基于t混合模型的医学图像分割方法研究
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摘要
核磁共振成像(Magnetic Resonance Imaging, MRI)技术以其无创伤,软组织分辨率高,成像数据丰富等特点,已广泛应用于医学图像的获取,并在临床医学诊断上也起到越来越重要的作用。MRI图像分割在生物医学领域和临床应用中具有重要意义,在解剖结构研究、组织量化测定、病灶定位和疾病诊断等方面有广泛的应用。精确的分割是后续图像分析和诊断的基础。大脑是人体最重要的部分,因此脑部MRI图像分割因其重要的应用价值成为医学图像分割的热点研究领域。
本文在前人研究成果的基础上,总结和概括了医学图像分割的目的和实际意义。在深入理解MRI的成像原理和MRI图像的特点后,本文选择了基于概率统计理论的分割方法,即有限混合模型作为医学图像分割的主要框架。
有限混合模型是分析复杂数据集的一个灵活而强有力的建模工具,它提供了用简单密度函数模拟复杂密度函数的一个有效方法。有限混合模型在模式识别、机器视觉及机器学习等领域都得到了广泛应用。在统计模式识别中有限混合模型常被用于无监督学习(如聚类)。基于高斯分布密度函数比较简单,参数估计容易以及比较贴近实际数据集的分布形状等原因,使得高斯混合模型成为最常用的建模工具。然而高斯混合模型受非典型(atypical)样本或野值(outlier)的影响很大,不能适应MRI图像高噪声的特点。t分布具有较高斯分布重(heavy)的尾部,抗噪性能好,能够在一定程度上改善高斯分布所遇到的问题,提供了一种比高斯分布更稳健的建模方法。本文通过实验表明t混合模型比高斯混合模型更能适应MRI图像的灰度特点。
马尔可夫随机场理论(Markov Random Field, MRF)是研究物理现象空间或上下文依赖关系的概率理论的一个分支。MRF理论提供了一种便捷而连续的方法来对像素或特征之间的上下文依赖关系进行建模。虽然t混合模型能在一定程度上改善高斯分布遇到的问题,但是混合模型是基于直方图模型的,即只考虑了图像中像素的灰度信息而没有考虑像素之间的空间位置之间的相互关系信息。为了解决这个问题,本文在混合模型的估计中引入随机场理论来对分类施加空间约束,弥补了混合模型的不足。
由于MRI是一种多参数,多核种的成像技术,可以得到关于同一人体组织三种不同侧重特点的图像：T1加权像,T2加权像,质子密度(PD)加权像。不同加权像关于同一组织的信息有些是冗余的,但有些也有是互补的,正符合了基于数据融合思想的图像分割方法的条件。由于MRI图像高噪声、边界模糊和伪影等特点,错误分割的像素点主要集中在不同组织的过渡区域。这是由于大多数的脑组织磁共振图像在不同组织的过渡区域总是存在灰度值的交叠现象(也即伪影现象),尤其在脑脊液(CSF)和灰质(GM),灰质(GM)和白质(WM)的过渡区域,这使得处于边缘地带的像素的类别确定有着较大的不确定性和未知性。而DS证据理论能很好的描述未知的和不确定性信息,再使用Dempster合成法则综合多方面的信息以提高分割的效果。因而在本文中先使用混合模型进行分割,然后在使用DS证据理论对分割的结果进行综合,以最终提高正确分割的效果。
The technology of Magnetic Resonance Imaging (MRI) with high soft tissue resolution, non-invasive and rich imaging data, and so on, have been widely used in medical image acquisition, and also has played an increasingly important role in the clinical diagnosis. Segmentation of MRI images has a great significance in biomedical and clinical fields, and so has been extensively applied in the study of anatomical structure, tissue quantification, lesion localization and disease diagnosis. Thus an accurate segmentation is the basis of subsequent image analysis and diagnosis. Because the brain is the most important part of human body, segmentation of MRI brain images has become the research focus of medical image segmentation with its great value.
In this thesis, we summarize the purpose of medical image segmentation and practical significance based on the results of previous researches. After deeply understanding the principles of magnetic resonance imaging and the characteristics of MRI images, finite mixture model is choosen as the main framework for segmentation, which is based on theory of Probability and Statistics,.
Finite mixture model is a flexible and powerful tool for analyzing complicated dataset, which provides an efficient method of simulating a complicated density function by simple density functions. It has been widely used in pattern recognition, machine vision, machine learning and other fields. Finite mixture model is often used for unsupervised learning (such as clustering) in statistical pattern recognition. Because gaussian density function has a simple expression, easily-estimating parameters and is similar to the shape of the actual data sets, the gaussian mixture model is one of the most popular modeling tools. However, gaussian mixture model can not be applied to the MRI images with high noise in view of the affection by atypical samples or outliers,t-distribution with heavier tails and good properties of anti-noising is a modeling tool more robust than the gaussian mixture model, which can solve the problems of gaussian mixture model to a certain extent. The experiments in the thsis show that the t mixture model can adapt better than the Gaussian mixture model due to the intensity characteristics of MRI images
Markov random field (MRF) theory is a branch of probability theories for analyzing the spatial or contextual dependencies of physical phenomena. MRF theory provides a convenient and consistent way of modeling context-dependent entities such as image pixels and correlated features. Although t-distribution can deal with the problems of gaussian mixture model to some extent, finite mixture model does not take spatial information into account, which is a histogram-based model. To overcome this difficulty, we import spatial information constraints by incorporating estimation of mixture model with MRF theory to make up the deficiency of finite mixture model.
Since MRI is a multi-parameter, multi-core kind of imaging technology, we can acquire three different kinds of images:T1 weighted images, T2-weighted images and proton density (PD) weighted images, which provide different information of the same human tissue. The information provided by different weightsed images on tissue is redundant and also some are complementary, so it meets the condition of image segmentation based on data fusion for MRI image segmentation. Pixels misclassified concentrate in the transitional region of different tissues owing to the characteristics of MRI images with high noise, fuzzy boundaries and artifacts. Classification of pixels in the transitional region of different tissues has a greater uncertainty and unpredictability, because the gray values of the region between different tissues in brain magnetic resonance images are overlapped, which are known as "artifacts". The phenomenon of artifacts particularly occurs in the transitional region between cerebrospinal fluid (CSF) and gray matter (GM) or Gray matter (GM) and white matter (WM). Due to the unknown and uncertainty of information can be well described by DS evidence theory, we can use Dempster's rule to integrate multi-information in order to improve the segmentation results. Therefore, in this thesis, we firstly use finite mixture model to classify the MRI image, and then employ the DS evidence theory to integrate the classified results, which can finally improve the accuracy of segmentation results.
本文在前人研究成果的基础上,总结和概括了医学图像分割的目的和实际意义。在深入理解MRI的成像原理和MRI图像的特点后,本文选择了基于概率统计理论的分割方法,即有限混合模型作为医学图像分割的主要框架。
有限混合模型是分析复杂数据集的一个灵活而强有力的建模工具,它提供了用简单密度函数模拟复杂密度函数的一个有效方法。有限混合模型在模式识别、机器视觉及机器学习等领域都得到了广泛应用。在统计模式识别中有限混合模型常被用于无监督学习(如聚类)。基于高斯分布密度函数比较简单,参数估计容易以及比较贴近实际数据集的分布形状等原因,使得高斯混合模型成为最常用的建模工具。然而高斯混合模型受非典型(atypical)样本或野值(outlier)的影响很大,不能适应MRI图像高噪声的特点。t分布具有较高斯分布重(heavy)的尾部,抗噪性能好,能够在一定程度上改善高斯分布所遇到的问题,提供了一种比高斯分布更稳健的建模方法。本文通过实验表明t混合模型比高斯混合模型更能适应MRI图像的灰度特点。
马尔可夫随机场理论(Markov Random Field, MRF)是研究物理现象空间或上下文依赖关系的概率理论的一个分支。MRF理论提供了一种便捷而连续的方法来对像素或特征之间的上下文依赖关系进行建模。虽然t混合模型能在一定程度上改善高斯分布遇到的问题,但是混合模型是基于直方图模型的,即只考虑了图像中像素的灰度信息而没有考虑像素之间的空间位置之间的相互关系信息。为了解决这个问题,本文在混合模型的估计中引入随机场理论来对分类施加空间约束,弥补了混合模型的不足。
由于MRI是一种多参数,多核种的成像技术,可以得到关于同一人体组织三种不同侧重特点的图像：T1加权像,T2加权像,质子密度(PD)加权像。不同加权像关于同一组织的信息有些是冗余的,但有些也有是互补的,正符合了基于数据融合思想的图像分割方法的条件。由于MRI图像高噪声、边界模糊和伪影等特点,错误分割的像素点主要集中在不同组织的过渡区域。这是由于大多数的脑组织磁共振图像在不同组织的过渡区域总是存在灰度值的交叠现象(也即伪影现象),尤其在脑脊液(CSF)和灰质(GM),灰质(GM)和白质(WM)的过渡区域,这使得处于边缘地带的像素的类别确定有着较大的不确定性和未知性。而DS证据理论能很好的描述未知的和不确定性信息,再使用Dempster合成法则综合多方面的信息以提高分割的效果。因而在本文中先使用混合模型进行分割,然后在使用DS证据理论对分割的结果进行综合,以最终提高正确分割的效果。
The technology of Magnetic Resonance Imaging (MRI) with high soft tissue resolution, non-invasive and rich imaging data, and so on, have been widely used in medical image acquisition, and also has played an increasingly important role in the clinical diagnosis. Segmentation of MRI images has a great significance in biomedical and clinical fields, and so has been extensively applied in the study of anatomical structure, tissue quantification, lesion localization and disease diagnosis. Thus an accurate segmentation is the basis of subsequent image analysis and diagnosis. Because the brain is the most important part of human body, segmentation of MRI brain images has become the research focus of medical image segmentation with its great value.
In this thesis, we summarize the purpose of medical image segmentation and practical significance based on the results of previous researches. After deeply understanding the principles of magnetic resonance imaging and the characteristics of MRI images, finite mixture model is choosen as the main framework for segmentation, which is based on theory of Probability and Statistics,.
Finite mixture model is a flexible and powerful tool for analyzing complicated dataset, which provides an efficient method of simulating a complicated density function by simple density functions. It has been widely used in pattern recognition, machine vision, machine learning and other fields. Finite mixture model is often used for unsupervised learning (such as clustering) in statistical pattern recognition. Because gaussian density function has a simple expression, easily-estimating parameters and is similar to the shape of the actual data sets, the gaussian mixture model is one of the most popular modeling tools. However, gaussian mixture model can not be applied to the MRI images with high noise in view of the affection by atypical samples or outliers,t-distribution with heavier tails and good properties of anti-noising is a modeling tool more robust than the gaussian mixture model, which can solve the problems of gaussian mixture model to a certain extent. The experiments in the thsis show that the t mixture model can adapt better than the Gaussian mixture model due to the intensity characteristics of MRI images
Markov random field (MRF) theory is a branch of probability theories for analyzing the spatial or contextual dependencies of physical phenomena. MRF theory provides a convenient and consistent way of modeling context-dependent entities such as image pixels and correlated features. Although t-distribution can deal with the problems of gaussian mixture model to some extent, finite mixture model does not take spatial information into account, which is a histogram-based model. To overcome this difficulty, we import spatial information constraints by incorporating estimation of mixture model with MRF theory to make up the deficiency of finite mixture model.
Since MRI is a multi-parameter, multi-core kind of imaging technology, we can acquire three different kinds of images:T1 weighted images, T2-weighted images and proton density (PD) weighted images, which provide different information of the same human tissue. The information provided by different weightsed images on tissue is redundant and also some are complementary, so it meets the condition of image segmentation based on data fusion for MRI image segmentation. Pixels misclassified concentrate in the transitional region of different tissues owing to the characteristics of MRI images with high noise, fuzzy boundaries and artifacts. Classification of pixels in the transitional region of different tissues has a greater uncertainty and unpredictability, because the gray values of the region between different tissues in brain magnetic resonance images are overlapped, which are known as "artifacts". The phenomenon of artifacts particularly occurs in the transitional region between cerebrospinal fluid (CSF) and gray matter (GM) or Gray matter (GM) and white matter (WM). Due to the unknown and uncertainty of information can be well described by DS evidence theory, we can use Dempster's rule to integrate multi-information in order to improve the segmentation results. Therefore, in this thesis, we firstly use finite mixture model to classify the MRI image, and then employ the DS evidence theory to integrate the classified results, which can finally improve the accuracy of segmentation results.
引文
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[2]http://radiology. xjtu. edu. cn/ct/zong/2. pdf
[3]C. R. Meyer, P. H. Hland, and J. Pipe, "Retrospective correction of intensity inhomogeneities in MRI", IEEE Trans. Med. Imag., vol.14, no.1, pp.36-41,1995.
[4]林瑶,田捷,医学图像分割方法综述[J],模式识别与人工智能,2002,15(2)：192-204.
[5]范勇,脑图像配准与分割研究[D],2003,北京：中国科学院研究生院。
[6]贾富仓,生物医学图像组织统计分类研究[D].2004,北京：中国科学院计算技术研究所.
[7]Redner RA, Walker HF. Mixture Densities, Maximum Likelihood and the Em Algorithm [J].SIAM Review,1984.26(2):195-239.
[8]Bilmes JA. A Gentle Tutorial of the EM Algorithm and its Application to Parameter Estimation for Gaussian Mixture and Hidden Markov Models[J]. International Computer Science Institute,1998.4:1-13.
[9]A. K.Jain, R. P. W. Duin, J.Mao. Statistical pattern recognition:a review [J]. IEEE Trans Panttern Analysis and Machine Intelligence.2000,22:4-37.
[10]Richard O. Duda. Pattern Classification (Second Edition). New York:Wiley,2003.
[11]G. J. McLachlan, D. Peel. Finite Mixture Models[M]. New York:Wiley,2000.
[12]A. P. Dempster, N. M. Laird, D. B. Rubin. Maximum likelihood from incomplete data using the EM algorithm (with discussion)[J]. Journal of the Royal Statistical Society (B).1977,39(4):1-38.
[13]陈思宝,基于t_混合模型和扩展保局投影的聚类与降维方法研究[D].2007.合肥：安徽大学博士论文。
[14]Ueda, N, Nakano, R. Deterministic annealing EM algorithm. Neural Networks,1998, 11:271-282.
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