冠脉造影图像的二维信息处理及三维重建研究
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摘要
X射线冠状动脉造影检查是目前国际上公认的诊断冠心病的常用手段,但基于二维造影图像的传统诊治方法存在很大的局限性。血管的三维重建技术不仅能为医生提供形象、直观的三维血管形状图像,而目可以辅助测量血管的有关参数(如直径大小、血管长度和截面积等),从而有助于冠心病的诊断和治疗。本文主要研究冠脉造影图像的血管提取、骨架和血管直径信息提取及三维重建和三维重建优化。
血管分割是冠脉造影图像处理中的一个难点。本文充分利用血管的运动、形状、尺度、灰度四方面的信息对冠状动脉造影图像进行分割。借助于背景组织的缓慢运动和目标动脉的剧烈运动,高通频域滤波器被选作用于减弱噪声并且增强血管。随后,改进的形态学方法和相对阈值比较被用来去除接近于静止的噪声并提取出动脉树。对多个造影图像序列进行实验后,证明本文的方法能够从低信噪比造影图像中自动地提取整支动脉树,对于细小血管部分或者血管末尾部分也有很好表现。
在分割出二维血管的结果基础上,本文采用形态学细化方法提取了心血管的骨架并用8连通链码加以数学表达;采用垂直线提取法和圆盘滚动法提取出了血管的直径。本方法经实验验证,对于二值血管图有着很好的效果。
在三维重建方面,首先研究了冠脉造影系统的几何模型以及空间中的三维坐标变换,进一步推导出在已知造影角度时点的三维重建方法。随后通过B样条拟合有限的三维点,插值出更多的血管点,使三维骨架连续,具有很好的可视性并减少了计算量。
最后是重建优化方面,采用自适应模拟退火优化方法对造影系统的外参进行优化。该方法优化时间效率高,优化结果相比于优化之前有很大提高。
X-ray angiography is one of the significant imaging techniques to diagnose coronary artery disease. However, the traditional treatment methods based on two-dimensional image have serious limitations. The automatic computation of the 3D coronary arterial tree allows the clinicians to visualize the arteries and can also support the geometric measurements for better prediction of stenosis. The main work of this thesis is carried out about the extraction of the coronary artery, vessel skeleton, diameter and 3-D reconstruction and optimization. The works can be included in four parts as follows:
Vessel segmentation is difficulty in angiogram image processing. Our method makes full use of the information of the vessel movement, shape, scale and intensity. For the case of slow movement of the background tissue and the more dramatic activity of the target artery, a sharpening frequency domain filter is employed to improve the image contrast. Then, the improved morphological method is used to remove nearly stationary noise and highlight the artery tree. At last, after relative-threshold comparison and multi-scale images combination, we obtain the result. By the method in this paper, we can automatically extract almost entire coronary artery tree from the low S/N x-ray angiographies, especially for the small and distal vessel part.
In the aspect of 2D information processing, morphologic thinning method is employed on the segmented results to pick up the vessel skeleton and 8 chain code is used to represent the skeleton. Then we separately use‘vertical line’and‘disk rolling’method to extract the vessel diameter along skeleton. Experiments validate our method yield good performance on binary image.
In the 3D reconstruction of coronary artery, we firstly discuss the geometry model of angiographic system and the 3D coordinates transformation to educe the 3D point reconstruction method. Then B-Spline interpolation method is used to increase the original sampling rate to make skeleton smoother and have better visibility.
Finally, we optimize the exterior geometric parameter of the angiography system. The adaptive simulated annealing method is used to search the optimization solutions. The optimization method has good efficiency and the optimization results are improved compared to the original parameters.
血管分割是冠脉造影图像处理中的一个难点。本文充分利用血管的运动、形状、尺度、灰度四方面的信息对冠状动脉造影图像进行分割。借助于背景组织的缓慢运动和目标动脉的剧烈运动,高通频域滤波器被选作用于减弱噪声并且增强血管。随后,改进的形态学方法和相对阈值比较被用来去除接近于静止的噪声并提取出动脉树。对多个造影图像序列进行实验后,证明本文的方法能够从低信噪比造影图像中自动地提取整支动脉树,对于细小血管部分或者血管末尾部分也有很好表现。
在分割出二维血管的结果基础上,本文采用形态学细化方法提取了心血管的骨架并用8连通链码加以数学表达;采用垂直线提取法和圆盘滚动法提取出了血管的直径。本方法经实验验证,对于二值血管图有着很好的效果。
在三维重建方面,首先研究了冠脉造影系统的几何模型以及空间中的三维坐标变换,进一步推导出在已知造影角度时点的三维重建方法。随后通过B样条拟合有限的三维点,插值出更多的血管点,使三维骨架连续,具有很好的可视性并减少了计算量。
最后是重建优化方面,采用自适应模拟退火优化方法对造影系统的外参进行优化。该方法优化时间效率高,优化结果相比于优化之前有很大提高。
X-ray angiography is one of the significant imaging techniques to diagnose coronary artery disease. However, the traditional treatment methods based on two-dimensional image have serious limitations. The automatic computation of the 3D coronary arterial tree allows the clinicians to visualize the arteries and can also support the geometric measurements for better prediction of stenosis. The main work of this thesis is carried out about the extraction of the coronary artery, vessel skeleton, diameter and 3-D reconstruction and optimization. The works can be included in four parts as follows:
Vessel segmentation is difficulty in angiogram image processing. Our method makes full use of the information of the vessel movement, shape, scale and intensity. For the case of slow movement of the background tissue and the more dramatic activity of the target artery, a sharpening frequency domain filter is employed to improve the image contrast. Then, the improved morphological method is used to remove nearly stationary noise and highlight the artery tree. At last, after relative-threshold comparison and multi-scale images combination, we obtain the result. By the method in this paper, we can automatically extract almost entire coronary artery tree from the low S/N x-ray angiographies, especially for the small and distal vessel part.
In the aspect of 2D information processing, morphologic thinning method is employed on the segmented results to pick up the vessel skeleton and 8 chain code is used to represent the skeleton. Then we separately use‘vertical line’and‘disk rolling’method to extract the vessel diameter along skeleton. Experiments validate our method yield good performance on binary image.
In the 3D reconstruction of coronary artery, we firstly discuss the geometry model of angiographic system and the 3D coordinates transformation to educe the 3D point reconstruction method. Then B-Spline interpolation method is used to increase the original sampling rate to make skeleton smoother and have better visibility.
Finally, we optimize the exterior geometric parameter of the angiography system. The adaptive simulated annealing method is used to search the optimization solutions. The optimization method has good efficiency and the optimization results are improved compared to the original parameters.
引文
[1] Haris K., Efstratiadis S. N, Maglaveras N., et al, Automated coronary artery extraction using watersheds, IEEE Computers in Cardiology, 1997, 24: 741~744
[2]高上凯,医学成像系统.北京:清华出版社, 2000. 10~41
[3] Sarwal A, Dhawan AP. 3D reconstruction of coronary arteries. Proceedings of the 16th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 1994, 1:504~505
[4] O’Brien JF, Ezquerra NF, Automated segmentation of coronary vessels in angiographic image sequences utilizing temporal, spatial structural constraints. SPIE, 1994, 2359: 25~37
[5] Chen J, Sato Y, Tamura S. Orientation space filtering for multiple orientation line segmentation. IEEE Pattern Analysis and Machine Intelligence, 2000, 22: 417~429
[6] Eiho S, Qian Y. Detection of coronary artery tree using morphological operator. IEEE Computers in Cardiology, 1997, 24: 525~528
[7] Park SH, Cha JH, Lee JJ, et a1. Flexible background. Texture analysis for coronary artery extraction based on digital subtraction angiography. ICCSA 2005, 3480: l1~18
[8] Aylward S, Pizer S, Bullitt E, et a1. Intensity ridge and widths for tabular object segmentation and registration. Wksp on Math Methods in Biomed Image Analysis, 1996: 131~138
[9] Lu JR, Chen DQ, Yu DY. Extraction of edge feature in cardio vascular image. SPIE, 2001, 4549: 141~148
[10] Hart M, Holley L. A method of automated coronary artery tracking in unsaturated angiograms. IEEE Computers in Cardiology, 1993, 20: 93~96
[11] Haris K, Efstratiadis SN, Maglaveras N, et a1. Automated coronary artery extraction using watersheds. IEEE Computers in Cardiology, 1997, 24: 741~744
[12] Lu S, Eiho S. Automatic detection of the coronary arterial contours with sub—branches from an X-ray angiogram. IEEE Computers in Cardiology, 1993, 20:575~578
[13] Klein A. K., Lee F., Amini A. Quantitative coronary angiography with deformable spine models. IEEE Transactions on medical imaging, 1997, 16(5): 468~482
[14] Hyun Wook Park, Todd Schoepfline, Yongmin Kim. Active contour model with gradient directional information: directional snake. IEEE Transactions on Circuits and Systems for Video Technology, 2001, 11(2): 252~256
[15] Amit Chakraboty, Lawrence, H. Staib. Deformable Boundary Finding in Medical images by integrating gradient and region information. IEEE Transactions on Medical Imaging, Dec, 1996, 15(6): 859~870
[16] Stansfiled S. A., ANGY. A rule-Based expert System for automatic segmentation of coronary vessels from digital subtracted angiograms. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1986, 8(2):188~199
[17] Smets C., Verbeeck G., Suetens P. A knowledge-based system for the delineation of blood vessels on subtraction angiograms. Pattern Recognition Letters,1998, 8(2): 113~121
[18] Nekovei R., Sun Y. Back-propagation network and its configuration for blood vessel detection in angiograms. IEEE Transactions on neural networks, 1995, 6(1): 64~72
[19] Caselles V, Cate F., Coll T, A geometric model for active contours in image processing, Numerische Mathematik, 1993, 66(1): 1~31
[20] Malladi R., Sethian J. A., Vemuri B.C. Shape modeling with front propagation: A level set approach. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1995, 17(2): 158~175
[21] Akira UCHIDA, Takao AKATSUKA, Tohoru TAKEDA. Identification of Coronary Arteries from Time Series of Angiogram and its 3D Understanding. SPIE Vol. 2298 :673~683
[22] CHIH-YANG LIN, YU-TAI CHING. Extraction Of Coronary Arterial Tree Using Cine X-Ray Angiograms. Biomedical Engineering Applications, Basis & Communications. 2005, 17(3): 111~121
[23] Longuet-Higgins H. C. A computer algorithm for reconstructing a scene from two projections. Nature, 1981, 293(10): 133~135
[24] Metz, C. E. Fencil L. E. Determination of three-dimensional structure in biplane radiography without prior knowledge of the relationship between the two views: Theory. Med. Phys., 1989, 16(1): 45~51
[25] Fencil, L. E. Metz C. E. Propagation and reduction of error in three dimensional structure determined from biplane views of unknown orientation. Med. Phys., 1990, 17(6): 951~961
[26] Radeva C., Toledo P., Von Land R., et al. 3D vessel reconstruction from biplane angiograms using snakes. IEEE Computers in Cardiology, 1998, 25: 773~776
[27] Cristina Ca?ero, Fernando Vilari?o, Josepa Mauri, et al. Predictive (un)distortion model and 3-D reconstruction by biplane snakes. IEEE Trans. Med. Imag., 2002, 21(9): 1188~1201
[28] Pellot C. P., Herment A., Sigelle M., et al. A 3-D reconstruction of vascular structures from two x-ray angiograms using an adapted simulated annealing algorithm. IEEE Trans. Med. Imag., 1994, 13: 48~60
[29] Yanagihara Y., Hashimoto T., Sugahara T., et al. A new method for automatic identification of coronary arteries in standard biplane angiograms. Int. J. Cardiac Imag., 1994, 10: 253~261
[30] Temel Kayikeioglu, Ali Gangal, Mehmet Turhal. Reconstructing coronary arterial segments from three projection boundaries. Pattern Recognition Letters, 2001, 22: 611~624
[31] Guggenheim N., Doriot P. A., Dorsaz P. A., et al. Spatial reconstruction of coronary arteries from angiographic images. Phys. Med. Biol., 1991, 36: 99~110
[32] Sarwal A., Dhawan P. Three dimensional reconstruction of coronary arteries from two views. Computer Methods and Programs in Biomedicine, 2001, 65: 25~43
[33] Nguyen T. V., Sklansky J. Reconstructing the 3-D medial axes of coronary arteries in single-view cine-angiograms. IEEE Trans. Med. Imag., 1994, 13: 61~73
[34] Kim H. C., Min B. G., Lee T. S., et al. 3-D digital subtraction angiography. IEEE Trans. Med. Imag., 1982, 1:52~158
[35] Parker D. L., Pope D., van’Bree L, R., et al. 3-D reconstruction of moving arterial beds from digital subtraction angiography. Comput. Biomed. Res., 1987, 20:166~185
[36] Kitamura K., Tobis J. M., Sklansky J. Estimating the 3-D skeletons and transverse areas of coronary arteries from biplane angiograms. IEEE Trans. Med. Imag., 1988, 7: 173~187
[37] Saito T., Misaki M., Shirato K., et al. Three-dimensional quantitative coronary angiography. IEEE Trans. Biomed. Eng., 1990, 37(8): 768~777
[38] Seiler C., Kirkeeide R. L., Gould K. L. Basic structure-function relations of the epicedial coronary vascular tree. Circulation, 1992, 85: 1987~2003
[39] Coatrieux J. L., Rong J., Collorec R. A framework for automatic analysis of the dynamic behavior of coronary angiograms. Int. J. Cardiac Imag., 1992, 8: 1~10
[40] Dumay A. C. M., Reiber J. H. C., Gerbrands J. Determination of optimal angiographic viewing angles. Basic principles and evaluation study, IEEE Trans. Med. Imag., 1994, 13: 13~24
[41] Wahle A., Wellnhofer E., Mugaragu I., et al. Assessment of diffuse coronary artery disease by quantitative analysis of coronary morphology based upon 3-D reconstruction from biplane angiograms. IEEE Trans. Med. Imag., 1995, 14: 230~241
[42] Chen S. James, Carroll John D. 3-D Reconstruction of Coronary Arterial Tree to Optimize Angiographic Visualization IEEE Trans. Med. Imag., 2000, 19: 318~335
[43] Sprague K., Drangova M., Lehmann G, et al, Coronary x-ray angiographic reconstruction and image orientation, Medical physics (Med. phys.) 2006, 33: 707-718
[44] Perrey W., Bojara M., Lindstaedt C., Fischer H., Evaluation of intracoronary pressure and blood flow velocity for the assessment of coronary stenos severity. Computers in Cardiology, vol.30, 2003: 247~ 250
[45] Blondel C., Vaillant R., Devernay F., Automatic trinocular 3D reconstruction of coronary artery centerlines from rotational X-ray angiography, In Proc. of CARS, Springer , Paris, 2002, 832~837
[46] Sang N. Li H., Peng WX et al. Adaptive thresholding of digital subtraction angiography images. In: Deren Li, Hongchao Ma, ed. Proc. of SPIE, MIPPR 2005:Image Analysis Techniques. Wuhan, China: 2005. 60441L-1-60441L-9
[47] Sonka M., Winniford M. D., Zhang X. M., et al, Lumen centerline detection in complex coronary angiogram, IEEE Transaction on Biomedical Engineering, 1994, 41(6): 520~527
[48]艾海舟,武勃.图像处理、分析与机器视觉.北京:北京人民邮电出版社, 2003. 96~97
[49]陆建荣,斯海臣,郁道银.冠状动脉血管直径测量方法的研究.中国生物医学工程学报, 2005, 24: 510~512
[50] Chen S.Y. James, Carroll D. John., Messenger J. C., Quantitative analysis of reconstruction 3-D coronary arterial tree and intracoronary devices, IEEE Transaction on Medical Imaging, 2002, 21(7): 724~740
[51] Hart W. E., Michael Goldbaum, et al. Measurement and classification of retinal vascular tortuosity. International Journal of Medical Informatics, 1999, 53: 239~252
[52] Dougherty G., J. Varro. A quantitative index for the measurement of the tortuosity of blood vessels, Medical Engineering&Physics, 2000, 22: 567~574
[53]施法中.计算机辅助几何设计与非均匀有理B样条.北京:北京航空航天大学出版社,1994. 272~280
[54] Sang N. Li H., Peng WX et al. 3D Reconstruction of the Coronary Tree from Two X-Ray Angiographic Views. Joseph M. Reinhardt, Josien P. W. Pluim, ed. Proc. of SPIE, Medical Imaging 2006: Image Processing. San Diego: 2006, 6144Y-1-6144Y-8
[55]郁道银,黄家祥,谢洪波等.冠状动脉树三维重建理论模型的研究.工程图学学报, 2003, 4, 83~89
[56]王凌.智能优化算法及其应用.北京:清华大学出版社, 2001. 15~35
[57] Ingber L. Adaptive simulated annealing (ASA):lessons learned. J Control and Cyberaetic.s, 1996, 25(1): 33~54
[2]高上凯,医学成像系统.北京:清华出版社, 2000. 10~41
[3] Sarwal A, Dhawan AP. 3D reconstruction of coronary arteries. Proceedings of the 16th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 1994, 1:504~505
[4] O’Brien JF, Ezquerra NF, Automated segmentation of coronary vessels in angiographic image sequences utilizing temporal, spatial structural constraints. SPIE, 1994, 2359: 25~37
[5] Chen J, Sato Y, Tamura S. Orientation space filtering for multiple orientation line segmentation. IEEE Pattern Analysis and Machine Intelligence, 2000, 22: 417~429
[6] Eiho S, Qian Y. Detection of coronary artery tree using morphological operator. IEEE Computers in Cardiology, 1997, 24: 525~528
[7] Park SH, Cha JH, Lee JJ, et a1. Flexible background. Texture analysis for coronary artery extraction based on digital subtraction angiography. ICCSA 2005, 3480: l1~18
[8] Aylward S, Pizer S, Bullitt E, et a1. Intensity ridge and widths for tabular object segmentation and registration. Wksp on Math Methods in Biomed Image Analysis, 1996: 131~138
[9] Lu JR, Chen DQ, Yu DY. Extraction of edge feature in cardio vascular image. SPIE, 2001, 4549: 141~148
[10] Hart M, Holley L. A method of automated coronary artery tracking in unsaturated angiograms. IEEE Computers in Cardiology, 1993, 20: 93~96
[11] Haris K, Efstratiadis SN, Maglaveras N, et a1. Automated coronary artery extraction using watersheds. IEEE Computers in Cardiology, 1997, 24: 741~744
[12] Lu S, Eiho S. Automatic detection of the coronary arterial contours with sub—branches from an X-ray angiogram. IEEE Computers in Cardiology, 1993, 20:575~578
[13] Klein A. K., Lee F., Amini A. Quantitative coronary angiography with deformable spine models. IEEE Transactions on medical imaging, 1997, 16(5): 468~482
[14] Hyun Wook Park, Todd Schoepfline, Yongmin Kim. Active contour model with gradient directional information: directional snake. IEEE Transactions on Circuits and Systems for Video Technology, 2001, 11(2): 252~256
[15] Amit Chakraboty, Lawrence, H. Staib. Deformable Boundary Finding in Medical images by integrating gradient and region information. IEEE Transactions on Medical Imaging, Dec, 1996, 15(6): 859~870
[16] Stansfiled S. A., ANGY. A rule-Based expert System for automatic segmentation of coronary vessels from digital subtracted angiograms. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1986, 8(2):188~199
[17] Smets C., Verbeeck G., Suetens P. A knowledge-based system for the delineation of blood vessels on subtraction angiograms. Pattern Recognition Letters,1998, 8(2): 113~121
[18] Nekovei R., Sun Y. Back-propagation network and its configuration for blood vessel detection in angiograms. IEEE Transactions on neural networks, 1995, 6(1): 64~72
[19] Caselles V, Cate F., Coll T, A geometric model for active contours in image processing, Numerische Mathematik, 1993, 66(1): 1~31
[20] Malladi R., Sethian J. A., Vemuri B.C. Shape modeling with front propagation: A level set approach. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1995, 17(2): 158~175
[21] Akira UCHIDA, Takao AKATSUKA, Tohoru TAKEDA. Identification of Coronary Arteries from Time Series of Angiogram and its 3D Understanding. SPIE Vol. 2298 :673~683
[22] CHIH-YANG LIN, YU-TAI CHING. Extraction Of Coronary Arterial Tree Using Cine X-Ray Angiograms. Biomedical Engineering Applications, Basis & Communications. 2005, 17(3): 111~121
[23] Longuet-Higgins H. C. A computer algorithm for reconstructing a scene from two projections. Nature, 1981, 293(10): 133~135
[24] Metz, C. E. Fencil L. E. Determination of three-dimensional structure in biplane radiography without prior knowledge of the relationship between the two views: Theory. Med. Phys., 1989, 16(1): 45~51
[25] Fencil, L. E. Metz C. E. Propagation and reduction of error in three dimensional structure determined from biplane views of unknown orientation. Med. Phys., 1990, 17(6): 951~961
[26] Radeva C., Toledo P., Von Land R., et al. 3D vessel reconstruction from biplane angiograms using snakes. IEEE Computers in Cardiology, 1998, 25: 773~776
[27] Cristina Ca?ero, Fernando Vilari?o, Josepa Mauri, et al. Predictive (un)distortion model and 3-D reconstruction by biplane snakes. IEEE Trans. Med. Imag., 2002, 21(9): 1188~1201
[28] Pellot C. P., Herment A., Sigelle M., et al. A 3-D reconstruction of vascular structures from two x-ray angiograms using an adapted simulated annealing algorithm. IEEE Trans. Med. Imag., 1994, 13: 48~60
[29] Yanagihara Y., Hashimoto T., Sugahara T., et al. A new method for automatic identification of coronary arteries in standard biplane angiograms. Int. J. Cardiac Imag., 1994, 10: 253~261
[30] Temel Kayikeioglu, Ali Gangal, Mehmet Turhal. Reconstructing coronary arterial segments from three projection boundaries. Pattern Recognition Letters, 2001, 22: 611~624
[31] Guggenheim N., Doriot P. A., Dorsaz P. A., et al. Spatial reconstruction of coronary arteries from angiographic images. Phys. Med. Biol., 1991, 36: 99~110
[32] Sarwal A., Dhawan P. Three dimensional reconstruction of coronary arteries from two views. Computer Methods and Programs in Biomedicine, 2001, 65: 25~43
[33] Nguyen T. V., Sklansky J. Reconstructing the 3-D medial axes of coronary arteries in single-view cine-angiograms. IEEE Trans. Med. Imag., 1994, 13: 61~73
[34] Kim H. C., Min B. G., Lee T. S., et al. 3-D digital subtraction angiography. IEEE Trans. Med. Imag., 1982, 1:52~158
[35] Parker D. L., Pope D., van’Bree L, R., et al. 3-D reconstruction of moving arterial beds from digital subtraction angiography. Comput. Biomed. Res., 1987, 20:166~185
[36] Kitamura K., Tobis J. M., Sklansky J. Estimating the 3-D skeletons and transverse areas of coronary arteries from biplane angiograms. IEEE Trans. Med. Imag., 1988, 7: 173~187
[37] Saito T., Misaki M., Shirato K., et al. Three-dimensional quantitative coronary angiography. IEEE Trans. Biomed. Eng., 1990, 37(8): 768~777
[38] Seiler C., Kirkeeide R. L., Gould K. L. Basic structure-function relations of the epicedial coronary vascular tree. Circulation, 1992, 85: 1987~2003
[39] Coatrieux J. L., Rong J., Collorec R. A framework for automatic analysis of the dynamic behavior of coronary angiograms. Int. J. Cardiac Imag., 1992, 8: 1~10
[40] Dumay A. C. M., Reiber J. H. C., Gerbrands J. Determination of optimal angiographic viewing angles. Basic principles and evaluation study, IEEE Trans. Med. Imag., 1994, 13: 13~24
[41] Wahle A., Wellnhofer E., Mugaragu I., et al. Assessment of diffuse coronary artery disease by quantitative analysis of coronary morphology based upon 3-D reconstruction from biplane angiograms. IEEE Trans. Med. Imag., 1995, 14: 230~241
[42] Chen S. James, Carroll John D. 3-D Reconstruction of Coronary Arterial Tree to Optimize Angiographic Visualization IEEE Trans. Med. Imag., 2000, 19: 318~335
[43] Sprague K., Drangova M., Lehmann G, et al, Coronary x-ray angiographic reconstruction and image orientation, Medical physics (Med. phys.) 2006, 33: 707-718
[44] Perrey W., Bojara M., Lindstaedt C., Fischer H., Evaluation of intracoronary pressure and blood flow velocity for the assessment of coronary stenos severity. Computers in Cardiology, vol.30, 2003: 247~ 250
[45] Blondel C., Vaillant R., Devernay F., Automatic trinocular 3D reconstruction of coronary artery centerlines from rotational X-ray angiography, In Proc. of CARS, Springer , Paris, 2002, 832~837
[46] Sang N. Li H., Peng WX et al. Adaptive thresholding of digital subtraction angiography images. In: Deren Li, Hongchao Ma, ed. Proc. of SPIE, MIPPR 2005:Image Analysis Techniques. Wuhan, China: 2005. 60441L-1-60441L-9
[47] Sonka M., Winniford M. D., Zhang X. M., et al, Lumen centerline detection in complex coronary angiogram, IEEE Transaction on Biomedical Engineering, 1994, 41(6): 520~527
[48]艾海舟,武勃.图像处理、分析与机器视觉.北京:北京人民邮电出版社, 2003. 96~97
[49]陆建荣,斯海臣,郁道银.冠状动脉血管直径测量方法的研究.中国生物医学工程学报, 2005, 24: 510~512
[50] Chen S.Y. James, Carroll D. John., Messenger J. C., Quantitative analysis of reconstruction 3-D coronary arterial tree and intracoronary devices, IEEE Transaction on Medical Imaging, 2002, 21(7): 724~740
[51] Hart W. E., Michael Goldbaum, et al. Measurement and classification of retinal vascular tortuosity. International Journal of Medical Informatics, 1999, 53: 239~252
[52] Dougherty G., J. Varro. A quantitative index for the measurement of the tortuosity of blood vessels, Medical Engineering&Physics, 2000, 22: 567~574
[53]施法中.计算机辅助几何设计与非均匀有理B样条.北京:北京航空航天大学出版社,1994. 272~280
[54] Sang N. Li H., Peng WX et al. 3D Reconstruction of the Coronary Tree from Two X-Ray Angiographic Views. Joseph M. Reinhardt, Josien P. W. Pluim, ed. Proc. of SPIE, Medical Imaging 2006: Image Processing. San Diego: 2006, 6144Y-1-6144Y-8
[55]郁道银,黄家祥,谢洪波等.冠状动脉树三维重建理论模型的研究.工程图学学报, 2003, 4, 83~89
[56]王凌.智能优化算法及其应用.北京:清华大学出版社, 2001. 15~35
[57] Ingber L. Adaptive simulated annealing (ASA):lessons learned. J Control and Cyberaetic.s, 1996, 25(1): 33~54