基于CTA影像的血管可视化技术研究
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摘要
心脑血管系统疾病已经成为当今世界上发病率、死亡率最高的疾病之一。计算机断层扫描与核磁共振成像等技术的出现使现代影像学检查技术成为血管疾病诊断的重要手段。在血管分析诊断系统中,血管的分割、提取与可视化技术发挥着极其重要的作用。目前的血管分割和提取算法因成像模式、应用领域以及其他一些因素的影响而各不相同,尚无任何一种通用的分割算法能够适用于所有的医学影像模式。在手术过程中,血管组织的可视化能够精确定位血管内部狭窄位置,为手术计划的定制提供依据。
虽然经历了二十多年的发展,但是血管可视化技术远未成熟,在理论和实际应用中还有许多亟待解决的问题。本文在目前存在的血管提取与可视化技术的基础上,以计算机断层扫描血管造影体数据作为研究对象,分别利用图形学理论和图像处理技术构建更精确的可视化技术和中心路径提取算法,并将两者进行结合,以便提供更多的血管内外部信息,为血管疾病的诊断提供足够的依据。本文所取得的主要研究成果和创新点如下:
(1)针对目前在曲面重建过程中采用多折线段模拟曲线带来的误差问题,根据任意设置的采样步长,采用B样条的方法将所有控制点拟合成曲线,实现了医学图像体数据的高精度曲面重建;并在此基础上引入一些曲面重建的辅助功能,如窗宽窗位调整、旋转曲面重建等,提升曲面重建的性能;
(2)为了能够在血管中更精确地观察病变,提出一种基于Snake模型的血管中心路径提取方法。首先,由用户手动在某一层上确定一个血管目标区域,并用初始化轮廓方法确定一个目标轮廓作为Snake模型的初始轮廓,加快了Snake模型的收敛速度;其次,求得该层Snake模型收敛的最终轮廓的中心点作为该层血管的中心点,并将该层的最终轮廓作为下一层的手动轮廓,以此类推,逐层取得血管中心点并连成中心路径;
(3)针对目前利用遍历方法提取血管速度较慢的缺点,引入八叉树分解方法以加速血管分割和血管边界距离场的计算,然后建立基于边界距离场的血管组织最大生成树,并对感兴趣的血管分支提取树的主干,即该分支的中心路径,最后用基于图形硬件处理器的三维纹理体绘制方法沿着中心路径实现血管虚拟内窥镜;
(4)针对传统边界距离场的计算以分割后的二值体数据为目标而丧失了原有数据特征的缺点,提出一种改进的基于距离场的中心路径提取算法。该算法利用原血管造影体数据中血管体素的梯度值倒数和拉普拉斯变换值作为边界距离场计算的初始值,并用重心法修正基于距离场提取的中心路径。与传统基于边界距离场的提取算法相比,该方法提取的血管中心路径更接近于实际应用中人工提取的路径;
(5)为了更准确的提取三维医学体数据中管状器官的中心路径,提出一种基于Hessian矩阵的中心路径提取算法。首先,计算输入的分割后二值数据中每个血管体素的Hessian矩阵;其次,利用每个血管体素Hessian矩阵的特征值和特征向量提取一条粗糙的中心路径;最后,对该中心路径上的每一点,利用尺度空间分析法在其所在的管腔横截面内进行修正,最终得到一条精确的中心路径。
上述研究成果分别从血管的可视化与血管的中心路径提取等方面给出了具体的研究方案和实验结果,为血管疾病的诊断提供了更为先进的辅助手段。此外,文中提出的曲面重建方法和不同的中心路径提取算法具有一定的通用性,为管腔可视化技术的理论研究与应用推广提供了新的思路。
Cardiovascular and cerebrovascular diseases have become one of the diseases with highest incidence and mortality rates. Computed tomography and magnetic resonance imaging techniques make the modern imaging technology become an important diagnosis means of blood vessel diseases. In the blood vessel analysis and diagnosis system, the extraction and visualization of blood vessels play a vita role. The segmentation and extraction algorithms vary depending on imaging modality, application field and other factors. However, there is no such a general segmentation algorithm that is suitable to all medical imaging modalities. In the blood vessel surgery, visualization can locate the stenosis position which is helpful for doctors making an appropriate surgery plan.
After twenty-year development, blood vessel visualization is still in its infancy and remains a great number of problems demanding prompt solution in both theory and application. Based on the existent vessel extraction and visualization techniques, this paper focuses on the research of computed tomography angiography vessel volume datasets. Computer graphics theory and image processing theory are utilized to realize more accurate visualization techniques and centerline extraction algorithms, respectively. The visualization and centerline extracted are also combined to provide more information for the diagnosis of blood vessel diseases. The main contributions and innovative ideas of this paper are summarized as follows:
(1) A high-precision curved planar reformation is realized against the errors caused by simulating curves using pieces of lines in curved planar reformation at present. In the high-precision method, all control points are used to produce curves with B-spline fitting according to the sampling steps specified. Based on this, some assistant functions of curved planar reformation are introduced to enhance the performance of the curved planar reformation, such as adjustments of window widths and window levels, rotating curved planar reformation.
(2) In order to make more accurate observations of the diseases in blood vessel, a centerline extraction method based on Snake model is proposed. First, a region of interest of blood vessel is determined by users in any slice of the volume data. And an initializing contour method is used to produce the initial contour for Snake model, which accelerates the convergence of the Snake model. Then, a final contour can be generated by the convergence of Snake model and a center point of the contour is obtained as the center of blood vessel in current slice. And the final contour in current slice is regarded as the initial contour of the next slice. In this way, a centerline can be obtained by connecting all the center points slice by slice.
(3) Aiming at the low speed in segmentation of blood vessel volume data using traversal method, an octree structure is introduced to accelerate the blood vessel segmentation process and the computation of distance from boundary field. Then, a maximum spanning tree of vascular structure is constructed based on the distance from boundary field and the trunk of the tree is extracted which is the centerline. Finally, a graphics processing unit-based 3D texture-mapping volume rendering method is utilized to show the virtual endoscopy of blood vessel along the centerline.
(4) To overcome the disadvantage in computation of the traditional distance from boundary field which loses the features of original data, an improved centerline extraction algorithm based on the distance from boundary field is proposed. In this algorithm, for each target voxel in original computed tomography angiography volume datasets, the sum of reverse of gradient and laplacian transformation value is regarded as the initial value, and the centerline extracted based on distance from boundary field is modified by center of gravity method. Compared to the traditional centerline extraction based on distance from boundary field, the centerline extracted by this algorithm is closer to the one extracted manually.
(5) In order to extract more accurate centerlines for vascular structures in 3D medical volume data, a centerline extraction method based on Hessian matrix is proposed. Firstly, Hessian matrix is computed for each target voxel in the segmented data which is always binary. Then, a coarse centerline is generated according to the eigenvalues and the eigenvectors of each target voxel’s Hessian matrix. Finally, scale space analysis method is used to refine each point in the coarse centerline in its cross-section plane. Thus, an accurate centerline is obtained.
All achievements above have presented research schemes and experimental results in blood vessel visualization and extraction, which will provide more advanced assistant methods for blood vessel diseases diagnosis. Besides, curved planar reformation and several different centerline extraction algorithms proposed in this paper have generality and enrich the theories and applications of vascular structures visualization.
虽然经历了二十多年的发展,但是血管可视化技术远未成熟,在理论和实际应用中还有许多亟待解决的问题。本文在目前存在的血管提取与可视化技术的基础上,以计算机断层扫描血管造影体数据作为研究对象,分别利用图形学理论和图像处理技术构建更精确的可视化技术和中心路径提取算法,并将两者进行结合,以便提供更多的血管内外部信息,为血管疾病的诊断提供足够的依据。本文所取得的主要研究成果和创新点如下:
(1)针对目前在曲面重建过程中采用多折线段模拟曲线带来的误差问题,根据任意设置的采样步长,采用B样条的方法将所有控制点拟合成曲线,实现了医学图像体数据的高精度曲面重建;并在此基础上引入一些曲面重建的辅助功能,如窗宽窗位调整、旋转曲面重建等,提升曲面重建的性能;
(2)为了能够在血管中更精确地观察病变,提出一种基于Snake模型的血管中心路径提取方法。首先,由用户手动在某一层上确定一个血管目标区域,并用初始化轮廓方法确定一个目标轮廓作为Snake模型的初始轮廓,加快了Snake模型的收敛速度;其次,求得该层Snake模型收敛的最终轮廓的中心点作为该层血管的中心点,并将该层的最终轮廓作为下一层的手动轮廓,以此类推,逐层取得血管中心点并连成中心路径;
(3)针对目前利用遍历方法提取血管速度较慢的缺点,引入八叉树分解方法以加速血管分割和血管边界距离场的计算,然后建立基于边界距离场的血管组织最大生成树,并对感兴趣的血管分支提取树的主干,即该分支的中心路径,最后用基于图形硬件处理器的三维纹理体绘制方法沿着中心路径实现血管虚拟内窥镜;
(4)针对传统边界距离场的计算以分割后的二值体数据为目标而丧失了原有数据特征的缺点,提出一种改进的基于距离场的中心路径提取算法。该算法利用原血管造影体数据中血管体素的梯度值倒数和拉普拉斯变换值作为边界距离场计算的初始值,并用重心法修正基于距离场提取的中心路径。与传统基于边界距离场的提取算法相比,该方法提取的血管中心路径更接近于实际应用中人工提取的路径;
(5)为了更准确的提取三维医学体数据中管状器官的中心路径,提出一种基于Hessian矩阵的中心路径提取算法。首先,计算输入的分割后二值数据中每个血管体素的Hessian矩阵;其次,利用每个血管体素Hessian矩阵的特征值和特征向量提取一条粗糙的中心路径;最后,对该中心路径上的每一点,利用尺度空间分析法在其所在的管腔横截面内进行修正,最终得到一条精确的中心路径。
上述研究成果分别从血管的可视化与血管的中心路径提取等方面给出了具体的研究方案和实验结果,为血管疾病的诊断提供了更为先进的辅助手段。此外,文中提出的曲面重建方法和不同的中心路径提取算法具有一定的通用性,为管腔可视化技术的理论研究与应用推广提供了新的思路。
Cardiovascular and cerebrovascular diseases have become one of the diseases with highest incidence and mortality rates. Computed tomography and magnetic resonance imaging techniques make the modern imaging technology become an important diagnosis means of blood vessel diseases. In the blood vessel analysis and diagnosis system, the extraction and visualization of blood vessels play a vita role. The segmentation and extraction algorithms vary depending on imaging modality, application field and other factors. However, there is no such a general segmentation algorithm that is suitable to all medical imaging modalities. In the blood vessel surgery, visualization can locate the stenosis position which is helpful for doctors making an appropriate surgery plan.
After twenty-year development, blood vessel visualization is still in its infancy and remains a great number of problems demanding prompt solution in both theory and application. Based on the existent vessel extraction and visualization techniques, this paper focuses on the research of computed tomography angiography vessel volume datasets. Computer graphics theory and image processing theory are utilized to realize more accurate visualization techniques and centerline extraction algorithms, respectively. The visualization and centerline extracted are also combined to provide more information for the diagnosis of blood vessel diseases. The main contributions and innovative ideas of this paper are summarized as follows:
(1) A high-precision curved planar reformation is realized against the errors caused by simulating curves using pieces of lines in curved planar reformation at present. In the high-precision method, all control points are used to produce curves with B-spline fitting according to the sampling steps specified. Based on this, some assistant functions of curved planar reformation are introduced to enhance the performance of the curved planar reformation, such as adjustments of window widths and window levels, rotating curved planar reformation.
(2) In order to make more accurate observations of the diseases in blood vessel, a centerline extraction method based on Snake model is proposed. First, a region of interest of blood vessel is determined by users in any slice of the volume data. And an initializing contour method is used to produce the initial contour for Snake model, which accelerates the convergence of the Snake model. Then, a final contour can be generated by the convergence of Snake model and a center point of the contour is obtained as the center of blood vessel in current slice. And the final contour in current slice is regarded as the initial contour of the next slice. In this way, a centerline can be obtained by connecting all the center points slice by slice.
(3) Aiming at the low speed in segmentation of blood vessel volume data using traversal method, an octree structure is introduced to accelerate the blood vessel segmentation process and the computation of distance from boundary field. Then, a maximum spanning tree of vascular structure is constructed based on the distance from boundary field and the trunk of the tree is extracted which is the centerline. Finally, a graphics processing unit-based 3D texture-mapping volume rendering method is utilized to show the virtual endoscopy of blood vessel along the centerline.
(4) To overcome the disadvantage in computation of the traditional distance from boundary field which loses the features of original data, an improved centerline extraction algorithm based on the distance from boundary field is proposed. In this algorithm, for each target voxel in original computed tomography angiography volume datasets, the sum of reverse of gradient and laplacian transformation value is regarded as the initial value, and the centerline extracted based on distance from boundary field is modified by center of gravity method. Compared to the traditional centerline extraction based on distance from boundary field, the centerline extracted by this algorithm is closer to the one extracted manually.
(5) In order to extract more accurate centerlines for vascular structures in 3D medical volume data, a centerline extraction method based on Hessian matrix is proposed. Firstly, Hessian matrix is computed for each target voxel in the segmented data which is always binary. Then, a coarse centerline is generated according to the eigenvalues and the eigenvectors of each target voxel’s Hessian matrix. Finally, scale space analysis method is used to refine each point in the coarse centerline in its cross-section plane. Thus, an accurate centerline is obtained.
All achievements above have presented research schemes and experimental results in blood vessel visualization and extraction, which will provide more advanced assistant methods for blood vessel diseases diagnosis. Besides, curved planar reformation and several different centerline extraction algorithms proposed in this paper have generality and enrich the theories and applications of vascular structures visualization.
引文
[1] ACR-NEMA Committee. Digital Imaging and Communications in Medicine (DICOM), 2003.
[2] The Visible Human Project. http://www.nlm.nih.gov/research/visible/visible_human.html, 1986.
[3] P. Lacroute, M. Levoy. Fast volume rendering using a shear-warp factorization of the viewing transformation. Proc. of ACM SIGGRAPH, Florida, Orlando, USA. 1994: 451-458.
[4] Kirbas C, Quek F. A review of vessel extraction techniques and algorithms. ACM Computing Surveys. 2004, 36(2): 81-121.
[5]主海文,刘有军,曾衍钧.血管图像分割技术的研究进展.北京生物医学工程. 2005, 24(2): 155-159.
[6] Sarwal A, Dhawan A. 3D reconstruction of coronary arteries. Proc. of IEEE Conference Engineering in Medicine and Biology Society, Baltimore, Maryland. 1994, 1: 504–505.
[7] Chwialkowski M, Ibrahim Y, Hong F, et al. A method for fully automated quantitative analysis of arterial flow using flow-sensitized MR images. Computeriezed Medical Imaging and Graphics. 1996, 20(5): 365–378.
[8] Niki N, Kawata Y, Satoh H, et al. 3D imaging of blood vessels using x-ray rotationalangiographic system. IEEE Nuclear Science Symposium Medical Imaging Conference, San Francisco, USA. 1993, 3: 1873–1877.
[9] Gullberg G, Zeng G. A cone-beam filtered backpropagation reconstruction algorithm for cardiac single photon emission computed tomography. IEEE Transactions on Medical Imaging. 1992, MI-11: 91–101.
[10] Tozaki T, Kawata Y, N. Niki, et al. 3D visualization of blood vessels and tumor using thin slice CT. IEEE Nuclear Science Symposium and Medical Imaging Conference, San Francisco, CA, USA. 1995, 3: 1470–1474.
[11] Kawata Y, Niki N, Kumazaki T. An approach for detecting blood vessel diseases from cone-beam CT image. Proc. of IEEE International Conference on Image Processing, Washington, DC, USA. 1995, 2: 500–503.
[12] Eberly D, Gardner R, Morse R, et al. Ridges for image analysis. Journal of Mathematical Imaging and Vision. 1994, 4(4): 351–371.
[13] Bullitt E, Aylward S. Analysis of time-varying images using 3D vascular models. Proc. of Applied Imagery Pattern Recogonition Workshop, Washington, DC, USA. 2001: 9–14.
[14] Guo D, Richardson P. Automatic vessel extraction from angiogram images. Proc. of IEEE Computers in Cardiology, Vienna, Austria. 1998, 25: 441–444.
[15] Schmitt H, Grass M, Rasche V, et al. An x-ray-based method for the determination of the contrast agent propagation in 3D vessel structures. IEEE Transactions on Medical Imaging. 2002, 21(3): 251–262.
[16] Obrien J, Ezquerra N. Automated segmentation of coronary vessels in angiographic image sequences utilizing temporal, spatial structural constraints. Proc. of SPIE Conference Visualization in Biomedical Computing. 1994, 2359(25): 25-37.
[17] Higgins W, Spyra W, Ritman E, et al. Automatic extraction of the arterial tree from 3D angiograms. Proc. of IEEE Conference Engineering in Medicine and Biology, Seatle, USA. 1989, 2: 563–564.
[18] Guéziec A, Pennec X, Ayache N. Medical image registration using geometric hashing. IEEE Computational Science & Engineering. 1997, 4(4): 29–41.
[19] Guéziec A, Ayache N. Smoothing and matching of 3D space curves. International Journal of Computer Vision. 1994, 12(1): 79–104.
[20] Ayache N, Guéziec A, Thirion J, et al. Evaluating 3D registration of CT scan images using crest lines. Mathematical Methods in Medical Imaging II. 1993, 2035(60): 60–71.
[21] Do Carmo M. Differential geometry of curves and surfaces. NewJersy: Prentice-Hall Englewood Cliffs, 1976.
[22] Koenderink J. Solid shapes. USA: MIT Press Cambridge, 1990.
[23] Prinet V, Monga O, Rocchisani J. Multi-dimensional vessel extraction using crest lines. Proc. of IEEE Conference Engineering in Medicine and Biology, Chicago, USA. 1997, 1: 393-394.
[24] Armande N, Montesinos P, Monga O. Thin nets extraction using multi-scale approach. Computer Vision and Image Understanding. 1999, 73(2): 248–257.
[25] Sato Y, Nakajima S, Shiraga N, et al. 3D multi-scale line filter for segmentation and visualization of curvilinear structures in medical images. IEEE Medical Image Analysis, 1998, 2(2): 143–168.
[26] Poli R, Valli G. An algorithm for real-time vessel enhancement and detection. Computer Methods and Programs in Biomedicine. 1997, 52(1): 1–22.
[27] Umbaugh S. Computer vision and machine processing. NewJersy: Prentice Hall PTR Upper Saddle River, 1998.
[28] Jain R, Kasturi R, Schunck B. Machine vision. New York: McGraw-Hill, 1995.
[29]刘党辉,沈兰荪,王兴伟.一种角膜新生血管图像论的分割方法.计算机工程与设计. 2002, 23(6): 52-55.
[30] Taleb-Ahmed A, Leclerc X, Michel T. Semi-automatic segmentation of vessels by mathematical morphology: application in MRI. Proc. of IEEE International Conference on Image Processing, Thessaloniki, Greece. 2001, 3: 1063-1066.
[31] McInerney T, Terzopoulos D. Deformable models in medical image analysis: a survey. Medical Image Analysis. 1996, 1(2): 91–108.
[32] Kass M, Witkin A, Terzoopoulos D. Snakes: active contour models. International Journal of Computer Vision. 1988, 1(4): 321–331.
[33] Luo H, Lu Q, Acharya R, et al. Robust snake model. Proc. of IEEE Conference on Computer Vison and Pattern Recognition, Hilton Head, SC, USA. 2000, 1: 452-457.
[34] Rueckert D, Burger P. Contour fitting using stochastic and probabilistic relaxation for cine MR images. Computer Assisted Radiology. 1995: 137–142.
[35] Osher S, Sethian J. Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulation. Journal of Computational Physics. 1988, 79(11): 12–49.
[36] Malladi R, Sethian J, Vemuri B. Shape modeling with front propagation: a level set approach. IEEE Transactions on Pattern Aanlysis and Machine Intelligence. 1995, 17(2): 158–175.
[37]田捷,包尚联,周明全.医学图像处理与分析.北京:电子工业出版社, 2003. 73-75.
[38]高齐新,于洋,赵大哲,等.一种基于水平集的肺部血管快速分割方法.东北大学学报(自然科学版). 2008, 29(6): 807-810.
[39] Peilot C,Herment A, Sigeile M. A 3D reconstruction of vascular structures from two x-ray angiograms using an adapted simulated annealing algorithm. IEEE Transactions on Medical Imaging. 1994, 13(1): 48-60.
[40] Petrocelli R, Elion J, Manbeck K. A new method for structure recognition in unsubtracted digital angiograms. Proc. of IEEE Computers in Cardiology, Durham, North Carolina, USA. 1992: 207–210.
[41] Petrocelli R, Manbeck K, Elion J. Three dimensional structure recognition in digital angiograms using gauss-markov methods. Proc. of IEEE Computers in Cardiology, London, UK. 1993: 101–104.
[42] O’Donnell, Boult T, Fang X, et al. The extruded generalized cylinder: A deformable model for object recovery. Proc. of IEEE Conference on Computer Vision and Pattern Recognition, Seattle, USA. 1994: 174–181.
[43] O’Donnell T, Gupta A, Boult T. A new model for the recovery of cylindrical structures from medical image data. Joint Conference Computer Vision, Virtual Reality and Robotics in Medicine and Robotics, and Computer-Assisted Surgery, Grenoble, France. 1997: 223–232.
[44] Park S, Lee J, Koo J, et al. Adaptive tracking algorithm based on direction field using ML estimation in angiogram. Proc. of IEEE Conference on Speech and Image Technologies for Computing and Telecommunications, Brisbane, Austrialia. 1997, 2: 671-675.
[45] Lu S, Eiho S. Automatic detection of the coronary arterial contours with sub-branches from an x-ray angiogram. Proc. of IEEE Computers in Cardiology, London, UK. 1993: 575–578.
[46] Smets C, Verbeeck G, Suetens P, et al. A knowledge-based system for the delineation of blood vessels on subtraction angiograms, Pattern Recognition Letters. 1988, 8(2): 113–121.
[47] Stanfiled S. Angy: A rule-based expert system for automatic segmentation of coronary vessels from digital substracted angiograms. IEEE Transactions on Pattern Analysis and Machine Intelligence. 1986, 8(2): 188-199.
[48] Ripley B. Pattern recognition and neural networks. British: Cambridge University press, 1996.
[49] Haykin S. Neural networks: a comprehensive foundation. USA: Printice Hall, 1999.
[50] Shiffman S, Rubin G, Napel S. Semiautomated editing of computed tomography sections for visualization of vascular. Proc. of SPIE Medical Imaging Conference. 1996, 2507: 140-151.
[51]郑杰.基于GPU的高质量交互式大规模数据场可视化技术研究.西安电子科技大学博士论文. 2007, 4.
[52] Preim B, Oeltze S. 3D visualization of vasculature: an overview. Visualization in Medicine and Life Sciences. Berlin: Springer-Verlag, 2007.
[53]张尤赛,陈福民.三维医学图像的体绘制技术综述.计算机工程与应用. 2002, 38(8): 18-20.
[54] Zou H, Gao X, Lv X. A block-layout structure for texture-based volume rendering. Journal of Information and Computational Science. 2008, 5(4): 1619-1628.
[55]邹华,高新波,吕新荣.一种八叉树编码加速的3D纹理体绘制算法.西安交通大学学报(自然科学版). 2008, 42(12): 1490-1494.
[56]邹华,高新波,吕新荣.基于层次包围盒的纹理体绘制加速算法.武汉大学学报(信息科学版). 2009, 34(3):321-325.
[57]邹华,高新波,吕新荣.一种新的GPU光线投射方法.计算机辅助设计与图形学学报. 2009, 21(2): 172-178.
[58]管伟光.体视化技术及其应用.北京:电子工业出版社. 1998.
[59]管伟光.体数据可视化及其在医学重的应用.中国科学院自动化研究所博士论文. 1995.
[60]帅捷,谭永强,孙健永,等.医学三维图像自由视角多平面重建(Free-MPR)显示技术的研究.中国医疗器械杂志. 2007, 31(1): 14-16.
[61] Kanitsar A, Fleischmann D, Wegenkittl R, et al. CPR-curved planar reformation. Proc. of IEEE Visualization, Boston, MA, USA. 2002: 37-44.
[62] Kanitsar A, Wegenkittl R, Fleischmann D, et al. Advanced curved planar reformation: flattening of vascular structures. Proc. of IEEE Visualization, Seatle, WA, USA. 2003: 43-50.
[63]吕新荣,高新波,邹华.医学图像体数据多平(曲)面重建.系统仿真学报. 2009, 21(1): 166-169, 173.
[64] Lorensen W, Cline H. Marching Cubes: A high resolution 3D surface construction algorithm. ACM Siggraph Computer Graphics. 1987, 21(4): 163-169.
[65] Cabral B, Cam N, Foran, J. Accelerated Volume Rendering and Tomographic Reconstruction Using Texture Mapping Hardware. Proc. of IEEE Visualization, Tysons Corner, Virginia, USA. 1994: 91-98.
[66] Nvidia Developer Relation Site. Available online at http://developer.nvidia.com.
[67]基尔加德,等著,洪伟,等译. Cg教程:可编程实施图形权威指南.第一版.北京:人民邮电出版社. 2004.
[68]姚德民,宋志坚.虚拟内窥镜关键技术的研究与临床应用.生物医学工程学杂志. 2008, 25(1): 18-22.
[69]彭延军,王元红,石教英,等.虚拟内窥镜关键技术研究.计算机应用研究. 2005, 5: 37-39.
[70]李乃弘,于文雪.三维人体虚拟内窥镜的实验研究.航天医学与医学工程. 1999, 12: 209-213.
[71]张惠,舒华忠.交互式虚拟内窥镜系统.中国图象图形学报. 2002, 7(1): 36-43.
[72]王刚.交互式虚拟内窥镜系统研究.西安电子科技大学硕士论文. 2003, 1.
[73] Hong L, Kaufman A, Wie Y, et al. 3D virtual colonoscopy. Proc. of IEEE symposium on Biomedical Visualization. 1995, 1: 26-32.
[1]常宏.多排CT的最新进展.医疗设备信息. 2005, 20(7): 69-69.
[2]帅捷,谭永强,孙健永,等.医学三维图像自由视角多平面重建(Free-MPR)显示技术的研究.中国医疗器械杂志. 2007, 31(1): 14-16.
[3]笪良龙,杨廷武,李玉阳,等.基于PC硬件加速的三维数据场直接体可视化.系统仿真学报. 2005, 17(10): 2422-2425.
[4]郑杰,姬红兵,杨万海.一种基于per-pixel光照的高质量体绘制算法.系统仿真学报. 2007, 19(1): 21-25.
[5]沈傲东.医学影像三维重建方法研究.西安电子科技大学硕士论文. 2003, 1.
[6] Lorensen W, Cline H. Marching Cubes: a high resolution 3D surface construction algorithm. ACM Siggraph Computer Graphics. 1987, 21(4): 163-169.
[7]王刚.交互式虚拟内窥镜系统研究.西安电子科技大学硕士论文. 2003, 1.
[8]周礼平.三维数据场虚拟内窥镜技术研究.西安电子科技大学硕士论文. 2004, 1.
[9]谭光喜,余成新,张晓磷,等.多层螺旋CT的MPR、SSD和CPR重建用于颌骨肿瘤.实用医学进修杂志. 2005, 33(3): 184-188.
[10] Kanitsar A, Fleischmann D, Wegenkittl R, et al. CPR-curved planar reformation. Proc. of IEEE Visualization, Boston, MA, USA. 2002: 37-44.
[11] Kanitsar A, Wegenkittl R, Fleischmann D, et al. Advanced curved planar reformation: flattening of vascular structures. Proc. of IEEE Visualization, Seatle, WA, USA. 2003: 43-50.
[12]吕新荣,高新波,邹华.医学图像体数据多平(曲)面重建.系统仿真学报. 2009, 21(1): 166-169, 173.
[13]孙家广,杨长贵.计算机图形学.第三版.北京:清华大学出版社, 1995. 284-294.
[14]刘旭敏,黄厚宽,王刘强,等.带形状参数样条曲线的研究.计算机研究与发展. 2007, 44(3): 487-496.
[15] Michael Mei?ner. http://www.gris.uni-tuebingen.de/edu/areas/scivis/volren/datasets/new.html.
[16] Taubin G. A signal processing approach to fair surface design. Proc. of ACM Siggraph, Los Angeles, CA, USA.1995: 351-358.
[17] Vollmer J, Mencel R, Mueller H. Improved Laplacian smoothing of noisy surface meshes. Proc. of EuroGraphics, Vienna, Austria. 1999: 131-138.
[18] Cebral J, Lohner R. From medical images to anatomically accurate finite element grids. International Journal of Numerical Methdos in Engineering. 2001, 51(8): 985-1008.
[19] Gibson S. Constrained elastic surface nets: Generating smooth surfaces from binary segmented data. Proc. of MICCAI, Springer, volume 1496 of LNCS, Cambridge MA, USA. 1998: 888-898.
[20] Schumann C, Oeltze S, Bade S, et al. Model-free surface visualization of vascular trees. Proc. of Eurographics, Prague, Czech Republic. 2007.
[21] Masutani Y, Masamune K, Dohi T. Region-growing-based feature extraction algorithm for tree-like objects. Proc. of Visualizationin Biomedical Computing, Springer, volume 1131 of LNCS, Hamburg, Germany. 1996: 161-171.
[22] Hahn H, Preim B, Selle D, et al. Visualization and interaction techniques for the exploration of vascular structures. Proc. of IEEE Visualization, San Diego, CA, USA. 2001: 395-402.
[23] H?hne K, Pflesser B, Pommert A, et al. A Realistic model of the inner organs from the visible human data. Proc. of MICCAI, Springer, volume 1935 of LNCS, Pittsburgh, PA, USA. 2000: 776–785.
[24] Felkl P, Wegenkittl R, B?hler K. Surface models of tube trees. Proc. of Computer Graphics International, Hersonissos, Crete, Greece. 2004: 70-77.
[25] Fiebich M, Straus C, Sehgal V, et al. Automatic bone segmentation technique for CT angiographic studies. Journal of Computer Assisted Tomography. 1999, 23(1):155–161.
[26] Frangi A, Niessen W, Vincken K, et al. Multiscale vessel enhancement filtering. Proc. of Medical Image Computing and Computer-Assisted Intervention, volume 1496 of Lecture Notes in Computer Science, Cambridge MA, USA. 1998: 130–137.
[27] Siebert J, Rosenbaum T, Pernicone J. Automated segmentation and presentation algorithmsfor 3D MR Angiography. Proc. of 10th Annual Meeting of the Society of Magnetic Resonance in Medicine, San Francisco. Berkeley, USA. 1991.
[28] Zuiderveld K. Visualization of multimodality medical volume data using object-oriented Methods. PhD thesis, Universiteit Utrecht, 1995.
[29] Pommert A, Bomans M, H?hne K. Volume visualization in magnetic resonance angiography. IEEE Computer Graphics and Application. 1992, 12(5): 12-13.
[30] Ebert D, Morris C, Rheingans P, et al. Designing effective transfer functions for volume rendering from photographics volumes. IEEE Transactions on Visualization and Computer Graphics. 2002, 8(2): 183-197.
[31] He T, Hong L, Kaufman A, et al. Generation of transfer functions with stochastic search techniques. Proc. of IEEE Visualization, San Francisco, CA, USA. 1996: 227-234.
[32] Kindlmann G, Durkin W. Semi-automatic generation of transfer functions for direct volume rendering. Proc. of IEEE Volume Visualization Symposium, North Carolina, USA. 1998: 79-86.
[33] Kindlmann G, Whitaker R, Tasdizen T, et al. Curvature-based transfer functions for volume rendering: methods and applications. Proc. of IEEE Visualization, Seatle, WA, USA. 2003: 513-520.
[34] Kniss J, Kindlmann G, Hansen C. Interactive volume rendering using multi-dimensional transfer functions and direct manipulation widgets. Proc. of IEEE Visualization, San Diego, CA, USA. 2001: 255-262.
[35] Kniss J, Kindlmann G, Hansen C. Multidimensional transfer functions for interactive volume rendering. IEEE Transactions on Visualization and Computer Graphics. 2002, 8(4): 270-285.
[36] Kniss J, Premoze S, Ikits M, et al. Gaussian transfer functions for multi-field volume visualization. Proc. of IEEE Visualization, Seatle, WA, USA. 2003: 497-504.
[37] Knittel G. Using pre-integrated transfer functions in an interactive software system for volume rendering. Proc. of Short Presentations Eurographics, Saarbruecken, Germany. 2002: 119-123.
[38] K?nig A, Gr?ller E. Mastering transfer function specification by using VolumePro technology. Proc. of the 17th Spring Conference on Computer Graphics, Budmerice, Slovakia. 2001: 279-286.
[39] Vega F, Sauber N, Tomandl B, et al. Enhanced 3D-Visualization of intracranial aneurysms involving the skull base. Proc. of MICCAI, Springer, volume 2879 of LNCS, Montréal, Canada. 2003: 256-263.
[40]张怡,张加万,孙济州,等.基于可编程图形加速硬件的实时光线投射算法.系统仿真学报. 2007, 19(18): 4204-4208.
[41] Gelder V, Kim K. Direct volume rendering with shading via three-dimensional Texture. Proc.of 1996 Symposium on Volume Visualization. San Francisco, California, USA. 1996: 23-30.
[42] Nvidia Developer Relation Site. Available online at http://developer.nvidia.com.
[43]基尔加德,等著,洪伟,等译. Cg教程:可编程实施图形权威指南.第一版.北京:人民邮电出版社. 2004.
[44] Lee T, Lin P, Lin C, et al. Interactive 3-D virtual colonoscopy system. IEEE Transactions on Information Technology in Biomedicine. 1999, 3(2): 139-150.
[45] Hong L, Muraki S, Kaufman A, et al. Vitrual voyage: interactive navigation in the human colon. ACM Siggraph Computer Graphics, Los Angeles, CA, USA. 1997: 27-34.
[46]耿国华,周明全.交互式实时虚拟内窥镜系统中的关键技术.计算机应用. 2002, 22(11): 54-55.
[47]范江波,周明全,耿国华.虚拟内窥镜技术的研究与实现.微机发展. 2000, 6: 60-62.
[48]姚德民,宋志坚.虚拟内窥镜关键技术的研究与临床应用.生物医学工程学杂志. 2008, 25(1): 18-22.
[49]彭延军,王元红,石教英,等.虚拟内窥镜关键技术研究.计算机应用研究. 2005, 5: 37-39.
[50]李乃弘,于文雪.三维人体虚拟内窥镜的实验研究.航天医学与医学工程. 1999, 12: 209-213.
[51]张惠,舒华忠.交互式虚拟内窥镜系统.中国图象图形学报. 2002, 7(1): 36-43.
[52] Verroust A, Lazarus F. Extracting skeletal curves from 3D scattered data. Shape Modeling International, Aizu Wakamatsu. 1999: 16-25.
[53] Niblack W, Gibbons P, Capson D. Generating skeletons and centerlines from the distance transform. CVGIP: Graphical Models Image Processing. 1992, 54(5): 420-437.
[54]竺海,姬红兵,高新波.基于边界距离场的管腔中心路径自动提取算法.计算机辅助设计与图形学学报. 2006, 18(6): 860-864.
[55]胡英,侯悦,徐心和.基于双距离场的三维中心路径提取算法.中国图像图形学报. 2003, 8(11): 1272-1276.
[1] Sato Y, Shiraga N, Nakajima S, et al. Local maximum intensity projection (LMIP): a new rendering method for vascular visualization. Journal of Computer Aided Tomography. 1998, 22(6): 912-917.
[2] Drebin R, Carpenter L, Hanrahan P. Volume Rendering. Proc. of Computer Graphics and Interactive Techniques, New York, USA. 1988: 65-74
[3] Lichtenbelt B, Crane R, Naqvi S. Introduction to Volume Rendering. New Jersey: Prentice-Hall, 1998.
[4]彭延军,石教英.体绘制技术在医学可视化中的新发展.中国图象图形学报. 2002, 7(12): 1239-1246.
[5] Kanitsar A, Fleischmann D, Wegenkittl R, et al. CPR-curved planar reformation. Proc. of IEEE Visualization, Boston, MA, USA. 2002: 37-44.
[6] Kanitsar A, Wegenkittl R, Fleischmann D, et al. Advanced curved planar reformation: flattening of vascular structures. Proc. of IEEE Visualization, Seatle, WA, USA. 2003: 43-50.
[7] Cai W. 3D Planar Reformation of Vascular Central Axis Surface with Biconvex Slab. Computerized Medical Imaging and Graphics. 2007, 31(7): 570-576.
[8] Avants B, Williams J. An Adaptive Minimal Path Generation Technique for Vessel Tracking in CTA/CEMRA Volume Images. International Conference on Medical Image Computing and Computer-Assisted Intervention, Utrecht, The Netherlands. 2001: 707–716.
[9] He S, Dai R, Lu B, et al. Medial Axis Reformation: A New Visualization Method for CT Angiography. Academic Radiology. 2001, 8(8): 726–733.
[10] Kass M, Witkin A, Terzopoulos D. Snakes: Active contour model. Computer Vision. 1987, 1(4): 321-331.
[11]李培华,张田文.主动轮廓模型(蛇模型)综述.软件学报. 2000, 11(6): 751-757.
[12] Yezzi A, Kichenassamy S, Kumar A, et al. A Geometric Snake Model for Segmentation of Medical Imagery. IEEE Transactions on Medical Image. 1997, 16(2): 199-209.
[13] Luo Xiping, Tian Jie, Lin Yao. An Algorithm for Segmentation of Medical Image Series Based on Active Contour Mode. Journal of Software. 2002, 13(6): 1050-1058.
[14]周则明,王平安,夏德深.基于Snake模型的低对比度噪声心脏MRI图像分割.系统仿真学报. 2004, 16(11): 2493-2497.
[15] Huang Shaohui, Wang Boliang, Huang Xiaoyang. Using GVF Snake to Segment Liver from CT images. Proc. of the 3rd IEEE-EMBS, MIT, Boston, USA. 2006: 145-148.
[16] Liu F, Zhao B, Kijewski PK, et al. Liver segmentation for CT images using GVF snake. Medical Physics. 2005, 32(12): 3699-3706.
[17] Xu Chenyang, Prince J.L. Snakes, shapes, and gradient vector flow. IEEE Transactions on Image Processing. 1998, 7(3): 359-369.
[18]阮鹏.基于T-snake模型的冠状动脉血管提取和运动分析的方法研究.天津大学硕士论文. 2006, 1.
[19]张麒,汪源源,王威琪,等.基于梯度矢量流与多尺度分析的血管内超声图像轮廓提取.生命科学仪器. 2007, 5(8): 32-36.
[20] Lv X, Gao X, Zou H. Interactive curved planar reformation based on snake model. Computerized Medical Imaging and Graphics. 2008, 32(8): 662-669.
[21]王小林,刘宏申,秦锋.基于Snake模型的目标检测.华中科技大学学报(自然科学版). 2008, 36(1): 75-77.
[22]孙家广,杨长贵.计算机图形学.第三版.北京:清华大学出版社, 1995.
[23] Michael Mei?ner. http://www.gris.uni-tuebingen.de/edu/areas/scivis/volren/datasets/new.html.
[1] Schumann C, Oeltze S, Bade R, et al. Model-free surface visualization of vascular trees. Eurographics/IEEE-VGTC Symposium on Visualization, Norrk ? ping, Sweden. 2007: 283-290.
[2] Hoover A, Kouznetsova V, Goldbaum M. Locating blood vessels in retinal images by piecewise threshold probing of a matched filter response. IEEE Transactions on Medical Imaging. 2000, 19(3): 203-210.
[3] Xu Chenyang, Prince J. Snakes, shapes, and gradient vector flow. IEEE Transactions on Image Process. 1998, 7(3): 359-369.
[4] Sum K, Cheung P. Boundary vector field for parametric active contours. Pattern Recognition. 2007, 40(6): 1635-1645.
[5] Sum K, Cheung P. Vessel extraction under non-uniform illumination: a level set approach. IEEE Transactions on Biomedical Engineering. 2008, 55(1): 358-360.
[6] Tolias Y, Panas S. A fuzzy vessel tracking algorithm for retinal images based on fuzzy clustering. IEEE Transactions on Medical Imaging. 1998, 17(2): 263-273.
[7] Bombardier V, Jaluent M, Bubel A, et al. Cooperation of two fuzzy segmentation operators for digital subtracted angiograms analysis. Proc. of the 6th IEEE International Conference on Fuzzy Systems, Barcelona, Spain. 1997: 1057-1062.
[8] Rodíguez R, Alarcón T, Pacheco O. A new strategy to obtain robust markers for blood vessels segmentation by using the watersheds method. Computers in Biology and Medicine. 2005,35(8): 665-686.
[9]徐智,郁道银,谢洪波,等.心血管造影图像中的心血管提取.中国生物医学工程学报. 2003, 22(1): 6-11.
[10] Ritter F, Hansen C, Dicken V, et al. Real-time illustration of vascular structures. IEEE Transactions on Visualization and Computer Graphics. 2006, 12(5): 877-884.
[11] Lorensen W, Cline H. Marching cubes: a high resolution 3D surface construction algorithm. Proc. of the 14th Annual Conference on Computer Graphics and Interactive Techniques, New York, USA. 1987: 163-169.
[12] Sato Y, Shiraga N, Nakajima S, et al. Local maximum intensity projection (LMIP): a new rendering method for vascular visualization. Journal of Computer Aided Tomography. 1998, 22(6): 912-917.
[13] Preim B, Oeltze S. 3D visualization of vasculature: an overview. Visualization in Medicine and Life Sciences. Berlin: Springer-Verlag, 2007.
[14]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(4): 510-512.
[15]贾冬焱,郝立巍,周寿军,等.自动测量造影图像中血管中心线和宽度的新方法.中国生物医学工程学报. 2007, 26(2): 214-219,225.
[16]唐荣锡,汪嘉业,彭群生,等.计算机图形学教程.北京:科学出版社, 2000.
[17] Cullip T, Neumann U. Accelerating volume reconstruction with 3D texture mapping hardware. UNC-1993-027, 1993.
[18] Kanitsar A, Fleischmann D, Wegenkittl R, et al. CPR-curved planar reformation. Proc. of IEEE Visualization, Boston, MA, USA. 2002: 37-44.
[19] Kanitsar A, Wegenkittl R, Fleischmann D, et al. Advanced curved planar reformation: flattening of vascular structures. Proc. of IEEE Visualization, Seatle, WA, USA. 2003: 43-50.
[20]竺海,姬红兵,高新波.基于边界距离场的管腔中心路径自动提取算法.计算机辅助设计与图形学学报. 2006, 18(6): 860-864.
[21]胡英,侯悦,徐心和.基于双距离场的三维中心路径提取算法.中国图像图形学报. 2003, 8(11): 1272-1276.
[22] Shih F, Wu Y. Three-dimensional Euclidean distance transformation and its application to shortest path planning. Pattern Recognition. 2004, 37(1): 79-92.
[23] Wan Ming, Liang Zhengrong, Ke Qi, et al. Automatic centerline extraction for virtual colonoscopy. IEEE Transactions on Medical Imaging. 2002, 21(12): 1450-1460.
[24] Michael Mei?ner. http://www.gris.uni-tuebingen.de/edu/areas/scivis/volren/datasets/new.html.
[25] Ohtake Y, Belyaey A, Alexa M, et al. Multilevel partition of unity implicits. International Conference on Computer Graphics and Interactive Techniques, New York, USA. 2003:463-470.
[26] Engel K, Kraus M, Etrl T. High quality pre-integrated volume rendering using hardware accelerated pixel shading. Proc. of the ACM SIGGRAPH/EUROGRAPHICS Workshop on Graphics Hardware, New York, USA. 2001: 9-16.
[27] Roettger S, Ertl T. A two-step approach for interactive pre-integrated volume rendering of unstructured grids. Proc. of IEEE Visualization, Boston, MA, USA. 2002: 23-28.
[1]李光明,田捷,赵明昌,等.基于Hessian矩阵的中心路径提取算法.软件学报. 2003, 14(1): 1148-1156.
[2]胡英,侯悦,徐心和.基于双距离场的三维中心路径提取算法.中国图象图形学报. 2003, 8(11): 1272-1276.
[3]竺海,姬红兵,高新波.基于边界距离场的管腔中心路径自动提取算法.计算机辅助设计与图形学学报. 2006, 18(6): 860-864.
[4] Sundar H, Silver D, Gagvani N, et al. Skeleton based shape matching and retrieval. Proc. of the Shape Modeling International 2003, Seoul, Korea. 2003: 130-139.
[5] Bitter I, Sato M, Bender M, et al. CEASAR: A Smooth, Accurate and robust centerline extraction algorithm. Proc. of IEEE Visualization 2000, Salt Lake City, USA. 2000: 45-52.
[6] Sato M, Bitter I, Bender MA, et al. TEASAR: Tree-structure extraction algorithm for accurate and robust skeletons. Proc. of IEEE Pacific Graphics 2000, Hong Kong, China. 2000: 281-289.
[7] Egger J, Mostarki? Z, Gro?kopf S, et al. A fast vessel centerline extraction algorithm for catheter simulation. Twentieth IEEE International Symposium on Computer-Based Medical Systems, Maribor, Slovenia. 2007.
[8]唐荣锡,汪嘉业,彭群生,等.计算机图形学教程.北京:科学出版社, 2000.
[9] Cruz A. Accuracy evaluation of different centerline approximations of blood vessels. Proc. of IEEE Visualization, Konstanz, Germany. 2004: 1-11.
[10] Michael Mei?ner. http://www.gris.uni-tuebingen.de/edu/areas/scivis/volren/datasets/new.html.
[1] Ge Y, Stelts D, Wang J, et al. Computing the centerline of the colon: a robust and efficient method based on 3D skeletons. Journal of Computer Assisted Tomography. 1999, 23(5): 786-794.
[2] Borgefors G. Distance transformations in digital images. Computer Vision, Graphics, and Image Processing. 1986, 34(3): 344-371.
[3] Dijkstra E. A note on two problems in connection with graphs, Num. Math. 1. 1959. 269-271.
[4] Telea A, Vilanova A. A robust level-set algorithm for centerline extraction. IEEE TCVG Symposium on Visualization. 2003, 40: 185-194.
[5] Kirbas C, Quek F. A review of vessel extraction techniques and algorithms. ACM Computing Surveys. 2004, 36(2): 81-121.
[6]李光明,田捷,赵明昌,等.基于Hessian矩阵的中心路径提取算法.软件学报. 2003, 14(1): 1148-1156.
[7]胡英,侯悦,徐心和.基于双距离场的三维中心路径提取算法.中国图象图形学报. 2003, 8(11): 1272-1276.
[8]竺海,姬红兵,高新波.基于边界距离场的管腔中心路径自动提取算法.计算机辅助设计与图形学学报. 2006, 18(6): 860-864.
[9] Sundar H, Silver D, Gagvani N, Dickinson S. Skeleton based shape matching and retrieval. Proc. of the Shape Modeling International, Seoul, Korea. 2003: 130-139.
[10] Bitter I, Sato M, Bender M, et al. CEASAR: A smooth, accurate and robust centerline extraction algorithm. Proc. of IEEE Visualization, Salt Lake City, USA. 2000: 45-52.
[11] Sato M, Bitter I, Bender M, et al. TEASAR: Tree-structure extraction algorithm for accurate and robust skeletons. Proc. of IEEE Pacific Graphics, Hong Kong, China. 2000: 281-289.
[12] Egger J, Mostarki? Z, Gro?kopf S, et al. A fast vessel centerline extraction algorithm for catheter simulation. Twentieth IEEE International Symposium on Computer-Based Medical Systems, Maribor, Slovenia. 2007.
[13] Xu Y, Zhang H, Li H, et al. An improved algorithm for vessel centerline tracking in coronary angiograms. Computer Methods and Programs in Biomedicine. 2007, 88(2): 131-143.
[14] Mueller D, Maeder A. Robust semi-automated path extraction for visualizing stenosis of the coronary arteries. Computerized Medical Imaging and Graphics. 2008, 32(6): 463-475.
[15] Cruz A. Accuracy evaluation of different centerline approximations of blood vessels. IEEE TCVG Symposium on Visualization, Konstanz, Germany. 2004: 1-11.
[16] Wan M, Liang Z, Ke Q, et al. Automatic centerline extraction for virtual colonoscopy. IEEE Transactions on Medical Images. 2002, 21(12): 1450-1460.
[17] Deschamps T, Cohent L. Fast extraction of minimal paths in 3D images and applications to virtual endoscopy. Medical Images Analysis. 2001, 5(4): 281-299.
[18] Morse B, Pizer S, Liu A. Multiscale medical analysis of medical images. Image & Vision Computing. 1993, 12(6): 327-338.
[19] He S, Yang X, Dai R. Medial axis extraction from blurred and noisy images. Journal of Image and Graphics. 2000, 5(5): 420-424.
[20] Michael Mei?ner. http://www.gris.uni-tuebingen.de/edu/areas/scivis/volren/datasets/new.html.
[2] The Visible Human Project. http://www.nlm.nih.gov/research/visible/visible_human.html, 1986.
[3] P. Lacroute, M. Levoy. Fast volume rendering using a shear-warp factorization of the viewing transformation. Proc. of ACM SIGGRAPH, Florida, Orlando, USA. 1994: 451-458.
[4] Kirbas C, Quek F. A review of vessel extraction techniques and algorithms. ACM Computing Surveys. 2004, 36(2): 81-121.
[5]主海文,刘有军,曾衍钧.血管图像分割技术的研究进展.北京生物医学工程. 2005, 24(2): 155-159.
[6] Sarwal A, Dhawan A. 3D reconstruction of coronary arteries. Proc. of IEEE Conference Engineering in Medicine and Biology Society, Baltimore, Maryland. 1994, 1: 504–505.
[7] Chwialkowski M, Ibrahim Y, Hong F, et al. A method for fully automated quantitative analysis of arterial flow using flow-sensitized MR images. Computeriezed Medical Imaging and Graphics. 1996, 20(5): 365–378.
[8] Niki N, Kawata Y, Satoh H, et al. 3D imaging of blood vessels using x-ray rotationalangiographic system. IEEE Nuclear Science Symposium Medical Imaging Conference, San Francisco, USA. 1993, 3: 1873–1877.
[9] Gullberg G, Zeng G. A cone-beam filtered backpropagation reconstruction algorithm for cardiac single photon emission computed tomography. IEEE Transactions on Medical Imaging. 1992, MI-11: 91–101.
[10] Tozaki T, Kawata Y, N. Niki, et al. 3D visualization of blood vessels and tumor using thin slice CT. IEEE Nuclear Science Symposium and Medical Imaging Conference, San Francisco, CA, USA. 1995, 3: 1470–1474.
[11] Kawata Y, Niki N, Kumazaki T. An approach for detecting blood vessel diseases from cone-beam CT image. Proc. of IEEE International Conference on Image Processing, Washington, DC, USA. 1995, 2: 500–503.
[12] Eberly D, Gardner R, Morse R, et al. Ridges for image analysis. Journal of Mathematical Imaging and Vision. 1994, 4(4): 351–371.
[13] Bullitt E, Aylward S. Analysis of time-varying images using 3D vascular models. Proc. of Applied Imagery Pattern Recogonition Workshop, Washington, DC, USA. 2001: 9–14.
[14] Guo D, Richardson P. Automatic vessel extraction from angiogram images. Proc. of IEEE Computers in Cardiology, Vienna, Austria. 1998, 25: 441–444.
[15] Schmitt H, Grass M, Rasche V, et al. An x-ray-based method for the determination of the contrast agent propagation in 3D vessel structures. IEEE Transactions on Medical Imaging. 2002, 21(3): 251–262.
[16] Obrien J, Ezquerra N. Automated segmentation of coronary vessels in angiographic image sequences utilizing temporal, spatial structural constraints. Proc. of SPIE Conference Visualization in Biomedical Computing. 1994, 2359(25): 25-37.
[17] Higgins W, Spyra W, Ritman E, et al. Automatic extraction of the arterial tree from 3D angiograms. Proc. of IEEE Conference Engineering in Medicine and Biology, Seatle, USA. 1989, 2: 563–564.
[18] Guéziec A, Pennec X, Ayache N. Medical image registration using geometric hashing. IEEE Computational Science & Engineering. 1997, 4(4): 29–41.
[19] Guéziec A, Ayache N. Smoothing and matching of 3D space curves. International Journal of Computer Vision. 1994, 12(1): 79–104.
[20] Ayache N, Guéziec A, Thirion J, et al. Evaluating 3D registration of CT scan images using crest lines. Mathematical Methods in Medical Imaging II. 1993, 2035(60): 60–71.
[21] Do Carmo M. Differential geometry of curves and surfaces. NewJersy: Prentice-Hall Englewood Cliffs, 1976.
[22] Koenderink J. Solid shapes. USA: MIT Press Cambridge, 1990.
[23] Prinet V, Monga O, Rocchisani J. Multi-dimensional vessel extraction using crest lines. Proc. of IEEE Conference Engineering in Medicine and Biology, Chicago, USA. 1997, 1: 393-394.
[24] Armande N, Montesinos P, Monga O. Thin nets extraction using multi-scale approach. Computer Vision and Image Understanding. 1999, 73(2): 248–257.
[25] Sato Y, Nakajima S, Shiraga N, et al. 3D multi-scale line filter for segmentation and visualization of curvilinear structures in medical images. IEEE Medical Image Analysis, 1998, 2(2): 143–168.
[26] Poli R, Valli G. An algorithm for real-time vessel enhancement and detection. Computer Methods and Programs in Biomedicine. 1997, 52(1): 1–22.
[27] Umbaugh S. Computer vision and machine processing. NewJersy: Prentice Hall PTR Upper Saddle River, 1998.
[28] Jain R, Kasturi R, Schunck B. Machine vision. New York: McGraw-Hill, 1995.
[29]刘党辉,沈兰荪,王兴伟.一种角膜新生血管图像论的分割方法.计算机工程与设计. 2002, 23(6): 52-55.
[30] Taleb-Ahmed A, Leclerc X, Michel T. Semi-automatic segmentation of vessels by mathematical morphology: application in MRI. Proc. of IEEE International Conference on Image Processing, Thessaloniki, Greece. 2001, 3: 1063-1066.
[31] McInerney T, Terzopoulos D. Deformable models in medical image analysis: a survey. Medical Image Analysis. 1996, 1(2): 91–108.
[32] Kass M, Witkin A, Terzoopoulos D. Snakes: active contour models. International Journal of Computer Vision. 1988, 1(4): 321–331.
[33] Luo H, Lu Q, Acharya R, et al. Robust snake model. Proc. of IEEE Conference on Computer Vison and Pattern Recognition, Hilton Head, SC, USA. 2000, 1: 452-457.
[34] Rueckert D, Burger P. Contour fitting using stochastic and probabilistic relaxation for cine MR images. Computer Assisted Radiology. 1995: 137–142.
[35] Osher S, Sethian J. Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulation. Journal of Computational Physics. 1988, 79(11): 12–49.
[36] Malladi R, Sethian J, Vemuri B. Shape modeling with front propagation: a level set approach. IEEE Transactions on Pattern Aanlysis and Machine Intelligence. 1995, 17(2): 158–175.
[37]田捷,包尚联,周明全.医学图像处理与分析.北京:电子工业出版社, 2003. 73-75.
[38]高齐新,于洋,赵大哲,等.一种基于水平集的肺部血管快速分割方法.东北大学学报(自然科学版). 2008, 29(6): 807-810.
[39] Peilot C,Herment A, Sigeile M. A 3D reconstruction of vascular structures from two x-ray angiograms using an adapted simulated annealing algorithm. IEEE Transactions on Medical Imaging. 1994, 13(1): 48-60.
[40] Petrocelli R, Elion J, Manbeck K. A new method for structure recognition in unsubtracted digital angiograms. Proc. of IEEE Computers in Cardiology, Durham, North Carolina, USA. 1992: 207–210.
[41] Petrocelli R, Manbeck K, Elion J. Three dimensional structure recognition in digital angiograms using gauss-markov methods. Proc. of IEEE Computers in Cardiology, London, UK. 1993: 101–104.
[42] O’Donnell, Boult T, Fang X, et al. The extruded generalized cylinder: A deformable model for object recovery. Proc. of IEEE Conference on Computer Vision and Pattern Recognition, Seattle, USA. 1994: 174–181.
[43] O’Donnell T, Gupta A, Boult T. A new model for the recovery of cylindrical structures from medical image data. Joint Conference Computer Vision, Virtual Reality and Robotics in Medicine and Robotics, and Computer-Assisted Surgery, Grenoble, France. 1997: 223–232.
[44] Park S, Lee J, Koo J, et al. Adaptive tracking algorithm based on direction field using ML estimation in angiogram. Proc. of IEEE Conference on Speech and Image Technologies for Computing and Telecommunications, Brisbane, Austrialia. 1997, 2: 671-675.
[45] Lu S, Eiho S. Automatic detection of the coronary arterial contours with sub-branches from an x-ray angiogram. Proc. of IEEE Computers in Cardiology, London, UK. 1993: 575–578.
[46] Smets C, Verbeeck G, Suetens P, et al. A knowledge-based system for the delineation of blood vessels on subtraction angiograms, Pattern Recognition Letters. 1988, 8(2): 113–121.
[47] Stanfiled S. Angy: A rule-based expert system for automatic segmentation of coronary vessels from digital substracted angiograms. IEEE Transactions on Pattern Analysis and Machine Intelligence. 1986, 8(2): 188-199.
[48] Ripley B. Pattern recognition and neural networks. British: Cambridge University press, 1996.
[49] Haykin S. Neural networks: a comprehensive foundation. USA: Printice Hall, 1999.
[50] Shiffman S, Rubin G, Napel S. Semiautomated editing of computed tomography sections for visualization of vascular. Proc. of SPIE Medical Imaging Conference. 1996, 2507: 140-151.
[51]郑杰.基于GPU的高质量交互式大规模数据场可视化技术研究.西安电子科技大学博士论文. 2007, 4.
[52] Preim B, Oeltze S. 3D visualization of vasculature: an overview. Visualization in Medicine and Life Sciences. Berlin: Springer-Verlag, 2007.
[53]张尤赛,陈福民.三维医学图像的体绘制技术综述.计算机工程与应用. 2002, 38(8): 18-20.
[54] Zou H, Gao X, Lv X. A block-layout structure for texture-based volume rendering. Journal of Information and Computational Science. 2008, 5(4): 1619-1628.
[55]邹华,高新波,吕新荣.一种八叉树编码加速的3D纹理体绘制算法.西安交通大学学报(自然科学版). 2008, 42(12): 1490-1494.
[56]邹华,高新波,吕新荣.基于层次包围盒的纹理体绘制加速算法.武汉大学学报(信息科学版). 2009, 34(3):321-325.
[57]邹华,高新波,吕新荣.一种新的GPU光线投射方法.计算机辅助设计与图形学学报. 2009, 21(2): 172-178.
[58]管伟光.体视化技术及其应用.北京:电子工业出版社. 1998.
[59]管伟光.体数据可视化及其在医学重的应用.中国科学院自动化研究所博士论文. 1995.
[60]帅捷,谭永强,孙健永,等.医学三维图像自由视角多平面重建(Free-MPR)显示技术的研究.中国医疗器械杂志. 2007, 31(1): 14-16.
[61] Kanitsar A, Fleischmann D, Wegenkittl R, et al. CPR-curved planar reformation. Proc. of IEEE Visualization, Boston, MA, USA. 2002: 37-44.
[62] Kanitsar A, Wegenkittl R, Fleischmann D, et al. Advanced curved planar reformation: flattening of vascular structures. Proc. of IEEE Visualization, Seatle, WA, USA. 2003: 43-50.
[63]吕新荣,高新波,邹华.医学图像体数据多平(曲)面重建.系统仿真学报. 2009, 21(1): 166-169, 173.
[64] Lorensen W, Cline H. Marching Cubes: A high resolution 3D surface construction algorithm. ACM Siggraph Computer Graphics. 1987, 21(4): 163-169.
[65] Cabral B, Cam N, Foran, J. Accelerated Volume Rendering and Tomographic Reconstruction Using Texture Mapping Hardware. Proc. of IEEE Visualization, Tysons Corner, Virginia, USA. 1994: 91-98.
[66] Nvidia Developer Relation Site. Available online at http://developer.nvidia.com.
[67]基尔加德,等著,洪伟,等译. Cg教程:可编程实施图形权威指南.第一版.北京:人民邮电出版社. 2004.
[68]姚德民,宋志坚.虚拟内窥镜关键技术的研究与临床应用.生物医学工程学杂志. 2008, 25(1): 18-22.
[69]彭延军,王元红,石教英,等.虚拟内窥镜关键技术研究.计算机应用研究. 2005, 5: 37-39.
[70]李乃弘,于文雪.三维人体虚拟内窥镜的实验研究.航天医学与医学工程. 1999, 12: 209-213.
[71]张惠,舒华忠.交互式虚拟内窥镜系统.中国图象图形学报. 2002, 7(1): 36-43.
[72]王刚.交互式虚拟内窥镜系统研究.西安电子科技大学硕士论文. 2003, 1.
[73] Hong L, Kaufman A, Wie Y, et al. 3D virtual colonoscopy. Proc. of IEEE symposium on Biomedical Visualization. 1995, 1: 26-32.
[1]常宏.多排CT的最新进展.医疗设备信息. 2005, 20(7): 69-69.
[2]帅捷,谭永强,孙健永,等.医学三维图像自由视角多平面重建(Free-MPR)显示技术的研究.中国医疗器械杂志. 2007, 31(1): 14-16.
[3]笪良龙,杨廷武,李玉阳,等.基于PC硬件加速的三维数据场直接体可视化.系统仿真学报. 2005, 17(10): 2422-2425.
[4]郑杰,姬红兵,杨万海.一种基于per-pixel光照的高质量体绘制算法.系统仿真学报. 2007, 19(1): 21-25.
[5]沈傲东.医学影像三维重建方法研究.西安电子科技大学硕士论文. 2003, 1.
[6] Lorensen W, Cline H. Marching Cubes: a high resolution 3D surface construction algorithm. ACM Siggraph Computer Graphics. 1987, 21(4): 163-169.
[7]王刚.交互式虚拟内窥镜系统研究.西安电子科技大学硕士论文. 2003, 1.
[8]周礼平.三维数据场虚拟内窥镜技术研究.西安电子科技大学硕士论文. 2004, 1.
[9]谭光喜,余成新,张晓磷,等.多层螺旋CT的MPR、SSD和CPR重建用于颌骨肿瘤.实用医学进修杂志. 2005, 33(3): 184-188.
[10] Kanitsar A, Fleischmann D, Wegenkittl R, et al. CPR-curved planar reformation. Proc. of IEEE Visualization, Boston, MA, USA. 2002: 37-44.
[11] Kanitsar A, Wegenkittl R, Fleischmann D, et al. Advanced curved planar reformation: flattening of vascular structures. Proc. of IEEE Visualization, Seatle, WA, USA. 2003: 43-50.
[12]吕新荣,高新波,邹华.医学图像体数据多平(曲)面重建.系统仿真学报. 2009, 21(1): 166-169, 173.
[13]孙家广,杨长贵.计算机图形学.第三版.北京:清华大学出版社, 1995. 284-294.
[14]刘旭敏,黄厚宽,王刘强,等.带形状参数样条曲线的研究.计算机研究与发展. 2007, 44(3): 487-496.
[15] Michael Mei?ner. http://www.gris.uni-tuebingen.de/edu/areas/scivis/volren/datasets/new.html.
[16] Taubin G. A signal processing approach to fair surface design. Proc. of ACM Siggraph, Los Angeles, CA, USA.1995: 351-358.
[17] Vollmer J, Mencel R, Mueller H. Improved Laplacian smoothing of noisy surface meshes. Proc. of EuroGraphics, Vienna, Austria. 1999: 131-138.
[18] Cebral J, Lohner R. From medical images to anatomically accurate finite element grids. International Journal of Numerical Methdos in Engineering. 2001, 51(8): 985-1008.
[19] Gibson S. Constrained elastic surface nets: Generating smooth surfaces from binary segmented data. Proc. of MICCAI, Springer, volume 1496 of LNCS, Cambridge MA, USA. 1998: 888-898.
[20] Schumann C, Oeltze S, Bade S, et al. Model-free surface visualization of vascular trees. Proc. of Eurographics, Prague, Czech Republic. 2007.
[21] Masutani Y, Masamune K, Dohi T. Region-growing-based feature extraction algorithm for tree-like objects. Proc. of Visualizationin Biomedical Computing, Springer, volume 1131 of LNCS, Hamburg, Germany. 1996: 161-171.
[22] Hahn H, Preim B, Selle D, et al. Visualization and interaction techniques for the exploration of vascular structures. Proc. of IEEE Visualization, San Diego, CA, USA. 2001: 395-402.
[23] H?hne K, Pflesser B, Pommert A, et al. A Realistic model of the inner organs from the visible human data. Proc. of MICCAI, Springer, volume 1935 of LNCS, Pittsburgh, PA, USA. 2000: 776–785.
[24] Felkl P, Wegenkittl R, B?hler K. Surface models of tube trees. Proc. of Computer Graphics International, Hersonissos, Crete, Greece. 2004: 70-77.
[25] Fiebich M, Straus C, Sehgal V, et al. Automatic bone segmentation technique for CT angiographic studies. Journal of Computer Assisted Tomography. 1999, 23(1):155–161.
[26] Frangi A, Niessen W, Vincken K, et al. Multiscale vessel enhancement filtering. Proc. of Medical Image Computing and Computer-Assisted Intervention, volume 1496 of Lecture Notes in Computer Science, Cambridge MA, USA. 1998: 130–137.
[27] Siebert J, Rosenbaum T, Pernicone J. Automated segmentation and presentation algorithmsfor 3D MR Angiography. Proc. of 10th Annual Meeting of the Society of Magnetic Resonance in Medicine, San Francisco. Berkeley, USA. 1991.
[28] Zuiderveld K. Visualization of multimodality medical volume data using object-oriented Methods. PhD thesis, Universiteit Utrecht, 1995.
[29] Pommert A, Bomans M, H?hne K. Volume visualization in magnetic resonance angiography. IEEE Computer Graphics and Application. 1992, 12(5): 12-13.
[30] Ebert D, Morris C, Rheingans P, et al. Designing effective transfer functions for volume rendering from photographics volumes. IEEE Transactions on Visualization and Computer Graphics. 2002, 8(2): 183-197.
[31] He T, Hong L, Kaufman A, et al. Generation of transfer functions with stochastic search techniques. Proc. of IEEE Visualization, San Francisco, CA, USA. 1996: 227-234.
[32] Kindlmann G, Durkin W. Semi-automatic generation of transfer functions for direct volume rendering. Proc. of IEEE Volume Visualization Symposium, North Carolina, USA. 1998: 79-86.
[33] Kindlmann G, Whitaker R, Tasdizen T, et al. Curvature-based transfer functions for volume rendering: methods and applications. Proc. of IEEE Visualization, Seatle, WA, USA. 2003: 513-520.
[34] Kniss J, Kindlmann G, Hansen C. Interactive volume rendering using multi-dimensional transfer functions and direct manipulation widgets. Proc. of IEEE Visualization, San Diego, CA, USA. 2001: 255-262.
[35] Kniss J, Kindlmann G, Hansen C. Multidimensional transfer functions for interactive volume rendering. IEEE Transactions on Visualization and Computer Graphics. 2002, 8(4): 270-285.
[36] Kniss J, Premoze S, Ikits M, et al. Gaussian transfer functions for multi-field volume visualization. Proc. of IEEE Visualization, Seatle, WA, USA. 2003: 497-504.
[37] Knittel G. Using pre-integrated transfer functions in an interactive software system for volume rendering. Proc. of Short Presentations Eurographics, Saarbruecken, Germany. 2002: 119-123.
[38] K?nig A, Gr?ller E. Mastering transfer function specification by using VolumePro technology. Proc. of the 17th Spring Conference on Computer Graphics, Budmerice, Slovakia. 2001: 279-286.
[39] Vega F, Sauber N, Tomandl B, et al. Enhanced 3D-Visualization of intracranial aneurysms involving the skull base. Proc. of MICCAI, Springer, volume 2879 of LNCS, Montréal, Canada. 2003: 256-263.
[40]张怡,张加万,孙济州,等.基于可编程图形加速硬件的实时光线投射算法.系统仿真学报. 2007, 19(18): 4204-4208.
[41] Gelder V, Kim K. Direct volume rendering with shading via three-dimensional Texture. Proc.of 1996 Symposium on Volume Visualization. San Francisco, California, USA. 1996: 23-30.
[42] Nvidia Developer Relation Site. Available online at http://developer.nvidia.com.
[43]基尔加德,等著,洪伟,等译. Cg教程:可编程实施图形权威指南.第一版.北京:人民邮电出版社. 2004.
[44] Lee T, Lin P, Lin C, et al. Interactive 3-D virtual colonoscopy system. IEEE Transactions on Information Technology in Biomedicine. 1999, 3(2): 139-150.
[45] Hong L, Muraki S, Kaufman A, et al. Vitrual voyage: interactive navigation in the human colon. ACM Siggraph Computer Graphics, Los Angeles, CA, USA. 1997: 27-34.
[46]耿国华,周明全.交互式实时虚拟内窥镜系统中的关键技术.计算机应用. 2002, 22(11): 54-55.
[47]范江波,周明全,耿国华.虚拟内窥镜技术的研究与实现.微机发展. 2000, 6: 60-62.
[48]姚德民,宋志坚.虚拟内窥镜关键技术的研究与临床应用.生物医学工程学杂志. 2008, 25(1): 18-22.
[49]彭延军,王元红,石教英,等.虚拟内窥镜关键技术研究.计算机应用研究. 2005, 5: 37-39.
[50]李乃弘,于文雪.三维人体虚拟内窥镜的实验研究.航天医学与医学工程. 1999, 12: 209-213.
[51]张惠,舒华忠.交互式虚拟内窥镜系统.中国图象图形学报. 2002, 7(1): 36-43.
[52] Verroust A, Lazarus F. Extracting skeletal curves from 3D scattered data. Shape Modeling International, Aizu Wakamatsu. 1999: 16-25.
[53] Niblack W, Gibbons P, Capson D. Generating skeletons and centerlines from the distance transform. CVGIP: Graphical Models Image Processing. 1992, 54(5): 420-437.
[54]竺海,姬红兵,高新波.基于边界距离场的管腔中心路径自动提取算法.计算机辅助设计与图形学学报. 2006, 18(6): 860-864.
[55]胡英,侯悦,徐心和.基于双距离场的三维中心路径提取算法.中国图像图形学报. 2003, 8(11): 1272-1276.
[1] Sato Y, Shiraga N, Nakajima S, et al. Local maximum intensity projection (LMIP): a new rendering method for vascular visualization. Journal of Computer Aided Tomography. 1998, 22(6): 912-917.
[2] Drebin R, Carpenter L, Hanrahan P. Volume Rendering. Proc. of Computer Graphics and Interactive Techniques, New York, USA. 1988: 65-74
[3] Lichtenbelt B, Crane R, Naqvi S. Introduction to Volume Rendering. New Jersey: Prentice-Hall, 1998.
[4]彭延军,石教英.体绘制技术在医学可视化中的新发展.中国图象图形学报. 2002, 7(12): 1239-1246.
[5] Kanitsar A, Fleischmann D, Wegenkittl R, et al. CPR-curved planar reformation. Proc. of IEEE Visualization, Boston, MA, USA. 2002: 37-44.
[6] Kanitsar A, Wegenkittl R, Fleischmann D, et al. Advanced curved planar reformation: flattening of vascular structures. Proc. of IEEE Visualization, Seatle, WA, USA. 2003: 43-50.
[7] Cai W. 3D Planar Reformation of Vascular Central Axis Surface with Biconvex Slab. Computerized Medical Imaging and Graphics. 2007, 31(7): 570-576.
[8] Avants B, Williams J. An Adaptive Minimal Path Generation Technique for Vessel Tracking in CTA/CEMRA Volume Images. International Conference on Medical Image Computing and Computer-Assisted Intervention, Utrecht, The Netherlands. 2001: 707–716.
[9] He S, Dai R, Lu B, et al. Medial Axis Reformation: A New Visualization Method for CT Angiography. Academic Radiology. 2001, 8(8): 726–733.
[10] Kass M, Witkin A, Terzopoulos D. Snakes: Active contour model. Computer Vision. 1987, 1(4): 321-331.
[11]李培华,张田文.主动轮廓模型(蛇模型)综述.软件学报. 2000, 11(6): 751-757.
[12] Yezzi A, Kichenassamy S, Kumar A, et al. A Geometric Snake Model for Segmentation of Medical Imagery. IEEE Transactions on Medical Image. 1997, 16(2): 199-209.
[13] Luo Xiping, Tian Jie, Lin Yao. An Algorithm for Segmentation of Medical Image Series Based on Active Contour Mode. Journal of Software. 2002, 13(6): 1050-1058.
[14]周则明,王平安,夏德深.基于Snake模型的低对比度噪声心脏MRI图像分割.系统仿真学报. 2004, 16(11): 2493-2497.
[15] Huang Shaohui, Wang Boliang, Huang Xiaoyang. Using GVF Snake to Segment Liver from CT images. Proc. of the 3rd IEEE-EMBS, MIT, Boston, USA. 2006: 145-148.
[16] Liu F, Zhao B, Kijewski PK, et al. Liver segmentation for CT images using GVF snake. Medical Physics. 2005, 32(12): 3699-3706.
[17] Xu Chenyang, Prince J.L. Snakes, shapes, and gradient vector flow. IEEE Transactions on Image Processing. 1998, 7(3): 359-369.
[18]阮鹏.基于T-snake模型的冠状动脉血管提取和运动分析的方法研究.天津大学硕士论文. 2006, 1.
[19]张麒,汪源源,王威琪,等.基于梯度矢量流与多尺度分析的血管内超声图像轮廓提取.生命科学仪器. 2007, 5(8): 32-36.
[20] Lv X, Gao X, Zou H. Interactive curved planar reformation based on snake model. Computerized Medical Imaging and Graphics. 2008, 32(8): 662-669.
[21]王小林,刘宏申,秦锋.基于Snake模型的目标检测.华中科技大学学报(自然科学版). 2008, 36(1): 75-77.
[22]孙家广,杨长贵.计算机图形学.第三版.北京:清华大学出版社, 1995.
[23] Michael Mei?ner. http://www.gris.uni-tuebingen.de/edu/areas/scivis/volren/datasets/new.html.
[1] Schumann C, Oeltze S, Bade R, et al. Model-free surface visualization of vascular trees. Eurographics/IEEE-VGTC Symposium on Visualization, Norrk ? ping, Sweden. 2007: 283-290.
[2] Hoover A, Kouznetsova V, Goldbaum M. Locating blood vessels in retinal images by piecewise threshold probing of a matched filter response. IEEE Transactions on Medical Imaging. 2000, 19(3): 203-210.
[3] Xu Chenyang, Prince J. Snakes, shapes, and gradient vector flow. IEEE Transactions on Image Process. 1998, 7(3): 359-369.
[4] Sum K, Cheung P. Boundary vector field for parametric active contours. Pattern Recognition. 2007, 40(6): 1635-1645.
[5] Sum K, Cheung P. Vessel extraction under non-uniform illumination: a level set approach. IEEE Transactions on Biomedical Engineering. 2008, 55(1): 358-360.
[6] Tolias Y, Panas S. A fuzzy vessel tracking algorithm for retinal images based on fuzzy clustering. IEEE Transactions on Medical Imaging. 1998, 17(2): 263-273.
[7] Bombardier V, Jaluent M, Bubel A, et al. Cooperation of two fuzzy segmentation operators for digital subtracted angiograms analysis. Proc. of the 6th IEEE International Conference on Fuzzy Systems, Barcelona, Spain. 1997: 1057-1062.
[8] Rodíguez R, Alarcón T, Pacheco O. A new strategy to obtain robust markers for blood vessels segmentation by using the watersheds method. Computers in Biology and Medicine. 2005,35(8): 665-686.
[9]徐智,郁道银,谢洪波,等.心血管造影图像中的心血管提取.中国生物医学工程学报. 2003, 22(1): 6-11.
[10] Ritter F, Hansen C, Dicken V, et al. Real-time illustration of vascular structures. IEEE Transactions on Visualization and Computer Graphics. 2006, 12(5): 877-884.
[11] Lorensen W, Cline H. Marching cubes: a high resolution 3D surface construction algorithm. Proc. of the 14th Annual Conference on Computer Graphics and Interactive Techniques, New York, USA. 1987: 163-169.
[12] Sato Y, Shiraga N, Nakajima S, et al. Local maximum intensity projection (LMIP): a new rendering method for vascular visualization. Journal of Computer Aided Tomography. 1998, 22(6): 912-917.
[13] Preim B, Oeltze S. 3D visualization of vasculature: an overview. Visualization in Medicine and Life Sciences. Berlin: Springer-Verlag, 2007.
[14]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(4): 510-512.
[15]贾冬焱,郝立巍,周寿军,等.自动测量造影图像中血管中心线和宽度的新方法.中国生物医学工程学报. 2007, 26(2): 214-219,225.
[16]唐荣锡,汪嘉业,彭群生,等.计算机图形学教程.北京:科学出版社, 2000.
[17] Cullip T, Neumann U. Accelerating volume reconstruction with 3D texture mapping hardware. UNC-1993-027, 1993.
[18] Kanitsar A, Fleischmann D, Wegenkittl R, et al. CPR-curved planar reformation. Proc. of IEEE Visualization, Boston, MA, USA. 2002: 37-44.
[19] Kanitsar A, Wegenkittl R, Fleischmann D, et al. Advanced curved planar reformation: flattening of vascular structures. Proc. of IEEE Visualization, Seatle, WA, USA. 2003: 43-50.
[20]竺海,姬红兵,高新波.基于边界距离场的管腔中心路径自动提取算法.计算机辅助设计与图形学学报. 2006, 18(6): 860-864.
[21]胡英,侯悦,徐心和.基于双距离场的三维中心路径提取算法.中国图像图形学报. 2003, 8(11): 1272-1276.
[22] Shih F, Wu Y. Three-dimensional Euclidean distance transformation and its application to shortest path planning. Pattern Recognition. 2004, 37(1): 79-92.
[23] Wan Ming, Liang Zhengrong, Ke Qi, et al. Automatic centerline extraction for virtual colonoscopy. IEEE Transactions on Medical Imaging. 2002, 21(12): 1450-1460.
[24] Michael Mei?ner. http://www.gris.uni-tuebingen.de/edu/areas/scivis/volren/datasets/new.html.
[25] Ohtake Y, Belyaey A, Alexa M, et al. Multilevel partition of unity implicits. International Conference on Computer Graphics and Interactive Techniques, New York, USA. 2003:463-470.
[26] Engel K, Kraus M, Etrl T. High quality pre-integrated volume rendering using hardware accelerated pixel shading. Proc. of the ACM SIGGRAPH/EUROGRAPHICS Workshop on Graphics Hardware, New York, USA. 2001: 9-16.
[27] Roettger S, Ertl T. A two-step approach for interactive pre-integrated volume rendering of unstructured grids. Proc. of IEEE Visualization, Boston, MA, USA. 2002: 23-28.
[1]李光明,田捷,赵明昌,等.基于Hessian矩阵的中心路径提取算法.软件学报. 2003, 14(1): 1148-1156.
[2]胡英,侯悦,徐心和.基于双距离场的三维中心路径提取算法.中国图象图形学报. 2003, 8(11): 1272-1276.
[3]竺海,姬红兵,高新波.基于边界距离场的管腔中心路径自动提取算法.计算机辅助设计与图形学学报. 2006, 18(6): 860-864.
[4] Sundar H, Silver D, Gagvani N, et al. Skeleton based shape matching and retrieval. Proc. of the Shape Modeling International 2003, Seoul, Korea. 2003: 130-139.
[5] Bitter I, Sato M, Bender M, et al. CEASAR: A Smooth, Accurate and robust centerline extraction algorithm. Proc. of IEEE Visualization 2000, Salt Lake City, USA. 2000: 45-52.
[6] Sato M, Bitter I, Bender MA, et al. TEASAR: Tree-structure extraction algorithm for accurate and robust skeletons. Proc. of IEEE Pacific Graphics 2000, Hong Kong, China. 2000: 281-289.
[7] Egger J, Mostarki? Z, Gro?kopf S, et al. A fast vessel centerline extraction algorithm for catheter simulation. Twentieth IEEE International Symposium on Computer-Based Medical Systems, Maribor, Slovenia. 2007.
[8]唐荣锡,汪嘉业,彭群生,等.计算机图形学教程.北京:科学出版社, 2000.
[9] Cruz A. Accuracy evaluation of different centerline approximations of blood vessels. Proc. of IEEE Visualization, Konstanz, Germany. 2004: 1-11.
[10] Michael Mei?ner. http://www.gris.uni-tuebingen.de/edu/areas/scivis/volren/datasets/new.html.
[1] Ge Y, Stelts D, Wang J, et al. Computing the centerline of the colon: a robust and efficient method based on 3D skeletons. Journal of Computer Assisted Tomography. 1999, 23(5): 786-794.
[2] Borgefors G. Distance transformations in digital images. Computer Vision, Graphics, and Image Processing. 1986, 34(3): 344-371.
[3] Dijkstra E. A note on two problems in connection with graphs, Num. Math. 1. 1959. 269-271.
[4] Telea A, Vilanova A. A robust level-set algorithm for centerline extraction. IEEE TCVG Symposium on Visualization. 2003, 40: 185-194.
[5] Kirbas C, Quek F. A review of vessel extraction techniques and algorithms. ACM Computing Surveys. 2004, 36(2): 81-121.
[6]李光明,田捷,赵明昌,等.基于Hessian矩阵的中心路径提取算法.软件学报. 2003, 14(1): 1148-1156.
[7]胡英,侯悦,徐心和.基于双距离场的三维中心路径提取算法.中国图象图形学报. 2003, 8(11): 1272-1276.
[8]竺海,姬红兵,高新波.基于边界距离场的管腔中心路径自动提取算法.计算机辅助设计与图形学学报. 2006, 18(6): 860-864.
[9] Sundar H, Silver D, Gagvani N, Dickinson S. Skeleton based shape matching and retrieval. Proc. of the Shape Modeling International, Seoul, Korea. 2003: 130-139.
[10] Bitter I, Sato M, Bender M, et al. CEASAR: A smooth, accurate and robust centerline extraction algorithm. Proc. of IEEE Visualization, Salt Lake City, USA. 2000: 45-52.
[11] Sato M, Bitter I, Bender M, et al. TEASAR: Tree-structure extraction algorithm for accurate and robust skeletons. Proc. of IEEE Pacific Graphics, Hong Kong, China. 2000: 281-289.
[12] Egger J, Mostarki? Z, Gro?kopf S, et al. A fast vessel centerline extraction algorithm for catheter simulation. Twentieth IEEE International Symposium on Computer-Based Medical Systems, Maribor, Slovenia. 2007.
[13] Xu Y, Zhang H, Li H, et al. An improved algorithm for vessel centerline tracking in coronary angiograms. Computer Methods and Programs in Biomedicine. 2007, 88(2): 131-143.
[14] Mueller D, Maeder A. Robust semi-automated path extraction for visualizing stenosis of the coronary arteries. Computerized Medical Imaging and Graphics. 2008, 32(6): 463-475.
[15] Cruz A. Accuracy evaluation of different centerline approximations of blood vessels. IEEE TCVG Symposium on Visualization, Konstanz, Germany. 2004: 1-11.
[16] Wan M, Liang Z, Ke Q, et al. Automatic centerline extraction for virtual colonoscopy. IEEE Transactions on Medical Images. 2002, 21(12): 1450-1460.
[17] Deschamps T, Cohent L. Fast extraction of minimal paths in 3D images and applications to virtual endoscopy. Medical Images Analysis. 2001, 5(4): 281-299.
[18] Morse B, Pizer S, Liu A. Multiscale medical analysis of medical images. Image & Vision Computing. 1993, 12(6): 327-338.
[19] He S, Yang X, Dai R. Medial axis extraction from blurred and noisy images. Journal of Image and Graphics. 2000, 5(5): 420-424.
[20] Michael Mei?ner. http://www.gris.uni-tuebingen.de/edu/areas/scivis/volren/datasets/new.html.