基于马尔可夫随机场的膝关节磁共振图像分割方法的研究
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摘要
医学图像分割是正常组织和病变组织的定量分析、三维重建等医学图像分析的基础,也是临床医学应用的瓶颈,分割结果的准确性对医生判断疾病的真实情况并作出正确的诊断计划至关重要。然而,在临床分割中,由于医学图像的复杂性、多样性和各种不确定因素造成的退化现象,导致医学图像分割本身是不适定的。
基于马尔可夫随机场的先验模型是引入先验信息来解决这一不适定问题的强有力工具,在贝叶斯图像分割中得到广泛运用。本文以膝关节MRI图像为研究对象,以自动、精确、快速分割作为研究目标,针对特定组织结构选择合理的分割算法和分割策略,得到了满意的分割结果,实现了膝关节骨骼和半月板的快速无监督分割,主要工作和贡献如下:
(1)膝关节MRI图像中骨骼的精确分割是进一步分割与定量分析膝部软组织的前提。目前膝关节骨骼分割的方法比较耗时或需要一定的人机交互。为解决这一问题,将多尺度MRF方法引入到膝关节MRI分割中,以实现快速无监督的分割。首先建立高斯混合的灰度统计模型,运用MDL准则自动确定类别的数目。建立多尺度MRF的先验模型时,利用尺度间的因果性给出非迭代的计算方法,由细尺度往粗尺度传递统计信息,再由粗尺度往细尺度计算每个像素的最大后验概率,从而实现快速准确的分割。实验结果表明,与单尺度MRF相比,多尺度MRF分割膝关节MRI所需时间大大减少,且精度与专家手动分割标准相当。算法通过建立多尺度马尔可夫随机场模型,完成了低信噪比膝关节MRI图像快速准确分割,可作为进一步自动分割软骨与半月板等软组织的基础。
(2)核磁共振成像(magnetic resonance imaging,MRI)图像形态、纹理均较为复杂,从图像中分割出感兴趣组织结构具有一定难度。本文提出一种“分割—粗定位—提取”思路,充分利用MRI成像特征和膝关节解剖学的先验知识,快速、自动地精确分割形态复杂、尺寸细小的膝关节半月板:首先利用多尺度马尔可夫随机场(markov random field,MRF)方法自动、快速地分割与目标有相似灰度分布的组织结构,然后结合Sobel算子和直方图投影方法粗定位半月板区域,最后通过判断连通区域面积提取出精确的半月板区域。实验结果表明,与目前手动、半自动的半月板分割等研究工作相比,本论文方法可以客观可重复地分割出半月板前后角等区域,并且算法耗时较低。
Medical image segmentation is not only the basis of medical image analysis such as quantitative analysis and the three-dimensional reconstruction of the normal and diseased tissues , but the bottleneck of clinical applications. Segmentation accuracy is vital for doctors to assess the real situation of diseases and make correct diagnosis plans. However,due to the complexity,diversity,and degradation of medical images,medical image segmentation itself is ill-posed.
A priori model based on Markov Random Field is a powerful method which is able to solve this ill-posed problem by employing priori information. It has been widely used for Bayesian image segmentation. In this dissertation,in order to segment knee Magnetic Resonance Imaging (MRI) images automatically ,accurately and quickly,we choose reasonable segmentation algorithm and strategy for particular tissues and get satisfactory results. The main work and contributions are as follows:
(1) Bone segmentation in knee MRI can be regarded as the groundwork of segmenting and analyzing soft tissue in knees. Usually this task is time-consuming and needs human intervention. To solve this problem automatically and rapidly,a multi-scale MRF is introduced into knee MRI segmentation in this dissertation. Gaussian mixture model is firstly built as the statistical model for the intensity image,with an estimation of index number using MDL. In the phase of building multi-scale MRF model,non-iterated computing based on causality between scales is implemented,where statistical information is transferred from fine scales to coarse scales and MAP of every pixel is computed from coarse scales to fine scales. As a result,fast and unsupervised bone segmentation on knee MRI can be achieved. The experiments show that the temporal cost of segmenting knee bones based on multi-scale MRF is relatively low and the segmentation error can be similar to manual segmentation by medical experts. In conclusion,the work presented here accomplishes fast and accurate segmentation on knee MRI of low SNR through building a multi-scale MRF model. Future work can be extended to further cartilage and meniscus segmentation.
(2) Magnetic resonance images have complex contents in both morphology and texture,which impose difficulty on effective image segmentation. To this end, the strategy of“segmenting-locating-extracting”is proposed,where MRI features and knee anatomical knowledge are made the most of as priori information. Firstly,multi-scale Markov Random Field method is used to implement an automatic and fast segmentation of tissues that have similar intensity distribution as menisci. Then the meniscus region is roughly located by combining Sobel operator with histogram projection. Finally,the areas of connective regions to extract the segmented meniscus anterior and posterior horns are determined accurately. Compared to related work on manually or semi-automatically segmenting menisci , the experiments show that the proposed algorithm automatically performs a repeatable and accurate segmentation on menisci,with relatively low temporal cost.
基于马尔可夫随机场的先验模型是引入先验信息来解决这一不适定问题的强有力工具,在贝叶斯图像分割中得到广泛运用。本文以膝关节MRI图像为研究对象,以自动、精确、快速分割作为研究目标,针对特定组织结构选择合理的分割算法和分割策略,得到了满意的分割结果,实现了膝关节骨骼和半月板的快速无监督分割,主要工作和贡献如下:
(1)膝关节MRI图像中骨骼的精确分割是进一步分割与定量分析膝部软组织的前提。目前膝关节骨骼分割的方法比较耗时或需要一定的人机交互。为解决这一问题,将多尺度MRF方法引入到膝关节MRI分割中,以实现快速无监督的分割。首先建立高斯混合的灰度统计模型,运用MDL准则自动确定类别的数目。建立多尺度MRF的先验模型时,利用尺度间的因果性给出非迭代的计算方法,由细尺度往粗尺度传递统计信息,再由粗尺度往细尺度计算每个像素的最大后验概率,从而实现快速准确的分割。实验结果表明,与单尺度MRF相比,多尺度MRF分割膝关节MRI所需时间大大减少,且精度与专家手动分割标准相当。算法通过建立多尺度马尔可夫随机场模型,完成了低信噪比膝关节MRI图像快速准确分割,可作为进一步自动分割软骨与半月板等软组织的基础。
(2)核磁共振成像(magnetic resonance imaging,MRI)图像形态、纹理均较为复杂,从图像中分割出感兴趣组织结构具有一定难度。本文提出一种“分割—粗定位—提取”思路,充分利用MRI成像特征和膝关节解剖学的先验知识,快速、自动地精确分割形态复杂、尺寸细小的膝关节半月板:首先利用多尺度马尔可夫随机场(markov random field,MRF)方法自动、快速地分割与目标有相似灰度分布的组织结构,然后结合Sobel算子和直方图投影方法粗定位半月板区域,最后通过判断连通区域面积提取出精确的半月板区域。实验结果表明,与目前手动、半自动的半月板分割等研究工作相比,本论文方法可以客观可重复地分割出半月板前后角等区域,并且算法耗时较低。
Medical image segmentation is not only the basis of medical image analysis such as quantitative analysis and the three-dimensional reconstruction of the normal and diseased tissues , but the bottleneck of clinical applications. Segmentation accuracy is vital for doctors to assess the real situation of diseases and make correct diagnosis plans. However,due to the complexity,diversity,and degradation of medical images,medical image segmentation itself is ill-posed.
A priori model based on Markov Random Field is a powerful method which is able to solve this ill-posed problem by employing priori information. It has been widely used for Bayesian image segmentation. In this dissertation,in order to segment knee Magnetic Resonance Imaging (MRI) images automatically ,accurately and quickly,we choose reasonable segmentation algorithm and strategy for particular tissues and get satisfactory results. The main work and contributions are as follows:
(1) Bone segmentation in knee MRI can be regarded as the groundwork of segmenting and analyzing soft tissue in knees. Usually this task is time-consuming and needs human intervention. To solve this problem automatically and rapidly,a multi-scale MRF is introduced into knee MRI segmentation in this dissertation. Gaussian mixture model is firstly built as the statistical model for the intensity image,with an estimation of index number using MDL. In the phase of building multi-scale MRF model,non-iterated computing based on causality between scales is implemented,where statistical information is transferred from fine scales to coarse scales and MAP of every pixel is computed from coarse scales to fine scales. As a result,fast and unsupervised bone segmentation on knee MRI can be achieved. The experiments show that the temporal cost of segmenting knee bones based on multi-scale MRF is relatively low and the segmentation error can be similar to manual segmentation by medical experts. In conclusion,the work presented here accomplishes fast and accurate segmentation on knee MRI of low SNR through building a multi-scale MRF model. Future work can be extended to further cartilage and meniscus segmentation.
(2) Magnetic resonance images have complex contents in both morphology and texture,which impose difficulty on effective image segmentation. To this end, the strategy of“segmenting-locating-extracting”is proposed,where MRI features and knee anatomical knowledge are made the most of as priori information. Firstly,multi-scale Markov Random Field method is used to implement an automatic and fast segmentation of tissues that have similar intensity distribution as menisci. Then the meniscus region is roughly located by combining Sobel operator with histogram projection. Finally,the areas of connective regions to extract the segmented meniscus anterior and posterior horns are determined accurately. Compared to related work on manually or semi-automatically segmenting menisci , the experiments show that the proposed algorithm automatically performs a repeatable and accurate segmentation on menisci,with relatively low temporal cost.
引文
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[2]翁璇,郑小林,姜海.医学图像分割技术研究进展[J].医疗卫生装备,2007,28(1):37-39.
[3]田捷,包尚联,周明全.医学影像处理与分析[M].北京:电子工业出版社,2003.
[4]陆明俊,王润生.计算机视觉中的Markov随机场方法[J].电子与信息学报,2000,22(6):1028-1037.
[5] Marroquin J,Mitter S,Poggio T. Probabilistic Solution of Ill-Posed Problems in Computational Vision[J]. Journal of the American Statistical Association, 1987,82(397):76-89.
[6] Hammersley J M,Clifford P. Markov field on finite graphs and lattices. Unpublished, 1971.
[7]李旭超,朱善安.图像分割中的马尔可夫随机场方法综述[J].中国图象图形学报,2007,12(5):789-798.
[8] Bertero M,Boccacci P. Introduction to Inverse Problems in Imaging[M]. Taylor & Francis Group,1998.
[9] Bouman C A,Shapiro M. A multiscale random field model for Bayesian image segmentation[J].IEEE Transactions on Image Processing,1994,3(2):162-177.
[10] Geman S, Geman D. Stochastic Relaxation,Gibbs Distributions,and the Bayesian Restoration of images[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,1984,PAMI-6(6):721-741.
[11] Poggi G, Ragozini A R P. Image segmentation by tree-structured Markov random fields[J]. IEEE signal processing Letters,1999,6(7):155-157.
[12] Laferte J M,Heitz F, Perez P. Discrete Markov image modeling and inference on the quadtree[J]. IEEE Transactions on Image Processing,2000,9(3):390- 404.
[13]汪西莉,刘芳,焦李成.一种分层马尔可夫图像模型及其推导算法[J].软件学报,2003,14(9):1558-1563.
[14]程兵,王莹.基于Markov随机场和FRAME模型的无监督图像分割[J].中国科学E辑,2004,34(4):391-400.
[15]郭慧敏.基于MRF的局部和全局最优化图象分割方法研究[D].硕士学位论文.南京师范大学,2007年.
[16] Lakshmanan S,Derin H. Simultaneous Parameter Estimation and Segmentation of Gibbs Random Fields Using Simulated Annealing[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,1989,PAMI- 11(8):799-813.
[17] Hastings W K. Monte Carlo sampling methods using Markov chains and their applications[J]. Biometrika,1970,57(1):97-109.
[18] Metropolis N,Rosenbluth A W,Rosenbluth M N,et al. Equation of state calculations by fast computing machines[J]. Journal of Chemical Physics,1953,21:1087-1092.
[19] Besag J. On the Statistical Analysis of Dirty Pictures[J].Journal of the Royal Statistical Society,1986, Series B-48:259~302.
[20] Blake A. Comparison of the efficiency of deterministic and stochastic algorithms for visual reconstruction[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,1989,11(1):2-12.
[21] Zerubia J,Chellappa R. Mean field annealing using compound Gauss-Markov random fields for edge detection and image estimation[J].IEEE Transactions on Neural Networks,1993,NN-4(4):703-709.
[22] Berthod M,Kato Z,Yu S,et al. Bayesian image classification using Markov random fields[J]. Image and Vision Computing,1996,4:285-295.
[23] Yuille A. Energy functions for early vision and analog networks[J].Biol Cybern, 1989,61(2):115-123.
[24] Derin H,Elliott H. Modeling and segmentation of noisy and textured images using gibbs random fields[J]. IEEE Transactions on Pattern Analysis and Machine intelligence,1996,18(7):707～721.
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