基于模糊理论的医学图像分割算法研究
|
摘要
磁共振(MR)脑部图像的分割主要包括两个方面的内容:一是对正常脑组织的分割,就是要将MR脑部图像分割为灰质、白质和脑脊液等组织部分。这是医学图像配准、三维重建和可视化的基础;另一方面就是对包含有病灶的MR.脑部图像的分割,即将感兴趣的病灶从其它组织中分割出来。这样就能够对病灶的形状、边界、截面面积以及体积等进行测量,并通过在治疗前后对这些指标的测量和分析,帮助医生制定和修改治疗方案。
由于人体解剖的个体差异较大,临床应用对医学图像分割的准确度和算法的执行速度要求较高;又由于噪声、偏移场效应和部分容积效应等对图像的影响,使得已有的分割算法远未达到理想的效果。因此,MR脑部图像的分割一直是医学图像处理和分析的热点研究问题。
医学图像的部分容积效应和有些组织区域的不确定性,决定了医学图像的模糊性。基于模糊理论的图像分割算法将模糊概念引入到图像分割算法中,用隶属度表示像素占各种“纯组织”部分容积的比例。这已经广泛地应用于MR脑部图像的分割中,其中最具代表性的算法就是模糊C-均值聚类算法(FCM)。但传统的FCM聚类算法是一种仅利用灰度信息的聚类算法。它未考虑相邻像素之间相关性,未能利用图像的空间信息,在分割低信噪比图像时会产生较大的偏差。
本文对传统的FCM算法进行进行了深入的研究,在此基础上提出了两种改进算法,这些方法在提高图像分割精度和鲁棒性等方面具有显著效果。
多发性硬化症是一种严重威胁中枢神经功能的疾病,对其病灶的分割方法研究正受到越来越多的关注。但由于实际的临床图像存在较严重的不确定噪声、不均匀性以及多发性硬化症病灶表现复杂等原因,使得现有的算法的分割效果不尽人意。本文利用改进的算法对多发硬化症进行了分割,取得了满意的分割效果。
本文首先对医学图像分割的现状作了详尽的综述。这部分主要介绍了医学图像分割方法的各种分类方法,特别对近年来医学图像分割方面的新算法及其特点作了一个详细的总结。
第二章主要对近年来国际上出现的多种改进的FCM算法进行比较分析。将它们大体分为三类:第一类,改变隶属度的约束条件;第二类,引进空间信息约束项;第三类,引入核函数。对这些算法中比较典型的算法做了简单的分析和评价。
第三章是本文的重点内容,根据脑部MR图像真实的灰度值具有分片为常数的特性,按照合理利用空间信息的原则,提出了一种基于多目标规划的FCM聚类算法。在传统的FCM算法中增加了空间信息约束项,提出了新的目标函数,并运用Lagrange乘数法,得到该规划问题的解。通过对模拟方块图和脑部MR图像以及临床脑部MR图像的分割实验,表明该算法在分割被噪声污染图像时,比传统的FCM算法及其改进算法具有更精确的图像分割能力。
第四章是本文的又一重点内容,由于传统的模糊聚类算法,只考虑了当前象素的作用,对分割含噪声图像不敏感。本文在传统的模糊聚类算法中引入了核函数,同时引入了控制邻域作用的约束项,提出了改进的基于模糊核聚类的MR图像分割新算法。通过对模拟图和仿真的脑部MR图像的分割实验证明,该算法对被噪声污染图像亦具有鲁棒性,特别是对被椒盐噪声污染图像的分割,可以有效地滤除噪声得到良好的分割结果。
第五章将多发性硬化症的MR成像特点和解剖性质做为先验知识,提出了一种针对多发性硬化症病灶T2加权脑部磁共振(MR)图像的分割算法。根据多发性硬化症病灶和脑脊液在T2加权像上同表现为高亮度信号的特点,本文把模糊C均值分割算法与形态学方法相结合,提出了基于核模糊C均值的多发性硬化症病灶分割算法。该算法首先用第四章改进的核模糊C均值算法做基础分割,再用形态学方法提取出多发性硬化症病灶得到最终分割结果。通过对多发性硬化症模拟脑部MR图像的分割结果表明,本文算法能够比较准确的分割多发性硬化症病灶。其分割效果明显好于FCM聚类算法。该算法还具有无监督、运算速度快、稳健性好等优点,能够应用于多发性硬化症的临床辅助诊断。
第六章研究了基于马尔可夫随机场的DT-MRI图像分割算法。在DT-MR扫描下,大脑中的灰质和脑脊液表现出各向同性,而白质由于其存在具有髓鞘的神经轴突而限制了水分子,使弥散仅沿着神经纤维轴方向进行,表现出显著的各向异性。根据此特性,DT-MRI技术在显示脑白质的微观组织结构和纤维束走向等方面具有极大的优越性,作为目前唯一的非侵入性分析大脑内部结构的重要工具,DT-MRI已经在中风、老年痴呆症、精神分裂症、脑缺血以及多发性硬化症和其他一些脑部肿瘤的研究和诊断中发挥了重要的作用。本章利用图像空间的相关信息作为先验知识,引入新的距离判别标准,基于马尔可夫场(MRF)模型,运用Gibbs场和最大后验概率(MAP)实现了一种DT-MRI图像分割的新算法。该算法具有无监督、稳健性好、收敛速度快、对低信噪比图像具有良好的分割结果等特点。
There are two purposes for the segmentation of MR brain images. The first one is to segment MR brain images into different tissue classes, especially gray matter (GM), white matter (WM) and cerebrospinal fluid (CSF), which is crucial to the image registration, 3D reconstruction and medical image visualization. The second one is to extract the focal region of interesting (ROI) from other tissues in order to assist physicians in making right diagnosis, and working out the therapeutic strategy.
The research on MR brain image segmentation has been an important field in medical image processing and analysis. There are a number of factors that cause current segmentation algorithms fail to satisfy the need of clinical practice, including 1) the individual differences in the tissue anatomy; 2) slow calculating speed and inaccuracy; and 3) poor image quality affected by noise, intensive inhomogeneity and partial volume effect (PVE), etc.
Medical images behave fuzziness duo to PVE artifacts and the uncertainty in some focal regions. The idea of using membership function associated with fuzzy-set theory to represent partial volume proportions of each "pure" tissue has been a quite popular and widely used model, in which Fuzzy c-means (FCM) clustering algorithm is the well-established approach to the implementation of the image segmentation. However, the conventional FCM fails to incorporate the spatial information of the image leading to aberrant consequences in the case of dealing with low signal-to-noise ratio (SNR) MR images.
In the thesis, two improved models of FCM algorithms are proposed. The performance of these algorithms is remarkably superior to the conventional ones in terms of accuracy and robustness.
we investigate the segmentation of MS lesions—an inflammatory demyelinating disease that would damage central nervous system. There is a growing attention to this area for the conventional segmentation algorithms are not working well due to the effects of noises, intensive inhomogeneities, the behavior of MS lesions etc. The testing results for T2-weighted MR brain images show the proposed algorithm is robust and accurate enough for clinical use.
Chapter 1 provides an overview of image segmentation methods. We describe the wide variety of medical image segmentation methods and applications. The thesis is devoted to general study of medical image segmentation, including the theory, the classification and the method of segmentation.
In chapter 2, we present many improved methods of the FCM algorithm in recent years in the lecture. There are generally classed into three kinds: the first one, the constraints on membership function is changed, the second one, the term of spatial information is introduced, the third one, the kernel method is introduced. Finally, the typical ones of these algorithms are analysed and appraised simply.
The main emphasis is on chapter 3, we develop a modified FCM clustering for brain MR image segmentation based on multiple objective programming, considering the intensities of ideal MR image which is piecewise constant. The proposed algorithm can reasonably use the spatial of image and improve the accuracy of segmentation. The new mathematical programming formula can thus be solved by the Lagrange multiplier. The results obtained by testing both simulated and clinical data, show that the proposed algorithm is more robust to noise and other artifacts than the conventional fuzzy image segmentation algorithms.
Another main emphasis is on chapter 4, when the conventional fuzzy clustering algorithm is used for image segmentation, the algorithm strictly depending on the current pixels, works only on images with less noise. In the paper, we presented a modified fuzzy kernel clustering algorithm for MR images segmentation. The new algorithm incorporates a kernel-induced distance mertric and a penalty term that controls the neighborhood effect to the objective function. Experiment results on both synthetic images and simulation MR images show that the proposed algorithm more robust to noise than the standard fuzzy image segmentation algorithms.
A novel approach to the segmentation of multiple sclerosis (MS) lesions in T2-weighted magnetic resonance (MR) images is presented in Chap5. According to the characteristic of MS lesions show the same high brightness with cerebrospinal fluid (CSF) in T2-weighted images, combining the strengths of the kernel fuzzy c-means algorithm and morphology characteristics of MS lesion tissues we present the segmentation of MS lesions based on kernel fuzzy c-means algorithm. The modified kernel fuzzy c-means algorithm is used to basic segmentation. Then the MS lesions are extracted by morphological method. The MS segmentation in simulated T2-weighted MR images show that the proposed algorithm can provide a powerful segmentation.
In Chap6, we develop a MRF-based algorithm for DT-MRI image segmentation. As a new technology which can reflect the direction of molecule diffusion, DTI can show the information of the structure of the tissues and the exchanges of water molecule with each tissues in pathology. It has great advantages on showing the distribution of white matter fiber pathway and its three-dimensional structures because of the distinct anisotropy of the diffusion in water molecule of the brain white matter. Without any other methods can measure the character of the live white matter presently, DTI has great significance for the study of the anatomization of the brain and the diagnosis of the diseases of white matter. In this chapter, using the priori knowledge of the spatial correlations of the image and a new tensor distance, applied Gibbs random field and MAP method to the segmentation problem can achieve a novel segmentation of DT-MRI. The results obtained by testing clinical DT-MRI datasets show that MRF can segment them more accurately than FCM.
由于人体解剖的个体差异较大,临床应用对医学图像分割的准确度和算法的执行速度要求较高;又由于噪声、偏移场效应和部分容积效应等对图像的影响,使得已有的分割算法远未达到理想的效果。因此,MR脑部图像的分割一直是医学图像处理和分析的热点研究问题。
医学图像的部分容积效应和有些组织区域的不确定性,决定了医学图像的模糊性。基于模糊理论的图像分割算法将模糊概念引入到图像分割算法中,用隶属度表示像素占各种“纯组织”部分容积的比例。这已经广泛地应用于MR脑部图像的分割中,其中最具代表性的算法就是模糊C-均值聚类算法(FCM)。但传统的FCM聚类算法是一种仅利用灰度信息的聚类算法。它未考虑相邻像素之间相关性,未能利用图像的空间信息,在分割低信噪比图像时会产生较大的偏差。
本文对传统的FCM算法进行进行了深入的研究,在此基础上提出了两种改进算法,这些方法在提高图像分割精度和鲁棒性等方面具有显著效果。
多发性硬化症是一种严重威胁中枢神经功能的疾病,对其病灶的分割方法研究正受到越来越多的关注。但由于实际的临床图像存在较严重的不确定噪声、不均匀性以及多发性硬化症病灶表现复杂等原因,使得现有的算法的分割效果不尽人意。本文利用改进的算法对多发硬化症进行了分割,取得了满意的分割效果。
本文首先对医学图像分割的现状作了详尽的综述。这部分主要介绍了医学图像分割方法的各种分类方法,特别对近年来医学图像分割方面的新算法及其特点作了一个详细的总结。
第二章主要对近年来国际上出现的多种改进的FCM算法进行比较分析。将它们大体分为三类:第一类,改变隶属度的约束条件;第二类,引进空间信息约束项;第三类,引入核函数。对这些算法中比较典型的算法做了简单的分析和评价。
第三章是本文的重点内容,根据脑部MR图像真实的灰度值具有分片为常数的特性,按照合理利用空间信息的原则,提出了一种基于多目标规划的FCM聚类算法。在传统的FCM算法中增加了空间信息约束项,提出了新的目标函数,并运用Lagrange乘数法,得到该规划问题的解。通过对模拟方块图和脑部MR图像以及临床脑部MR图像的分割实验,表明该算法在分割被噪声污染图像时,比传统的FCM算法及其改进算法具有更精确的图像分割能力。
第四章是本文的又一重点内容,由于传统的模糊聚类算法,只考虑了当前象素的作用,对分割含噪声图像不敏感。本文在传统的模糊聚类算法中引入了核函数,同时引入了控制邻域作用的约束项,提出了改进的基于模糊核聚类的MR图像分割新算法。通过对模拟图和仿真的脑部MR图像的分割实验证明,该算法对被噪声污染图像亦具有鲁棒性,特别是对被椒盐噪声污染图像的分割,可以有效地滤除噪声得到良好的分割结果。
第五章将多发性硬化症的MR成像特点和解剖性质做为先验知识,提出了一种针对多发性硬化症病灶T2加权脑部磁共振(MR)图像的分割算法。根据多发性硬化症病灶和脑脊液在T2加权像上同表现为高亮度信号的特点,本文把模糊C均值分割算法与形态学方法相结合,提出了基于核模糊C均值的多发性硬化症病灶分割算法。该算法首先用第四章改进的核模糊C均值算法做基础分割,再用形态学方法提取出多发性硬化症病灶得到最终分割结果。通过对多发性硬化症模拟脑部MR图像的分割结果表明,本文算法能够比较准确的分割多发性硬化症病灶。其分割效果明显好于FCM聚类算法。该算法还具有无监督、运算速度快、稳健性好等优点,能够应用于多发性硬化症的临床辅助诊断。
第六章研究了基于马尔可夫随机场的DT-MRI图像分割算法。在DT-MR扫描下,大脑中的灰质和脑脊液表现出各向同性,而白质由于其存在具有髓鞘的神经轴突而限制了水分子,使弥散仅沿着神经纤维轴方向进行,表现出显著的各向异性。根据此特性,DT-MRI技术在显示脑白质的微观组织结构和纤维束走向等方面具有极大的优越性,作为目前唯一的非侵入性分析大脑内部结构的重要工具,DT-MRI已经在中风、老年痴呆症、精神分裂症、脑缺血以及多发性硬化症和其他一些脑部肿瘤的研究和诊断中发挥了重要的作用。本章利用图像空间的相关信息作为先验知识,引入新的距离判别标准,基于马尔可夫场(MRF)模型,运用Gibbs场和最大后验概率(MAP)实现了一种DT-MRI图像分割的新算法。该算法具有无监督、稳健性好、收敛速度快、对低信噪比图像具有良好的分割结果等特点。
There are two purposes for the segmentation of MR brain images. The first one is to segment MR brain images into different tissue classes, especially gray matter (GM), white matter (WM) and cerebrospinal fluid (CSF), which is crucial to the image registration, 3D reconstruction and medical image visualization. The second one is to extract the focal region of interesting (ROI) from other tissues in order to assist physicians in making right diagnosis, and working out the therapeutic strategy.
The research on MR brain image segmentation has been an important field in medical image processing and analysis. There are a number of factors that cause current segmentation algorithms fail to satisfy the need of clinical practice, including 1) the individual differences in the tissue anatomy; 2) slow calculating speed and inaccuracy; and 3) poor image quality affected by noise, intensive inhomogeneity and partial volume effect (PVE), etc.
Medical images behave fuzziness duo to PVE artifacts and the uncertainty in some focal regions. The idea of using membership function associated with fuzzy-set theory to represent partial volume proportions of each "pure" tissue has been a quite popular and widely used model, in which Fuzzy c-means (FCM) clustering algorithm is the well-established approach to the implementation of the image segmentation. However, the conventional FCM fails to incorporate the spatial information of the image leading to aberrant consequences in the case of dealing with low signal-to-noise ratio (SNR) MR images.
In the thesis, two improved models of FCM algorithms are proposed. The performance of these algorithms is remarkably superior to the conventional ones in terms of accuracy and robustness.
we investigate the segmentation of MS lesions—an inflammatory demyelinating disease that would damage central nervous system. There is a growing attention to this area for the conventional segmentation algorithms are not working well due to the effects of noises, intensive inhomogeneities, the behavior of MS lesions etc. The testing results for T2-weighted MR brain images show the proposed algorithm is robust and accurate enough for clinical use.
Chapter 1 provides an overview of image segmentation methods. We describe the wide variety of medical image segmentation methods and applications. The thesis is devoted to general study of medical image segmentation, including the theory, the classification and the method of segmentation.
In chapter 2, we present many improved methods of the FCM algorithm in recent years in the lecture. There are generally classed into three kinds: the first one, the constraints on membership function is changed, the second one, the term of spatial information is introduced, the third one, the kernel method is introduced. Finally, the typical ones of these algorithms are analysed and appraised simply.
The main emphasis is on chapter 3, we develop a modified FCM clustering for brain MR image segmentation based on multiple objective programming, considering the intensities of ideal MR image which is piecewise constant. The proposed algorithm can reasonably use the spatial of image and improve the accuracy of segmentation. The new mathematical programming formula can thus be solved by the Lagrange multiplier. The results obtained by testing both simulated and clinical data, show that the proposed algorithm is more robust to noise and other artifacts than the conventional fuzzy image segmentation algorithms.
Another main emphasis is on chapter 4, when the conventional fuzzy clustering algorithm is used for image segmentation, the algorithm strictly depending on the current pixels, works only on images with less noise. In the paper, we presented a modified fuzzy kernel clustering algorithm for MR images segmentation. The new algorithm incorporates a kernel-induced distance mertric and a penalty term that controls the neighborhood effect to the objective function. Experiment results on both synthetic images and simulation MR images show that the proposed algorithm more robust to noise than the standard fuzzy image segmentation algorithms.
A novel approach to the segmentation of multiple sclerosis (MS) lesions in T2-weighted magnetic resonance (MR) images is presented in Chap5. According to the characteristic of MS lesions show the same high brightness with cerebrospinal fluid (CSF) in T2-weighted images, combining the strengths of the kernel fuzzy c-means algorithm and morphology characteristics of MS lesion tissues we present the segmentation of MS lesions based on kernel fuzzy c-means algorithm. The modified kernel fuzzy c-means algorithm is used to basic segmentation. Then the MS lesions are extracted by morphological method. The MS segmentation in simulated T2-weighted MR images show that the proposed algorithm can provide a powerful segmentation.
In Chap6, we develop a MRF-based algorithm for DT-MRI image segmentation. As a new technology which can reflect the direction of molecule diffusion, DTI can show the information of the structure of the tissues and the exchanges of water molecule with each tissues in pathology. It has great advantages on showing the distribution of white matter fiber pathway and its three-dimensional structures because of the distinct anisotropy of the diffusion in water molecule of the brain white matter. Without any other methods can measure the character of the live white matter presently, DTI has great significance for the study of the anatomization of the brain and the diagnosis of the diseases of white matter. In this chapter, using the priori knowledge of the spatial correlations of the image and a new tensor distance, applied Gibbs random field and MAP method to the segmentation problem can achieve a novel segmentation of DT-MRI. The results obtained by testing clinical DT-MRI datasets show that MRF can segment them more accurately than FCM.
引文
[1]Peter A.Rinck,宋英儒.医学磁共振(第五版)[M].北京:人民卫生出版社,2007.
[2]宋枭禹,包尚联.医学的诺贝尔奖授予两位MRI物理学家所带来的思考[J].世界医疗器械,2004,10(1):16-17.
[3]Moseley ME,Cohen Y,Mintrovitch J,et al,Early detection of regional cerebral ischemia in cats:comparison of diffusion-and T2-weighted MRI and spectroscopy.Magn Reson Med,1990,14:330-346.
[4]Moseley ME,Kucharczyk J,Mintrovitch J,Cohen Y,Kuhanewicz J,Derugin N,Asgari H,Norman D.Diffusion-weighted MR imaging of acute stroke:Correlation with T2-weighted and magnetic susceptibility-enhanced MR imaging in cats.AJNR,1990,11:423-429.
[5]谢静霞.核磁共振新技术研究与临床应用[M].北京:北京医科大学出版社,2001.
[6]Basser PJ,Mattiello J,and LeBihan D.MR diffusion tensor spectroscopy and imaging.Biophysical Journal,1994,66(1):259-267.
[7]章毓晋.图象分割[M].北京:科学出版社,2001.
[8]罗述谦,周果宏.医学图象处理与分析[M].北京:科学出版社,2003.
[9]Pham DL,Xu C,Prince JL.A survey of current methods in medical image segmentation[J].Annual Review of Biomedical Engineering,2000,2,315-337.
[10]Liew,Alan WC,Yan H.Current methods in the automatic tissue segmentation of 3D magnetic resonance brain images[J],Current Medical Imaging Reviews.2006,2(1):91-103.
[11]颜刚.基于模糊马尔可夫场的图像算法研究[D].广州:南方医科大学,2005.
[12]赵荣椿,迟耀斌,朱重光.图像分割技术进展[J].中国体视学和图像分析,1998,3(2):121-128.
[13]赵志峰,张尤赛.医学图像分割综述[J].华东船舶工业学院学报,2003,17(3):43-48.
[14]聂斌.医学图像分割技术及其进展[J].泰山医学院学报,2002,23(4):422-426.
[15]Bezdek J,Hall L,Clarke L.Review of MR image segmentation techniques using pattern recognition[J].Medical Physics,1993;20:1033-1048.
[16]Clarke LP,Velthuizen RP.MRI segmentation:methods and applications[J].Magnetic Resonance Imaging.1995,13(3):343-368.
[17]李璟,朱善安,He B.医学图像分割技术[J].生物医学工程学杂志,2006,23(4):891-894.
[18]Goshtasby A,Turner DA.Segmentation of cardiac cine MR images for extraction of right and left ventricular chamber[J].IEEE Trans.On Medical Imaging,1995,14(1):56-64.
[19]Thedens DR,Skorton DJ,Fleagle SR.Methods of graph searching for border detection in image sequences with applications to cardiac magnetic resonance imaging[J].IEEE Trans.On Medical Imaging,1995,14(1):42-55.
[20]Canny J.A computational approach to edge detection[J].IEEE Trans.On Pattern Analysis and Machine Intelligence,1986,8(6):679-698.
[21]Deng W,Iyengar SS.A new probabilistic relaxation scheme and its application to edge detection[J].IEEE Trans.On Pattern Analysis and machine Intelligence,1996,18(4):432-437.
[22]Qian RJ,Huang TS.Optimal edge detection in two-dimensional images[J].IEEE Trans.On Image Processing,1996,5(7):1215-1220.
[23]付宜利,高文朋,王树国.颅脑磁共振图像分割评价的统计学方法[J].医学影像学杂志,2005,15(8):644-647.
[24]Bansal R,Staib LH,Chen Z,et al.Entropy-based,multipleportal-to-3D CT registration for prostate radiotherapy using iteratively estimated segmentation[A].In:Proceedings of Medical Image Computing and Computer-Assisted Intervention[C],Cambridge,UK,1999:567-578.
[25]Sahoo P,Wilkins C,Ueager J.Threshold selection using Rrenyi's entropy[J].Pattern Recognition,1997,30(1):71-84.
[26]M.Singh,P.Patel,D.Khosla,and T.Kim,Segmentation of functional MRI by K-means clustering [J],IEEE Trans.Nucl.Sci.,1996,43(6):2030-2036.
[27]Mohamed NA,Sameh MY,Nevin M.A modified fuzzy C-means algorithm for bias field estimation and segmentation of MRI data [J].IEEE Trans.On Medical Imaging,21(3),2002:193-199.
[28]Liew AW,Yan H,An adaptive spatial fuzzy clustering algorithm for 3-D MR image segmentation [J],IEEE Trans.On Medical Imaging,2003,22(9):1063-1075.
[29]Zhao YQ,Li ML.A modified fuzzy C-Means algorithm for segmentation of MRI[C].Proceedings of the 5th ICCIMA'03,2003.
[30]Nie SD,Chen Y,Gu SD,et al.The study of fast fuzzy clustering segmentation algorithm of head MRI [J].Chinese Journal of Biomedical Engineering,2001,20(2):104-109.
[31]M.Wiegell,D.Tuch,H.Larson,and V.Wedeen.Automatic Segmentation of Tha-lamic Nuclei from Diffusion Tensor Magnetic Resonance Imaging.NeuroImage,2003,19:391- 402.
[32]J.Weickert.Diffusion and Regularization Methods for Tensor-valued Images.In First SIAM-EMS Conf Appl Math,in Our Changing World,2001.
[33]C.Chefd'hotel,O.Faugeras,D.Tschumperl?,and R.Deriche.Constrained flows of matrix-valued functions:application to diffusion tensor regularization.In ECCV,2002,pages251-265.
[34]C.Alexander,C.Gee,and R.Bajcsy.Similarity Measure for Matching Diffusion Tensor images.In British Machine Vision Conference,1999,pages 93-102.
[35]Wan S Y,William H.Symmetric region growing [J].IEEE Trans,on Image Processing,2003,12(9):1007-1015.
[36]Rosenfeld A.Fuzzy digital topology [J].Inform & Control,1979,40:76-87.
[37]Rosenfeld A.On connectivity properties of grayscale pictures [J].Pattern Recognition,1983,16(l):47-50.
[38]J.K.Udupa,S.Samarasekera.Fuzzy connectedness and object definition:theory,algorithms,and applications in image segmentation [J].Graphical model and Image processing,1996,58(3):246-261.
[39]J.K.Udupa.Fuzzy connectedness and image segmentation [J].Proceedings of the IEEE,2003,91(10):1649-1669.
[40]Yang FG,Tianzi Jiang TZ,Pixon-based image segmentation with Markov random fields[J],IEEE Trans,on Image Processing,2003,12(12):1552-1559.
[41]Geman S,Geman D.Stochatic relaxation,Gibbs distributions,and the bayesian restoration of images [J].IEEE Trans.On Pattern Analysis and Machine Intelligence,1984,6(6),721-741.
[42]Zhang Y,Brady M,Smith S.Segmentation of brain images through a hidden Markov random field model and the expectation-maximization algorithm [J].IEEE Trans.On Medical Imaging,2001,20(1):45-57.
[43]Li SZ.Markov random field modeling in image analysis [M].Springer-Verlag,2001.
[44]Lakshmanan S,Derin H.Simultaneous parameter estimation and segmentation of Gibbs random fields using simulated annealing [J].IEEE Trans.On Pattern Analysis and machine Intelligence,1989,121(8):799-813.
[45]Melas DE,Wilson SP.Double Markov random fields and bayesian image segmentation [J].IEEE Trans.On Signal Process,2002,50(2):357-365.
[46]Kass M,Witkin A,Terzopoulos D.Snakes:active contour models[C].In:Proc of First Int Confon Computer Vision.London,1987.259-269.
[47]Osher S,Sethian JA.Fronts propagating with curvature-dependent speed:algorithms based on Hamilton- Jacobi formulations [J].Journal of Computarional Physics,79(1),1988:12:49.
[48]Wang Z,Vemuri BC.DTI segmentation using an information theoretic tensor dissimilarity measure[J].IEEE Trans.On Medical Imaging,2005,24(10):1267-1277.
[49]陈强,周则明,王平安等.带标记线左心室MR图像的自动分割[J],中国图形图像学报,2004,9(6):666-673.
[50]Zhukov L,Museth K,Breen D,et al.Level set modeling and segmentation of.DT-MRI brain data[J],Journal of Electronic Imaging,2003,12(1):125-133.
[51]Wang Z,Vemuri BC.DTI segmentation using an information theoretic tensor dissimilarity measure[J].IEEE Trans.On Medical Imaging,2005,24(10):1267-1277.
[52]孙优贤,卢建刚,许锋.神经网络在图像处理中的应用[J],信息与控制,2003,32(4):344-350.
[53]Ahmed MN,Farag AA.Two-stage neural network for volume segmentation of medical images[J].Proceedings of IEEE International Conference On Neural Networks,1997(3):1373-1377.
[54]Chen CT.Medical image segmentation by a constraint satisfaction neural network[J].IEEE Trans.On Nuclear Science,1991,38(2):678-686.
[55]Cheng KS.The application of competitive Hopfield neural network to medical image segmentation[J].IEEE Trans.On Medical Imaging,1996(15):560-567.
[56]Mallat S.A theory for multiresolution signal decomposition:the wavelet representation[J].IEEE Trans.On Pattern Analysis and machine Intelligence,1989,11(7):647-693.
[57]Laine A,Fna J.Texture classification by wavelet packet signatures[J].IEEE Trans.On Pattern Analysis and machine Intelligence,1993,15(11):1186-1191.
[58]Chun DN,Yang HS.Robust image segmentation using genetic algorithm with a fuzzy measure [J].Pattern Recognition,1996,29(7):1195-1211.
[59]Bram VG,Alejandro FF,Joes JS,et al.Active shape model segmentation with optimal features [J].IEEE Trans.On Medical Imaging,21(8):924-933.
[60]Vincent L,Soille P.Watersheds in digital spaces:an efficient algorithm based on immersion simulations [J].IEEE Trans.On Pattern Analysis and machine Intelligence,1991,13(6):583-598.
[61]Udupa JK,Leblanc VR,Zhu Y,et al.A framwork for evaluating imagesegmentation algorithms [J].Computerized Medical Imaging and Graphics,2006,30(l):75-87.
[62]Zhang YJ.A survey on evaluation methods for image segmentation [J].Pattern Recognition,1996,29(8):1335-1346.
[1]Zadeh LA.Fuzzy sets[J].Information Control,1965(8):338-353.
[2]谢季坚,刘承平.模糊数学方法及其应用(第三版)[M].武汉:华中科技大学出版社,2006.
[3]颜刚.基于模糊马尔可夫场的图像算法研究[D].广州:南方医科大学,2005.
[4]胡宝清.模糊理论基础[M].武汉:武汉大学出版社,2004.
[5]Kanel,M.S,Selim,S.Z.,New algorithms for solving the fuzzy clustering problem[J],Pattern Recognition,1994,27(3):421-428.
[6]Zhu C,Jiang T.Multi-context fuzzy clustering for separation of brain tissues in MR images[J],NeuroImage,2003,18(3):685-696.
[7]Carvalho BM,Gau C J,Herman GT,et al.Algorithms for fuzzy segmentation[J].Pattern Analysis & Applications,1999,2(1):73-81.
[8]Karmakar GC,Dooley LS.A generic fuzzy rule based image segmentation algorithm[J].Pattern Recognition Letters 2002,23(10):1215-1227.
[9]Pham DL,Prince JL.Adaptive fuzzy segmentation of magenetic resonace images[J].IEEE Trans.on Medical Imaging,1999,18(9):737-752.
[10]Prewer D,Kitchen LJ.Soft image segmentation by weighted linked pyramid[J].Pattern Recognition Letters,2001,22(2):123-132.
[11]Bezdek JC,Pal SK.Fuzzy models for pattern recognition[M].Piscataway,NJ:IEEE Press,1999.
[12]Bezdek J,Hall L,Clarke L.Review of MR image segmentation techniques using pattern recognition[J].Medical Physics,1993,20:1033-1048.
[13]边肇祺,张学工等.模式识别[M].清华大学出版社.1999.
[14]R.Krishnapuram,J.M Keller.A possibilistic approach to clustering[J].IEEE Trans.Fuzzy Systems,1993:98-110.
[15]Barni M,Cappellini V,Mecocci A.Comments on‘A possibilistic approach to clustering'[J].IEEE Trans.on Fuzzy Systems,1996,4(3):393-396.
[16]D.L.Pham.Spatial models for fuzzy clustering[J].Comput.Vis.Imag.Understand.2001,84,285-297.
[17]M.N.Ahmed,S.M.Yamany,N.Mohamed,A.A.Farag,and T.Moriarty.A modified fuzzyc-menas algorithm for bias field estimation and segmentation of MRI data[J].IEEE Trans.Med.Imag,2002,21(3):193-199.
[18]D.L.Pham and J.L.Prince.Adaptive fuzzy segmentation of magnetic resonance images[J].IEEE Trans.Med.Imag.1999,18(9):737-752.
[19]Lei Jiang,Wenhui Yang.A Modified Fuzzy C-Means Algorithm for Segmentation of Magnetic Resonance Images[C].Proceedings Ⅶ Digital Image Computing:Techniques and Applications(DICTA'03):225-231.
[20]Zhang D Q,Chen S C.Kernel based fuzzy and possibilistic c-means clustering [J].Accepted by the International Conference on Artificial Neural Network (ICANN'03),Istanbul,Turkey,June,2003
[21]Zhang D Q,Chen S C.Kernel-based fuzzy clustering incorporating spatial constraints for image segmentation[C].Proceedings of the Second International Conference on Machine Learning and Cybernetic,Xi'an,2-5 November 2003.
[22]Zhang D Q,Chen S C.A novel kernelized fuzzy c-means algorithm with application in medical image segmentation [J].Artif.Intell.2004,32,37-52,
[1]田捷,韩博闻,王岩,罗希平.模糊C-均值聚类法在医学图像分析中的应用[J],软件学报,2001,12(11):1623-1629.
[2]D.Q.Zhang and S.C.Chen.A novel kernelized fuzzy c-means algorithm and segmentation of MRI data[J],Artif.Intell.Med.,2004,(32):37-52.
[3]D.L.Pham,J.L Prince.Adaptive fuzzy segmentation of magnetic resonance images[J],IEEE Trans.Med.Im..,1999,18(9):737-752.
[4]Dzung L.Pham.Spatial models for fuzzy clustering[J],Computer Vision and Image Understand.,2001,84:285-297.
[5]Mohamed N.Ahmed.A modified fuzzy c-means algorithm for bias field estimation and segmentation of MRI data[J],IEEE Trans.Med.Im.,2002,21(3):193-199.
[6]Alan Wee-Chung Liew,Hong Yan.An adaptive spatial fuzzy clustering algorithm for 3-D MR image segmentation[J],IEEE Trans.Med.Im.,2003,22(9):1063-1075.
[7]Shan shen,William Sandharm.MRI fuzzy segmentation of brain tissue using neighborhood attraction with nueral-network optimization[J].IEEE,Transaction on information technology in biomedicine.2005,9(3):459-467.
[8]Keh-shih Chuang,Hong-Long Tzeng.Fuzzy c-means clustering with spatial information for image segmentation[J].Computerized medical imaging and graphic 2006:9-15.
[9]SONG Xue Feng,WEI Xiao Ping.Operations research[M].NangJing:Southeast University Press.2003:108-123.(in Chinese)
[10]Brain Web[online].Available:www.bic.mni.megill.ca/brainweb/
[1]王爱民,沈兰荪.图像分割研究综述[J].测控技术,2000,19(5):1-16
[1]J.C.Bezek.Pattem recognition with fuzzy object function algorithms[M].New York:Plenum.1981.
[2]张莉,周伟达,焦李成.核聚类算法[J].计算机学报,2002,25(6):587-590
[3]林亚忠,程跃斌,陈武凡.基于修正的分段模糊吉伯斯随机场模型的图像分割[J].计算机应用,2005,(11)
[4]D.Q.Zhang and S.C.Chen.Kernel-based fuzzy clustering incorporating spatial constraints for image segmentation[C].In:Proceedings of the Second International Conference on Machine Learning and Cybernetics,Xi'an,2-5November 2003
[5]D.L.Pham.Spatial models for fuzzy clustering[J].Comput.Vis.Imag.Understand.,2001,84:285-297.
[6]Mohamed N.Ahmed.A modified fuzzy c-means algorithm for bias field estimation and segmentation of MRI data[J].IEEE Trans.Med.Im.,2002,21(3):193-199.
[7]Alan Wee-Chung Liew,Hong Yan.An adaptive spatial fuzzy clustering algorithm for 3-D MR image segmentation[J].IEEE Trans.Med.Im.,2003,22(9):1063-1075.
[8]D.Q.Zhang and S.C.Chen.A novel kernelized fuzzy c-means algorithm and segmentation of MRI data[J].Artif.Intell.Med.,2004,32:37-52.
[9]Keh-Shih Chuang,Hong-Long Tzeng,Sharon Chen,Jay Wu,Tzong-Jer Chen,Fuzzyc-meansclusteringwithspatialinformationforimagesegmentation[J].Computerized Medical Imaging and Graphics,2006,30:9-15
[10]冯前进 陈武凡,模糊马尔可夫场模型与图像分割新算法[J].南方医科大学学报,2006,26(5):579-583
[1]雷建明,黎朝茂,江先娣,廖耿.多发性硬化症36例临床分析[J].河北医学,2007,13(3):279-281.
[2]胡学强 麦卫华 王敦敬.多发性硬化症413例患者的临床表现特点[J],中华神经科杂志,2004,37(1):66-69.
[3]李宏增,魏龙晓.对多发性硬化症磁共振诊断标准的再认识[J].西南国防医学,2006,16(3).
[4]Ardizzone E,Pirrone R,Gambino O,et al.Two channels fuzzy C-means detection of multiple sclerosis lesions in multispectral MR images[C],IEEE ICIP,2002.
[5]AO B,Dehak SM,Zhu YM,et al.Automated segmentation of multiple sclerosis lesions in multispectral MR imageing using fuzzy clustering[J],Computers in Biology and Medicine,2000;30(1):23.
[6]Pachai C,Zhu YM,Grimaud J,et al.A pyramidal approach for automatic segmentation of multiple sclerosis lesions in brain MRI[J].Computerized Medical Imaging and Graphics,1998;22(5):399.
[7]Li L,Li X,Lu H,et al.MRI volumetric analysis of multiple sclerosis:methodology and validation[J],IEEE Trans.on Nuclear Science,2003;50(5): 1686.
[8]Leemput KV,Maes F,Vandermeulen D,et al.Automated segmentation of multiple sclerosis lesions by model outlier detection[J],IEEE Trans.on Medical Imaging,2001;20(8):677.
[9]J.C.Bezek.Pattern recognition with fuzzy object function algorithms[M].New York:Plenum,1981.
[10]余学飞,李彬,陈武凡,基于模糊核聚类的MR图像分割新算法[J],南方医科大学学报,2008,28(4):555-557
[11]D.Q.Zhang and S.C.Chen.A novel kernelized fuzzy c-means algorithm and segmentation of MRI data[J].Artif.Intell.Med.,2004,32:37-52.
[12]Keh-Shih Chuang,Hong-Long Tzeng,Sharon Chen,Jay Wu,Tzong-Jer Chen Fuzzyc-means clustering with spatial information for image segmentation[J].Computerized Medical Imaging and Graphics,2006,30:9-15
[1]Moseley ME,Cohen Y,Mintrovitch J,et al,Early detection of regional cerebral ischemia in cats:comparison of diffusion-and T2-weighted MRI and spectroscopy.Magn Reson Med,1990,14:330-346.
[2]Susumu Mori and Peter B.Barker.Diffusion magnetic resonance imaging:Its principle and applications.The Anatomical Record,1999,257(3):102-109.
[3]谢静霞.核磁共振新技术研究与临床应用[M].北京:北京医科大学出版社,2001.
[4]Celeux G,Forbes F,Peyrard N.EM procedures using mean field-like approximations for Markov model-based image segmentation[J].Pattern Recognition,2003,36(1):131-144.
[5]Z.Wange and B.C Vemuri.An affine invariant tensor dissimilarity measure and its application to tensor-valued image segmentation.In IEEE Conference on Computer Vision and Pattern Recognition,Washington,DC.,June 2004.
[6]G.K.Rohde et al.Comprehensive approach for correction of motion and distortion in diffusion-weighted MRI.Magn Reson Med,2004,51(1):103-114,.
[7]Sotak CH.The role of diffusion tensor imaging in the evaluation of ischemic brain injury.NMR Biomed,2002,15:561-569.
[8]Alexander AL,Hasan K,Kindlmann G,et al.A geometric analysis of diffusion tensor measurements of the human brain.Magn Reson Med,2000,44:283-291.
[9]D.H.Ballard and CM.Brown.Computer vision.Prentice-Hall, Inc.Englewood Cliffs,New Jersey,1982.
[10]Basser PJ,Pajevic S,Pierpaoli C,et al.In vivo tractography using DT-MRI data.Magn Reson Med,2000,44:625-632.
[11]Zhang S,Demiralp C,Laidlaw DH.Visualizing diffusion tensor MR images using streamtubes and streamsurfaces.IEEE Transactions on Visualization and Computer Graphics,2003,9(4):454-462.
[12]Zhang Y,Brady M,Smith S.Segmentation of brain images through a hidden Markov random field model and the expectation-maximization algorithm [J].IEEE Trans,on Medical Imaging,2001,20(1):45-57.
[13]Wyatt PP,Noble JA.MAP MRF joint segmentation and registration of medical images[J].Medical Image Analysis [J],2003,7(4):539-552.
[14]Wang Y,Adali T,Xuan J,et al.Magnetic resonance image analysis by information theoretic criteria and stochastic site models [J].IEEE Trans,on Information Technology in Biomedicine,2001,5(2):150-158.
[15]Yang F,Jiang T.Pixon-based image segmentation with Markov random fields[J].IEEE Trans,on Image Processing,2003,12(12):1552-1559.
[16]L.C.GRogers.D.Williams.Diffusions,Markov processes and Martingales(Volumn 1)[M].Beijing:World Publishing Company,2003.
[2]宋枭禹,包尚联.医学的诺贝尔奖授予两位MRI物理学家所带来的思考[J].世界医疗器械,2004,10(1):16-17.
[3]Moseley ME,Cohen Y,Mintrovitch J,et al,Early detection of regional cerebral ischemia in cats:comparison of diffusion-and T2-weighted MRI and spectroscopy.Magn Reson Med,1990,14:330-346.
[4]Moseley ME,Kucharczyk J,Mintrovitch J,Cohen Y,Kuhanewicz J,Derugin N,Asgari H,Norman D.Diffusion-weighted MR imaging of acute stroke:Correlation with T2-weighted and magnetic susceptibility-enhanced MR imaging in cats.AJNR,1990,11:423-429.
[5]谢静霞.核磁共振新技术研究与临床应用[M].北京:北京医科大学出版社,2001.
[6]Basser PJ,Mattiello J,and LeBihan D.MR diffusion tensor spectroscopy and imaging.Biophysical Journal,1994,66(1):259-267.
[7]章毓晋.图象分割[M].北京:科学出版社,2001.
[8]罗述谦,周果宏.医学图象处理与分析[M].北京:科学出版社,2003.
[9]Pham DL,Xu C,Prince JL.A survey of current methods in medical image segmentation[J].Annual Review of Biomedical Engineering,2000,2,315-337.
[10]Liew,Alan WC,Yan H.Current methods in the automatic tissue segmentation of 3D magnetic resonance brain images[J],Current Medical Imaging Reviews.2006,2(1):91-103.
[11]颜刚.基于模糊马尔可夫场的图像算法研究[D].广州:南方医科大学,2005.
[12]赵荣椿,迟耀斌,朱重光.图像分割技术进展[J].中国体视学和图像分析,1998,3(2):121-128.
[13]赵志峰,张尤赛.医学图像分割综述[J].华东船舶工业学院学报,2003,17(3):43-48.
[14]聂斌.医学图像分割技术及其进展[J].泰山医学院学报,2002,23(4):422-426.
[15]Bezdek J,Hall L,Clarke L.Review of MR image segmentation techniques using pattern recognition[J].Medical Physics,1993;20:1033-1048.
[16]Clarke LP,Velthuizen RP.MRI segmentation:methods and applications[J].Magnetic Resonance Imaging.1995,13(3):343-368.
[17]李璟,朱善安,He B.医学图像分割技术[J].生物医学工程学杂志,2006,23(4):891-894.
[18]Goshtasby A,Turner DA.Segmentation of cardiac cine MR images for extraction of right and left ventricular chamber[J].IEEE Trans.On Medical Imaging,1995,14(1):56-64.
[19]Thedens DR,Skorton DJ,Fleagle SR.Methods of graph searching for border detection in image sequences with applications to cardiac magnetic resonance imaging[J].IEEE Trans.On Medical Imaging,1995,14(1):42-55.
[20]Canny J.A computational approach to edge detection[J].IEEE Trans.On Pattern Analysis and Machine Intelligence,1986,8(6):679-698.
[21]Deng W,Iyengar SS.A new probabilistic relaxation scheme and its application to edge detection[J].IEEE Trans.On Pattern Analysis and machine Intelligence,1996,18(4):432-437.
[22]Qian RJ,Huang TS.Optimal edge detection in two-dimensional images[J].IEEE Trans.On Image Processing,1996,5(7):1215-1220.
[23]付宜利,高文朋,王树国.颅脑磁共振图像分割评价的统计学方法[J].医学影像学杂志,2005,15(8):644-647.
[24]Bansal R,Staib LH,Chen Z,et al.Entropy-based,multipleportal-to-3D CT registration for prostate radiotherapy using iteratively estimated segmentation[A].In:Proceedings of Medical Image Computing and Computer-Assisted Intervention[C],Cambridge,UK,1999:567-578.
[25]Sahoo P,Wilkins C,Ueager J.Threshold selection using Rrenyi's entropy[J].Pattern Recognition,1997,30(1):71-84.
[26]M.Singh,P.Patel,D.Khosla,and T.Kim,Segmentation of functional MRI by K-means clustering [J],IEEE Trans.Nucl.Sci.,1996,43(6):2030-2036.
[27]Mohamed NA,Sameh MY,Nevin M.A modified fuzzy C-means algorithm for bias field estimation and segmentation of MRI data [J].IEEE Trans.On Medical Imaging,21(3),2002:193-199.
[28]Liew AW,Yan H,An adaptive spatial fuzzy clustering algorithm for 3-D MR image segmentation [J],IEEE Trans.On Medical Imaging,2003,22(9):1063-1075.
[29]Zhao YQ,Li ML.A modified fuzzy C-Means algorithm for segmentation of MRI[C].Proceedings of the 5th ICCIMA'03,2003.
[30]Nie SD,Chen Y,Gu SD,et al.The study of fast fuzzy clustering segmentation algorithm of head MRI [J].Chinese Journal of Biomedical Engineering,2001,20(2):104-109.
[31]M.Wiegell,D.Tuch,H.Larson,and V.Wedeen.Automatic Segmentation of Tha-lamic Nuclei from Diffusion Tensor Magnetic Resonance Imaging.NeuroImage,2003,19:391- 402.
[32]J.Weickert.Diffusion and Regularization Methods for Tensor-valued Images.In First SIAM-EMS Conf Appl Math,in Our Changing World,2001.
[33]C.Chefd'hotel,O.Faugeras,D.Tschumperl?,and R.Deriche.Constrained flows of matrix-valued functions:application to diffusion tensor regularization.In ECCV,2002,pages251-265.
[34]C.Alexander,C.Gee,and R.Bajcsy.Similarity Measure for Matching Diffusion Tensor images.In British Machine Vision Conference,1999,pages 93-102.
[35]Wan S Y,William H.Symmetric region growing [J].IEEE Trans,on Image Processing,2003,12(9):1007-1015.
[36]Rosenfeld A.Fuzzy digital topology [J].Inform & Control,1979,40:76-87.
[37]Rosenfeld A.On connectivity properties of grayscale pictures [J].Pattern Recognition,1983,16(l):47-50.
[38]J.K.Udupa,S.Samarasekera.Fuzzy connectedness and object definition:theory,algorithms,and applications in image segmentation [J].Graphical model and Image processing,1996,58(3):246-261.
[39]J.K.Udupa.Fuzzy connectedness and image segmentation [J].Proceedings of the IEEE,2003,91(10):1649-1669.
[40]Yang FG,Tianzi Jiang TZ,Pixon-based image segmentation with Markov random fields[J],IEEE Trans,on Image Processing,2003,12(12):1552-1559.
[41]Geman S,Geman D.Stochatic relaxation,Gibbs distributions,and the bayesian restoration of images [J].IEEE Trans.On Pattern Analysis and Machine Intelligence,1984,6(6),721-741.
[42]Zhang Y,Brady M,Smith S.Segmentation of brain images through a hidden Markov random field model and the expectation-maximization algorithm [J].IEEE Trans.On Medical Imaging,2001,20(1):45-57.
[43]Li SZ.Markov random field modeling in image analysis [M].Springer-Verlag,2001.
[44]Lakshmanan S,Derin H.Simultaneous parameter estimation and segmentation of Gibbs random fields using simulated annealing [J].IEEE Trans.On Pattern Analysis and machine Intelligence,1989,121(8):799-813.
[45]Melas DE,Wilson SP.Double Markov random fields and bayesian image segmentation [J].IEEE Trans.On Signal Process,2002,50(2):357-365.
[46]Kass M,Witkin A,Terzopoulos D.Snakes:active contour models[C].In:Proc of First Int Confon Computer Vision.London,1987.259-269.
[47]Osher S,Sethian JA.Fronts propagating with curvature-dependent speed:algorithms based on Hamilton- Jacobi formulations [J].Journal of Computarional Physics,79(1),1988:12:49.
[48]Wang Z,Vemuri BC.DTI segmentation using an information theoretic tensor dissimilarity measure[J].IEEE Trans.On Medical Imaging,2005,24(10):1267-1277.
[49]陈强,周则明,王平安等.带标记线左心室MR图像的自动分割[J],中国图形图像学报,2004,9(6):666-673.
[50]Zhukov L,Museth K,Breen D,et al.Level set modeling and segmentation of.DT-MRI brain data[J],Journal of Electronic Imaging,2003,12(1):125-133.
[51]Wang Z,Vemuri BC.DTI segmentation using an information theoretic tensor dissimilarity measure[J].IEEE Trans.On Medical Imaging,2005,24(10):1267-1277.
[52]孙优贤,卢建刚,许锋.神经网络在图像处理中的应用[J],信息与控制,2003,32(4):344-350.
[53]Ahmed MN,Farag AA.Two-stage neural network for volume segmentation of medical images[J].Proceedings of IEEE International Conference On Neural Networks,1997(3):1373-1377.
[54]Chen CT.Medical image segmentation by a constraint satisfaction neural network[J].IEEE Trans.On Nuclear Science,1991,38(2):678-686.
[55]Cheng KS.The application of competitive Hopfield neural network to medical image segmentation[J].IEEE Trans.On Medical Imaging,1996(15):560-567.
[56]Mallat S.A theory for multiresolution signal decomposition:the wavelet representation[J].IEEE Trans.On Pattern Analysis and machine Intelligence,1989,11(7):647-693.
[57]Laine A,Fna J.Texture classification by wavelet packet signatures[J].IEEE Trans.On Pattern Analysis and machine Intelligence,1993,15(11):1186-1191.
[58]Chun DN,Yang HS.Robust image segmentation using genetic algorithm with a fuzzy measure [J].Pattern Recognition,1996,29(7):1195-1211.
[59]Bram VG,Alejandro FF,Joes JS,et al.Active shape model segmentation with optimal features [J].IEEE Trans.On Medical Imaging,21(8):924-933.
[60]Vincent L,Soille P.Watersheds in digital spaces:an efficient algorithm based on immersion simulations [J].IEEE Trans.On Pattern Analysis and machine Intelligence,1991,13(6):583-598.
[61]Udupa JK,Leblanc VR,Zhu Y,et al.A framwork for evaluating imagesegmentation algorithms [J].Computerized Medical Imaging and Graphics,2006,30(l):75-87.
[62]Zhang YJ.A survey on evaluation methods for image segmentation [J].Pattern Recognition,1996,29(8):1335-1346.
[1]Zadeh LA.Fuzzy sets[J].Information Control,1965(8):338-353.
[2]谢季坚,刘承平.模糊数学方法及其应用(第三版)[M].武汉:华中科技大学出版社,2006.
[3]颜刚.基于模糊马尔可夫场的图像算法研究[D].广州:南方医科大学,2005.
[4]胡宝清.模糊理论基础[M].武汉:武汉大学出版社,2004.
[5]Kanel,M.S,Selim,S.Z.,New algorithms for solving the fuzzy clustering problem[J],Pattern Recognition,1994,27(3):421-428.
[6]Zhu C,Jiang T.Multi-context fuzzy clustering for separation of brain tissues in MR images[J],NeuroImage,2003,18(3):685-696.
[7]Carvalho BM,Gau C J,Herman GT,et al.Algorithms for fuzzy segmentation[J].Pattern Analysis & Applications,1999,2(1):73-81.
[8]Karmakar GC,Dooley LS.A generic fuzzy rule based image segmentation algorithm[J].Pattern Recognition Letters 2002,23(10):1215-1227.
[9]Pham DL,Prince JL.Adaptive fuzzy segmentation of magenetic resonace images[J].IEEE Trans.on Medical Imaging,1999,18(9):737-752.
[10]Prewer D,Kitchen LJ.Soft image segmentation by weighted linked pyramid[J].Pattern Recognition Letters,2001,22(2):123-132.
[11]Bezdek JC,Pal SK.Fuzzy models for pattern recognition[M].Piscataway,NJ:IEEE Press,1999.
[12]Bezdek J,Hall L,Clarke L.Review of MR image segmentation techniques using pattern recognition[J].Medical Physics,1993,20:1033-1048.
[13]边肇祺,张学工等.模式识别[M].清华大学出版社.1999.
[14]R.Krishnapuram,J.M Keller.A possibilistic approach to clustering[J].IEEE Trans.Fuzzy Systems,1993:98-110.
[15]Barni M,Cappellini V,Mecocci A.Comments on‘A possibilistic approach to clustering'[J].IEEE Trans.on Fuzzy Systems,1996,4(3):393-396.
[16]D.L.Pham.Spatial models for fuzzy clustering[J].Comput.Vis.Imag.Understand.2001,84,285-297.
[17]M.N.Ahmed,S.M.Yamany,N.Mohamed,A.A.Farag,and T.Moriarty.A modified fuzzyc-menas algorithm for bias field estimation and segmentation of MRI data[J].IEEE Trans.Med.Imag,2002,21(3):193-199.
[18]D.L.Pham and J.L.Prince.Adaptive fuzzy segmentation of magnetic resonance images[J].IEEE Trans.Med.Imag.1999,18(9):737-752.
[19]Lei Jiang,Wenhui Yang.A Modified Fuzzy C-Means Algorithm for Segmentation of Magnetic Resonance Images[C].Proceedings Ⅶ Digital Image Computing:Techniques and Applications(DICTA'03):225-231.
[20]Zhang D Q,Chen S C.Kernel based fuzzy and possibilistic c-means clustering [J].Accepted by the International Conference on Artificial Neural Network (ICANN'03),Istanbul,Turkey,June,2003
[21]Zhang D Q,Chen S C.Kernel-based fuzzy clustering incorporating spatial constraints for image segmentation[C].Proceedings of the Second International Conference on Machine Learning and Cybernetic,Xi'an,2-5 November 2003.
[22]Zhang D Q,Chen S C.A novel kernelized fuzzy c-means algorithm with application in medical image segmentation [J].Artif.Intell.2004,32,37-52,
[1]田捷,韩博闻,王岩,罗希平.模糊C-均值聚类法在医学图像分析中的应用[J],软件学报,2001,12(11):1623-1629.
[2]D.Q.Zhang and S.C.Chen.A novel kernelized fuzzy c-means algorithm and segmentation of MRI data[J],Artif.Intell.Med.,2004,(32):37-52.
[3]D.L.Pham,J.L Prince.Adaptive fuzzy segmentation of magnetic resonance images[J],IEEE Trans.Med.Im..,1999,18(9):737-752.
[4]Dzung L.Pham.Spatial models for fuzzy clustering[J],Computer Vision and Image Understand.,2001,84:285-297.
[5]Mohamed N.Ahmed.A modified fuzzy c-means algorithm for bias field estimation and segmentation of MRI data[J],IEEE Trans.Med.Im.,2002,21(3):193-199.
[6]Alan Wee-Chung Liew,Hong Yan.An adaptive spatial fuzzy clustering algorithm for 3-D MR image segmentation[J],IEEE Trans.Med.Im.,2003,22(9):1063-1075.
[7]Shan shen,William Sandharm.MRI fuzzy segmentation of brain tissue using neighborhood attraction with nueral-network optimization[J].IEEE,Transaction on information technology in biomedicine.2005,9(3):459-467.
[8]Keh-shih Chuang,Hong-Long Tzeng.Fuzzy c-means clustering with spatial information for image segmentation[J].Computerized medical imaging and graphic 2006:9-15.
[9]SONG Xue Feng,WEI Xiao Ping.Operations research[M].NangJing:Southeast University Press.2003:108-123.(in Chinese)
[10]Brain Web[online].Available:www.bic.mni.megill.ca/brainweb/
[1]王爱民,沈兰荪.图像分割研究综述[J].测控技术,2000,19(5):1-16
[1]J.C.Bezek.Pattem recognition with fuzzy object function algorithms[M].New York:Plenum.1981.
[2]张莉,周伟达,焦李成.核聚类算法[J].计算机学报,2002,25(6):587-590
[3]林亚忠,程跃斌,陈武凡.基于修正的分段模糊吉伯斯随机场模型的图像分割[J].计算机应用,2005,(11)
[4]D.Q.Zhang and S.C.Chen.Kernel-based fuzzy clustering incorporating spatial constraints for image segmentation[C].In:Proceedings of the Second International Conference on Machine Learning and Cybernetics,Xi'an,2-5November 2003
[5]D.L.Pham.Spatial models for fuzzy clustering[J].Comput.Vis.Imag.Understand.,2001,84:285-297.
[6]Mohamed N.Ahmed.A modified fuzzy c-means algorithm for bias field estimation and segmentation of MRI data[J].IEEE Trans.Med.Im.,2002,21(3):193-199.
[7]Alan Wee-Chung Liew,Hong Yan.An adaptive spatial fuzzy clustering algorithm for 3-D MR image segmentation[J].IEEE Trans.Med.Im.,2003,22(9):1063-1075.
[8]D.Q.Zhang and S.C.Chen.A novel kernelized fuzzy c-means algorithm and segmentation of MRI data[J].Artif.Intell.Med.,2004,32:37-52.
[9]Keh-Shih Chuang,Hong-Long Tzeng,Sharon Chen,Jay Wu,Tzong-Jer Chen,Fuzzyc-meansclusteringwithspatialinformationforimagesegmentation[J].Computerized Medical Imaging and Graphics,2006,30:9-15
[10]冯前进 陈武凡,模糊马尔可夫场模型与图像分割新算法[J].南方医科大学学报,2006,26(5):579-583
[1]雷建明,黎朝茂,江先娣,廖耿.多发性硬化症36例临床分析[J].河北医学,2007,13(3):279-281.
[2]胡学强 麦卫华 王敦敬.多发性硬化症413例患者的临床表现特点[J],中华神经科杂志,2004,37(1):66-69.
[3]李宏增,魏龙晓.对多发性硬化症磁共振诊断标准的再认识[J].西南国防医学,2006,16(3).
[4]Ardizzone E,Pirrone R,Gambino O,et al.Two channels fuzzy C-means detection of multiple sclerosis lesions in multispectral MR images[C],IEEE ICIP,2002.
[5]AO B,Dehak SM,Zhu YM,et al.Automated segmentation of multiple sclerosis lesions in multispectral MR imageing using fuzzy clustering[J],Computers in Biology and Medicine,2000;30(1):23.
[6]Pachai C,Zhu YM,Grimaud J,et al.A pyramidal approach for automatic segmentation of multiple sclerosis lesions in brain MRI[J].Computerized Medical Imaging and Graphics,1998;22(5):399.
[7]Li L,Li X,Lu H,et al.MRI volumetric analysis of multiple sclerosis:methodology and validation[J],IEEE Trans.on Nuclear Science,2003;50(5): 1686.
[8]Leemput KV,Maes F,Vandermeulen D,et al.Automated segmentation of multiple sclerosis lesions by model outlier detection[J],IEEE Trans.on Medical Imaging,2001;20(8):677.
[9]J.C.Bezek.Pattern recognition with fuzzy object function algorithms[M].New York:Plenum,1981.
[10]余学飞,李彬,陈武凡,基于模糊核聚类的MR图像分割新算法[J],南方医科大学学报,2008,28(4):555-557
[11]D.Q.Zhang and S.C.Chen.A novel kernelized fuzzy c-means algorithm and segmentation of MRI data[J].Artif.Intell.Med.,2004,32:37-52.
[12]Keh-Shih Chuang,Hong-Long Tzeng,Sharon Chen,Jay Wu,Tzong-Jer Chen Fuzzyc-means clustering with spatial information for image segmentation[J].Computerized Medical Imaging and Graphics,2006,30:9-15
[1]Moseley ME,Cohen Y,Mintrovitch J,et al,Early detection of regional cerebral ischemia in cats:comparison of diffusion-and T2-weighted MRI and spectroscopy.Magn Reson Med,1990,14:330-346.
[2]Susumu Mori and Peter B.Barker.Diffusion magnetic resonance imaging:Its principle and applications.The Anatomical Record,1999,257(3):102-109.
[3]谢静霞.核磁共振新技术研究与临床应用[M].北京:北京医科大学出版社,2001.
[4]Celeux G,Forbes F,Peyrard N.EM procedures using mean field-like approximations for Markov model-based image segmentation[J].Pattern Recognition,2003,36(1):131-144.
[5]Z.Wange and B.C Vemuri.An affine invariant tensor dissimilarity measure and its application to tensor-valued image segmentation.In IEEE Conference on Computer Vision and Pattern Recognition,Washington,DC.,June 2004.
[6]G.K.Rohde et al.Comprehensive approach for correction of motion and distortion in diffusion-weighted MRI.Magn Reson Med,2004,51(1):103-114,.
[7]Sotak CH.The role of diffusion tensor imaging in the evaluation of ischemic brain injury.NMR Biomed,2002,15:561-569.
[8]Alexander AL,Hasan K,Kindlmann G,et al.A geometric analysis of diffusion tensor measurements of the human brain.Magn Reson Med,2000,44:283-291.
[9]D.H.Ballard and CM.Brown.Computer vision.Prentice-Hall, Inc.Englewood Cliffs,New Jersey,1982.
[10]Basser PJ,Pajevic S,Pierpaoli C,et al.In vivo tractography using DT-MRI data.Magn Reson Med,2000,44:625-632.
[11]Zhang S,Demiralp C,Laidlaw DH.Visualizing diffusion tensor MR images using streamtubes and streamsurfaces.IEEE Transactions on Visualization and Computer Graphics,2003,9(4):454-462.
[12]Zhang Y,Brady M,Smith S.Segmentation of brain images through a hidden Markov random field model and the expectation-maximization algorithm [J].IEEE Trans,on Medical Imaging,2001,20(1):45-57.
[13]Wyatt PP,Noble JA.MAP MRF joint segmentation and registration of medical images[J].Medical Image Analysis [J],2003,7(4):539-552.
[14]Wang Y,Adali T,Xuan J,et al.Magnetic resonance image analysis by information theoretic criteria and stochastic site models [J].IEEE Trans,on Information Technology in Biomedicine,2001,5(2):150-158.
[15]Yang F,Jiang T.Pixon-based image segmentation with Markov random fields[J].IEEE Trans,on Image Processing,2003,12(12):1552-1559.
[16]L.C.GRogers.D.Williams.Diffusions,Markov processes and Martingales(Volumn 1)[M].Beijing:World Publishing Company,2003.