基于模糊随机模型的磁共振脑部图像分割算法研究
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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。
基于马尔可夫场(MRF)模型的图像分割算法，是一类重要的图像分割算法。该类算法利用了图像空间的相关信息作为先验知识，运用Gibbs场和最大后验概率(MAP)实现图像分割，能够有效地对迭加了噪声的低信噪比图像进行分割。但基于MRF模型的分割算法也存在一些问题，例如不能有效地处理图像的模糊性、存在过分割现象、参数估计困难等。
本文深入研究了基于模糊理论和基于MRF模型的图像分割算法，主要取得下列成果：(1)针对FCM算法存在的问题，提出了一种能够合理利用空间信息的改进的FCM算法；(2)将模糊理论和MRF结合，提出了一种模糊MRF模型，并对模型的建立、参数估计和优化方法进行了深入的研究；(3)研究了多发性硬化症病灶的分割算法，分别提出了一种基于模糊连接度和一种基于MRF模型的多发性硬化症病灶的分割算法；(4)研究了基于非齐次MRF模型的图像分割算法，并提出了一种用模糊连接度对非齐次MRF进行参数估计的方法。这些方法在提高图像分割的精度和鲁棒性等方面具有显著的效果。
第二章根据MR脑部图像真实的灰度值具有分片常数的特性，按照合理利用图像空间信息的原则，提出了一种基于隶属度光滑约束的FCM聚类算法。在传统FCM的目标函数中增加了使隶属度趋向于分片光滑的约束项，提出了新的目标函数，得到了新的数学规划问题，并运用Lagrange乘数法，得到了该规划问题的解。以此提出了一种FCM聚类算法的改进算法。通过对模拟和临床MR脑部图像的分割实验，表明该算法在分割被噪声污染的图像时，比传统的FCM算法及其改进算法等多种图像分割算法具有更精确的图像分割能力，并且运算简单、运算速度快、稳健性好。
第三章分析了基于模糊理论和基于MRF模型的图像分割算法各自的优势和存在的问题。在传统MRF模型的基础上，引入模糊概念，建立了一种模糊MRF模型，并运用MAP方法将图像的分割问题转化为一个数学规划问题。通过对该规划问题的求解，得到了图像像素对不同组织的隶属度计算方法，提出了一种高效、无监督的图像分割算法，从而实现了对MR脑部图像的精确分割。通过对模拟MR脑部图像和临床MR脑部图像分割实验，表明该基于模糊MRF模型的图像分割新算法比基于传统MRF模型的图像分割算法和模糊C-均值等图像分割算法能够更精确地分割图像。
第四章和第五章研究了多发性硬化症病灶的分割方法。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。
第四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，提出了一种基于模糊连接度的多发性硬化症病灶的分割算法。模糊连接度用模糊关系描述了图像中两个像素之间的关联程度。通过选取种子像素，运用像素间的模糊连接度进行增长区域，能够实现对病灶的分割。但基于模糊连接度的分割算法需要人工选择种子点，这样就制约了该方法的应用。本章提出了一种实现种子像素自动选取的方法，实现了多发性硬化症病灶的自动分割。作为多发性硬化症病灶分割的预处理，针对FLAIR MR脑部图像的特征，还巧妙地提出了一种基于区域增长方法的脑部组织提取算法，能够自动地去除头骨、头皮等非脑部组织。通过对临床患者FLAIR MR图像的分割实验，表明该分割算法能够比较准确地分割多发性硬化症病灶，其分割效果明显好于FCM聚类算法和基于MRF的分割算法。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。
第五章提出了一种基于MRF模型，利用了多发性硬化症形态学特性的多发性硬化症病灶的分割算法。首先运用基于MRF模型的分割算法和区域增长法，分割出脑白质所包围的区域。然后对脑白质所包围的区域再次分割，就实现了对MR脑部图像的多发性硬化症病灶分割。通过对多发性硬化症模拟和临床T_2加权MR脑部图像的分割实验，表明该算法能够比较准确地分割多发性硬化症病灶，并且具有稳健性好等优点，能够应用于多发性硬化症的临床辅助诊断。
第六章提出了一种基于非齐次MRF的图像分割算法，并运用模糊空间元素的模糊连接度模型，估计非齐次MRF中控制像素对空间信息依赖程度的参数，改进了传统的基于MRF模型的图像分割算法。在传统的基于MRF模型的图像分割算法中，总是假设对应的MRF具有齐次性，即像素对空间信息的依赖程度与其空间位置无关。由于图像中不同位置的像素对空间信息的依赖程度是不同，因此，运用非齐次MRF来描述图像会更合理。通过对模拟MR脑部图像和临床MR脑部图像分割实验，表明该算法比传统的基于齐次MRF模型的图像分割算法和FCM聚类算法等图像分割算法有更精确的图像分割能力。
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.
The Markov random field (MRF) segmentation has been successfully applied to this issue in the presence of noise by taking into account a priori knowledge of the spatial correlations of the image using Gibbs distribution and maximum a posteriori (MAP). However, there are still problems associated with MRF, such as the difficulty in dealing with fuzzy characteristics of images, parameter estimation, and the tendency of over-segmentation.
In this paper, we look into the segmentation algorithms based on fuzzy set and MRF, and the main contributions to which are as follows: 1) a modified FCM clustering algorithm is proposed to improve the segmentation accuracy of FCM; 2) a Fuzzy Markov random field (FMRF) model is introduced by combining fuzzy set and MRF, and the modeling, parameter estimate, optimization methods and algorithm about FMRF are studied; 3) a fuzzy connectedness-based segmentation method of multiple sclerosis (MS) lesions and a MRF-based segmentation method of MS lesions are developed; 4) inhomogeneous MRF (IMRF) model is studied and the parameter in IMRF is estimated using fuzzy connectedness. The performance of these algorithms is remarkably superior to the conventional ones in terms of accuracy and robustness.
In chapterⅡ, we present a modified FCM clustering algorithm for brain image segmentation with a membership smoothing constraint (MC-FCM). The rationale of which is that in general an ideal MR image is assumed to be piecewise constant, a membership smoothing constraint is therefore appended to the object function of conventional FCM so as to incorporate the spatial information of the image. The new mathematical programming formula can thus be solved by the Lagrange multiplier. The validity of this algorithm is evaluated using simulated brain MR images with different noise level and real brain MR image. The results show that MC-FCM is overperformed than the conventional counterparts, and is as well as simple, fast, and robust.
In chapterⅢ, we inspect the properties of both fuzzy set and MRF, then introduce the notion of fuzzy membership to the conventional MRF model---therefore forms a Fuzzy Markov random field (FMRF) model. Applying MAP method to the segmentation problem leads to a mathematical programming problem, which can be solved by deriving the formula of determining the membership values for each voxel to indicate the partial volume degree. The results obtained by testing both simulated and clinical data, show that FMRF can segment them more accurately than the conventional model-based and FCM do as well.
In chapterⅣandⅤ, 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.
In chapterⅣ, An automatic segmentation algorithm of MS lesions for MR FLAIR images is presented based on fuzzy connectedness by using a priori knowledge of characteristics of MS lesions and anatomical structures. The connectedness employs fuzzy relationship to describe the analogy of two neighboring pixels. The segmentation of focal regions is accomplished by choosing pixel-seeds, and then expanding regions using connectedness between the pixels. The pixel-seed selection is done automatically to facilitate practical applications. A novel brain tissue extraction algorithm is also presented using region expanding method as the preprocessing, which is able to automatically remove tissues other than those of brain, such as skull, scalp etc. The testing results using clinical MR FLAIR brain images demonstrate that the performance of the proposed algorithm is significantly improved over the conventional FCM clustering and MRF model-based algorithms. This unsupervised algorithm can be used in clinical practice with adequate calculating speed, and robustness.
In chapterⅤ, we develop a MRF-based algorithm for MS lesions segmentation by utilizing the morphological characteristics of MS lesion tissues. The regions circumscribed by white matter are extracted at first by MRF segmentation and region growing methods; the abstracted regions are then segmented again using MRF algorithm. The testing results for T_2-weighted MR brain images show the proposed algorithm is robust and accurate enough for clinical use.
In chapterⅥ, A improved unsupervised algorithm for image segmentation is proposed using an inhomogeneous MRF model, in which the parameter is estimated in fuzzy connectedness. The conventional MRF-based segmentation algorithms always assume the MRF is homogeneous, i.e., the pixels are uncorrelated spatially. This assumption is usually not satisfied in practice, which requires a more precise model like inhomogeneous MRF to represent the context information. Simulated brain MR images with different noise level and real brain MR images are tested. The results show that the proposed algorithm is more accurate in comparison with others.
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。
基于马尔可夫场(MRF)模型的图像分割算法，是一类重要的图像分割算法。该类算法利用了图像空间的相关信息作为先验知识，运用Gibbs场和最大后验概率(MAP)实现图像分割，能够有效地对迭加了噪声的低信噪比图像进行分割。但基于MRF模型的分割算法也存在一些问题，例如不能有效地处理图像的模糊性、存在过分割现象、参数估计困难等。
本文深入研究了基于模糊理论和基于MRF模型的图像分割算法，主要取得下列成果：(1)针对FCM算法存在的问题，提出了一种能够合理利用空间信息的改进的FCM算法；(2)将模糊理论和MRF结合，提出了一种模糊MRF模型，并对模型的建立、参数估计和优化方法进行了深入的研究；(3)研究了多发性硬化症病灶的分割算法，分别提出了一种基于模糊连接度和一种基于MRF模型的多发性硬化症病灶的分割算法；(4)研究了基于非齐次MRF模型的图像分割算法，并提出了一种用模糊连接度对非齐次MRF进行参数估计的方法。这些方法在提高图像分割的精度和鲁棒性等方面具有显著的效果。
第二章根据MR脑部图像真实的灰度值具有分片常数的特性，按照合理利用图像空间信息的原则，提出了一种基于隶属度光滑约束的FCM聚类算法。在传统FCM的目标函数中增加了使隶属度趋向于分片光滑的约束项，提出了新的目标函数，得到了新的数学规划问题，并运用Lagrange乘数法，得到了该规划问题的解。以此提出了一种FCM聚类算法的改进算法。通过对模拟和临床MR脑部图像的分割实验，表明该算法在分割被噪声污染的图像时，比传统的FCM算法及其改进算法等多种图像分割算法具有更精确的图像分割能力，并且运算简单、运算速度快、稳健性好。
第三章分析了基于模糊理论和基于MRF模型的图像分割算法各自的优势和存在的问题。在传统MRF模型的基础上，引入模糊概念，建立了一种模糊MRF模型，并运用MAP方法将图像的分割问题转化为一个数学规划问题。通过对该规划问题的求解，得到了图像像素对不同组织的隶属度计算方法，提出了一种高效、无监督的图像分割算法，从而实现了对MR脑部图像的精确分割。通过对模拟MR脑部图像和临床MR脑部图像分割实验，表明该基于模糊MRF模型的图像分割新算法比基于传统MRF模型的图像分割算法和模糊C-均值等图像分割算法能够更精确地分割图像。
第四章和第五章研究了多发性硬化症病灶的分割方法。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。
第四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，提出了一种基于模糊连接度的多发性硬化症病灶的分割算法。模糊连接度用模糊关系描述了图像中两个像素之间的关联程度。通过选取种子像素，运用像素间的模糊连接度进行增长区域，能够实现对病灶的分割。但基于模糊连接度的分割算法需要人工选择种子点，这样就制约了该方法的应用。本章提出了一种实现种子像素自动选取的方法，实现了多发性硬化症病灶的自动分割。作为多发性硬化症病灶分割的预处理，针对FLAIR MR脑部图像的特征，还巧妙地提出了一种基于区域增长方法的脑部组织提取算法，能够自动地去除头骨、头皮等非脑部组织。通过对临床患者FLAIR MR图像的分割实验，表明该分割算法能够比较准确地分割多发性硬化症病灶，其分割效果明显好于FCM聚类算法和基于MRF的分割算法。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。
第五章提出了一种基于MRF模型，利用了多发性硬化症形态学特性的多发性硬化症病灶的分割算法。首先运用基于MRF模型的分割算法和区域增长法，分割出脑白质所包围的区域。然后对脑白质所包围的区域再次分割，就实现了对MR脑部图像的多发性硬化症病灶分割。通过对多发性硬化症模拟和临床T_2加权MR脑部图像的分割实验，表明该算法能够比较准确地分割多发性硬化症病灶，并且具有稳健性好等优点，能够应用于多发性硬化症的临床辅助诊断。
第六章提出了一种基于非齐次MRF的图像分割算法，并运用模糊空间元素的模糊连接度模型，估计非齐次MRF中控制像素对空间信息依赖程度的参数，改进了传统的基于MRF模型的图像分割算法。在传统的基于MRF模型的图像分割算法中，总是假设对应的MRF具有齐次性，即像素对空间信息的依赖程度与其空间位置无关。由于图像中不同位置的像素对空间信息的依赖程度是不同，因此，运用非齐次MRF来描述图像会更合理。通过对模拟MR脑部图像和临床MR脑部图像分割实验，表明该算法比传统的基于齐次MRF模型的图像分割算法和FCM聚类算法等图像分割算法有更精确的图像分割能力。
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.
The Markov random field (MRF) segmentation has been successfully applied to this issue in the presence of noise by taking into account a priori knowledge of the spatial correlations of the image using Gibbs distribution and maximum a posteriori (MAP). However, there are still problems associated with MRF, such as the difficulty in dealing with fuzzy characteristics of images, parameter estimation, and the tendency of over-segmentation.
In this paper, we look into the segmentation algorithms based on fuzzy set and MRF, and the main contributions to which are as follows: 1) a modified FCM clustering algorithm is proposed to improve the segmentation accuracy of FCM; 2) a Fuzzy Markov random field (FMRF) model is introduced by combining fuzzy set and MRF, and the modeling, parameter estimate, optimization methods and algorithm about FMRF are studied; 3) a fuzzy connectedness-based segmentation method of multiple sclerosis (MS) lesions and a MRF-based segmentation method of MS lesions are developed; 4) inhomogeneous MRF (IMRF) model is studied and the parameter in IMRF is estimated using fuzzy connectedness. The performance of these algorithms is remarkably superior to the conventional ones in terms of accuracy and robustness.
In chapterⅡ, we present a modified FCM clustering algorithm for brain image segmentation with a membership smoothing constraint (MC-FCM). The rationale of which is that in general an ideal MR image is assumed to be piecewise constant, a membership smoothing constraint is therefore appended to the object function of conventional FCM so as to incorporate the spatial information of the image. The new mathematical programming formula can thus be solved by the Lagrange multiplier. The validity of this algorithm is evaluated using simulated brain MR images with different noise level and real brain MR image. The results show that MC-FCM is overperformed than the conventional counterparts, and is as well as simple, fast, and robust.
In chapterⅢ, we inspect the properties of both fuzzy set and MRF, then introduce the notion of fuzzy membership to the conventional MRF model---therefore forms a Fuzzy Markov random field (FMRF) model. Applying MAP method to the segmentation problem leads to a mathematical programming problem, which can be solved by deriving the formula of determining the membership values for each voxel to indicate the partial volume degree. The results obtained by testing both simulated and clinical data, show that FMRF can segment them more accurately than the conventional model-based and FCM do as well.
In chapterⅣandⅤ, 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.
In chapterⅣ, An automatic segmentation algorithm of MS lesions for MR FLAIR images is presented based on fuzzy connectedness by using a priori knowledge of characteristics of MS lesions and anatomical structures. The connectedness employs fuzzy relationship to describe the analogy of two neighboring pixels. The segmentation of focal regions is accomplished by choosing pixel-seeds, and then expanding regions using connectedness between the pixels. The pixel-seed selection is done automatically to facilitate practical applications. A novel brain tissue extraction algorithm is also presented using region expanding method as the preprocessing, which is able to automatically remove tissues other than those of brain, such as skull, scalp etc. The testing results using clinical MR FLAIR brain images demonstrate that the performance of the proposed algorithm is significantly improved over the conventional FCM clustering and MRF model-based algorithms. This unsupervised algorithm can be used in clinical practice with adequate calculating speed, and robustness.
In chapterⅤ, we develop a MRF-based algorithm for MS lesions segmentation by utilizing the morphological characteristics of MS lesion tissues. The regions circumscribed by white matter are extracted at first by MRF segmentation and region growing methods; the abstracted regions are then segmented again using MRF algorithm. The testing results for T_2-weighted MR brain images show the proposed algorithm is robust and accurate enough for clinical use.
In chapterⅥ, A improved unsupervised algorithm for image segmentation is proposed using an inhomogeneous MRF model, in which the parameter is estimated in fuzzy connectedness. The conventional MRF-based segmentation algorithms always assume the MRF is homogeneous, i.e., the pixels are uncorrelated spatially. This assumption is usually not satisfied in practice, which requires a more precise model like inhomogeneous MRF to represent the context information. Simulated brain MR images with different noise level and real brain MR images are tested. The results show that the proposed algorithm is more accurate in comparison with others.
引文
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[1] 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.
[2] Wyatt PP, Noble JA. MAP MRF joint segmentation and registration of medical images[J]. Medical Image Analysis[J], 2003, 7(4):539-552.
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[1] Deng H, Clausi DA. Unsupervised image segmentation using a simple MRF model with a new implementation scheme [J]. Pattern Recognition, 2004, 37(12):2323-2335.
[2] Descombes X. Estimation of Markov random field prior parameters using Markov chain Monte Carlo maximum likelihood [J]. IEEE Trans. on Image Processing, 1999, 8(7):954-963.
[3] 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.
[4] Salzenstein F, Pieczynski W. Parameter estimation in hidden fuzzy Markov random fields and image segmentation [J]. Graphical Models and Image Processing, 1997, 59(4): 205-220.
[5] Udupa J K, Samarasekera S. Fuzzy connectedness and object definition: theory, algorithms, and applications in image segmentation[J]. Graphical Model and Image Processing, 1996, 58(3): 246-261.
[6] Udupa J K. Fuzzy connectedness and image segmentation[J]. Proceedings of the IEEE, 2003, 91(10): 1649-1669.
[2] 张雪林．磁共振成像(MRI)诊断学[M]．北京：人民军医出版社，2004．
[3] 俎栋林．磁共振成像学[M]．北京：高等教育出版社，2004．
[4] 章毓晋．图象分割[M]．北京：科学出版社，2001．
[5] 罗述谦，周果宏．医学图象处理与分析[M]．北京：科学出版社，2003．
[6] 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.
[7] Liew, Alan WC, Yah H. Current methods in the automatic tissue segmentation of 3D magnetic resonance brain images [J], Current Medical Imaging Reviews. 2006,2(1):91-103.
[8] 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．
[9] 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．
[10] 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．
[11] 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)：492-426
[12] Bezdek J, Hall L, Clarke L. Review of MR image segmentation techniques using pattern recognition[J].Medical Physics, 1993;20:1033-1048.
[13] Clarke LP, Velthuizen RP. MRI segmentation: methods and applications [J]. Magnetic Resonance Imaging. 1995, 13(3):343-368.
[14] 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．
[15] 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.
[16] 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.
[17] Canny J. A computational approach to edge detection [J]. IEEE Trans. On Pattern Analysis and Machine Intelligence, 1986, 8(6): 679-698.
[18] 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.
[19] Qian RJ, Huang TS. Optimal edge detection in two-dimensional images[J]. IEEE Trans. On Image Processing, 1996, 5(7): 1215-1220.
[20] 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．
[21] 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.
[22] Sahoo P, Wilkins C, Ueager J. Threshold selection using Rrenyi's entropy [J]. Pattern Recognition, 1997, 30(1): 71-84.
[23] 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.
[24] 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.
[25] 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.
[26] Zhao YQ, Li ML. A modified fuzzy C-Means algorithm for segmentation of MRI[C]. Proceedings of the 5th ICCIMA'03,2003.
[27] 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.
[28] Wan S Y, William H. Symmetric region growing [J]. IEEE Trans. on Image Processing, 2003,12(9): 1007-1015.
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[2] Descombes X. Estimation of Markov random field prior parameters using Markov chain Monte Carlo maximum likelihood [J]. IEEE Trans. on Image Processing, 1999, 8(7):954-963.
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