MRI颅脑图像分割算法研究
|
摘要
随着各种影像检查设备在临床上的应用,医学图像的后处理技术成为近年来图像处理领域中的研究热点问题,而图像分割是图像的三维重建、可视化、配准、融合和定量分析等技术的前提和基础。本文在研究常用图像分割算法的基础上,主要探讨图割(Graph Cut)算法在MRI脑组织图像分割中的应用问题,任务是实现脑灰质(Gray Matter, GM)、脑白质(white matter, WM)和脑脊液(cerebrospinal fluid,CSF)等组织的分割。
对于最小割的求解问题,本文采用“预流”(preflow)算法求网络最大流,获得最小割集,实现图像的分割,提高了算法的运算速度。
针对归一割算法计算速度慢的弱点,本文将分水岭变换引入到图割(GraphCut)框架中,提出一种新的基于分水岭预分割的快速归一割(sNcut)算法。图割算法应用到图像分割中,其核心是根据某个模型将图像映射成一个加权无向图,并寻求图的最优割集,从而实现图像目标区域与背景区域的分割。将分水岭变换分割出来的若干个内部像素密切相关的小区域映射成图的顶点,可大大减少顶点的数目,运算速度较像素点的直接映射方法明显提高。
针对分水岭算法本身的过分割问题,以及噪声信号对过分割的助长现象,本文设计了一个多结构的自适应形态滤波器,消除图像中的噪声,并在分水岭分割之后采用添加标记点法进行区域合并,这种分割的前处理和后处理有效地抑制了过分割现象,保证预分割的结果是有意义的,为图的构建及最优割集的寻找提供前提条件。
另外,为了保证归一割算法分割的准确性,本文对权重的确定方法进行了改进,一般的方法是利用像素的灰度梯度确定权重,建立图模型,本文综合利用像素的灰度和空间两方面的信息确定顶点之间的权重,提出一个新的权重模型ISI(indensity and spatial information, ISI)。
为了验证算法的有效性,本文采用40套脑图像数据进行仿真实验,其中35套数据的分割结果达到预期目的,可以准确地将脑灰质、脑白质和脑脊液等组织分割出来,其它5套数据由于图像质量导致无法分割或分割错误,其分割的正确率为87.5%,该实验结果表明本文提出的算法是有效的。
With the clinical application of all kinds of imaging equipments, the medical image post-processing technology has become the hot issue in the recent image segmentation field, while the image segmentation is the premise and foundation of the three-dimensional reconstruction, visualization, registration, integration and quantitative analysis techniques. Based on the research of several usual image segmentation algorithm, the paper focuses on the use of Graph Cut algorithm in the MRI brain image. And the task is to achieve the partition of brain gray matter (GM), white matter (WM) and cerebrospinal fluid (CSF).
For the minimum cut solution of the problem, this paper adopts the "preflow" algorithm for the maximum flow of the graph network in order to attain the minimum cut set. The method achieves the image segmentation algorithm and improves computational speed.
Owing to the normalized cut (Ncut) algorithm's weakness of calculating slowly, the paper uses the watershed transformation algorithm in the graph cut framework and propose a new speedy normalized cut algorithm—sNcut algorithm. The graph cut is applied to the image segmentation, whose core is to map an image into a weighted undirected graph based on a certain model and then search for the optimal cut set in order to achieve the partition of the object region and background region. A number of small regions, split by the watershed transformation, whose internal pixels are closely related to one another, are mapped the vertices in the graph. This method can significantly reduce the number of vertices and the computing speed has improved significantly than the direct pixel mapping method.
Direct at the over-segmentation problem in the watershed processing and the phenomenon that noise signal encourages the over-segmentation, the paper designs a multi-structure adaptive morphological filters to remove the image noise and proceeds the region combination by adding marker points. The pre-processing and post-processing of segmentation effectively inhibits the phenomenon of over-segmentation to ensure that the result of the pre-segmentation is meaningful and to provide a prerequisite for the graph construction and searching for the optimal cut set.
In addition, in order to ensure the accuracy of the normalized cut segmentation, the paper improves the method of determining weights. The general approach is to use the pixels'gray gradient to determine the weight and establish the graph model. The paper combines the pixels'grayscale and space information to determine the weight between the vertices and proposes a new model of weight--indensity and spatial information (ISI).
In order to verify the effectiveness of the algorithm, this paper uses 40 sets of brain image data for simulation experiments. However the segmentation results of 35 sets of data achieves the intended purpose and cerebral gray matter, white matter and cerebrospinal fluid and other organizations can be partitioned accurately. The other five sets of the data can not be divided or split error due to image quality. The correct rate of segmentation is87.5%, and the experimental results show that the proposed algorithm is effective.
对于最小割的求解问题,本文采用“预流”(preflow)算法求网络最大流,获得最小割集,实现图像的分割,提高了算法的运算速度。
针对归一割算法计算速度慢的弱点,本文将分水岭变换引入到图割(GraphCut)框架中,提出一种新的基于分水岭预分割的快速归一割(sNcut)算法。图割算法应用到图像分割中,其核心是根据某个模型将图像映射成一个加权无向图,并寻求图的最优割集,从而实现图像目标区域与背景区域的分割。将分水岭变换分割出来的若干个内部像素密切相关的小区域映射成图的顶点,可大大减少顶点的数目,运算速度较像素点的直接映射方法明显提高。
针对分水岭算法本身的过分割问题,以及噪声信号对过分割的助长现象,本文设计了一个多结构的自适应形态滤波器,消除图像中的噪声,并在分水岭分割之后采用添加标记点法进行区域合并,这种分割的前处理和后处理有效地抑制了过分割现象,保证预分割的结果是有意义的,为图的构建及最优割集的寻找提供前提条件。
另外,为了保证归一割算法分割的准确性,本文对权重的确定方法进行了改进,一般的方法是利用像素的灰度梯度确定权重,建立图模型,本文综合利用像素的灰度和空间两方面的信息确定顶点之间的权重,提出一个新的权重模型ISI(indensity and spatial information, ISI)。
为了验证算法的有效性,本文采用40套脑图像数据进行仿真实验,其中35套数据的分割结果达到预期目的,可以准确地将脑灰质、脑白质和脑脊液等组织分割出来,其它5套数据由于图像质量导致无法分割或分割错误,其分割的正确率为87.5%,该实验结果表明本文提出的算法是有效的。
With the clinical application of all kinds of imaging equipments, the medical image post-processing technology has become the hot issue in the recent image segmentation field, while the image segmentation is the premise and foundation of the three-dimensional reconstruction, visualization, registration, integration and quantitative analysis techniques. Based on the research of several usual image segmentation algorithm, the paper focuses on the use of Graph Cut algorithm in the MRI brain image. And the task is to achieve the partition of brain gray matter (GM), white matter (WM) and cerebrospinal fluid (CSF).
For the minimum cut solution of the problem, this paper adopts the "preflow" algorithm for the maximum flow of the graph network in order to attain the minimum cut set. The method achieves the image segmentation algorithm and improves computational speed.
Owing to the normalized cut (Ncut) algorithm's weakness of calculating slowly, the paper uses the watershed transformation algorithm in the graph cut framework and propose a new speedy normalized cut algorithm—sNcut algorithm. The graph cut is applied to the image segmentation, whose core is to map an image into a weighted undirected graph based on a certain model and then search for the optimal cut set in order to achieve the partition of the object region and background region. A number of small regions, split by the watershed transformation, whose internal pixels are closely related to one another, are mapped the vertices in the graph. This method can significantly reduce the number of vertices and the computing speed has improved significantly than the direct pixel mapping method.
Direct at the over-segmentation problem in the watershed processing and the phenomenon that noise signal encourages the over-segmentation, the paper designs a multi-structure adaptive morphological filters to remove the image noise and proceeds the region combination by adding marker points. The pre-processing and post-processing of segmentation effectively inhibits the phenomenon of over-segmentation to ensure that the result of the pre-segmentation is meaningful and to provide a prerequisite for the graph construction and searching for the optimal cut set.
In addition, in order to ensure the accuracy of the normalized cut segmentation, the paper improves the method of determining weights. The general approach is to use the pixels'gray gradient to determine the weight and establish the graph model. The paper combines the pixels'grayscale and space information to determine the weight between the vertices and proposes a new model of weight--indensity and spatial information (ISI).
In order to verify the effectiveness of the algorithm, this paper uses 40 sets of brain image data for simulation experiments. However the segmentation results of 35 sets of data achieves the intended purpose and cerebral gray matter, white matter and cerebrospinal fluid and other organizations can be partitioned accurately. The other five sets of the data can not be divided or split error due to image quality. The correct rate of segmentation is87.5%, and the experimental results show that the proposed algorithm is effective.
引文
[1]吴恩惠,冯敢生,白人驹,韩萍.医学影像学[M].北京：人民卫生出版社,2008
[2]范立南,韩晓微,张广渊.图像处理与模式识别[M].北京：科学出版社,2007
[3]范立南,韩晓微,王忠实,等.基于多结构元的噪声污染灰度图像边缘检测研究[J],武汉大学学报,2003,36(3)：86-90
[4]付宜利,高文鹏,王树国.基于阈值分割的K-最近邻规则的磁共振脑图像分割算法的研究[J].医学影像学杂志,2008,15(8)：644-647
[5]谈国军,戎皓.基于二维最大熵与之图像分割技术的改进方法[J].软件导刊,2008,7(1)：3-4
[6]陈敏.一种全自动识别最优阈值的图像分割方法[J].计算机应用与软,2006,23(4)：85-86
[7]周德芳,张健.二维最大熵阈值分割的一种快速递推算法及应用[J].现代电子技术,2003,24：85-87
[8]施博,童小念.基于并行遗传算法的双阈值图像分割方法[J].图像处理,2009,25(1)：304-306
[9]张春丽.基于分层遗传算法的双阈值图像分割[J].微计算机应用,2008,29(1)：91-95
[10]Melkemi K E,Mohamed B,Sebti F. A multiagentsystem approach for image segmentation using genetic algorithms and extremal optimization heuris-tics[J]. Pattern Recognition Letters,2006,27,27 (11):1230-1238
[11]徐燕,关履泰.基于多小波变换的分水岭医学数字图像分割算法[J].数理医药学杂志,2007,20(3)：298-300
[12]宋军,邵谦明,周耀华.小波变换尺度过零点表征及在医学超声图像分割重的应用[J].复旦学报(自然科学版),2001,40(1)：40-43.
[13]杨丽君,王保保.一种基于小波和分水岭变换的图像分割方法[J].计算机应用2005,25(2)：253-254
[14]Sun M, Li C, Zhang Y, et al. Symmetric wavelet transforms for edge localization[J].Optical Engineering,1994,337,33(7):2272～2281
[15]蒋小标,汤光明,徐蕾.基于模糊理论的图像分割方法[J].计算机工程与设计,2007, 28(16)：3940-3942
[16]左奇,史忠科.基于模糊理论的图像分割方法[J].西北工业大学,2003,21(3)：313-316
[17]黄永锋等.模糊神经网络在颅脑磁共振图像分割中的应用研究[J].中国生物医学工程学报,2003,22(6)：508-512
[18]Horikawa S, Furuhashi T,Uchikawa Y.On fuzzy modeling using neural networds with the back propagation algorithm[J]. IEEE Trans. on Neural Networks,1992,3(5):801-806
[19]Bischof H, Schneider W, Pomz AJ. Multispectral classification of landsat-images using neural networks[J]. IEEE Trans, on Geoscience and Remote Sensing,1992,30(3):482-490.
[20]Lera G, Pinzolas M. Neighborhood based Levenberg-Marquardt algorithm for neural network training[J].IEEE Transactions on Neural Networks,2002,135,13(5):1200-1203
[21]孙炜等.基于自组织小波神经网路的磁共振图像分割方法[J].电子测量与仪器学报,2008,22(4)：26-29
[22]王妍玲,韩宏杰.基于小波神经网路的脑图像分割研究[J].计算机仿真,2008,25(6)：206-209
[23]贾富仓,李华.一种基于三阶中心矩的图像边缘检测方法[J].计算机工程应用,2004,9：11-12
[24]卜娟,王向阳,孙艺峰.基于模糊C均值聚类的多分量彩色图像分割算法[J].中国图象图形学报,2008,13(10)：1837-1840
[25]Zainal A A, Akira A. Image segmentation by histogram thresholding using hierarchical cluster analysis[J].Pattern Recognition Letters,2006,27,27 (13):1515-1521
[26]余学飞,李彬,陈武凡.基于模糊核聚类的MR图像分割新算法[J].南方医科大学学报,2008,28(4)：555-557
[27]Ahmed M N, Yamany S M, Mohamed N, etal. A modified fuzzy C-means algorithm for bias field estimation and segmentation of MRI data[J].IEEE Transactions on Multimudia.2002,21(3):193-199
[28]Pham D L. Spatialmodels for fuzzy clustering[J].Computer Vision and Image Understanding,2001,84 (2):285～297
[29]Alan Liew WC, Yan H. An adaptive spatial fuzzy clustering algorithm for3-D MR image segmentation[J].IEEE Trans Med Imag,2003,22 (9):1063-75
[30]刘旭,寿文德.颅脑磁共振图像分割评价的统计学方法[J].医疗卫生装备,2004,7：6-7
[31]ZhangY.J. A Survey on evaluation methods for image segmentation[J].Pattern Recognition,1996,29(8):1335-1346
[32]Kapur,et al.Segmentation of brain tissue from magnetic resonance images[J].Medical Image Analysis,1996,1(2):109-127
[33]Kikinis,et al. Statistical intensity correction and segmentation of magnetic resonance image data[J].Processing of the Third Conference on Visualization in Biomedical Coputing,1994,1(7):13-14
[34]史勇红,臧飞虎.一种自适应立体脑图像分割方法[J].中国医疗器杂志,2006,30(2)：87-89
[35]刘国英,傅明,唐贤英,孟爱国.一种基于多分辨率分析的简化的分裂-合并图像分割算法[J].长沙理工大学学报,2006,3(4)：77-80
[36]Jong-Bae Kim, Hang Joon Kim. Multiresolution-based watersheds for efficient image segmentation[J]. Pattern Recogn itionLetters,2003,24:473-488
[37]喻罡,李鹏,缪亚林,卞正中.多分辨超声心动图像分割模型[J].西安交通大学学报,2006,40(4)：432-436
[38]句彦伟,田铮,武新乾.基于广义多分辨似然比和混合多尺度自回归预报模型的图像无监督分割[J].计算机科学,2007,34(2)：234-237
[39]Comer ML,Delp E J. Segmentation of textured images using a multiresolution gaussian autoregressive model[J].IEEE Trans I mage Processing,1999,8 (3):408～ 420
[40]姜红军,王可佳,海鹰,张得龙,平子良.基于数学形态学的医学图像自动阈值分割[J].内蒙古师范大学学报(自然科学汉文版),2008,37(3)：397-402
[41]侯立华.改进Snake模型在医学超声图像分割中的应用[J].计算仿真,2008,25(8)：183-185
[42]廖亮,林土胜,张卫东.基于静电力方法的主动轮廓模型的脑部MRI图像分割[J].生物医学工程杂志,2008,25(4)：770-789
[43]栾红霞,戚飞虎.一种新的用于MR脑图像分割的主动轮廓模型[J].仪器仪表学报,2004,25(4)：558-580
[44]湛永松,雷德斌,潘春洪,石民勇.基于图切割的交互式图像分割算法[J].系统仿真报,2008,20(3)：799-803
[45]徐秋平.郭敏.田丽丽.基于梯度矢量流Snake模型与图割的目标边界提取[J].计算机工程与应用,2008,44(28)：158-160
[46]徐利娜,彭国华.图像分割中一种改进的图割模型[J].计算机技术,2006,6(18):2853-2858
[47]Xu N, Ahuja N, Bansal R. Object Segmentation Using Graph Cuts Based Active Contours[J].Computer Vision and Image Understanding,2007,107 (3):210-224
[48]Boykov Y,Funka-Lea G. Graph cuts and efficient N-D image segmentation[J].International Journal of Computer Vision,2006,70 (2):109-131
[49]刘嘉,王宏琦.一种基于图割的交互式图像分割方法[J].电子与信息学报,2008,30(8)：1973-1976
[50]Rother C,Kolmogorov V, Blake A. GrabCut—interactive foreground extraction using iterated graph cuts[J].ACM Trans.Graphics,Los Angeles,2004,23 (3):309-314
[51]Kolmogorov V,Zabih R. What energy functions can be minimized via graph cuts? [J].IEEE Trans.on Pattern Analysis and Machine Intelligence,2004,26 (2):147-159
[52]Xu N, Ahuja N, Bansal R. Object Segmentation Using Graph Cuts Based Active Contours[J].Computer Vision and Image Understanding,2007,107 (3):210-224
[53]Boykov Y,Funkalea G. Graph cuts and efficient N-D image segmentation [J]. International Journal of Computer Vision,2006,70 (2):109-131
[54]Rother C, Kolmogorov V, Blake A. Grabcut:Interactive foreground extraction using iterated graph cuts[J]. ACMTransac-tions on Graphics,2004,23 (3):309-314
[55]Boykov Y, Jolly MP. Interactive graph cuts for optimal boundary and region segmentation of objects in N-D images [J].Proceedings of Eighth IEEE International Conference on Computer Vi-sion. Washington: IEEE,2001,1:105-112
[56]杨帆,廖庆敏.基于图论的图像分割算法的分析与研究[J].视频技术应用与程,2006,7：80-83
[57]Zhen Wu, Richard Leahy. An Optimal Graph Theoretic Approach to Data Clustering: Theory and Its Application to Image Segmentation[J].IEEE transactions on pattern analysis and machine intelligence,1993,15(11):1101-1113
[58]Song Wang, Jeffrey Mark Siskind. Image Segmentation with Ratio Cut[J].IEEE transactions on pattern analysis and machine intelligence,2003,25(6):675-690
[59]Jianbo Shi, Jitendra Malik. Normalized Cuts and Image Segmentation.IEEE transactions on pattern analysis and machine intelligence,2000,22(8):888-905
[60]S Sarkar, K L Boyer. Quantitative Measures of Change Based on Feature Organization: Eigenvalues and Eigenvectors[J].Proc IEEE Conf Computer Vision and Pattern Recognition,1996
[61]C Ding,X F Ren,H Zha et al.Spectral Min-max Cut for Graph Partitioning and Data Clustering[J].Proc of the IEEE Intl Conf on Data Mining,2001:107～114
[62]O Veksler. Image Segmentation by Nested Cuts[J]. Proc IEEE CS Conf Computer Vision and Pattern Recognition,2000:339～344
[63]闫成新,桑农,张天序.基于图论的图像分割研究进展[J].计算机工程与应用,2006,42(5)：11-14
[64]Luc Vincent, Pierre Soille. Watersheds in Digital Spaces:An Efficient Algorithm Based on Immersion Simulations[J].IEEE transactions on pattern analysis and machine intelligence,1991,13(6):583-598
[65]Andrew V. Goldberg, Robert E. Tarjan. A new approach to the Maximum Flow Problem[J]. Princeton university,1988
[66]关新平,黄娜,唐英干.一种基于标记阈值的分水岭分割新算法[J].系统工程与电子技术,2009,31(4)：972-975
[67]罗玲,解梅,陈杉.基于多尺度形态滤波的分水岭图像分割方法[J].计算机辅助设计与图形学学报,2004,16(2)：168-175
[68]Haris K, Efstratiadis S. Hybrid image segmentation using watersheds and fast region merging[J].IEEE Transactions on Image Processing,1998,7(12):1684-1698
[2]范立南,韩晓微,张广渊.图像处理与模式识别[M].北京：科学出版社,2007
[3]范立南,韩晓微,王忠实,等.基于多结构元的噪声污染灰度图像边缘检测研究[J],武汉大学学报,2003,36(3)：86-90
[4]付宜利,高文鹏,王树国.基于阈值分割的K-最近邻规则的磁共振脑图像分割算法的研究[J].医学影像学杂志,2008,15(8)：644-647
[5]谈国军,戎皓.基于二维最大熵与之图像分割技术的改进方法[J].软件导刊,2008,7(1)：3-4
[6]陈敏.一种全自动识别最优阈值的图像分割方法[J].计算机应用与软,2006,23(4)：85-86
[7]周德芳,张健.二维最大熵阈值分割的一种快速递推算法及应用[J].现代电子技术,2003,24：85-87
[8]施博,童小念.基于并行遗传算法的双阈值图像分割方法[J].图像处理,2009,25(1)：304-306
[9]张春丽.基于分层遗传算法的双阈值图像分割[J].微计算机应用,2008,29(1)：91-95
[10]Melkemi K E,Mohamed B,Sebti F. A multiagentsystem approach for image segmentation using genetic algorithms and extremal optimization heuris-tics[J]. Pattern Recognition Letters,2006,27,27 (11):1230-1238
[11]徐燕,关履泰.基于多小波变换的分水岭医学数字图像分割算法[J].数理医药学杂志,2007,20(3)：298-300
[12]宋军,邵谦明,周耀华.小波变换尺度过零点表征及在医学超声图像分割重的应用[J].复旦学报(自然科学版),2001,40(1)：40-43.
[13]杨丽君,王保保.一种基于小波和分水岭变换的图像分割方法[J].计算机应用2005,25(2)：253-254
[14]Sun M, Li C, Zhang Y, et al. Symmetric wavelet transforms for edge localization[J].Optical Engineering,1994,337,33(7):2272～2281
[15]蒋小标,汤光明,徐蕾.基于模糊理论的图像分割方法[J].计算机工程与设计,2007, 28(16)：3940-3942
[16]左奇,史忠科.基于模糊理论的图像分割方法[J].西北工业大学,2003,21(3)：313-316
[17]黄永锋等.模糊神经网络在颅脑磁共振图像分割中的应用研究[J].中国生物医学工程学报,2003,22(6)：508-512
[18]Horikawa S, Furuhashi T,Uchikawa Y.On fuzzy modeling using neural networds with the back propagation algorithm[J]. IEEE Trans. on Neural Networks,1992,3(5):801-806
[19]Bischof H, Schneider W, Pomz AJ. Multispectral classification of landsat-images using neural networks[J]. IEEE Trans, on Geoscience and Remote Sensing,1992,30(3):482-490.
[20]Lera G, Pinzolas M. Neighborhood based Levenberg-Marquardt algorithm for neural network training[J].IEEE Transactions on Neural Networks,2002,135,13(5):1200-1203
[21]孙炜等.基于自组织小波神经网路的磁共振图像分割方法[J].电子测量与仪器学报,2008,22(4)：26-29
[22]王妍玲,韩宏杰.基于小波神经网路的脑图像分割研究[J].计算机仿真,2008,25(6)：206-209
[23]贾富仓,李华.一种基于三阶中心矩的图像边缘检测方法[J].计算机工程应用,2004,9：11-12
[24]卜娟,王向阳,孙艺峰.基于模糊C均值聚类的多分量彩色图像分割算法[J].中国图象图形学报,2008,13(10)：1837-1840
[25]Zainal A A, Akira A. Image segmentation by histogram thresholding using hierarchical cluster analysis[J].Pattern Recognition Letters,2006,27,27 (13):1515-1521
[26]余学飞,李彬,陈武凡.基于模糊核聚类的MR图像分割新算法[J].南方医科大学学报,2008,28(4)：555-557
[27]Ahmed M N, Yamany S M, Mohamed N, etal. A modified fuzzy C-means algorithm for bias field estimation and segmentation of MRI data[J].IEEE Transactions on Multimudia.2002,21(3):193-199
[28]Pham D L. Spatialmodels for fuzzy clustering[J].Computer Vision and Image Understanding,2001,84 (2):285～297
[29]Alan Liew WC, Yan H. An adaptive spatial fuzzy clustering algorithm for3-D MR image segmentation[J].IEEE Trans Med Imag,2003,22 (9):1063-75
[30]刘旭,寿文德.颅脑磁共振图像分割评价的统计学方法[J].医疗卫生装备,2004,7：6-7
[31]ZhangY.J. A Survey on evaluation methods for image segmentation[J].Pattern Recognition,1996,29(8):1335-1346
[32]Kapur,et al.Segmentation of brain tissue from magnetic resonance images[J].Medical Image Analysis,1996,1(2):109-127
[33]Kikinis,et al. Statistical intensity correction and segmentation of magnetic resonance image data[J].Processing of the Third Conference on Visualization in Biomedical Coputing,1994,1(7):13-14
[34]史勇红,臧飞虎.一种自适应立体脑图像分割方法[J].中国医疗器杂志,2006,30(2)：87-89
[35]刘国英,傅明,唐贤英,孟爱国.一种基于多分辨率分析的简化的分裂-合并图像分割算法[J].长沙理工大学学报,2006,3(4)：77-80
[36]Jong-Bae Kim, Hang Joon Kim. Multiresolution-based watersheds for efficient image segmentation[J]. Pattern Recogn itionLetters,2003,24:473-488
[37]喻罡,李鹏,缪亚林,卞正中.多分辨超声心动图像分割模型[J].西安交通大学学报,2006,40(4)：432-436
[38]句彦伟,田铮,武新乾.基于广义多分辨似然比和混合多尺度自回归预报模型的图像无监督分割[J].计算机科学,2007,34(2)：234-237
[39]Comer ML,Delp E J. Segmentation of textured images using a multiresolution gaussian autoregressive model[J].IEEE Trans I mage Processing,1999,8 (3):408～ 420
[40]姜红军,王可佳,海鹰,张得龙,平子良.基于数学形态学的医学图像自动阈值分割[J].内蒙古师范大学学报(自然科学汉文版),2008,37(3)：397-402
[41]侯立华.改进Snake模型在医学超声图像分割中的应用[J].计算仿真,2008,25(8)：183-185
[42]廖亮,林土胜,张卫东.基于静电力方法的主动轮廓模型的脑部MRI图像分割[J].生物医学工程杂志,2008,25(4)：770-789
[43]栾红霞,戚飞虎.一种新的用于MR脑图像分割的主动轮廓模型[J].仪器仪表学报,2004,25(4)：558-580
[44]湛永松,雷德斌,潘春洪,石民勇.基于图切割的交互式图像分割算法[J].系统仿真报,2008,20(3)：799-803
[45]徐秋平.郭敏.田丽丽.基于梯度矢量流Snake模型与图割的目标边界提取[J].计算机工程与应用,2008,44(28)：158-160
[46]徐利娜,彭国华.图像分割中一种改进的图割模型[J].计算机技术,2006,6(18):2853-2858
[47]Xu N, Ahuja N, Bansal R. Object Segmentation Using Graph Cuts Based Active Contours[J].Computer Vision and Image Understanding,2007,107 (3):210-224
[48]Boykov Y,Funka-Lea G. Graph cuts and efficient N-D image segmentation[J].International Journal of Computer Vision,2006,70 (2):109-131
[49]刘嘉,王宏琦.一种基于图割的交互式图像分割方法[J].电子与信息学报,2008,30(8)：1973-1976
[50]Rother C,Kolmogorov V, Blake A. GrabCut—interactive foreground extraction using iterated graph cuts[J].ACM Trans.Graphics,Los Angeles,2004,23 (3):309-314
[51]Kolmogorov V,Zabih R. What energy functions can be minimized via graph cuts? [J].IEEE Trans.on Pattern Analysis and Machine Intelligence,2004,26 (2):147-159
[52]Xu N, Ahuja N, Bansal R. Object Segmentation Using Graph Cuts Based Active Contours[J].Computer Vision and Image Understanding,2007,107 (3):210-224
[53]Boykov Y,Funkalea G. Graph cuts and efficient N-D image segmentation [J]. International Journal of Computer Vision,2006,70 (2):109-131
[54]Rother C, Kolmogorov V, Blake A. Grabcut:Interactive foreground extraction using iterated graph cuts[J]. ACMTransac-tions on Graphics,2004,23 (3):309-314
[55]Boykov Y, Jolly MP. Interactive graph cuts for optimal boundary and region segmentation of objects in N-D images [J].Proceedings of Eighth IEEE International Conference on Computer Vi-sion. Washington: IEEE,2001,1:105-112
[56]杨帆,廖庆敏.基于图论的图像分割算法的分析与研究[J].视频技术应用与程,2006,7：80-83
[57]Zhen Wu, Richard Leahy. An Optimal Graph Theoretic Approach to Data Clustering: Theory and Its Application to Image Segmentation[J].IEEE transactions on pattern analysis and machine intelligence,1993,15(11):1101-1113
[58]Song Wang, Jeffrey Mark Siskind. Image Segmentation with Ratio Cut[J].IEEE transactions on pattern analysis and machine intelligence,2003,25(6):675-690
[59]Jianbo Shi, Jitendra Malik. Normalized Cuts and Image Segmentation.IEEE transactions on pattern analysis and machine intelligence,2000,22(8):888-905
[60]S Sarkar, K L Boyer. Quantitative Measures of Change Based on Feature Organization: Eigenvalues and Eigenvectors[J].Proc IEEE Conf Computer Vision and Pattern Recognition,1996
[61]C Ding,X F Ren,H Zha et al.Spectral Min-max Cut for Graph Partitioning and Data Clustering[J].Proc of the IEEE Intl Conf on Data Mining,2001:107～114
[62]O Veksler. Image Segmentation by Nested Cuts[J]. Proc IEEE CS Conf Computer Vision and Pattern Recognition,2000:339～344
[63]闫成新,桑农,张天序.基于图论的图像分割研究进展[J].计算机工程与应用,2006,42(5)：11-14
[64]Luc Vincent, Pierre Soille. Watersheds in Digital Spaces:An Efficient Algorithm Based on Immersion Simulations[J].IEEE transactions on pattern analysis and machine intelligence,1991,13(6):583-598
[65]Andrew V. Goldberg, Robert E. Tarjan. A new approach to the Maximum Flow Problem[J]. Princeton university,1988
[66]关新平,黄娜,唐英干.一种基于标记阈值的分水岭分割新算法[J].系统工程与电子技术,2009,31(4)：972-975
[67]罗玲,解梅,陈杉.基于多尺度形态滤波的分水岭图像分割方法[J].计算机辅助设计与图形学学报,2004,16(2)：168-175
[68]Haris K, Efstratiadis S. Hybrid image segmentation using watersheds and fast region merging[J].IEEE Transactions on Image Processing,1998,7(12):1684-1698