
[148]Wang Y, Audli T, Xuan. Magnetic resonance image analysis by information theoretic criteria and stochastic site models. IEEE Transactions on Imag Processing,2001, 5(2):150-158
[149]Kiknis R, Shenton M, Jolesz F. A, et al. Quantitative analysis of brain and cerebrospinal fliud spaces with MR imaging, J. Magn. Res. Imag.,1992:619-629.
[150]Miki'c I, Krucinski S, Thomas J. D. Segmentation and tracking in echocardiographic sequences:Active contours guided by optical flow estimates. IEEE Transcations on Medical Imaging,1998,17(2):274-283
[151]Yongye Zhang, Brady M, Smith S. Segmentation of brain MR images through a hidden markov random field model and the expectation-maximization algorithm. IEEE Transactions on Image Processing,2000,20(1):45-57
[152]Melnerney T, Terzopoulos D. Deformable models in medical image analysis. Proceedings of the workshop on methematical methods in biomedical image analysis, San Francisco, CAUSA,21-22 June 1996,171-180
[153]Knickmeyer R, Gousttard S, Kang C, Evans D, Wilber K, Smith J, Hamer R, Lin W, Gerig G, Gilmore J. A structural MRI study of human brain developement from birth to 2 years. J Neurosci,2008,28(47):121176-12182
[154]Isaacs E, Edmonds C, Chong W, Lucas A, Morley R, Gadian D. Brain morphometry and IQ measurements in preterm children, Brain,2004,127(12):2595-2607
[155]Goldenberg R, Kimmel R, Rivlin E, Rudzsky M. Cotex segmentation: fast variational geometric approach. IEEE Trans Med Imag,2002,21(2):1544-1551.
[156]Dale A, Fischl B, Sereno M. Cortical Surface-Based Analysis: Ⅰ. Segmentation and Surface Reconstruction. NeuroImage,1999,9(2):179-194.
[157]B. P. F. Lelieveldt, et al. Multi-views active appearance models for consistent segmentation of multiple standard views:application to long- and short-axis cardiac MR images. in Proceedings of the 17th International Congress and Exhibition.2003. London, United Kingdom.
[158]Bazin P. L, Pham D. L. Topology-preserving tissue classification of magenetic resonance brain images. IEEE Trans Med Imag,2007,26(4):487-496
[159]Sethian J. A. Algorithms for tracking interfaces in CFD and material science. Annu. Rev. Comput. Fluid Mechanics,1995.
[160]Wollschleger H, Tenspiel RW et al. Reliable automatic frame-by-frame contour detection of digitized LV cine-angiograms. IEEE Computers in Cardiology, 1998:353-356
[161]Nishida M, Makris N, Kennedy D. N, Vangel M, Fischl B, Krishnamoorthy K. S, Caviness V. S, Grant P. E. Detailed semiautomated MRI based morphometry of the neonatal brain:preliminary results. Nero Image,2006,32(3):1041-1049
[162]Miki'c I, Krucinski S, Thomas J. D. Segmentation and tracking in echocardiographic sequences:Active contours guided by optical flow estimates. IEEE Transcations on Medical Imaging,1998,17(2):274-283
[163]Yongye Zhang, Brady M, Smith S. Segmentation of brain MR images through a hidden markov random field model and the expectation-maximization algorithm. IEEE Transactions on Image Processing,2000,20(1):45-57
[164]Melnerney T, Terzopoulos D. Deformable models in medical image analysis. Proceedings of the workshop on methematical methods in biomedical image analysis, San Francisco, CA USA,21-22 June 1996,171-180
[165]Knickmeyer R, Gousttard S, Kang C, Evans D, Wilber K, Smith J, Hamer R, Lin W, Gerig G, Gilmore J. A structural MRI study of human brain developement from birth to 2 years. J Neurosci,2008,28(47):121176-12182
[166]Song Z, Awate S. P, Licht D, J, Gee J. C. Clinical Neonatal Brain MRI Segmentation Using Adaptive Nonparametric Data Models and Intensity-Based Makov Priors. Proceedings of Medical Image Computing and Computer Aided Intervention, 2007:883-890
[167]Aljabar P, Heckemann R, Hammers A, Hajnal J, Rueckert D. Multi-atlas based segmentation of brain images:Atlas selection and its effect on accuracy. NeroImage, 2009,46(3):726-738
[168]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.
[169]Zeng X, Staib L, Schultz R, Duncan J. Segmentation and Measurement of the Cotex from 3D MR Images Using Coupled Surfaces Propagation. IEEE Trans Med Imag, 1999,18(10):100-111.
[170]Guillemaud R, Brady M. Esitmating bias field of MR images. IEEE Trans Med Imag, June 1997,16(3):238-251.
[171]Ahmed M, Yamany S, Mohamed N, Frag 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
[172]Pham D, Prince J. Adaptive fuzzy segmentation of magnetic resonance images. IEEE Trans Med Imag, September 1999,18(9):737-752.
[173]Li C. Active contours with local binary fitting energy. IMA workshop on New Mathematics and Algorithms for 3-D Image Analysis, January 2006.
[174]N. Paragios and R. Deriche, Geodesic active regions:A new paradigm to deal with frame partition problems in computer vision. Joournal of Visual Communication and Image Representation,2002,13(1-2):249-268.
[175]Y. Q. Wang, W. F. Chen, T. L. Yu, Y. T Zhang, Hessian Based Image Structure Adaptive Gradient Vector Flow For Parametric Active Contours, Proceeding of 2010 IEEE 17th International Conference on Image Processing, HongKong,2010,649-652.