基于体绘制算法的心脏数据三维可视化
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摘要
科学计算可视化是近年来蓬勃发展的一个新兴科研范畴,其中体绘制方法是可视化研究的重要手段。它被广泛的应用于地质、气象、流体力学及医学影像等多个学术领域。其中虚拟组织器官重建是可视化领域的热点课题,在医学诊断等方面有重要的应用。
为实现对心脏解剖结构的精确模拟,保留心脏内部的组织细节,以便直观有效地显示心脏内部在组织和器官层次上各种生理病理现象的演变过程。本文对光线投射体绘制算法进行了深入分析,并通过光线投射算法完成了对虚拟人心脏、羊心脏MRI数据集的三维可视化。传统的医学影像技术如CT和MRI等只能获取沿着特定方向的组织切片序列,而实际医学诊治过程中往往需要从不同方位从整体和切片等角度对器官组织进行观察分析。针对该问题,本文实现了心脏数据标准切片的提取、标准方向切面的显示和任意视点切面的显示。
针对已分类的虚拟人心脏数据集,本文对数据进行预处理,确定出边界体元素集和内部体元素集后进行绘制。该方法在一定程度上解决了心脏内部不同组织相互遮挡的问题,方便观察心脏内部不同结构。
体绘制算法在绘制过程中对每个体元素进行处理,因此对于较大的数据集来说,体绘制在获得高质量的结果图象的同时,存在绘制速度慢、交互时间长的问题。本文提出了基于图象空间和基于物体空间的两种光线投射加速算法,运用一维传递函数以及二维传递函数进行三维可视化,在不同数据集上进行验证。结果表明自适应的加速算法在一定程度上解决了光线投射算法成像速度慢的问题。
Scientific visualization is a new research field under vigorous development emerging in recent years.Volume rendering is an important research means in scientific visualization which is widely applied in Geology, Meteorology, Hydrodynamic and Medical Imaging and some other acedmic fields.Three-dimentional visualization of virtual tissues and organs is a current research focus and has important application in medical diagnosis.
In order to realize the accurate simulation of cardiac anatomical structure and retain the tissue details of cardiac data so as to display the evolution process of physiological and pathological phenomenons of heart on level of tissue and organ intuitivly and effectively,this paper made an in-depth analysis on ray casting and adopt this method to realize the three-dimensional visualization of human cardiac and sheep cardiac MRI data. Since slices produced by traditional medical imaging technologies, such as CT and MRI, are along some fixed direction, During medical practice, however, doctors usually require to observe the organ,tissue and slices from different viewpoints to make a decision. To address this problem, this paper realised the extraction of typical slices and the displaying of virtual sections of cardiac data from standard directions and arbitrary viewpoint.
Aimed at classified human cardiac MRI data, this paper preprocessed the input data so as to determine the boundary voxels and the internal voxels and then did the volume rendering. This method solves the problem of occlusion between different tissues to some extent and provides convenience for observing the different cardiac tissues.
In volume rendering, we deal with each voxel to obtain the high rendering quality,so when dealing with large datasets, this method has the problem of slow rendering speed and interaction difficulty .To address this problem,this paper proposed two accelerating algorithms of ray casting.One is image-space based and the other is object-space based.Tested with different datasets and using both one-dimentional and two-dimentional transfer function, the results showed that the adaptive accelerating algorithms solve the problem of slow rendering speed to some extent.
为实现对心脏解剖结构的精确模拟,保留心脏内部的组织细节,以便直观有效地显示心脏内部在组织和器官层次上各种生理病理现象的演变过程。本文对光线投射体绘制算法进行了深入分析,并通过光线投射算法完成了对虚拟人心脏、羊心脏MRI数据集的三维可视化。传统的医学影像技术如CT和MRI等只能获取沿着特定方向的组织切片序列,而实际医学诊治过程中往往需要从不同方位从整体和切片等角度对器官组织进行观察分析。针对该问题,本文实现了心脏数据标准切片的提取、标准方向切面的显示和任意视点切面的显示。
针对已分类的虚拟人心脏数据集,本文对数据进行预处理,确定出边界体元素集和内部体元素集后进行绘制。该方法在一定程度上解决了心脏内部不同组织相互遮挡的问题,方便观察心脏内部不同结构。
体绘制算法在绘制过程中对每个体元素进行处理,因此对于较大的数据集来说,体绘制在获得高质量的结果图象的同时,存在绘制速度慢、交互时间长的问题。本文提出了基于图象空间和基于物体空间的两种光线投射加速算法,运用一维传递函数以及二维传递函数进行三维可视化,在不同数据集上进行验证。结果表明自适应的加速算法在一定程度上解决了光线投射算法成像速度慢的问题。
Scientific visualization is a new research field under vigorous development emerging in recent years.Volume rendering is an important research means in scientific visualization which is widely applied in Geology, Meteorology, Hydrodynamic and Medical Imaging and some other acedmic fields.Three-dimentional visualization of virtual tissues and organs is a current research focus and has important application in medical diagnosis.
In order to realize the accurate simulation of cardiac anatomical structure and retain the tissue details of cardiac data so as to display the evolution process of physiological and pathological phenomenons of heart on level of tissue and organ intuitivly and effectively,this paper made an in-depth analysis on ray casting and adopt this method to realize the three-dimensional visualization of human cardiac and sheep cardiac MRI data. Since slices produced by traditional medical imaging technologies, such as CT and MRI, are along some fixed direction, During medical practice, however, doctors usually require to observe the organ,tissue and slices from different viewpoints to make a decision. To address this problem, this paper realised the extraction of typical slices and the displaying of virtual sections of cardiac data from standard directions and arbitrary viewpoint.
Aimed at classified human cardiac MRI data, this paper preprocessed the input data so as to determine the boundary voxels and the internal voxels and then did the volume rendering. This method solves the problem of occlusion between different tissues to some extent and provides convenience for observing the different cardiac tissues.
In volume rendering, we deal with each voxel to obtain the high rendering quality,so when dealing with large datasets, this method has the problem of slow rendering speed and interaction difficulty .To address this problem,this paper proposed two accelerating algorithms of ray casting.One is image-space based and the other is object-space based.Tested with different datasets and using both one-dimentional and two-dimentional transfer function, the results showed that the adaptive accelerating algorithms solve the problem of slow rendering speed to some extent.
引文
1唐泽圣等.三维数据场可视化.北京:清华大学出版社,1999,12:8~12
2 W E Lorensen, H E Cline. Marching Cubes:a high resolution 3D surface construction algorithm[C].SIGGRAPH 87,1987:163~169
3 R Drebin, L Carpenter, P Hanrahan.Volume rendering[C].Proc.SIGGRAPH 88,1988:65~74
4 S. P. Callahan, J. H. Callahan, C. E. Scheidegger, C. T. Silva. Direct Volume Rendering: A 3D Plotting Technique for Scientific Data.Computing in Science & Engineering.2008,10(1):88 ~92
5 H. Scharsach. Advanced GPU raycasting[C] .Proceedings of Central European Seminar on Computer Graphics 2005. Budmerice Castle. 2005 :69~76
6安新军,彭延军,何明祥.空间跳跃的光线投射加速算法研究[J].系统仿真学报,2006,18(S):304~307
7 W. L. Cai, J. Y. Shi. Composed scattering model for direct volume rendering [J]. Journal of Computer Science & Technology, 1996, 11(5) : 433~442
8 C. Bajaj, V. Pascacci, D. Schikore. The contour spectrum [A]. IEEE V isualization’97[C]. Philadelphia: IEEE Computer Society Press, 1997: 167~173
9张建勋,孙济洲,韩逢庆,张加万.基于相邻层间相似性加速Splatting算法[J].系统仿真学报,2005(02):421~428
10 P. Lacroute, M. Levoy. Fast volume rendering using a shear-warp factorization of viewing transformation [J]. Computer Graphics,1994, 28 (4) : 451~459
11 W. J. Schroeder. The VTK User's Guide [M].version 4.New York, USA:Kitware,Inc.2001:1~377
12赵明昌,田捷,薛健.医学影像处理与分析开发包MITK的设计与实现[J].软件学报,2005,16(4):485~495
13 W. L. Cai, J. Y. Shi. A Data Flow Architecture for Scientific Visualization. International Confon CAD&Graphics'93,Beijing,1993:433~442
14管伟光.体视化技术及其应用.电子工业出版社,1998:153~166
15 M. Levoy, Display of surfaces from volume data, IEEE Comput.Graph.Appl., May 1988. 8(3):29~37
16 K. Muller, E. J. Swan. Splatting errors and antialiasing [J]. IEEE Transaction on Visualization and Computer Granphics, 1998,4(2) : 178~191
17 L Westover.Footprint ecaluation for volume rendering,In Computer Graphics Proceedings[C].In:Annual Conference Series,ACM SIGGRAPH,1990:367~376
18 G. Cameron, P. E. Undrill. Rendering volumetric medical image data on a SIMD-architecture computer[C].In:Proceedings of the Third Eurographics Workshop on Rendering,Bristol,UK,1992:135~145
19 G. Schlosser. Fast visualization by shear-warp on quadratic super-spline models using wavelet data decompositions. IEEE Visualization‘05. 2005:351~358
20 Li Guo, Xie Mei. Implementation and Improvement Based on Shear-Warp Volume Rendering Algorithm. Computer Engineering and Technology, 2009. ICCET '08. International Conference on Volume 1, 22-24 Jan. 2009:182 ~185
21 Rudiger Westermann, Bemd Sevenich,Accelerated Volume Ray-Casting using Texture Mapping.12th IEEE Visualization 2001 Conference,2001:24~26
22 T. Moeller, R. Machiraju, K. Mueller, R. Yagel.Classification and local error estimation of interpolation and derivative filters. Proceedings of IEEE Symposium on Volume Visualization,1996:71~78
23 J. F. Blinn. Light reflection functions for simulation of clouds and dusty surfaces,Computer Graphics,1982,16(3):83~87
24 H.Gouraud. Continuous shading of curved surfaces,IEEE Transactions on Computers,1971,20(6):623~629
25 B.T.Phong,Illumination for computer generated pictures,Communcations of the ACM,1975,18(6):311~317
26郭圣文.利用VTK与ITK的集成实现医学图象可视化[J].计算机工程与应用, 2006,(30):183~184
27周芳芳,樊晓平,杨斌.体绘制中传递函数设计的研究现状与展望[J].中国图象图形学报, 2008,(06):1034~1047
28 F. Yang, W. M. Zuo, K. Q. Wang, H. Zhang. 3D cardiac MRI data visualization based on volume data preprocessing and transfer function design. Computers in Cardiology, 2008 14-17 Sept. 2008:717~720
29 Han-qing Huang, Ze-sheng Tang. An interactive volume rendering tool for transfer function specification [J]. Chinese Journal of Computers, 2005, 28 (6) : 1063~1067
30 P. Sereda. The Transfer Function Design for Volume Data Rendering [A]. In: Proceedings of the Advanced School for Computing and Imaging[C]. Heijen, Netherlands, 2004: 17~28
31 E. B. Lum, K. L. Ma. Lighting Transfer Functions using Gradient Aligned Sampling. In: Proc. of IEEE Visualization , 2004:289~296
32 O. Soldea, G. Elber, E. Rivlin. Global segmentation and curvature analysis of volumetric data sets using trivariate B-spline functions [J]. IEEE Transactions on Pattern Analysis and MachineIntelligence, 2006, 28(2): 265~278
33 G. Kindlmann, J. W. Durkin. Semi-automatic generation of transfer functions for direct volume rendering. In : Proceedings of IEEE Symposium on Volume Visualization , Research Triangle Park , North Carolina , USA , 1998 :79~86
34 S. Roettger, M. Bauer, M. Stamminger. Spatialized transfer functions [A]. In: Proceedings of IEEE/EUROGRAPHICS Symposium onVisualization 2005 [C] , Minneapolis, MN, USA, 2005:271~278
35 P. Sereda, A. V. Bartroli, W. O. Serlie, A. Gerritsen, Visualization of boundaries in volumetric datasets using LH histograms [J]. IEEE Transactions on Visualization and Computer Graphics, 2006,12 (2) : 208～218
36 J. Kniss, R. U. Van, A. Stephens. Statistically quantitative volume visualization [A]. In: Proceedings of IEEE Visualization2005 [C] , Minneapolis, MN, USA , 2005: 37~45
37 Y. Wu, H. Qu. Interactive transfer function design based on editing direct volume rendered images, IEEE Trans.Visualization and Computer Graphics, 2007, 13(5):1027~1040
38 R. Avlia, L. Sobierajski, A. Kaufman. Towards a comprehensive volume visualization system [A]. In: IEEE Visualization’92[C].Washington: IEEE Computer Society Press, 1992: 13~20
39胡英,王怀志.基于光线投射技术的医学图象三维重建[J],东北大学学报(自然科学版),2004,25(1):1~4
40邹华,高新波,吕新荣.层次包围盒与GPU实现相结合的光线投射算法[J].计算机辅助设计与图形学学报, 2009(02):172~178
41 H. W. Shen, L. J. Chiang. A fast volume rendering algorithm for time-varying fields using a time-space partitioning (TSP) tree[A]. In: IEEE Visualization’99 [C]. Boston: IEEE Computer Society Press, 1999: 371~545
42董峰,蔡文立.基于空间分割的三维不规则数据场的体绘制算法,计算机辅助设计与图形学学,1997,9(3):241~248
43苏超轼,赵明昌,张向文.GPU加速的八叉树体绘制算法[J].计算机应用,2008(05):1232~1239
44 M. Levoy. Efficient ray tracing for volume data [J]. Computer Graphics, 1990, 9 (3): 245~261
45 J. Wilhelms, V. Gelder. A coherent projection approach for direct volume rendering [J]. Computer Graphics, 1991, 25 (4): 275~281
46周勇,唐圣泽.通过区域块投影方法直接绘制三维数据场[J].计算机辅助设计与图形学报, 1996, 8 (3) : 161~168
47 Y. Zhou, W. Chen, Z. S. Tang. Subvolume projection: a full exploration of function coherence for volume rendering [J]. The Journal of Visualization and Computer Animation, 1995, 12 (6):207~218
48 T. Etrl, R. Westermann, R. Grsso. Multi-resolution and hierarchical methods for the visualization of volume data [J]. Future Generation Computer System, 1999, 15 (1): 31~42
49 T. Y. Kim, Y. G. Shin. An efficient wavelet-based compression method for vo lume rendering [A]. In: Computer Graphics and Applications, Proceedings, Seventh Pacific Conference[C]. Singapore: IEEE Computer Society Press, 1999: 147~156
50 A. W. Michel, B. T. Jos. X-ray volume rendering by hierarchical wavelet splatting [A]. In: Pattern Recognition, Proceedings, 15th International Conference[C]. Washington: IEEE Computer Society Press, 2000: 159~162
51 D. Laur, P. Hanrahan. Hierarchical splatting: A progressive refinement algorithm for volume rendering [J]. Computer Graphics, 1991, 25 (4): 275~288
52 B. Liu, G. D. Nelson. A simplified energy projection and applications of transfer function in isometric volume rendering [A]. In: IEEE Canadian Conference on Computer Engineering[C]. 1999. Canada: IEEE Computer Society Press, 1999:1728~ 1733
53 A. Kostas, T. A. Tim. 4D volume rendering with the shear warp factorisation extensions and quantitative results [A]. In: Information Visualization, P roceedings, Fifth International Conference [C]. New York: IEEE Computer Society Press, 2001: 435~443
54 I. Ihm, R. Lee. Indexing data structures for faster volume rendering [J]. Computers & Graphics, 1997, 21 (4): 497~506
55陈慧,何兴恒.体视化中LOD技术思想的应用与实现[J].计算机工程与设计, 2008,29(22):5860~5865
56陈礼民,梁晓辉,邵志东.基于数据场相关性的光线投射算法.中国图象图形学报,1999,4(9):566~567
57张怡,孙济州,张如万.基于片段的光线投射算法,中国图象图形学报,2007,12(8):1418~1422
2 W E Lorensen, H E Cline. Marching Cubes:a high resolution 3D surface construction algorithm[C].SIGGRAPH 87,1987:163~169
3 R Drebin, L Carpenter, P Hanrahan.Volume rendering[C].Proc.SIGGRAPH 88,1988:65~74
4 S. P. Callahan, J. H. Callahan, C. E. Scheidegger, C. T. Silva. Direct Volume Rendering: A 3D Plotting Technique for Scientific Data.Computing in Science & Engineering.2008,10(1):88 ~92
5 H. Scharsach. Advanced GPU raycasting[C] .Proceedings of Central European Seminar on Computer Graphics 2005. Budmerice Castle. 2005 :69~76
6安新军,彭延军,何明祥.空间跳跃的光线投射加速算法研究[J].系统仿真学报,2006,18(S):304~307
7 W. L. Cai, J. Y. Shi. Composed scattering model for direct volume rendering [J]. Journal of Computer Science & Technology, 1996, 11(5) : 433~442
8 C. Bajaj, V. Pascacci, D. Schikore. The contour spectrum [A]. IEEE V isualization’97[C]. Philadelphia: IEEE Computer Society Press, 1997: 167~173
9张建勋,孙济洲,韩逢庆,张加万.基于相邻层间相似性加速Splatting算法[J].系统仿真学报,2005(02):421~428
10 P. Lacroute, M. Levoy. Fast volume rendering using a shear-warp factorization of viewing transformation [J]. Computer Graphics,1994, 28 (4) : 451~459
11 W. J. Schroeder. The VTK User's Guide [M].version 4.New York, USA:Kitware,Inc.2001:1~377
12赵明昌,田捷,薛健.医学影像处理与分析开发包MITK的设计与实现[J].软件学报,2005,16(4):485~495
13 W. L. Cai, J. Y. Shi. A Data Flow Architecture for Scientific Visualization. International Confon CAD&Graphics'93,Beijing,1993:433~442
14管伟光.体视化技术及其应用.电子工业出版社,1998:153~166
15 M. Levoy, Display of surfaces from volume data, IEEE Comput.Graph.Appl., May 1988. 8(3):29~37
16 K. Muller, E. J. Swan. Splatting errors and antialiasing [J]. IEEE Transaction on Visualization and Computer Granphics, 1998,4(2) : 178~191
17 L Westover.Footprint ecaluation for volume rendering,In Computer Graphics Proceedings[C].In:Annual Conference Series,ACM SIGGRAPH,1990:367~376
18 G. Cameron, P. E. Undrill. Rendering volumetric medical image data on a SIMD-architecture computer[C].In:Proceedings of the Third Eurographics Workshop on Rendering,Bristol,UK,1992:135~145
19 G. Schlosser. Fast visualization by shear-warp on quadratic super-spline models using wavelet data decompositions. IEEE Visualization‘05. 2005:351~358
20 Li Guo, Xie Mei. Implementation and Improvement Based on Shear-Warp Volume Rendering Algorithm. Computer Engineering and Technology, 2009. ICCET '08. International Conference on Volume 1, 22-24 Jan. 2009:182 ~185
21 Rudiger Westermann, Bemd Sevenich,Accelerated Volume Ray-Casting using Texture Mapping.12th IEEE Visualization 2001 Conference,2001:24~26
22 T. Moeller, R. Machiraju, K. Mueller, R. Yagel.Classification and local error estimation of interpolation and derivative filters. Proceedings of IEEE Symposium on Volume Visualization,1996:71~78
23 J. F. Blinn. Light reflection functions for simulation of clouds and dusty surfaces,Computer Graphics,1982,16(3):83~87
24 H.Gouraud. Continuous shading of curved surfaces,IEEE Transactions on Computers,1971,20(6):623~629
25 B.T.Phong,Illumination for computer generated pictures,Communcations of the ACM,1975,18(6):311~317
26郭圣文.利用VTK与ITK的集成实现医学图象可视化[J].计算机工程与应用, 2006,(30):183~184
27周芳芳,樊晓平,杨斌.体绘制中传递函数设计的研究现状与展望[J].中国图象图形学报, 2008,(06):1034~1047
28 F. Yang, W. M. Zuo, K. Q. Wang, H. Zhang. 3D cardiac MRI data visualization based on volume data preprocessing and transfer function design. Computers in Cardiology, 2008 14-17 Sept. 2008:717~720
29 Han-qing Huang, Ze-sheng Tang. An interactive volume rendering tool for transfer function specification [J]. Chinese Journal of Computers, 2005, 28 (6) : 1063~1067
30 P. Sereda. The Transfer Function Design for Volume Data Rendering [A]. In: Proceedings of the Advanced School for Computing and Imaging[C]. Heijen, Netherlands, 2004: 17~28
31 E. B. Lum, K. L. Ma. Lighting Transfer Functions using Gradient Aligned Sampling. In: Proc. of IEEE Visualization , 2004:289~296
32 O. Soldea, G. Elber, E. Rivlin. Global segmentation and curvature analysis of volumetric data sets using trivariate B-spline functions [J]. IEEE Transactions on Pattern Analysis and MachineIntelligence, 2006, 28(2): 265~278
33 G. Kindlmann, J. W. Durkin. Semi-automatic generation of transfer functions for direct volume rendering. In : Proceedings of IEEE Symposium on Volume Visualization , Research Triangle Park , North Carolina , USA , 1998 :79~86
34 S. Roettger, M. Bauer, M. Stamminger. Spatialized transfer functions [A]. In: Proceedings of IEEE/EUROGRAPHICS Symposium onVisualization 2005 [C] , Minneapolis, MN, USA, 2005:271~278
35 P. Sereda, A. V. Bartroli, W. O. Serlie, A. Gerritsen, Visualization of boundaries in volumetric datasets using LH histograms [J]. IEEE Transactions on Visualization and Computer Graphics, 2006,12 (2) : 208～218
36 J. Kniss, R. U. Van, A. Stephens. Statistically quantitative volume visualization [A]. In: Proceedings of IEEE Visualization2005 [C] , Minneapolis, MN, USA , 2005: 37~45
37 Y. Wu, H. Qu. Interactive transfer function design based on editing direct volume rendered images, IEEE Trans.Visualization and Computer Graphics, 2007, 13(5):1027~1040
38 R. Avlia, L. Sobierajski, A. Kaufman. Towards a comprehensive volume visualization system [A]. In: IEEE Visualization’92[C].Washington: IEEE Computer Society Press, 1992: 13~20
39胡英,王怀志.基于光线投射技术的医学图象三维重建[J],东北大学学报(自然科学版),2004,25(1):1~4
40邹华,高新波,吕新荣.层次包围盒与GPU实现相结合的光线投射算法[J].计算机辅助设计与图形学学报, 2009(02):172~178
41 H. W. Shen, L. J. Chiang. A fast volume rendering algorithm for time-varying fields using a time-space partitioning (TSP) tree[A]. In: IEEE Visualization’99 [C]. Boston: IEEE Computer Society Press, 1999: 371~545
42董峰,蔡文立.基于空间分割的三维不规则数据场的体绘制算法,计算机辅助设计与图形学学,1997,9(3):241~248
43苏超轼,赵明昌,张向文.GPU加速的八叉树体绘制算法[J].计算机应用,2008(05):1232~1239
44 M. Levoy. Efficient ray tracing for volume data [J]. Computer Graphics, 1990, 9 (3): 245~261
45 J. Wilhelms, V. Gelder. A coherent projection approach for direct volume rendering [J]. Computer Graphics, 1991, 25 (4): 275~281
46周勇,唐圣泽.通过区域块投影方法直接绘制三维数据场[J].计算机辅助设计与图形学报, 1996, 8 (3) : 161~168
47 Y. Zhou, W. Chen, Z. S. Tang. Subvolume projection: a full exploration of function coherence for volume rendering [J]. The Journal of Visualization and Computer Animation, 1995, 12 (6):207~218
48 T. Etrl, R. Westermann, R. Grsso. Multi-resolution and hierarchical methods for the visualization of volume data [J]. Future Generation Computer System, 1999, 15 (1): 31~42
49 T. Y. Kim, Y. G. Shin. An efficient wavelet-based compression method for vo lume rendering [A]. In: Computer Graphics and Applications, Proceedings, Seventh Pacific Conference[C]. Singapore: IEEE Computer Society Press, 1999: 147~156
50 A. W. Michel, B. T. Jos. X-ray volume rendering by hierarchical wavelet splatting [A]. In: Pattern Recognition, Proceedings, 15th International Conference[C]. Washington: IEEE Computer Society Press, 2000: 159~162
51 D. Laur, P. Hanrahan. Hierarchical splatting: A progressive refinement algorithm for volume rendering [J]. Computer Graphics, 1991, 25 (4): 275~288
52 B. Liu, G. D. Nelson. A simplified energy projection and applications of transfer function in isometric volume rendering [A]. In: IEEE Canadian Conference on Computer Engineering[C]. 1999. Canada: IEEE Computer Society Press, 1999:1728~ 1733
53 A. Kostas, T. A. Tim. 4D volume rendering with the shear warp factorisation extensions and quantitative results [A]. In: Information Visualization, P roceedings, Fifth International Conference [C]. New York: IEEE Computer Society Press, 2001: 435~443
54 I. Ihm, R. Lee. Indexing data structures for faster volume rendering [J]. Computers & Graphics, 1997, 21 (4): 497~506
55陈慧,何兴恒.体视化中LOD技术思想的应用与实现[J].计算机工程与设计, 2008,29(22):5860~5865
56陈礼民,梁晓辉,邵志东.基于数据场相关性的光线投射算法.中国图象图形学报,1999,4(9):566~567
57张怡,孙济州,张如万.基于片段的光线投射算法,中国图象图形学报,2007,12(8):1418~1422