基于IVUS图像分割和CAG三维重建技术的数据融合研究
|
摘要
冠状动脉疾病中常见的动脉粥样硬化是危害人类健康的首要疾病之一,其主要的临床诊断方式为:X射线冠脉造影图像(Coronary angiography, CAG)和血管内超声成像(Intravascular Ultrasound, IVUS)。CAG可以对冠状动脉的结构和血管狭窄进行客观诊断,并可以通过三维重建获得具有空间形态结构的三维骨架,以便直接观察冠状动脉形貌特征。IVUS不仅可以对血管腔的直径、面积等参数进行精确测量,而且可以发现早期的冠状动脉粥样硬化斑块,进而对斑块的偏心距,壁厚及成分含量进行检测。融合CAG和IVUS图像数据,可以使两种方法的优势得到互补,在获得完全的冠状动脉实体模型的同时,不仅可以观察到血管段的空间位置,而且可以获得感兴趣血管段的内外膜及斑块量化数据,从而辅助临床诊断治疗。
本文的研究内容主要包括以下几个方面:
1.基于改进的Snake模型的血管内超声图像内外膜分割利用时空滤波器对IVUS图像进行图像增强。基于传统的Snake模型,通过改进内部能量函数和设计外部图像力,降低Snake函数曲线对斑块噪声和椒盐噪声的敏感度,在改善局部分割效果的同时,用贪婪法对Snake能量函数进行全局优化计算。
2.感兴趣血管段导引丝和血管骨架的三维重建及其优化提出了对感兴趣血管段导引丝三维重建的优化方法:即分别进行匹配点优化和几何变换矩阵优化。利用弦长公式设置六对初始匹配点,设计匹配点对的目标能量函数,并利用动态规划算法进行优化求解。
3. IVUS图像序列在三维导引丝上的定位计算提出了IVUS图像序列在三维导引丝上的定位方法:对导引丝序列点进行三次均匀B样条的光顺拟合,利用最佳垂平面法求取对应点的切矢量,并通过坐标变换关系,实现IVUS图像序列在导引丝上的定位。
4. IVUS图像序列在三维导引丝上的定向计算提出了IVUS图像序列在三维导引丝上的定向方法:利用空间曲线模型对相邻帧图像间的相对角度进行计算,根据匹配点对的空间几何关系求取偏心角,并用四元数和复合矩阵变换实现IVUS图像在导引丝上的准确定向。
5. IVUS图像序列与冠脉造影图像的数据融合实验利用模拟实验验证了定位、定向算法的正确性;利用临床获得的CAG和IVUS图像进行了数据融合实验,验证了融合算法的准确可行性。
Atherosclerosis which is a common disease in coronary artery disease is one of the primary human health hazards. It has two major clinical diagnostic methods: X-ray coronary angiography and intravascular ultrasound images. X-ray coronary angiography images can make an objective diagnosis for the structure of coronary artery and vascular stenosis. So we can obtain the three-dimensional spatial structure skeleton for direct observation about the coronary morphology through 3D reconstruction. Intravascular ultrasound can not only accurately measure the parameters of the lumen diameter and area, but also find the early coronary atherosclerotic plaque. So we can detect the eccentricity, wall thickness and the composition about plaque. We can make the advantages of both methods complement each other, through the data fusion between CAG and IVUS. We can obtain the solid model of coronary artery. At the same time, we can not only observe the spatial position of vessels, but also get the quantitative data of plaque for interested segment to help clinical diagnosis and treatment.
The main contents of this dissertation include five parts as follows:
1. Segmentation of lumen and media-adventitia border in intravascular ultrasound images based on improved Snake model
We firstly use a spatio-temporal filter to reduce the effect of speckles and enhance the images. Then, we ameliorate the internal energy and design the image energy for reducing the sensitivity. Finally, through experiment we improve the local segmentation. At the same time, we give a optimization calculation for the energy function of Snake by greedy method.
2. 3D reconstruction and optimization for catheter and vessel centerline in interested coronary artery
This paper proposes a method to optimize the 3D reconstruction of interested vessels: optimization of matched points and GT. Through setting six pairs of initial matched points by chord formula, designing the energy function for matched points optimization, we can solve it using dynamic programming algorithm.
3. Position calculation for IVUS image sequences located in 3D catheter
The methods are presented for IVUS image sequences to locate in 3D catheter. The point sequences of catheter are smoothed by B-spline curve fitting. We figure out the cut vector by the method of optimal vertical plane. Then, we can realize the location of IVUS image sequences in 3D catheter through the coordinate transformation.
4. Oriention calculation for IVUS image sequences located in 3D catheter
The methods are presented for IVUS image sequences to determine the orientation in 3D catheter. Relative twists are figured out by geometrical model of spatial curve between the adjacent frames. The eccentric angles can be figured out by the spatial relationship between matched points. Finally, we estimate the absolute orientation of IVUS image sequences in 3D catheter through quaternion and complex matrix translation respectively.
5. Experiment of data fusion between the IVUS image sequences and the coronary angiogram
The data fusion between the simulated, clinical IVUS images and coronary angiogram are experimented respectively, and the accuracy of the method is validated using error analysis.
本文的研究内容主要包括以下几个方面:
1.基于改进的Snake模型的血管内超声图像内外膜分割利用时空滤波器对IVUS图像进行图像增强。基于传统的Snake模型,通过改进内部能量函数和设计外部图像力,降低Snake函数曲线对斑块噪声和椒盐噪声的敏感度,在改善局部分割效果的同时,用贪婪法对Snake能量函数进行全局优化计算。
2.感兴趣血管段导引丝和血管骨架的三维重建及其优化提出了对感兴趣血管段导引丝三维重建的优化方法:即分别进行匹配点优化和几何变换矩阵优化。利用弦长公式设置六对初始匹配点,设计匹配点对的目标能量函数,并利用动态规划算法进行优化求解。
3. IVUS图像序列在三维导引丝上的定位计算提出了IVUS图像序列在三维导引丝上的定位方法:对导引丝序列点进行三次均匀B样条的光顺拟合,利用最佳垂平面法求取对应点的切矢量,并通过坐标变换关系,实现IVUS图像序列在导引丝上的定位。
4. IVUS图像序列在三维导引丝上的定向计算提出了IVUS图像序列在三维导引丝上的定向方法:利用空间曲线模型对相邻帧图像间的相对角度进行计算,根据匹配点对的空间几何关系求取偏心角,并用四元数和复合矩阵变换实现IVUS图像在导引丝上的准确定向。
5. IVUS图像序列与冠脉造影图像的数据融合实验利用模拟实验验证了定位、定向算法的正确性;利用临床获得的CAG和IVUS图像进行了数据融合实验,验证了融合算法的准确可行性。
Atherosclerosis which is a common disease in coronary artery disease is one of the primary human health hazards. It has two major clinical diagnostic methods: X-ray coronary angiography and intravascular ultrasound images. X-ray coronary angiography images can make an objective diagnosis for the structure of coronary artery and vascular stenosis. So we can obtain the three-dimensional spatial structure skeleton for direct observation about the coronary morphology through 3D reconstruction. Intravascular ultrasound can not only accurately measure the parameters of the lumen diameter and area, but also find the early coronary atherosclerotic plaque. So we can detect the eccentricity, wall thickness and the composition about plaque. We can make the advantages of both methods complement each other, through the data fusion between CAG and IVUS. We can obtain the solid model of coronary artery. At the same time, we can not only observe the spatial position of vessels, but also get the quantitative data of plaque for interested segment to help clinical diagnosis and treatment.
The main contents of this dissertation include five parts as follows:
1. Segmentation of lumen and media-adventitia border in intravascular ultrasound images based on improved Snake model
We firstly use a spatio-temporal filter to reduce the effect of speckles and enhance the images. Then, we ameliorate the internal energy and design the image energy for reducing the sensitivity. Finally, through experiment we improve the local segmentation. At the same time, we give a optimization calculation for the energy function of Snake by greedy method.
2. 3D reconstruction and optimization for catheter and vessel centerline in interested coronary artery
This paper proposes a method to optimize the 3D reconstruction of interested vessels: optimization of matched points and GT. Through setting six pairs of initial matched points by chord formula, designing the energy function for matched points optimization, we can solve it using dynamic programming algorithm.
3. Position calculation for IVUS image sequences located in 3D catheter
The methods are presented for IVUS image sequences to locate in 3D catheter. The point sequences of catheter are smoothed by B-spline curve fitting. We figure out the cut vector by the method of optimal vertical plane. Then, we can realize the location of IVUS image sequences in 3D catheter through the coordinate transformation.
4. Oriention calculation for IVUS image sequences located in 3D catheter
The methods are presented for IVUS image sequences to determine the orientation in 3D catheter. Relative twists are figured out by geometrical model of spatial curve between the adjacent frames. The eccentric angles can be figured out by the spatial relationship between matched points. Finally, we estimate the absolute orientation of IVUS image sequences in 3D catheter through quaternion and complex matrix translation respectively.
5. Experiment of data fusion between the IVUS image sequences and the coronary angiogram
The data fusion between the simulated, clinical IVUS images and coronary angiogram are experimented respectively, and the accuracy of the method is validated using error analysis.
引文
[1].江一清,刘朝中,朱国英,现代冠心病学,北京:人民军医出版社,2001,3~11
[2].胡春红,郁道银,黄家祥等,冠脉树中感兴趣血管段最佳造影角度的计算,津大学学报,2006,39(3):343~348
[3]. PLiebson PR , Klein LW etc , Intravascular ultrasound in coronary atherosclerosis: A new approach to clinical assessment,Am Heart J,1991,123:1643~1660
[4]. Wahle A, Mitchell SC, Olszewski ME etc,Accurate visualization and quantification of coronary vasculature by 3-D/4-D fusion from biplane angiography and intravascular ultrasound,2001,4158:144~154
[5].陈在嘉,徐义枢,孔华宇,临床冠心病学,北京:人民卫生出版社,1994,121~125
[6].陈国伟,郑宗鍔,现代心脏内科学,长沙:湖南科学技术出版社,1994,932~941
[7].王贤才(译),简明希氏内科学,青岛:青岛出版社,1993,3~10
[8].蔚挺,现代临床心脏病学,北京:人民军医出版社,1991,451~460
[9].张玉顺,马淑坤,冠脉造影的现状,医师进修杂志,2000,23(2),4~5
[10].李占全,冠脉造影法在冠心病诊断中的价值,医师进修杂志,2003,26(9):9~10
[11].李俊峡,鹰津良树,宫本忠司等,冠脉病变中血管内超声与冠脉造影的比较,第四军医大学学报,2005,26(13):1194~1196
[12].朱天刚,胡大一,冠脉内超声的临床应用价值,第四军医大学学报,2000,16(3):208~210
[13]. Zhang X, McKay CR,Sonka M.,Tissue characterization in intravascular ultrasound images, Trans.Med.Imag,1998,17:889~898
[14]. Takagi A, Hibi K.,Zhang X,Automated contour detection for high-frequency intravascular ultrasound imaging: a techinique with blood noise reduction for edge enhancement, Ultrasound Med. Biol,2000,26(6):4352~4355
[15]. Movassaghi B,Rasche V,Florent R,3D Coronary reconstruction from calibrated motion-compensated 2d projections,International Congress Series,2003,23:1079~1084
[16]. Cherieta F,Self-calibration of a biplane X-ray imaging system for an optimalthree dimensional reconstruction , Computerized Medical Imaging and Graphics,1999,23:133~141
[17]. Kristiansen G,Wunderlich W,Fischer F etc,Accuracy and precision of the analytic calibration method in quantitative coronary arteriography,IEEE Computers in Cardiology,1996,23:401~404
[18]. Nobl EJ,Boukerrouid,Ultrasound image segmentation: a survey,Trans. Med. Imag.,2006,25(8):987~1009
[19]. Sanz-requena R,Moratal D,Garcia-sanchez DR,Automatic segmentation and 3D reconstruction of intravascular ultrasound images for a fast preliminary evaluation of vessel pathologies , Computerized Medical Imaging and Graphics,2007,31(2):71~80
[20]. Glannoglou GD,Chatzizisis YS,Koutkias V,A novel active contour model for fully automated segmentation of intravascular ultrasound images Computers in Biology and Medicine,2007,37(9):1292~1302
[21].徐智,心血管造影图像的二维信息处理及其三维重建研究:[博士学位论文],天津:天津大学,2003
[22]. Temel K,Ali G,Mehmet T,A surface-based method for diction of coronary vessel boundaries in poor quality X-ray angiogram images , Pattern Recognition Letters,2002,23:783~802
[23]. Qian Y,Eiho S,Sugimoto N,Automatic extraction of coronary artery tree on coronary angiograms by morphological operators , IEEE Computer in Cardiology,2002,23:783~802
[24]. Chen SJ,Carroll JD,3-D reconstruction of coronary arterial tree to optimize angiographic visualization,IEEE Transaction on Medical Imaging,2000,19(4):318~336
[25]. Chen SJ,Carroll JD,Kinematic and deformation analysis of 4-D coronary arterial trees reconstructed from cine angiograms,IEEE Transaction on Medical Imaging,2003,22(6):710~721
[26].黄家祥,冠状动脉树三维骨架重建方法的研究:[硕士学位论文],天津:天津大学,2003
[27].黄家祥,基于造影图像的冠状动脉三维重建和定量分析方法的研究:[博士学位论文],天津:天津大学,2003
[28]. Christiaens J,Vande R,Determination of optimal angiographic viewing angles for QCA,International Congress Series,2001,1230:909~915
[29]. Sato Y,Araki T,Hanayama M,A viewpoint determination for stenosis diagnosis and quantification in coronary angiographic image acquisition, IEEE Transaction on Medical Imaging,1998,17(1):121~137
[30]. Chen SJ,Hoffmann KR,Carroll JD,Computer assisted coronary intervention:3D reconstruction and determination of optimal views,IEEE Computer in Cardiology,1996,23:117~120
[31].胡春红,感兴趣血管段最佳视角和血管内超声与冠脉造影融合研究:[博士学位论文],天津:天津大学,2006
[32]. Chatzizisis YS,Giannoglou GD,Ziakas A,In vivo comparative study of linear versus geometrically correct three-dimensional reconstruction of coronary arteries,Elsevier Inc,2008,101:263~267
[33]. Cothren RM,Shekhar R,Tuzcu EM,Three-dimensional reconstruction of the coronary artery wall by image fusion of intravascular ultrasound and bi-plane angiography,International Journal of Cardiac Imaging,2000,16:69~85
[34]. Rotger D,Radeva P,Canero C,Corresponding IVUS and angiogram image data,Computers in Cardiology,2001,28:273~276
[35]. Prause GP,Dejong SC,Mckay CR,Towards a geometrically correct 3D reconstruction of tortuous coronary arteries based on biplane angiography and intravascular ultrasound,International Journal of Cardiac Imaging,1997,13:451~462
[36]. Wahle A,Steven C,Mark E,Accurate visualization and quantification of coronary vasculature by 3D/4D fusion from biplane angiography and intravascular ultrasound , Biomonitoring and Endoscopy Technologies ,EBiOS2000:144~155
[37]. Wahle A,Lopez JJ,Edward C,Effects of vessel geometry and catheter position on dose delivery in intracoronary brachytherapy,IEEE Transactions on Biomedical Engineering,2003,50(11):1286~1296
[38]. Wahle A , Guido PM , Rainmund Erbel , Fusion of angiography and intravascular ultrasound in vivo:establishing the absolute 3-D frame orientation,IEEE Transactions on Biomedical Engineering,1999,46(10):1176~1182
[39]. Wahle A,Mark E,Interactive virtual endoscopy in coronary ateries based on multimodality fusion,IEEE Transactions on Biomedical Engineering,2004,43(11):1391~1405
[40]. Wahle A,Guido PM,Steven C,Geometrically correct 3D reconstruction of intravascular ultrasound images by fusion with biplane angiography-methods and validation,IEEE Transactions on Biomedical Engineering,1999,18(8):686~699
[41]. Wahle A,Lopez JJ,Mark E,Plaque development, vessel curvature, and wall shear stress in coronary arteries assessed by X-ray angiography and intravascular ultrasound,Medical Image Analysis,2006,10:615~631
[42]. Bourantas CV,Kourtis IC,Plissiti ME,A method for 3D reconstruction ofcoronary arteries using biplane angiography and intravascular ultrasound images,Computerized Medical Imaging and Graphics,2005,29:597~606
[43]. Cothren RM,Shekhar R,Tuzcu EM,Three-dimensional reconstruction of the coronary artery wall by image fusion of intravascular ultrasound and bi-plane angiography,International Journal of Cardiac Imaging,2000,16:69~85
[44]. Takagi A,Hibi K,Zhang X,Automated contour detection for high-frequency intravascular ultrasound imaging: a techinique with blood noise reduction for edge enhancement, Ultrasound Med. Biol,2000,26(6):4352~4355
[45]. Zhang X,McKay CR,Sonka M,Tissue characterization in intravascular ultrasound images,IEEE Trans.Med.Imag,1998,17:889~898
[46]. Gil D,Radeva P,Saludes J,Automatic segmentation of artery wall in coronary IVUS images: A probabilistic approach,in Proc.CIC 2000,Cambridge,MA,2000,4352~4355
[47]. Haas C,Ermert H,Holt S,Segmentation of 3D intravascular ultrasound images based on a random field model,Ultrasound Med.Biol,2000,26(2) :361~364
[48]. Plissiti ME,Fotiadis DI,Michalis LK,An automated method for lumen and media-adventitia border detection in a sequence of IVUS frames,IEEE Transactions on Information Technology in Biomedicine,2004,8(2):131~141
[49]. Zhu H,Liang Y,Friedman MH,IVUS image segmentation based on contrast , Processing of SPIE 2002(C),USA:Durham NC, 2002,1727~1733
[50]. Brusseau E,DeKorte CL,Mastik F,Fully automatic luminal contour segmentation in intracoronary ultrasound imaging-A statistical approach,IEEE Transaction on Medical Imaging,2004,23(5):554~566
[51]. Roelandt J.R.T.C , Mario C. Di , Pandian N.G , Three-dimensional reconstruction of intracoronary ultrasound images; rational, approaches, problems, and directions,Circulation,1994,90(2):1044~1055
[52]. Maurincomme E,Finet G,What are the advantages and limitations of three-dimensional intracoronary ultrasound imaging,Cardiovascular Imaging,1996,186:243~255
[53].纪承寅,姚勇,现代心血管病显像诊断学,北京:人民军医出版社,2004,91~365
[54].余建明,医学影像技术学,北京:科学出版社,2009,81~433
[55].潘景韬,邵建华,潘其兴,心血管病诊断新技术,济南:山东科技出版社,1992,52~243
[56].万明习,医学超声学原理与技术,西安:西安交通大学出版社,1992,9~33
[57].林书玉,超声换能器的原理及设计,北京:科学出版社,2004,1~36,207~258
[58].栾桂冬,张金铎,王仁乾,压电换能器和换能器阵,北京:北京大学出版设,1990
[59].高上凯,医学成像系统,北京:清华出版社,2000,10~41
[60]. Canero C,Vilarino F,Mauri J,Predictive (un)distortion model and 3-D reconstruction by biplane snakes,IEEE Transactions on Medical Imaging,2002,21(9):1188~1201
[61]. Kaus MR,Berg J,Jurgen W,Automated segmentation of the left ventricle in cardia MRI,MedIA,2004,8(3):245~254
[62]. Kass M,Witkin A,Terzopoulouse D,Snake:active contour model,London:Ro senfield Aeds Proceedings of the 1st International Conference on Computer Vision,1987,259~268
[63].孙晓阳,SNAKE-主动轮廓模型的算法研究与应用:[硕士学位论文],上海:上海交通大学,1997
[64].王大中,变分法基础,北京:国防工业出版社,2004,36~180
[65]. Maurice RL,Bertrand M,Lagrangian speckle model and tissue-motion estimation-Theory,IEEE Transaction on Medical Imaging,1999,18(7):593~603
[66]. Crerwinski RN,Jones DL,Obrien WD,Detection of lines and boundaries in speckle images-application to medical ultrasound,IEEE Transaction on Medical Imaging,1999,18(2):126~136
[67].闫敬文,数字图像处理技术与图像图形学基本教程,北京:科学出版社,2002,100~250
[68].阮秋琦(译),数字图像处理(第二版),北京:电子工业出版社,2004,117~220
[69].朱其刚,刘明尹,曹茂永,基于自适应邻域的超声图像加权中值滤波,中国生物医学工程学报,2005,24(2):186~188
[70].李军,丁明跃,一种改进的B超图像自适应加权中值滤波,华中理工大学学报,2000,28(6):71~73
[71]. Williams DJ,Shah M,A fast algorithm for active contours and curvature estimation,Image Understanding,1992,55(1):14~26
[72].王立功,于甬华,基于Snake模型的图像目标轮廓自动跟踪方法,东南大学学报(自然科学版),2003,33(2):215~218
[73].杨勇,黄波,一种基于内容表示的图像序列运动分割算法,通信学报,2001,32(6):102~106
[74]. Hom BKP,Schunck BG,Determining Optical Flow,Artificial Intelligence,1981,17,185~203
[75]. Amini AA,Tehrani S,Weymouth TE,Using dynamic programming for minimizing the energy of active contours in the presence of hard constraints,Second International Conference on Computer Vision,1998,95~99
[76].王晓东,计算机算法设计与分析,北京:电子工业出版社,2007,201~210
[77].霍红卫,算法设计与分析,西安:西安电子科技大学出版社,2005,156~182
[78]. Wang L , Yu DL , Chen XD , Quantitative analysis for lumen and media-adventitia border detection in intravascular ultrasound images ,International Conference on Optical Instruments and Technology,2008,7156:71561D~71561D-9
[79].马振鹤,万柏坤,王瑞平等,冠状动脉造影图像降噪处理的3种方法比较,生物医学工程与临床,2002,6(3):129~131
[80].李轶,陈滨津,张谦等,小波变换在冠状动脉造影图像处理中的应用,医疗卫生装备,2005,26(8):18~19
[81].徐智,心血管造影图像的二维信息处理及其三维重建研究:[博士学位论文],天津:天津大学,2003
[82]. Detre KM,Wright E,Murphu ML,Observer agreement in evaluating coronary angiograms,Circulation,1975,25:979~986
[83]. Wunderlich W , Aqrawal R , Beneficial effects of pravastatin initiated immediately after a coronary event,the American Journal of Cardiology,2000,86(12):1293~1298
[84]. Yim PJ,Cebral JR,Lohner R,New methods forcomputational fluid dynamics of carotid artery from magnetic resosnance angiography,SPIE Medical Imaging,2001,4321(22)
[85]. Ritchings RT,Colchester ACF,Detection of abnormalities on carotid angiograms,Patter Recognization Letter,1986,4:367~374
[86]. Thackray BD,Nelson AC,Semi-automatic segmentation of vascular network images using a rotating structuring element(ROSE) with mathematical morphology and dual feature thresholding,IEEE Transactions on Medical Imaging,1993,l12:385~392
[87]. Liu I,Sun Y,Recursive tracking of vascular networks in angiograms based on the detection-deletion scheme,IEEE Transaction on medical imaging,1993,12:334~341
[88]. Park H,Schoepflin T,Kim Y,Active contour model with gradient directional information: directional snake,IEEE Transactions on Circuits and Systems for Video Technology,2001,11(2):252~256
[89]. Klein AK,Lee F,Amini AA,Quantitive coronary angiography with deformable spline models,IEEE Transactions on medical imaging,1997,16(5):468~482
[90]. Chakraborty A,Staib LH,Duncan JS,Deformable boundary finding in medical images by integrating gradient and region information , IEEE Transactions on Medical Imaging,1996,15(6):859~870
[91].贾云得,机器视觉,北京:科学出版社,2000,237~238
[92].张莹,运筹学基础,北京:清华大学出版社,1995,195~203
[93].《运筹学》教材编写组,运筹学(第三版),北京:清华大学出版社,2005,155~173
[94]. Brusseau E,DeKorte CL,Mastik F,Fully automatic luminal contour segmentation in intracoronary ultrasound imaging-A statistical approach ,IEEE Transaction on Medical Imaging,2004,23(5):554~566
[95]. Huang JX,Yu DY,Chen XD,Optimization of transformation for 3D reconstruction of coronary arterial tree,Proceedings of SPIE, the International Society for Optical Engineering,2004,5444:547~552
[96].王岭,陈晓冬,郁道银,基于冠脉造影图像的导引丝三维重建,传感器与微系统,2010,29(5):66~69
[97].王岭,陈晓冬,郁道银,基于CAG三维重建与超声图像的数据融合研究,中国生物医学工程学报,2009,28(6):834~839
[98].施法中,计算机辅助几何设计与非均匀有理B样条(CAGD&NURBS),北京:北京航空航天大学出版社,1994,27~280
[99].朱心雄,自由曲线曲面造型技术,北京:科学出版社,2000,1~16
[100].苏步青,刘鼎元,计算几何,上海:上海科学技术出版社,1981,23~68
[101]. Sapides N,Farin G,Automatic fairing algorithm for B-spline curves,Computer Graphics and Application,1989,9:48~56
[102]. Farin G,Rein G,Sapidis N,Fairing cubic B-spline curves,Computer Aided Geometric Design,1986,4:91~103
[103].满家巨,胡事民,B-样条曲线的节点去除与光顺,软件学报,2001,12(1):1109~1113
[104]. Eck M,Hadenfeld J,Local energy fairing of B-spline curves,Geometric Modelling,Springer-Verlag,U.K.,1995
[105].肖轶军,丁明跃,一种自由曲线三维重建的新方法研究,华中理工大学学报,2000,28(2):90~92
[106].黄文钧,迭代线性最近点参数非均匀B样条曲线拟合,广西科学院学报2002,18(4):165~170
[107].曲军,孙烨,B样条曲线参数重载的非线性整体逼近拟合法[J],机械设计与制造,2001,5:36~37
[108].张弢,一种求最小平面度的新方法,辽宁大学学报,2003,30(3):200~202
[109].陈维桓,微分几何初步,北京:北京大学出版社,1990,10~31
[110].孙家广,计算机图形学,北京:清华大学出版社,1998,365~377
[111].赵云,朱文玲,血管内超声成像及三维重建,中华心血管病杂志,1998,26(2):148~150
[112].舒先红,沈学东,施纯敏,血管腔内超声显像三维重建实验研究,中华超声影像学杂志,1996,5(5):224~226
[113]. Shiota T,Sinclair B,Ishii M,Three dimensional reconstruction of color Doppler flow convergence regions and regurgitant jets:an in vitro quantitative study,J Am Coll Cardiol,1996,27:1511~1518
[2].胡春红,郁道银,黄家祥等,冠脉树中感兴趣血管段最佳造影角度的计算,津大学学报,2006,39(3):343~348
[3]. PLiebson PR , Klein LW etc , Intravascular ultrasound in coronary atherosclerosis: A new approach to clinical assessment,Am Heart J,1991,123:1643~1660
[4]. Wahle A, Mitchell SC, Olszewski ME etc,Accurate visualization and quantification of coronary vasculature by 3-D/4-D fusion from biplane angiography and intravascular ultrasound,2001,4158:144~154
[5].陈在嘉,徐义枢,孔华宇,临床冠心病学,北京:人民卫生出版社,1994,121~125
[6].陈国伟,郑宗鍔,现代心脏内科学,长沙:湖南科学技术出版社,1994,932~941
[7].王贤才(译),简明希氏内科学,青岛:青岛出版社,1993,3~10
[8].蔚挺,现代临床心脏病学,北京:人民军医出版社,1991,451~460
[9].张玉顺,马淑坤,冠脉造影的现状,医师进修杂志,2000,23(2),4~5
[10].李占全,冠脉造影法在冠心病诊断中的价值,医师进修杂志,2003,26(9):9~10
[11].李俊峡,鹰津良树,宫本忠司等,冠脉病变中血管内超声与冠脉造影的比较,第四军医大学学报,2005,26(13):1194~1196
[12].朱天刚,胡大一,冠脉内超声的临床应用价值,第四军医大学学报,2000,16(3):208~210
[13]. Zhang X, McKay CR,Sonka M.,Tissue characterization in intravascular ultrasound images, Trans.Med.Imag,1998,17:889~898
[14]. Takagi A, Hibi K.,Zhang X,Automated contour detection for high-frequency intravascular ultrasound imaging: a techinique with blood noise reduction for edge enhancement, Ultrasound Med. Biol,2000,26(6):4352~4355
[15]. Movassaghi B,Rasche V,Florent R,3D Coronary reconstruction from calibrated motion-compensated 2d projections,International Congress Series,2003,23:1079~1084
[16]. Cherieta F,Self-calibration of a biplane X-ray imaging system for an optimalthree dimensional reconstruction , Computerized Medical Imaging and Graphics,1999,23:133~141
[17]. Kristiansen G,Wunderlich W,Fischer F etc,Accuracy and precision of the analytic calibration method in quantitative coronary arteriography,IEEE Computers in Cardiology,1996,23:401~404
[18]. Nobl EJ,Boukerrouid,Ultrasound image segmentation: a survey,Trans. Med. Imag.,2006,25(8):987~1009
[19]. Sanz-requena R,Moratal D,Garcia-sanchez DR,Automatic segmentation and 3D reconstruction of intravascular ultrasound images for a fast preliminary evaluation of vessel pathologies , Computerized Medical Imaging and Graphics,2007,31(2):71~80
[20]. Glannoglou GD,Chatzizisis YS,Koutkias V,A novel active contour model for fully automated segmentation of intravascular ultrasound images Computers in Biology and Medicine,2007,37(9):1292~1302
[21].徐智,心血管造影图像的二维信息处理及其三维重建研究:[博士学位论文],天津:天津大学,2003
[22]. Temel K,Ali G,Mehmet T,A surface-based method for diction of coronary vessel boundaries in poor quality X-ray angiogram images , Pattern Recognition Letters,2002,23:783~802
[23]. Qian Y,Eiho S,Sugimoto N,Automatic extraction of coronary artery tree on coronary angiograms by morphological operators , IEEE Computer in Cardiology,2002,23:783~802
[24]. Chen SJ,Carroll JD,3-D reconstruction of coronary arterial tree to optimize angiographic visualization,IEEE Transaction on Medical Imaging,2000,19(4):318~336
[25]. Chen SJ,Carroll JD,Kinematic and deformation analysis of 4-D coronary arterial trees reconstructed from cine angiograms,IEEE Transaction on Medical Imaging,2003,22(6):710~721
[26].黄家祥,冠状动脉树三维骨架重建方法的研究:[硕士学位论文],天津:天津大学,2003
[27].黄家祥,基于造影图像的冠状动脉三维重建和定量分析方法的研究:[博士学位论文],天津:天津大学,2003
[28]. Christiaens J,Vande R,Determination of optimal angiographic viewing angles for QCA,International Congress Series,2001,1230:909~915
[29]. Sato Y,Araki T,Hanayama M,A viewpoint determination for stenosis diagnosis and quantification in coronary angiographic image acquisition, IEEE Transaction on Medical Imaging,1998,17(1):121~137
[30]. Chen SJ,Hoffmann KR,Carroll JD,Computer assisted coronary intervention:3D reconstruction and determination of optimal views,IEEE Computer in Cardiology,1996,23:117~120
[31].胡春红,感兴趣血管段最佳视角和血管内超声与冠脉造影融合研究:[博士学位论文],天津:天津大学,2006
[32]. Chatzizisis YS,Giannoglou GD,Ziakas A,In vivo comparative study of linear versus geometrically correct three-dimensional reconstruction of coronary arteries,Elsevier Inc,2008,101:263~267
[33]. Cothren RM,Shekhar R,Tuzcu EM,Three-dimensional reconstruction of the coronary artery wall by image fusion of intravascular ultrasound and bi-plane angiography,International Journal of Cardiac Imaging,2000,16:69~85
[34]. Rotger D,Radeva P,Canero C,Corresponding IVUS and angiogram image data,Computers in Cardiology,2001,28:273~276
[35]. Prause GP,Dejong SC,Mckay CR,Towards a geometrically correct 3D reconstruction of tortuous coronary arteries based on biplane angiography and intravascular ultrasound,International Journal of Cardiac Imaging,1997,13:451~462
[36]. Wahle A,Steven C,Mark E,Accurate visualization and quantification of coronary vasculature by 3D/4D fusion from biplane angiography and intravascular ultrasound , Biomonitoring and Endoscopy Technologies ,EBiOS2000:144~155
[37]. Wahle A,Lopez JJ,Edward C,Effects of vessel geometry and catheter position on dose delivery in intracoronary brachytherapy,IEEE Transactions on Biomedical Engineering,2003,50(11):1286~1296
[38]. Wahle A , Guido PM , Rainmund Erbel , Fusion of angiography and intravascular ultrasound in vivo:establishing the absolute 3-D frame orientation,IEEE Transactions on Biomedical Engineering,1999,46(10):1176~1182
[39]. Wahle A,Mark E,Interactive virtual endoscopy in coronary ateries based on multimodality fusion,IEEE Transactions on Biomedical Engineering,2004,43(11):1391~1405
[40]. Wahle A,Guido PM,Steven C,Geometrically correct 3D reconstruction of intravascular ultrasound images by fusion with biplane angiography-methods and validation,IEEE Transactions on Biomedical Engineering,1999,18(8):686~699
[41]. Wahle A,Lopez JJ,Mark E,Plaque development, vessel curvature, and wall shear stress in coronary arteries assessed by X-ray angiography and intravascular ultrasound,Medical Image Analysis,2006,10:615~631
[42]. Bourantas CV,Kourtis IC,Plissiti ME,A method for 3D reconstruction ofcoronary arteries using biplane angiography and intravascular ultrasound images,Computerized Medical Imaging and Graphics,2005,29:597~606
[43]. Cothren RM,Shekhar R,Tuzcu EM,Three-dimensional reconstruction of the coronary artery wall by image fusion of intravascular ultrasound and bi-plane angiography,International Journal of Cardiac Imaging,2000,16:69~85
[44]. Takagi A,Hibi K,Zhang X,Automated contour detection for high-frequency intravascular ultrasound imaging: a techinique with blood noise reduction for edge enhancement, Ultrasound Med. Biol,2000,26(6):4352~4355
[45]. Zhang X,McKay CR,Sonka M,Tissue characterization in intravascular ultrasound images,IEEE Trans.Med.Imag,1998,17:889~898
[46]. Gil D,Radeva P,Saludes J,Automatic segmentation of artery wall in coronary IVUS images: A probabilistic approach,in Proc.CIC 2000,Cambridge,MA,2000,4352~4355
[47]. Haas C,Ermert H,Holt S,Segmentation of 3D intravascular ultrasound images based on a random field model,Ultrasound Med.Biol,2000,26(2) :361~364
[48]. Plissiti ME,Fotiadis DI,Michalis LK,An automated method for lumen and media-adventitia border detection in a sequence of IVUS frames,IEEE Transactions on Information Technology in Biomedicine,2004,8(2):131~141
[49]. Zhu H,Liang Y,Friedman MH,IVUS image segmentation based on contrast , Processing of SPIE 2002(C),USA:Durham NC, 2002,1727~1733
[50]. Brusseau E,DeKorte CL,Mastik F,Fully automatic luminal contour segmentation in intracoronary ultrasound imaging-A statistical approach,IEEE Transaction on Medical Imaging,2004,23(5):554~566
[51]. Roelandt J.R.T.C , Mario C. Di , Pandian N.G , Three-dimensional reconstruction of intracoronary ultrasound images; rational, approaches, problems, and directions,Circulation,1994,90(2):1044~1055
[52]. Maurincomme E,Finet G,What are the advantages and limitations of three-dimensional intracoronary ultrasound imaging,Cardiovascular Imaging,1996,186:243~255
[53].纪承寅,姚勇,现代心血管病显像诊断学,北京:人民军医出版社,2004,91~365
[54].余建明,医学影像技术学,北京:科学出版社,2009,81~433
[55].潘景韬,邵建华,潘其兴,心血管病诊断新技术,济南:山东科技出版社,1992,52~243
[56].万明习,医学超声学原理与技术,西安:西安交通大学出版社,1992,9~33
[57].林书玉,超声换能器的原理及设计,北京:科学出版社,2004,1~36,207~258
[58].栾桂冬,张金铎,王仁乾,压电换能器和换能器阵,北京:北京大学出版设,1990
[59].高上凯,医学成像系统,北京:清华出版社,2000,10~41
[60]. Canero C,Vilarino F,Mauri J,Predictive (un)distortion model and 3-D reconstruction by biplane snakes,IEEE Transactions on Medical Imaging,2002,21(9):1188~1201
[61]. Kaus MR,Berg J,Jurgen W,Automated segmentation of the left ventricle in cardia MRI,MedIA,2004,8(3):245~254
[62]. Kass M,Witkin A,Terzopoulouse D,Snake:active contour model,London:Ro senfield Aeds Proceedings of the 1st International Conference on Computer Vision,1987,259~268
[63].孙晓阳,SNAKE-主动轮廓模型的算法研究与应用:[硕士学位论文],上海:上海交通大学,1997
[64].王大中,变分法基础,北京:国防工业出版社,2004,36~180
[65]. Maurice RL,Bertrand M,Lagrangian speckle model and tissue-motion estimation-Theory,IEEE Transaction on Medical Imaging,1999,18(7):593~603
[66]. Crerwinski RN,Jones DL,Obrien WD,Detection of lines and boundaries in speckle images-application to medical ultrasound,IEEE Transaction on Medical Imaging,1999,18(2):126~136
[67].闫敬文,数字图像处理技术与图像图形学基本教程,北京:科学出版社,2002,100~250
[68].阮秋琦(译),数字图像处理(第二版),北京:电子工业出版社,2004,117~220
[69].朱其刚,刘明尹,曹茂永,基于自适应邻域的超声图像加权中值滤波,中国生物医学工程学报,2005,24(2):186~188
[70].李军,丁明跃,一种改进的B超图像自适应加权中值滤波,华中理工大学学报,2000,28(6):71~73
[71]. Williams DJ,Shah M,A fast algorithm for active contours and curvature estimation,Image Understanding,1992,55(1):14~26
[72].王立功,于甬华,基于Snake模型的图像目标轮廓自动跟踪方法,东南大学学报(自然科学版),2003,33(2):215~218
[73].杨勇,黄波,一种基于内容表示的图像序列运动分割算法,通信学报,2001,32(6):102~106
[74]. Hom BKP,Schunck BG,Determining Optical Flow,Artificial Intelligence,1981,17,185~203
[75]. Amini AA,Tehrani S,Weymouth TE,Using dynamic programming for minimizing the energy of active contours in the presence of hard constraints,Second International Conference on Computer Vision,1998,95~99
[76].王晓东,计算机算法设计与分析,北京:电子工业出版社,2007,201~210
[77].霍红卫,算法设计与分析,西安:西安电子科技大学出版社,2005,156~182
[78]. Wang L , Yu DL , Chen XD , Quantitative analysis for lumen and media-adventitia border detection in intravascular ultrasound images ,International Conference on Optical Instruments and Technology,2008,7156:71561D~71561D-9
[79].马振鹤,万柏坤,王瑞平等,冠状动脉造影图像降噪处理的3种方法比较,生物医学工程与临床,2002,6(3):129~131
[80].李轶,陈滨津,张谦等,小波变换在冠状动脉造影图像处理中的应用,医疗卫生装备,2005,26(8):18~19
[81].徐智,心血管造影图像的二维信息处理及其三维重建研究:[博士学位论文],天津:天津大学,2003
[82]. Detre KM,Wright E,Murphu ML,Observer agreement in evaluating coronary angiograms,Circulation,1975,25:979~986
[83]. Wunderlich W , Aqrawal R , Beneficial effects of pravastatin initiated immediately after a coronary event,the American Journal of Cardiology,2000,86(12):1293~1298
[84]. Yim PJ,Cebral JR,Lohner R,New methods forcomputational fluid dynamics of carotid artery from magnetic resosnance angiography,SPIE Medical Imaging,2001,4321(22)
[85]. Ritchings RT,Colchester ACF,Detection of abnormalities on carotid angiograms,Patter Recognization Letter,1986,4:367~374
[86]. Thackray BD,Nelson AC,Semi-automatic segmentation of vascular network images using a rotating structuring element(ROSE) with mathematical morphology and dual feature thresholding,IEEE Transactions on Medical Imaging,1993,l12:385~392
[87]. Liu I,Sun Y,Recursive tracking of vascular networks in angiograms based on the detection-deletion scheme,IEEE Transaction on medical imaging,1993,12:334~341
[88]. Park H,Schoepflin T,Kim Y,Active contour model with gradient directional information: directional snake,IEEE Transactions on Circuits and Systems for Video Technology,2001,11(2):252~256
[89]. Klein AK,Lee F,Amini AA,Quantitive coronary angiography with deformable spline models,IEEE Transactions on medical imaging,1997,16(5):468~482
[90]. Chakraborty A,Staib LH,Duncan JS,Deformable boundary finding in medical images by integrating gradient and region information , IEEE Transactions on Medical Imaging,1996,15(6):859~870
[91].贾云得,机器视觉,北京:科学出版社,2000,237~238
[92].张莹,运筹学基础,北京:清华大学出版社,1995,195~203
[93].《运筹学》教材编写组,运筹学(第三版),北京:清华大学出版社,2005,155~173
[94]. Brusseau E,DeKorte CL,Mastik F,Fully automatic luminal contour segmentation in intracoronary ultrasound imaging-A statistical approach ,IEEE Transaction on Medical Imaging,2004,23(5):554~566
[95]. Huang JX,Yu DY,Chen XD,Optimization of transformation for 3D reconstruction of coronary arterial tree,Proceedings of SPIE, the International Society for Optical Engineering,2004,5444:547~552
[96].王岭,陈晓冬,郁道银,基于冠脉造影图像的导引丝三维重建,传感器与微系统,2010,29(5):66~69
[97].王岭,陈晓冬,郁道银,基于CAG三维重建与超声图像的数据融合研究,中国生物医学工程学报,2009,28(6):834~839
[98].施法中,计算机辅助几何设计与非均匀有理B样条(CAGD&NURBS),北京:北京航空航天大学出版社,1994,27~280
[99].朱心雄,自由曲线曲面造型技术,北京:科学出版社,2000,1~16
[100].苏步青,刘鼎元,计算几何,上海:上海科学技术出版社,1981,23~68
[101]. Sapides N,Farin G,Automatic fairing algorithm for B-spline curves,Computer Graphics and Application,1989,9:48~56
[102]. Farin G,Rein G,Sapidis N,Fairing cubic B-spline curves,Computer Aided Geometric Design,1986,4:91~103
[103].满家巨,胡事民,B-样条曲线的节点去除与光顺,软件学报,2001,12(1):1109~1113
[104]. Eck M,Hadenfeld J,Local energy fairing of B-spline curves,Geometric Modelling,Springer-Verlag,U.K.,1995
[105].肖轶军,丁明跃,一种自由曲线三维重建的新方法研究,华中理工大学学报,2000,28(2):90~92
[106].黄文钧,迭代线性最近点参数非均匀B样条曲线拟合,广西科学院学报2002,18(4):165~170
[107].曲军,孙烨,B样条曲线参数重载的非线性整体逼近拟合法[J],机械设计与制造,2001,5:36~37
[108].张弢,一种求最小平面度的新方法,辽宁大学学报,2003,30(3):200~202
[109].陈维桓,微分几何初步,北京:北京大学出版社,1990,10~31
[110].孙家广,计算机图形学,北京:清华大学出版社,1998,365~377
[111].赵云,朱文玲,血管内超声成像及三维重建,中华心血管病杂志,1998,26(2):148~150
[112].舒先红,沈学东,施纯敏,血管腔内超声显像三维重建实验研究,中华超声影像学杂志,1996,5(5):224~226
[113]. Shiota T,Sinclair B,Ishii M,Three dimensional reconstruction of color Doppler flow convergence regions and regurgitant jets:an in vitro quantitative study,J Am Coll Cardiol,1996,27:1511~1518