MR图像脑白质区域提取及纤维跟踪研究
摘要
人脑是自然界中最复杂的系统之一,对人类认知过程的探索也是目前科学研究最具有挑战性的问题之一,而现代脑影像技术的发展为研究人脑提供了便利的非侵入性手段。早期基于EEG、MEG和fMRI等影像技术的许多研究都指出,人脑在不同区域具有相对不同的功能,即“功能分化”。但人脑如果要完成一项简单的任务,也总是需要多个不同的功能区域相互作用和协调,共同构成一个网络来完成指令和任务,即“功能整合”。因为人脑可以被看作是一个复杂的网络,所以从网络的角度来研究人脑的功能是极为必要的。
最近几年涌现出很多关于脑网络构建的文章,使得从网络的角度来研究大脑认知的过程成为目前国际上的研究热点。而脑网络构建过程中最关键一步就是白质纤维跟踪,所以精确的白质纤维跟踪是有效的脑网络构建的基本前提。目前,有多种脑白质纤维跟踪的计算方法,但主要分成两大类:决定性跟踪和概率性跟踪。其中传统的决定性跟踪算法是基于线性延展的思想,计算快速但在纤维交叉的位置计算不精确。概率性跟踪能够解决纤维交叉的问题,但其计算结果不够直观且计算费时,不适合临床应用。本文基于磁共振(MRI)脑图像,研究能对脑白质区域进行正确跟踪并在此基础上实施纤维跟踪的方法。论文完成了如下这些有新意的研究工作:
1.提出了能同时兼顾到脑白质跟踪的准确性和算法速度的基于双张量模型的组合跟踪算法。由于双张量模型能够解决纤维交叉问题,从而能够提高算法的准确性;同时由于决定性算法计算快速,使得本文提出的算法时间复杂度降低。总之,该算法找到了计算结果准确性和计算过程快速性之间的平衡点,从而使得脑白质纤维跟踪能够更好地被应用到临床实践中。
2.为防止算法在跟踪白质纤维束的时候超出脑白质区域,本文利用改进的Random Walks算法提取脑白质区域,形成二值掩模并应用于纤维跟踪过程中,从而使跟踪的白质纤维束限制在脑白质区域内。由于人脑结构的复杂性,原始的Random Walks被应用于脑白质提取时并不能取得很好的分割结果,为了提取更准确的脑白质区域,本文引入了局部二值模式和先验概率模型,从而提高了分割脑白质的准确性。
3.分别采用合成的测试数据和真实的MRI数据集验证了本文算法的性能。实验结果表明,本文提出的组合跟踪算法不仅很好地解决了纤维交叉问题,并且能够有效的应用于临床研究中。
本论文的研究工作得到了国家自然科学基金(60771007)和中国科学院研究生创新基金的资助。
Human brain is one of the most complicated systems in the world, and the exploration in the mechanism of human brain information processing is also one of the most chanllenging problems among science reserch. The development of modern imaging technique makes the research of human brain in a non-invasive way become available. From previous research based on EEG, MEG and fMRI techniques, it indicates that human brain has different functions in differnt regions, which means "functional segregation". However, even when the human brain implements an extremely process, it always involves many different regions interacting and cooperating with each other, thereby constructing a network to complete the task, and this is called "functional integration". As the human brain can be considered as a very complicated network, it is necessary for us to investigate the function of human brain on the basis of network.
There were numerous papers about the construction of brain network in recent years, which makes this topic become the most welcomed one among science research. The essential step in the process of constructing the brain network is tracing the white matter bundles, which is called tractography. Therefore, accurate tractography is of critical significance for efficient brain network construcation. So far, there are numerous tractography techniques, and they can generally be classified into two catigories: deterministic tractography and probabilistic tractography. Traditional deterministic tractography is very fast but inaccurate in regions where fibers cross or twist within the voxel. Probabilistic tracking methods are accurate but a time-consuming process and difficult to interpret, making the clinical use unavailable. Therefore, this thesis focused on investigating the latest techniques of tractography and exploring the application of tractography. The major contributions in this thesis are the following points:
1. Considering both the accuracy and speed of the algorithm, in this thesis we proposed a combinatorial method based on a two-tensor model. As the two-tensor model is able to address the fiber crossing problem, it will improve the accuracy of the algorithm. Also the deterministic method is very fast so it is possible to decrease the computational time. The proposed Combinatorial Streamline Tractography (CST) is a tradeoff for speed and accuracy, so that the tractography can be used in clinical practice more efficiently and accurately.
2. Simultaneously, in order to stop the white matter bundles from tracking outside the white matter (WM) region, we extracted the WM region by using an improved Random Walks method and achieved a binary template, thereby limiting the white matter bundles in the WM region. However, due to the complex anatomical structure of brain tissue, the original Random Walks cannot achieve a good extraction result. In order to achieve a more accurate WM region, we introduced Local Binary Pattern (LBP) and Prior Probability Model to Random Walks to improve the accuracy of this algorithm.
3. We evaluated the performance of our proposed Combinatorial Streamline Tractography both on synthetic datasets and real brain diffusion MRI datasets. The results demonstrate that this approach not only successfully reveals structure in crossing regions over a broad range of crossing angles and curvatures, but also it is efficient and robust for clinical use.
This research was sponsored by Nature and Science Foundation of China (Project No.60771007) and Chinese Academy of Science Graduate Innovation Funding.
最近几年涌现出很多关于脑网络构建的文章,使得从网络的角度来研究大脑认知的过程成为目前国际上的研究热点。而脑网络构建过程中最关键一步就是白质纤维跟踪,所以精确的白质纤维跟踪是有效的脑网络构建的基本前提。目前,有多种脑白质纤维跟踪的计算方法,但主要分成两大类:决定性跟踪和概率性跟踪。其中传统的决定性跟踪算法是基于线性延展的思想,计算快速但在纤维交叉的位置计算不精确。概率性跟踪能够解决纤维交叉的问题,但其计算结果不够直观且计算费时,不适合临床应用。本文基于磁共振(MRI)脑图像,研究能对脑白质区域进行正确跟踪并在此基础上实施纤维跟踪的方法。论文完成了如下这些有新意的研究工作:
1.提出了能同时兼顾到脑白质跟踪的准确性和算法速度的基于双张量模型的组合跟踪算法。由于双张量模型能够解决纤维交叉问题,从而能够提高算法的准确性;同时由于决定性算法计算快速,使得本文提出的算法时间复杂度降低。总之,该算法找到了计算结果准确性和计算过程快速性之间的平衡点,从而使得脑白质纤维跟踪能够更好地被应用到临床实践中。
2.为防止算法在跟踪白质纤维束的时候超出脑白质区域,本文利用改进的Random Walks算法提取脑白质区域,形成二值掩模并应用于纤维跟踪过程中,从而使跟踪的白质纤维束限制在脑白质区域内。由于人脑结构的复杂性,原始的Random Walks被应用于脑白质提取时并不能取得很好的分割结果,为了提取更准确的脑白质区域,本文引入了局部二值模式和先验概率模型,从而提高了分割脑白质的准确性。
3.分别采用合成的测试数据和真实的MRI数据集验证了本文算法的性能。实验结果表明,本文提出的组合跟踪算法不仅很好地解决了纤维交叉问题,并且能够有效的应用于临床研究中。
本论文的研究工作得到了国家自然科学基金(60771007)和中国科学院研究生创新基金的资助。
Human brain is one of the most complicated systems in the world, and the exploration in the mechanism of human brain information processing is also one of the most chanllenging problems among science reserch. The development of modern imaging technique makes the research of human brain in a non-invasive way become available. From previous research based on EEG, MEG and fMRI techniques, it indicates that human brain has different functions in differnt regions, which means "functional segregation". However, even when the human brain implements an extremely process, it always involves many different regions interacting and cooperating with each other, thereby constructing a network to complete the task, and this is called "functional integration". As the human brain can be considered as a very complicated network, it is necessary for us to investigate the function of human brain on the basis of network.
There were numerous papers about the construction of brain network in recent years, which makes this topic become the most welcomed one among science research. The essential step in the process of constructing the brain network is tracing the white matter bundles, which is called tractography. Therefore, accurate tractography is of critical significance for efficient brain network construcation. So far, there are numerous tractography techniques, and they can generally be classified into two catigories: deterministic tractography and probabilistic tractography. Traditional deterministic tractography is very fast but inaccurate in regions where fibers cross or twist within the voxel. Probabilistic tracking methods are accurate but a time-consuming process and difficult to interpret, making the clinical use unavailable. Therefore, this thesis focused on investigating the latest techniques of tractography and exploring the application of tractography. The major contributions in this thesis are the following points:
1. Considering both the accuracy and speed of the algorithm, in this thesis we proposed a combinatorial method based on a two-tensor model. As the two-tensor model is able to address the fiber crossing problem, it will improve the accuracy of the algorithm. Also the deterministic method is very fast so it is possible to decrease the computational time. The proposed Combinatorial Streamline Tractography (CST) is a tradeoff for speed and accuracy, so that the tractography can be used in clinical practice more efficiently and accurately.
2. Simultaneously, in order to stop the white matter bundles from tracking outside the white matter (WM) region, we extracted the WM region by using an improved Random Walks method and achieved a binary template, thereby limiting the white matter bundles in the WM region. However, due to the complex anatomical structure of brain tissue, the original Random Walks cannot achieve a good extraction result. In order to achieve a more accurate WM region, we introduced Local Binary Pattern (LBP) and Prior Probability Model to Random Walks to improve the accuracy of this algorithm.
3. We evaluated the performance of our proposed Combinatorial Streamline Tractography both on synthetic datasets and real brain diffusion MRI datasets. The results demonstrate that this approach not only successfully reveals structure in crossing regions over a broad range of crossing angles and curvatures, but also it is efficient and robust for clinical use.
This research was sponsored by Nature and Science Foundation of China (Project No.60771007) and Chinese Academy of Science Graduate Innovation Funding.
引文
陈穗芬,刘哲星,江贵平,陈武凡.2007.基于扩散形状的DTI纤维跟踪算法研究[J].中国医学物理学杂志.24(3):173-176.
汤天宇,阮宗才.2007.基于FMT的扩散张量成像脑白质纤维跟踪算法[J].华中科技大学学报.35:182-186.
王明时,高伟,赵欣,路会生,刘海婴,王力群,李德彪.2006.白质纤维重建过程中像素内交叉问题解决方法[J].天津大学学报.39(3):354-359.
刘晓东,蔡子凡,王婷婷,姚力,卢洁.2008.全张量步长适应性脑白质纤维跟踪改进算法[J].北京师范大学学报.44(2):212-216.
于春水,李坤成.2004.弥散张量成像纤维跟踪技术的研究进展[J].中国医学影像技术.20(3):477-479.
何光武,张贵祥,王斌,项华,何江波,成中意,汪守中.2008.大脑白质纤维磁共振弥散张量成像扫描参数研究[J].中国中西医结合影像学杂志.6(6):163-166.
饶晶晶,漆剑频,王承缘.2008.扩散张量成像扩散梯度方向与DTI图像质量的相关性研究[J].放射学实践.23(3):320-323.
江贵平,刘哲星,冯前进,陈武凡.2005.基于DT-MRI的纤维跟踪及可视化研究[J].中国医学物理学杂志.22(3):514-518.
田捷,包尚联,周明全.2003.医学影像处理与分析[M].电子工业出版社.
Ardizzone E,Pirrone R,Gambino O,Alagna F.2009.Segmentation of MR Brain images with Bias Artifact [C].In: Proceedings of IEEE International Conference on Information Technology and Applications in Biomedicine.1- 4.
Ashburner J,Friston K.2005.Unified segmentation [J].NeuroImage.26(3) : 839– 851.
Barmpoutis,Bing Jian,and Baba C.Vemuri.2009.Adaptive Kernels for Multi-fiber Reconstruction [J].Process Med Imaging.21: 338–349.
Basser PJ,Matiello J,Le Bihan D.1994.Estimation of the effective self diffusion tensor from the NMR spin echo [J].J Magn Reson.103:247–54.
Behrens,T.,Woolrich,M.,Jenkinson,M.,Johansen-Berg,H.,Nunes,R.,Clare,S.,Matthews,P.,Brady,J.,Smith,S.2003.Characterization and propagation of uncertainty in diffusion-weighted MR imaging [J].Magn.Reson.Med.50:1077–1088.
Behrens,T.,Berg,H.J.,Jbabdi,S.,Rushworth,M.,Woolrich,M.2007.Probabilistic diffusion tractography with multiple fibre orientations: what can we gain? [J].NeuroImage.34:144–155.
Benoit C,Nicolas P,Piotr A H,Colin S,Fran?ois R.2010.A non-local fuzzy segmentation method: Application to brain MRI [J].Pattern Recognition.
Blyth R.2003.Tractography with multiple fiber directions.In proceeding of ISMRM[C],1-4.
Boykov Y,Jolly M P.2001.Interactive graph cuts for optimal boundary & region segmentation of objects in n-d images [C].In Proceedings of ICCV.1:105-112.
Bjornemo,M.,Brun,A.,Kikinis,R.,Westin,C.F.2002.Regularized stochastic white matter tractography using diffusion tensor MRI [C].In: Proc.MICCAI.pp.435-442.
Brun,A.,Bjornemo,M.,Kikinis,R.,Westin,C.F.2002.White matter tractography using sequential importance sampling [C].In: Proc.ISMRM Annual Meeting.pp.1131-1135.
Doyle P,Snell L.1984.Random Walks and Electric Networks,Volume 22 of Carus Mathematical [M].Mathematical Association of America,Washington DC.
Fletcher P.,Tao R.,Jeong W.,Whitaker R.T.2007.A volumetric approach to quantifying region-to-region white matter connectivity in diffusion tensor MRI [C]. In: Proc.Information Processing in Medical Imaging.pp.346–358.
Friman,O.,Farneback,G.,Westin,C.2006.A bayesian approach for stochastic white matter tractography [J].IEEE Trans.Med.Imag.25 (8),965–978.
Grady L,Funka-Lea G.2004.Multi-Label Image Segmentation for Medical Applications Based on Graph-Theoretic Electrical Potentials [C].Proc.Workshop Computer Vision and Math.Methods in Medical and Biomedical Image Analysis.230-245.
Grady L,Schiwietz T,Aharon S,Westermann R.2005.Random Walks for Interactive Organ Segmentation in Two and Three Dimensions [C].In: Proceedings of the 8th International Conference on Medical Image Computing and Computer-Assisted Intervention.773-780.
Grady L.2006.Random Walks for Image Segmentation [J].IEEE Transactions on Pattern Analysis and Machine Intelligence.28(11):1768-1783.
Gossl C.,Fahrmeir L.,Putz B.,Auer L.,Auer D.2002.Fiber tracking from DTI using linear state space models: detectability of the pyramidal tract [J].NeuroImage.16: 378–388.
Jenkinson M,Pechaud M,Smith S.2005.BET2: MR-based estimation of brain,skull and scalp surfaces [C].In: Proceedings of the 11th Annual Meeting of the Organization for Human Brain Mapping.
Kim K H,Ronen I,Formisano E.2004.Robust fiber tracking method by vector selection criterion in diffusion tensor images [C].Proceedings of the 26th Annual International Conference of the IEEE EMBS.San Francisco,USA,1080-1083.
Lazar,M.,Weinstein,D.,Tsuruda,J.,Hasan,K.,Arfanakis,K.,Meyerand,E.,Badie,B.,Rowley,H.,Haughton,V.,Field,A.,Witwer,B.,Alexander,A.,2003.White matter tractography using tensor deflection [J].Hum.Brain Mapp.18,306–321.
Lazar,M.,Alexander,A.,2005.Bootstrap white matter tractography (BOOT-TRAC) [J].NeuroImage 24,524–532.
Maenpaa T.Pietikainen M.2001.Texture analysis with local binary patterns.Handbook of Pattern Recognition and Computer Vision[M].3rd ed,World Scientific,Singapore.711-736.
Maier F,Wimmer A,Soza G,Kaftan J N,Fritz D,Dillmann R.2008.Automatic Liver Segmentation using the Random Walker Algorithm [J].Bildverarbeitung für die Medizin.
Mayer A,Greenspan H.2009.An Adaptive Mean-Shift Framework for MRI Brain Segmentation [J].IEEE Trans Medical Imaging,28(8):1238– 1250.
McInerney,T.,Terzopoulos,D.1996.Deformable models in medical image analysis [J].Medical Image Analysis,1:91–108
Mori,S.,Crain,B.,Chacko,V.,van Zijl,P.1999.Three-dimensional tracking of axonal rojections in the brain by magnetic resonance imaging [J].Ann.Neurol.5,265-269.
Mori S,van Zijl PCM.2002.Fiber tracking: principles and strategies—a technical review [J].NMR Biomed;15:468–80.
Mortensen E N,Barrett W A.1995.Intelligent scissors for image composition [C].Proceedings of the 22nd annual conference on Computer graphics and interactive techniques.191-198.
Moumen E,Hashim M.2009.Incorporating prior information in the fuzzy C-mean algorithm with application to brain tissues segmentation in MRI [C].In: Proceedings of IEEE International Conference on Image Processing.Cairo,Egypt,3393- 3396.
Murgasova M,Rueckert D,Edwards D,Hajnal J.2009.Robust segmentation of brain structures in MRI [C].IEEE International Symposium on Biomedical Imaging,17-20.
Nanni L,Lumini A,Brahnam S.2010.Local binary patterns variants as texture descriptors for medical image analysis [J].Artificial Intelligence in Medicine.49(2):117– 125
Ojala T,Pietikinen M.2002.Multiresolution Gray-scale and Rotation Invariant Texture Classification with Local Binary Patterns [J].IEEE Transaction On Pattern Analysis and Machine Intelligence.24(7):971-987.
Parker G.,Wheeler-Kingshott C.,Barker G.2002.Estimating distributed anatomical connectivity using fast marching methods and diffusion tensor imaging [J].IEEE Trans.Med.Imag.21 (5),505–512.
Parker,G.,Haroon,H.,Wheeler-Kingshott,C.,2003.A framework for a streamlinebased probabilistic index of connectivity (PICo) using a structural interpretation of MRI diffusion measurements [J].J.Magn.Reson.Imag.18,242–254.
Parker,G.,Alexander,D.,2003.Probabilistic Monte Carlo based mapping of cerebralconnections utilising whole-brain crossing fibre information [C].In: Proc.Information Processing in Medical Imaging,pp.684–695.
Parker,G.,Alexander,D.,2005.Probabilistic anatomical connectivity using persistent angular structure obtained from diffusion weighted imaging [J].Phil.Trans.Roy.Soc.Ser.B 360,893–902.
Peled,S.,Friman,O.,Jolesz,F.,Westin,C.F.2006.Geometrically constrained two-tensor model for crossing tracts in DWI [J].Magnetic Resonance Imaging,vol.24.1263-1270.
Pichon E.,Westin C.,Tannenbaum A.2005.A Hamilton–Jacobi–Bellman approach to high angular resolution diffusion tractography [C].In: Proc.MICCAI,pp.180-187.
Pohlman S,Powell K.A,Obuchowski N.A,et al.1996.Quantitative classification of breast tumors in digitized mammograms [J].Medical Physics.23:1337-1345.
Prados E.,Lenglet C.,Pons J.,Wotawa N.,Deriche R.,Faugeras O.,Soatto S.2006.Control theory and fast marching techniques for brain connectivity mapping [C].In: Proc.CVPR,pp.1076-1083.
Qazi A.A.,Radmanesh A.,O'Donnell L.,Kindlmann G.,Peled S.,Whalen S.2009.Resolving crossings in the corticospinal tract by two-tensor streamline tractography: Method and clinical assessment using fMRI [J].NeuroImage 47(supplement 2):T98-T106
Rother C,Blake A,Kolmogorov V.2004.Grabcut-Interactive foreground extraction using iterated graph cuts [J].Siggraph2004,ACM Transaction on Graphics.23(3):309-314.
Shi J B,Malik J.2000.Normalized cuts and image segmentation [J].IEEE Transactions on Pattern analysis and machine intelligence.22(8):888-905.
Unay D,Ekin A,Cetin M,Jasinschi R,Ercil A.2007.Robustness of Local Binary Patterns in Brain MR Image Analysis [C].In: Proceedings of the 29th Annual International Conference of the IEEE EMBS.CitéInternationale,Lyon,France,2098– 2101.
Van Leemput K,Maes F,Vandermeulen D.1999.Automated model-based bias field correction of MR images of the brain [J].IEEE Trans Med Imaging,18(10):885-896.
Weinstein D M ,Kindlmann G L ,Lundberg E C.1999.Tensorlines : advection2diffusion based propagation through diffusion tensor fields [C].IEEE Visualization Proceedings.San Francisco ,USA ,249-253.
Wighton P,Sadeghi M,Lee TK,Atkins MS.2009.A Fully Automatic Random Walker Segmentation for Skin Lesions in a Supervised Setting [C].In: Proceedings of the 12th International Conference on Medical Image Computing and Computer-Assisted Intervention.London,UK,1108 - 1115.
Yang,J.,Staib,L.,Duncan,J.2004.Neighbor-constrained segmentation with level set based3D deformable models [J].IEEE Trans.Medical Imaging,23(8):940-948
Zahn C.1971.Graph Theoretical Methods for Detecting and Describing Gestalt Clusters [J].IEEE Transactions on Computation.20:68-86.
Zeng X,Staib L,Schultz R,Duncan J.1999.Segmentation and measurement of the cortex from 3D MR images using coupled-surface propagation [J].IEEE Trans.Medical Imaging,18(10):74-86
Zhang,Y.,Brady,M.,Smith,S.2001.Segmentation of brain MR images through a hidden Markov model and the expectation-maximization algorithm [J].IEEE Trans.Medical Imaging,20(1):45-57
Zhengrong Liang,Su Wang.2009.An EM Approach to MAP Solution of Segmenting Tissue Mixtures: A Numerical Analysis [J].IEEE Transactions on Medical Imaging,28(2):297-310.
汤天宇,阮宗才.2007.基于FMT的扩散张量成像脑白质纤维跟踪算法[J].华中科技大学学报.35:182-186.
王明时,高伟,赵欣,路会生,刘海婴,王力群,李德彪.2006.白质纤维重建过程中像素内交叉问题解决方法[J].天津大学学报.39(3):354-359.
刘晓东,蔡子凡,王婷婷,姚力,卢洁.2008.全张量步长适应性脑白质纤维跟踪改进算法[J].北京师范大学学报.44(2):212-216.
于春水,李坤成.2004.弥散张量成像纤维跟踪技术的研究进展[J].中国医学影像技术.20(3):477-479.
何光武,张贵祥,王斌,项华,何江波,成中意,汪守中.2008.大脑白质纤维磁共振弥散张量成像扫描参数研究[J].中国中西医结合影像学杂志.6(6):163-166.
饶晶晶,漆剑频,王承缘.2008.扩散张量成像扩散梯度方向与DTI图像质量的相关性研究[J].放射学实践.23(3):320-323.
江贵平,刘哲星,冯前进,陈武凡.2005.基于DT-MRI的纤维跟踪及可视化研究[J].中国医学物理学杂志.22(3):514-518.
田捷,包尚联,周明全.2003.医学影像处理与分析[M].电子工业出版社.
Ardizzone E,Pirrone R,Gambino O,Alagna F.2009.Segmentation of MR Brain images with Bias Artifact [C].In: Proceedings of IEEE International Conference on Information Technology and Applications in Biomedicine.1- 4.
Ashburner J,Friston K.2005.Unified segmentation [J].NeuroImage.26(3) : 839– 851.
Barmpoutis,Bing Jian,and Baba C.Vemuri.2009.Adaptive Kernels for Multi-fiber Reconstruction [J].Process Med Imaging.21: 338–349.
Basser PJ,Matiello J,Le Bihan D.1994.Estimation of the effective self diffusion tensor from the NMR spin echo [J].J Magn Reson.103:247–54.
Behrens,T.,Woolrich,M.,Jenkinson,M.,Johansen-Berg,H.,Nunes,R.,Clare,S.,Matthews,P.,Brady,J.,Smith,S.2003.Characterization and propagation of uncertainty in diffusion-weighted MR imaging [J].Magn.Reson.Med.50:1077–1088.
Behrens,T.,Berg,H.J.,Jbabdi,S.,Rushworth,M.,Woolrich,M.2007.Probabilistic diffusion tractography with multiple fibre orientations: what can we gain? [J].NeuroImage.34:144–155.
Benoit C,Nicolas P,Piotr A H,Colin S,Fran?ois R.2010.A non-local fuzzy segmentation method: Application to brain MRI [J].Pattern Recognition.
Blyth R.2003.Tractography with multiple fiber directions.In proceeding of ISMRM[C],1-4.
Boykov Y,Jolly M P.2001.Interactive graph cuts for optimal boundary & region segmentation of objects in n-d images [C].In Proceedings of ICCV.1:105-112.
Bjornemo,M.,Brun,A.,Kikinis,R.,Westin,C.F.2002.Regularized stochastic white matter tractography using diffusion tensor MRI [C].In: Proc.MICCAI.pp.435-442.
Brun,A.,Bjornemo,M.,Kikinis,R.,Westin,C.F.2002.White matter tractography using sequential importance sampling [C].In: Proc.ISMRM Annual Meeting.pp.1131-1135.
Doyle P,Snell L.1984.Random Walks and Electric Networks,Volume 22 of Carus Mathematical [M].Mathematical Association of America,Washington DC.
Fletcher P.,Tao R.,Jeong W.,Whitaker R.T.2007.A volumetric approach to quantifying region-to-region white matter connectivity in diffusion tensor MRI [C]. In: Proc.Information Processing in Medical Imaging.pp.346–358.
Friman,O.,Farneback,G.,Westin,C.2006.A bayesian approach for stochastic white matter tractography [J].IEEE Trans.Med.Imag.25 (8),965–978.
Grady L,Funka-Lea G.2004.Multi-Label Image Segmentation for Medical Applications Based on Graph-Theoretic Electrical Potentials [C].Proc.Workshop Computer Vision and Math.Methods in Medical and Biomedical Image Analysis.230-245.
Grady L,Schiwietz T,Aharon S,Westermann R.2005.Random Walks for Interactive Organ Segmentation in Two and Three Dimensions [C].In: Proceedings of the 8th International Conference on Medical Image Computing and Computer-Assisted Intervention.773-780.
Grady L.2006.Random Walks for Image Segmentation [J].IEEE Transactions on Pattern Analysis and Machine Intelligence.28(11):1768-1783.
Gossl C.,Fahrmeir L.,Putz B.,Auer L.,Auer D.2002.Fiber tracking from DTI using linear state space models: detectability of the pyramidal tract [J].NeuroImage.16: 378–388.
Jenkinson M,Pechaud M,Smith S.2005.BET2: MR-based estimation of brain,skull and scalp surfaces [C].In: Proceedings of the 11th Annual Meeting of the Organization for Human Brain Mapping.
Kim K H,Ronen I,Formisano E.2004.Robust fiber tracking method by vector selection criterion in diffusion tensor images [C].Proceedings of the 26th Annual International Conference of the IEEE EMBS.San Francisco,USA,1080-1083.
Lazar,M.,Weinstein,D.,Tsuruda,J.,Hasan,K.,Arfanakis,K.,Meyerand,E.,Badie,B.,Rowley,H.,Haughton,V.,Field,A.,Witwer,B.,Alexander,A.,2003.White matter tractography using tensor deflection [J].Hum.Brain Mapp.18,306–321.
Lazar,M.,Alexander,A.,2005.Bootstrap white matter tractography (BOOT-TRAC) [J].NeuroImage 24,524–532.
Maenpaa T.Pietikainen M.2001.Texture analysis with local binary patterns.Handbook of Pattern Recognition and Computer Vision[M].3rd ed,World Scientific,Singapore.711-736.
Maier F,Wimmer A,Soza G,Kaftan J N,Fritz D,Dillmann R.2008.Automatic Liver Segmentation using the Random Walker Algorithm [J].Bildverarbeitung für die Medizin.
Mayer A,Greenspan H.2009.An Adaptive Mean-Shift Framework for MRI Brain Segmentation [J].IEEE Trans Medical Imaging,28(8):1238– 1250.
McInerney,T.,Terzopoulos,D.1996.Deformable models in medical image analysis [J].Medical Image Analysis,1:91–108
Mori,S.,Crain,B.,Chacko,V.,van Zijl,P.1999.Three-dimensional tracking of axonal rojections in the brain by magnetic resonance imaging [J].Ann.Neurol.5,265-269.
Mori S,van Zijl PCM.2002.Fiber tracking: principles and strategies—a technical review [J].NMR Biomed;15:468–80.
Mortensen E N,Barrett W A.1995.Intelligent scissors for image composition [C].Proceedings of the 22nd annual conference on Computer graphics and interactive techniques.191-198.
Moumen E,Hashim M.2009.Incorporating prior information in the fuzzy C-mean algorithm with application to brain tissues segmentation in MRI [C].In: Proceedings of IEEE International Conference on Image Processing.Cairo,Egypt,3393- 3396.
Murgasova M,Rueckert D,Edwards D,Hajnal J.2009.Robust segmentation of brain structures in MRI [C].IEEE International Symposium on Biomedical Imaging,17-20.
Nanni L,Lumini A,Brahnam S.2010.Local binary patterns variants as texture descriptors for medical image analysis [J].Artificial Intelligence in Medicine.49(2):117– 125
Ojala T,Pietikinen M.2002.Multiresolution Gray-scale and Rotation Invariant Texture Classification with Local Binary Patterns [J].IEEE Transaction On Pattern Analysis and Machine Intelligence.24(7):971-987.
Parker G.,Wheeler-Kingshott C.,Barker G.2002.Estimating distributed anatomical connectivity using fast marching methods and diffusion tensor imaging [J].IEEE Trans.Med.Imag.21 (5),505–512.
Parker,G.,Haroon,H.,Wheeler-Kingshott,C.,2003.A framework for a streamlinebased probabilistic index of connectivity (PICo) using a structural interpretation of MRI diffusion measurements [J].J.Magn.Reson.Imag.18,242–254.
Parker,G.,Alexander,D.,2003.Probabilistic Monte Carlo based mapping of cerebralconnections utilising whole-brain crossing fibre information [C].In: Proc.Information Processing in Medical Imaging,pp.684–695.
Parker,G.,Alexander,D.,2005.Probabilistic anatomical connectivity using persistent angular structure obtained from diffusion weighted imaging [J].Phil.Trans.Roy.Soc.Ser.B 360,893–902.
Peled,S.,Friman,O.,Jolesz,F.,Westin,C.F.2006.Geometrically constrained two-tensor model for crossing tracts in DWI [J].Magnetic Resonance Imaging,vol.24.1263-1270.
Pichon E.,Westin C.,Tannenbaum A.2005.A Hamilton–Jacobi–Bellman approach to high angular resolution diffusion tractography [C].In: Proc.MICCAI,pp.180-187.
Pohlman S,Powell K.A,Obuchowski N.A,et al.1996.Quantitative classification of breast tumors in digitized mammograms [J].Medical Physics.23:1337-1345.
Prados E.,Lenglet C.,Pons J.,Wotawa N.,Deriche R.,Faugeras O.,Soatto S.2006.Control theory and fast marching techniques for brain connectivity mapping [C].In: Proc.CVPR,pp.1076-1083.
Qazi A.A.,Radmanesh A.,O'Donnell L.,Kindlmann G.,Peled S.,Whalen S.2009.Resolving crossings in the corticospinal tract by two-tensor streamline tractography: Method and clinical assessment using fMRI [J].NeuroImage 47(supplement 2):T98-T106
Rother C,Blake A,Kolmogorov V.2004.Grabcut-Interactive foreground extraction using iterated graph cuts [J].Siggraph2004,ACM Transaction on Graphics.23(3):309-314.
Shi J B,Malik J.2000.Normalized cuts and image segmentation [J].IEEE Transactions on Pattern analysis and machine intelligence.22(8):888-905.
Unay D,Ekin A,Cetin M,Jasinschi R,Ercil A.2007.Robustness of Local Binary Patterns in Brain MR Image Analysis [C].In: Proceedings of the 29th Annual International Conference of the IEEE EMBS.CitéInternationale,Lyon,France,2098– 2101.
Van Leemput K,Maes F,Vandermeulen D.1999.Automated model-based bias field correction of MR images of the brain [J].IEEE Trans Med Imaging,18(10):885-896.
Weinstein D M ,Kindlmann G L ,Lundberg E C.1999.Tensorlines : advection2diffusion based propagation through diffusion tensor fields [C].IEEE Visualization Proceedings.San Francisco ,USA ,249-253.
Wighton P,Sadeghi M,Lee TK,Atkins MS.2009.A Fully Automatic Random Walker Segmentation for Skin Lesions in a Supervised Setting [C].In: Proceedings of the 12th International Conference on Medical Image Computing and Computer-Assisted Intervention.London,UK,1108 - 1115.
Yang,J.,Staib,L.,Duncan,J.2004.Neighbor-constrained segmentation with level set based3D deformable models [J].IEEE Trans.Medical Imaging,23(8):940-948
Zahn C.1971.Graph Theoretical Methods for Detecting and Describing Gestalt Clusters [J].IEEE Transactions on Computation.20:68-86.
Zeng X,Staib L,Schultz R,Duncan J.1999.Segmentation and measurement of the cortex from 3D MR images using coupled-surface propagation [J].IEEE Trans.Medical Imaging,18(10):74-86
Zhang,Y.,Brady,M.,Smith,S.2001.Segmentation of brain MR images through a hidden Markov model and the expectation-maximization algorithm [J].IEEE Trans.Medical Imaging,20(1):45-57
Zhengrong Liang,Su Wang.2009.An EM Approach to MAP Solution of Segmenting Tissue Mixtures: A Numerical Analysis [J].IEEE Transactions on Medical Imaging,28(2):297-310.