基于统计方法的核磁共振人脑图像的分割及三维数据的分析
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摘要
随着医疗诊断设备的不断进步,高分辨率核磁共振成像技术已成为目前医学诊断中非常有效的一种非入侵手段,在人体解剖结构的定量分析中占有越来越重要的地位。本文主要研究核磁共振脑部图像分析的两个核心问题：脑部各种组织的分割和对三维脑组织的形状描述及定量分析。
脑组织分割是在对磁共振图像分析中非常关键的一个处理过程。对于核磁共振图像的分割,我们需要克服图像本身的模糊性来提高图像分割的精度,并较好的确定适当的分割阈值,基于此,本文提出来了一种基于模糊理论与马尔可夫场相结合的高斯曲线拟合多阈值分割方法。该算法将模糊集合和马尔可夫随机场结合起来刻画邻域势团能量,并用其表征图像邻域的先验特征,其中在模糊集合的定义上,本文对图像像素的隶属度函数进行了重新定义,使其不仅仅依赖于像素点本身的灰度特性,而且还考虑了各种组织类别的均值、方差及其邻域灰度特征,并在此基础上建立了模糊的马尔可夫随机场。随后利用贝叶斯方法得到后验概率的最简化的能量模型,同时,以最大后验概率(MAP)作为分割准则来决定每一个像素的归类以及它属于该类的隶属度,然后采用条件迭代算法来寻求MAP的解,并利用解中的模糊类的质心来更新类的中心值。为了确定合适的分割阈值,我们需要将不同聚类类别最大程度的区分开,于是本文进一步根据二维直方图上灰度聚类的分布特征推导出二维直方图在各组别内方差达到最小(不同类别峰谷区分最明显)时的投影,同时将模糊马尔可夫场聚类所求得的类中心及类方差作为高斯拟合的参数对投影进行高斯曲线拟合,并把相邻两峰区拟合曲线的交点作为两类别的最佳分割阈值(即两峰区的谷点),最后在二维直方图中找到这些阈值点所确定的直线,并把这些直线作为区分不同类别的界线,完成对图像的分割。实验结果显示,该方法在抗模糊和噪声的能力方面有很好效果,并在一定程度上克服了分割区域连通性差的问题,从而得到了良好的核磁共振分割结果。
论文对脑部组织的三维形状问题也进行了初步研究,三维物体的表面参数化是形状分析中非常重要的研究表示方法之一,但是,传统的参数化方法只是在距离和角度方面保持了特征,没有将参数化后物体表面的对应关系考虑在内。因此,本文提出了一种基于形状特征的参数化方法,用于脑部海马体的香蕉形状的三维物体结构的统计形状分析。在此方法中,我们首先从核磁共振图像脑部的斜冠状面、矢状面和横切面的三个二维图像出发,手工提取海马体的形状特征,确定其二维边缘。第二步利用Mimics 10.01软件进行三维重建,并将海马体的三维表面映射到单位球面上,并根据海马体的二维边缘确定其表面的等纬度圈。第三步由一系列的等纬度圈的重心来获得三维海马体的中轴线。第四步对中轴线进行分析,并建立起中轴线坐标系和局部坐标系,同时利用局部坐标系为每一个等纬度圈确定一个起点,这些点共同形成了模型表面的经度起始线,并从它开始求取每条等纬度圈上的经度参数。最后,对参数化表面进行优化,提高参数精度。这一系列经纬线及其坐标就构成了表征海马体形状结构的参数化表面模型。结果显示,我们提出的这种表面模型基本上保证了不同个体的海马结构样本之间主要形状的对应关系。
在疾病相关的海马体分析中,我们通过对海马体的体积计算和海马体表面与中轴线距离的测量,并使用t检验的统计量分别对患有阿尔茨海默氏痴呆症的海马体的标准化体积均值以及海马体表面节点到它们的中轴线的距离的均值相对于正常海马体的显著性水平p进行检验,可得到一些有意义的统计结论。
With development of medical diagnostic equipment, the high resolution magnetic resonance (MR) imaging is a powerful non-invasive tool for medical diagnosis, it is plays an increasingly important role in the quantitative analysis of anatomical structures. This paper focuses on two topics of the MR brain image analysis. One is tissue segmentation and the other is three dimensional shapes of the brain description and quantitative analysis.
Tissue segmentation is a crucial processing in MR brain image analysis. For the MR image segmentation, we need to overcome the ambiguity of the image to improve the accuracy of segmentation, and find more accurate segmentation threshold, so a multi-threshold MR image segmentation method based on fuzzy Markov Random Field (MRF), clustering and Gaussian curves is proposed in this paper. In the approach, since the degradation of MRI, the neighborhood prior information was inducted by the energy of the cliques. First of all, Membership function of pixels was re-defined, which not only depended on gray features, but also had taken the type of variance and neighborhood information into consideration, and fuzzy MRF was developed; Second, the most simplified energy function of posterior probability was obtained with Bayesian, meanwhile, maximum a posteriori (MAP) was used as the statistical clustering criteria, and sought the solution of MAP by iterated conditional modes(ICM), then every class center was updated by the centroid of the fuzzy class. Third, two-dimensional histogram of image was produced, and projected into one-dimensional histogram by the optimum projection theorem. Fourth, the cluster center points obtained in fuzzy MRF clustering method were introduced into projection to define the gray scope of Gaussian curves, in which the projection histogram was fit with Gaussian curves, and several intersections were acquired at the point where two adjacent Gaussian curves meet. Finally, the lines identified by the intersections were found in the two-dimensional histogram to divide image as threshold values. Experiments show that the algorithm greatly improves the anti-blur and noise immunity compared to one-dimensional Otsu method and two-dimensional Otsu method, and it overcomes the problem of poor partition connectivity to a certain extent, thus an optimized segmentation result is obtained for MR image.
Preliminary study was completed on three-dimensional shape of the brain tissue in this paper. Parameterized surface model of three dimensional objects is an important representation method for the shape analysis and studies. However, the traditional parameterization methods only attempt to preserve the areas or angles in the mapping, which does not guarantee the correspondence between the surfaces. In the paper, we propose a shape-character-derived parameterization method for statistical shape analysis of banana like tree dimensional objects structure. In this algorithm, firstly we extracted the shape character and determined the two-dimensional edge of the hippocampus according to tree 2-D images of the sagittal, coronal and transverse of the brain MR images. Secondly, MR images were reconstructed in the tree dimensional areas by Mimics10.01 software, and the three-dimensional surface of the hippocampus was mapped onto the unit sphere, and determined their latitude circle in according with the edge of the hippocampus in the two-dimensional surface. Thirdly, the body axis of the hippocampus was got by the barycenter of a series of latitude circles. Fourthly, a dateline is extracted on the surface, which is used to get the longitude for each latitude circle. Lastly, this series of latitude and longitude lines and their coordinates formed parameterized shape surface model to represent the hippocampus. The result shows that our method preserves the correspondence between the parameterized surfaces.
In the disease related analysis of the hippocampus, this paper calculated the standardization volume of the hippocampus and measure the distance from the surface to the center axis, and using t statistics test the level of significance p of the two indicators above in Alzheimer's dementia hippocampus, which obtain meaningful statistical conclusions.
脑组织分割是在对磁共振图像分析中非常关键的一个处理过程。对于核磁共振图像的分割,我们需要克服图像本身的模糊性来提高图像分割的精度,并较好的确定适当的分割阈值,基于此,本文提出来了一种基于模糊理论与马尔可夫场相结合的高斯曲线拟合多阈值分割方法。该算法将模糊集合和马尔可夫随机场结合起来刻画邻域势团能量,并用其表征图像邻域的先验特征,其中在模糊集合的定义上,本文对图像像素的隶属度函数进行了重新定义,使其不仅仅依赖于像素点本身的灰度特性,而且还考虑了各种组织类别的均值、方差及其邻域灰度特征,并在此基础上建立了模糊的马尔可夫随机场。随后利用贝叶斯方法得到后验概率的最简化的能量模型,同时,以最大后验概率(MAP)作为分割准则来决定每一个像素的归类以及它属于该类的隶属度,然后采用条件迭代算法来寻求MAP的解,并利用解中的模糊类的质心来更新类的中心值。为了确定合适的分割阈值,我们需要将不同聚类类别最大程度的区分开,于是本文进一步根据二维直方图上灰度聚类的分布特征推导出二维直方图在各组别内方差达到最小(不同类别峰谷区分最明显)时的投影,同时将模糊马尔可夫场聚类所求得的类中心及类方差作为高斯拟合的参数对投影进行高斯曲线拟合,并把相邻两峰区拟合曲线的交点作为两类别的最佳分割阈值(即两峰区的谷点),最后在二维直方图中找到这些阈值点所确定的直线,并把这些直线作为区分不同类别的界线,完成对图像的分割。实验结果显示,该方法在抗模糊和噪声的能力方面有很好效果,并在一定程度上克服了分割区域连通性差的问题,从而得到了良好的核磁共振分割结果。
论文对脑部组织的三维形状问题也进行了初步研究,三维物体的表面参数化是形状分析中非常重要的研究表示方法之一,但是,传统的参数化方法只是在距离和角度方面保持了特征,没有将参数化后物体表面的对应关系考虑在内。因此,本文提出了一种基于形状特征的参数化方法,用于脑部海马体的香蕉形状的三维物体结构的统计形状分析。在此方法中,我们首先从核磁共振图像脑部的斜冠状面、矢状面和横切面的三个二维图像出发,手工提取海马体的形状特征,确定其二维边缘。第二步利用Mimics 10.01软件进行三维重建,并将海马体的三维表面映射到单位球面上,并根据海马体的二维边缘确定其表面的等纬度圈。第三步由一系列的等纬度圈的重心来获得三维海马体的中轴线。第四步对中轴线进行分析,并建立起中轴线坐标系和局部坐标系,同时利用局部坐标系为每一个等纬度圈确定一个起点,这些点共同形成了模型表面的经度起始线,并从它开始求取每条等纬度圈上的经度参数。最后,对参数化表面进行优化,提高参数精度。这一系列经纬线及其坐标就构成了表征海马体形状结构的参数化表面模型。结果显示,我们提出的这种表面模型基本上保证了不同个体的海马结构样本之间主要形状的对应关系。
在疾病相关的海马体分析中,我们通过对海马体的体积计算和海马体表面与中轴线距离的测量,并使用t检验的统计量分别对患有阿尔茨海默氏痴呆症的海马体的标准化体积均值以及海马体表面节点到它们的中轴线的距离的均值相对于正常海马体的显著性水平p进行检验,可得到一些有意义的统计结论。
With development of medical diagnostic equipment, the high resolution magnetic resonance (MR) imaging is a powerful non-invasive tool for medical diagnosis, it is plays an increasingly important role in the quantitative analysis of anatomical structures. This paper focuses on two topics of the MR brain image analysis. One is tissue segmentation and the other is three dimensional shapes of the brain description and quantitative analysis.
Tissue segmentation is a crucial processing in MR brain image analysis. For the MR image segmentation, we need to overcome the ambiguity of the image to improve the accuracy of segmentation, and find more accurate segmentation threshold, so a multi-threshold MR image segmentation method based on fuzzy Markov Random Field (MRF), clustering and Gaussian curves is proposed in this paper. In the approach, since the degradation of MRI, the neighborhood prior information was inducted by the energy of the cliques. First of all, Membership function of pixels was re-defined, which not only depended on gray features, but also had taken the type of variance and neighborhood information into consideration, and fuzzy MRF was developed; Second, the most simplified energy function of posterior probability was obtained with Bayesian, meanwhile, maximum a posteriori (MAP) was used as the statistical clustering criteria, and sought the solution of MAP by iterated conditional modes(ICM), then every class center was updated by the centroid of the fuzzy class. Third, two-dimensional histogram of image was produced, and projected into one-dimensional histogram by the optimum projection theorem. Fourth, the cluster center points obtained in fuzzy MRF clustering method were introduced into projection to define the gray scope of Gaussian curves, in which the projection histogram was fit with Gaussian curves, and several intersections were acquired at the point where two adjacent Gaussian curves meet. Finally, the lines identified by the intersections were found in the two-dimensional histogram to divide image as threshold values. Experiments show that the algorithm greatly improves the anti-blur and noise immunity compared to one-dimensional Otsu method and two-dimensional Otsu method, and it overcomes the problem of poor partition connectivity to a certain extent, thus an optimized segmentation result is obtained for MR image.
Preliminary study was completed on three-dimensional shape of the brain tissue in this paper. Parameterized surface model of three dimensional objects is an important representation method for the shape analysis and studies. However, the traditional parameterization methods only attempt to preserve the areas or angles in the mapping, which does not guarantee the correspondence between the surfaces. In the paper, we propose a shape-character-derived parameterization method for statistical shape analysis of banana like tree dimensional objects structure. In this algorithm, firstly we extracted the shape character and determined the two-dimensional edge of the hippocampus according to tree 2-D images of the sagittal, coronal and transverse of the brain MR images. Secondly, MR images were reconstructed in the tree dimensional areas by Mimics10.01 software, and the three-dimensional surface of the hippocampus was mapped onto the unit sphere, and determined their latitude circle in according with the edge of the hippocampus in the two-dimensional surface. Thirdly, the body axis of the hippocampus was got by the barycenter of a series of latitude circles. Fourthly, a dateline is extracted on the surface, which is used to get the longitude for each latitude circle. Lastly, this series of latitude and longitude lines and their coordinates formed parameterized shape surface model to represent the hippocampus. The result shows that our method preserves the correspondence between the parameterized surfaces.
In the disease related analysis of the hippocampus, this paper calculated the standardization volume of the hippocampus and measure the distance from the surface to the center axis, and using t statistics test the level of significance p of the two indicators above in Alzheimer's dementia hippocampus, which obtain meaningful statistical conclusions.
引文
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