基于模糊聚类的脑磁共振图像分割技术研究
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摘要
磁共振成像(Magnetic Resonance Imaging, MRI)技术以其非介入性、非损伤性、很少受目标物体运动影响等特点,成为脑疾病临床诊断的重要辅助手段。脑MR图像的精确分割对生物医学研究和临床应用具有重要的指导意义。然而,在实际应用中,脑MR图像中存在灰度不均匀性、噪声、脑组织的部分容积效应以及低对比度等缺陷,使脑MR图像的精确分割变得十分困难。为此,本文针对脑MR图像分割问题,采用模糊聚类模型,从目标函数的改进和数据不确定性描述两方面,深入研究了基于模糊聚类模型及其扩展模型的脑MR图像分割算法。本文所做的主要工作与创新性成果如下：
(1)提出了一种各向异性权重的模糊C均值聚类算法。深入探讨了含噪声脑MR图像的分割策略,分析了传统模糊聚类算法的主要缺陷以及现有改进算法的空间信息构造思路,通过引入新的邻域窗口权重的计算方法,使中心点邻域内各点具有各向异性的权重,有效地克服图像中噪声对于分割的影响,并使用基于灰度级的快速算法,达到精确分割带噪图像的目的。
(2)提出了一种基于局部和全局信息的概率模糊C均值聚类算法。通过探讨含偏移场脑MR图像的分割策略,给出了模糊聚类算法中估计偏移场的一般思路,综合利用了全局和局部的灰度拟合信息,使分割目标受到局部信息约束力和全局信息约束力两种力量的驱动。该算法在估计偏移场的同时,进一步提高了分割精度。
(3)提出了一个基于模糊C均值聚类的模型框架。该框架改进了算法聚类中心的初始化方法,有效地克服了噪声、偏移场等对图像的污染；利用局部空间邻域信息的处理,克服噪声保留更多图像细节信息；引入基函数估计偏移场,自动估计各控制参数,并有效克服了部分容积效应对于分割结果的影响；通过基于直方图统计的加速算法,最终达到快速精确分割脑MR图像的目的。该框架具有较强的实用性。
(4)为了进一步增强对于图像数据中不确定性的描述,在模糊聚类模型中分别引入粗糙集和二型模糊集,提出了广义的基于粗糙模糊集的聚类模型与基于区间二型模糊集的概率模糊C均值聚类模型。前一种模型能够根据图像数据自身内容自动确定各聚类类别的粗糙模糊集,通过多项式基函数拟合灰度不均匀性,自动确定上近似集合与下近似集合对于聚类中心的影响权重值,且该算法对于聚类中心的初始化十分鲁棒；后一种模型首次将区间二型模糊集引入到概率模糊C均值算法中,针对描述不确定性的模糊隶属度和概率典型性同时进行处理,提供了不确定性轨迹的构造,降型和去模糊化的处理,实验结果表明这两种算法各具优势,能够得到较精确的分割结果。
(5)针对脑MR图像中存在的低对比度的缺陷,提出了两种脑MR图像分割模型：将局部高斯概率模型引入到模糊聚类的目标函数中,提出了模糊局部高斯概率模型的聚类分割算法。该方法引入了二阶统计量局部方差,算法中局部均值和方差随着空间的改变而变化,并严格推导出相应的更新公式,因此该算法具有较强的自适应性。进一步,对图像中各像素点对应的邻域尺度进行自动估计,提出了自适应尺度模糊局部高斯概率模型的聚类分割算法,提高了模型的鲁棒性,达到精确分割的目的。
Magnetic resonance imaging (MRI) has several advantages over other medical imaging modalities, including high contrast among different soft tissues, relatively high spatial resolution across the entire field of view and multi-spectral characteristics. Therefore, it has been widely used in quantitative brain imaging studies. Quantitative volumetric measurement and three-dimensional visualization of brain tissues are helpful for pathological evolution analyses, where image segmentation plays an important role. However, MR images suffer from several major artifacts, including intensity inhomogeneity, noise, partial volume (PV) effect and low contrast, which make MR segmentation remain a challenging topic. Therefore, in this thesis, we focus on brain MR image segmentation based on fuzzy clustering model from two aspects, including the construction and improvement of objective function and the uncertainty description of data. All the algorithms proposed in this thesis can get an accurate segmentation result. Our work mainly includes the following parts:
(1) A novel anisotropic weighted fuzzy c-means clustering algorithm is proposed to over-come the impact of noise in the image during segmentation. Based on the discussion of the strategies for the segmentations of brain MR image with noise, we analysis the major drawbacks of conventional fuzzy clustering algorithm and the ideas of local information construction for current improved methods. Then we introduce a new method to compute the weights of the neighborhood which makes the pixels in the neighborhood have anisotropic weights. Mean-while, the algorithm is accelerated with histogram of the image. The experimental results show that our method has stronger anti-noise property and higher segmentation accuracy.
(2) A modified possibilistic fuzzy c-means clustering algorithm is presented by combining the local and global intensity information. Based on the discussion of the strategies for the segmentations of brain MR image with intensity inhomogeneity, we focus on the segmentation based intensity inhomogeneity correction methods. To estimate the intensity inhomogeneities in the image, the proposed algorithm introduces the global intensity into the coherent local intensity clustering algorithm and takes the local and global intensity information into account. The segmentation target therefore is driven by two forces, one induced by the coherent local intensity and the other by the coherent global intensity, to ensure the smoothness of the derived optimal bias field and improve the accuracy of the segmentations. Comparisons with other approaches demonstrate the superior performance of the proposed algorithm.
(3) A framework with modified fast fuzzy c-means clustering for brain MR images seg-mentation is proposed to overcome the intensity inhomogeneity, noise and partial volume effect simultaneously and improve image segmentation performance. A new automated method for centroids initialization is proposed to overcome the impact of intensity inhomogeneity and noise during initializing the centroids. An adaptive method to incorporate the local spatial continuity is proposed to overcome the noise effectively and prevent the edge from blurring. The frame-work is accelerated with histogram, and utilizes a set of basis function to estimate the bias field in the image. The weights of the regularization terms, which make the segmentations more accuracy, are all automatically computed to avoid the manually-tuned parameter and reduce the iteration steps of the algorithm. The proposed framework is fast and robust, thereby allowing for fully automatic applications.
(4) To improve the uncertainty description of the dataset, we introduce the rough sets and interval type-2fuzzy sets into the fuzzy clustering model, and propose a generalized rough fuzzy c-means algorithm and an interval possibilistic fuzzy c-means clustering algorithm. In the first algorithm, a novel hybrid rough fuzzy c-means algorithm is proposed for brain MR image segmentation. Each cluster is characterized by three automatically determined rough-fuzzy regions, and accordingly the membership of each pixel is estimated with respect to the region it locates. The importance of each region is balanced by a weighting parameter, and the bias field in MR images is modeled by a linear combination of orthogonal polynomials. The weighting parameter estimation and bias field correction have been incorporated into the itera- tive clustering process. Experimental results demonstrate that the proposed algorithm is more robust to the initialization, noise, and bias field, and can produce more accurate and reliable segmentations. In the second algorithm, we utilize the interval type-2fuzzy set, and focus on the representation and management of uncertainty which is present in both fuzzy memberships and possibilistic typicalities of the patterns associated with the varying of fuzzifiers. Therefore, we extend a pattern set to interval type-2fuzzy sets using two fuzzifiers for membership and two fuzzifiers for possibilistic. Consequently, the proposed algorithm can simultaneously overcome the drawbacks and inherit the advantages of current interval type-2fuzzy set based algorithms. Experiments demonstrate the advantages of the method over state-of-the-art.
(5) To overcome the low contrast in brain MR images, we introduce the second-order statistics (local variance) into the fuzzy clustering model, and propose two improved algorithms. By introducing the local Gaussian distribution fitting energy into the fuzzy clustering model, a fuzzy local Gaussian distribution fitting model is proposed to segment brain MR images. The means and standard deviation of local Gaussian distributions are updated iteratively and varying spatially, therefore the proposed model is more adaptive. Then, a new local scale computing method is introduced to estimate the local variances for local Gaussian distributions. Then the adaptive scale fuzzy local Gaussian distribution fitting model is proposed to improve the robust of the algorithm over the initializations. The experimental results show the advantages of the method over the state-of-the-art.
(1)提出了一种各向异性权重的模糊C均值聚类算法。深入探讨了含噪声脑MR图像的分割策略,分析了传统模糊聚类算法的主要缺陷以及现有改进算法的空间信息构造思路,通过引入新的邻域窗口权重的计算方法,使中心点邻域内各点具有各向异性的权重,有效地克服图像中噪声对于分割的影响,并使用基于灰度级的快速算法,达到精确分割带噪图像的目的。
(2)提出了一种基于局部和全局信息的概率模糊C均值聚类算法。通过探讨含偏移场脑MR图像的分割策略,给出了模糊聚类算法中估计偏移场的一般思路,综合利用了全局和局部的灰度拟合信息,使分割目标受到局部信息约束力和全局信息约束力两种力量的驱动。该算法在估计偏移场的同时,进一步提高了分割精度。
(3)提出了一个基于模糊C均值聚类的模型框架。该框架改进了算法聚类中心的初始化方法,有效地克服了噪声、偏移场等对图像的污染；利用局部空间邻域信息的处理,克服噪声保留更多图像细节信息；引入基函数估计偏移场,自动估计各控制参数,并有效克服了部分容积效应对于分割结果的影响；通过基于直方图统计的加速算法,最终达到快速精确分割脑MR图像的目的。该框架具有较强的实用性。
(4)为了进一步增强对于图像数据中不确定性的描述,在模糊聚类模型中分别引入粗糙集和二型模糊集,提出了广义的基于粗糙模糊集的聚类模型与基于区间二型模糊集的概率模糊C均值聚类模型。前一种模型能够根据图像数据自身内容自动确定各聚类类别的粗糙模糊集,通过多项式基函数拟合灰度不均匀性,自动确定上近似集合与下近似集合对于聚类中心的影响权重值,且该算法对于聚类中心的初始化十分鲁棒；后一种模型首次将区间二型模糊集引入到概率模糊C均值算法中,针对描述不确定性的模糊隶属度和概率典型性同时进行处理,提供了不确定性轨迹的构造,降型和去模糊化的处理,实验结果表明这两种算法各具优势,能够得到较精确的分割结果。
(5)针对脑MR图像中存在的低对比度的缺陷,提出了两种脑MR图像分割模型：将局部高斯概率模型引入到模糊聚类的目标函数中,提出了模糊局部高斯概率模型的聚类分割算法。该方法引入了二阶统计量局部方差,算法中局部均值和方差随着空间的改变而变化,并严格推导出相应的更新公式,因此该算法具有较强的自适应性。进一步,对图像中各像素点对应的邻域尺度进行自动估计,提出了自适应尺度模糊局部高斯概率模型的聚类分割算法,提高了模型的鲁棒性,达到精确分割的目的。
Magnetic resonance imaging (MRI) has several advantages over other medical imaging modalities, including high contrast among different soft tissues, relatively high spatial resolution across the entire field of view and multi-spectral characteristics. Therefore, it has been widely used in quantitative brain imaging studies. Quantitative volumetric measurement and three-dimensional visualization of brain tissues are helpful for pathological evolution analyses, where image segmentation plays an important role. However, MR images suffer from several major artifacts, including intensity inhomogeneity, noise, partial volume (PV) effect and low contrast, which make MR segmentation remain a challenging topic. Therefore, in this thesis, we focus on brain MR image segmentation based on fuzzy clustering model from two aspects, including the construction and improvement of objective function and the uncertainty description of data. All the algorithms proposed in this thesis can get an accurate segmentation result. Our work mainly includes the following parts:
(1) A novel anisotropic weighted fuzzy c-means clustering algorithm is proposed to over-come the impact of noise in the image during segmentation. Based on the discussion of the strategies for the segmentations of brain MR image with noise, we analysis the major drawbacks of conventional fuzzy clustering algorithm and the ideas of local information construction for current improved methods. Then we introduce a new method to compute the weights of the neighborhood which makes the pixels in the neighborhood have anisotropic weights. Mean-while, the algorithm is accelerated with histogram of the image. The experimental results show that our method has stronger anti-noise property and higher segmentation accuracy.
(2) A modified possibilistic fuzzy c-means clustering algorithm is presented by combining the local and global intensity information. Based on the discussion of the strategies for the segmentations of brain MR image with intensity inhomogeneity, we focus on the segmentation based intensity inhomogeneity correction methods. To estimate the intensity inhomogeneities in the image, the proposed algorithm introduces the global intensity into the coherent local intensity clustering algorithm and takes the local and global intensity information into account. The segmentation target therefore is driven by two forces, one induced by the coherent local intensity and the other by the coherent global intensity, to ensure the smoothness of the derived optimal bias field and improve the accuracy of the segmentations. Comparisons with other approaches demonstrate the superior performance of the proposed algorithm.
(3) A framework with modified fast fuzzy c-means clustering for brain MR images seg-mentation is proposed to overcome the intensity inhomogeneity, noise and partial volume effect simultaneously and improve image segmentation performance. A new automated method for centroids initialization is proposed to overcome the impact of intensity inhomogeneity and noise during initializing the centroids. An adaptive method to incorporate the local spatial continuity is proposed to overcome the noise effectively and prevent the edge from blurring. The frame-work is accelerated with histogram, and utilizes a set of basis function to estimate the bias field in the image. The weights of the regularization terms, which make the segmentations more accuracy, are all automatically computed to avoid the manually-tuned parameter and reduce the iteration steps of the algorithm. The proposed framework is fast and robust, thereby allowing for fully automatic applications.
(4) To improve the uncertainty description of the dataset, we introduce the rough sets and interval type-2fuzzy sets into the fuzzy clustering model, and propose a generalized rough fuzzy c-means algorithm and an interval possibilistic fuzzy c-means clustering algorithm. In the first algorithm, a novel hybrid rough fuzzy c-means algorithm is proposed for brain MR image segmentation. Each cluster is characterized by three automatically determined rough-fuzzy regions, and accordingly the membership of each pixel is estimated with respect to the region it locates. The importance of each region is balanced by a weighting parameter, and the bias field in MR images is modeled by a linear combination of orthogonal polynomials. The weighting parameter estimation and bias field correction have been incorporated into the itera- tive clustering process. Experimental results demonstrate that the proposed algorithm is more robust to the initialization, noise, and bias field, and can produce more accurate and reliable segmentations. In the second algorithm, we utilize the interval type-2fuzzy set, and focus on the representation and management of uncertainty which is present in both fuzzy memberships and possibilistic typicalities of the patterns associated with the varying of fuzzifiers. Therefore, we extend a pattern set to interval type-2fuzzy sets using two fuzzifiers for membership and two fuzzifiers for possibilistic. Consequently, the proposed algorithm can simultaneously overcome the drawbacks and inherit the advantages of current interval type-2fuzzy set based algorithms. Experiments demonstrate the advantages of the method over state-of-the-art.
(5) To overcome the low contrast in brain MR images, we introduce the second-order statistics (local variance) into the fuzzy clustering model, and propose two improved algorithms. By introducing the local Gaussian distribution fitting energy into the fuzzy clustering model, a fuzzy local Gaussian distribution fitting model is proposed to segment brain MR images. The means and standard deviation of local Gaussian distributions are updated iteratively and varying spatially, therefore the proposed model is more adaptive. Then, a new local scale computing method is introduced to estimate the local variances for local Gaussian distributions. Then the adaptive scale fuzzy local Gaussian distribution fitting model is proposed to improve the robust of the algorithm over the initializations. The experimental results show the advantages of the method over the state-of-the-art.
引文
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