体数据特征的高效可视化方法研究
|
摘要
体数据可视化借助于人眼视觉容易感知的二维图像形象、直观地展示体数据内部隐含的特征信息,帮助用户对数据做进一步的分析与处理,广泛应用于医学、气象、地质、科学仿真等领域。
传输函数是实现体数据分类的有效手段,即对体数据内部特征映射不同的光学属性,进而获取感兴趣特征的有效展示,这直接决定了体数据可视化的有效性。然而,定义一个能够有效展示体数据内部特征的传输函数是一个复杂而耗时的过程,制约了体数据可视化效率的提升,妨碍了体数据可视化在各个领域的拓展与应用。
本文旨在研究高效的体数据绘制方法和自动的体数据分类方法,其目的均是避免复杂的传输函数设计过程,提升体数据可视化效率。经典的最大密度投影法和最大标量差累积法是当前流行的高效体绘制方法,无需调节复杂的传输函数,即可获得感兴趣特征的有效展示。然而,最大密度投影法绘制结果中最大密度特征的视觉感知效果不佳,容易引起视觉歧义,而最大标量差累积法则无法完整展现视线方向上的重要特征。传输函数的自动优化是当前体数据分类领域的研究热点,但是需要用户对初始数据具有丰富的先验知识,交互地指定感兴趣的特征,对于那些对初始数据认识不足的用户来说,这仍然是一个反复尝试、复杂而耗时的过程,存在一定的局限性。针对上述问题,本文从绘制和分类两个角度出发,对上述算法进行改进,进一步提升了体数据特征的可视化与分析效率。
本文提出了一种视觉感知增强的最大密度投影法,以梯度模为衡量标准,查找最大密度特征的最佳法向,利用经典的光照模型对最大密度特征做光照处理,获得形状感知增强的最大密度特征图像。引入图像处理领域的色调映射技术增强局部特征的对比度。利用最佳法向特征的深度自适应更新光照系数,并且采用HSV颜色模型对其进行颜色映射,增强最大密度特征的深度感知。最后提出一种双阈值的区域增长策略,能够准确地提取感兴趣区域,突出地展示感兴趣的最大密度特征信息。该方法无需传输函数作用,即可获得最大密度特征的增强展示,提升了用户探索与分析体数据的效率。
本文亦提出了隐藏特征展示的体数据可视化方法。在最大标量差累积法的基础上,动态更新当前最大标量值,使得隐藏于当前最大标量值之后的特征能够有效展示于绘制结果中。进而提出一种有效展示隐藏特征的直接体绘制方法,在不透明度的累加值到达临界状态时,动态计算调整系数,降低可见特征在绘制结果图像中的贡献,使得隐藏特征能够展示于结果图像中。进一步定义了方便用户选取感兴趣特征的二值函数,增强感兴趣特征在绘制结果中的展示。该类方法在初始的线性传输函数作用下,即可完整地展示体数据内部的特征信息,方便用户快速地获取与分析体数据内部特征。
为简化体数据分类过程,本文提出一种体数据特征自动分析与可视化技术。对初始体数据做基于空间相似性的预分类,进而提供一种直观的体数据播放器交互手段,帮助用户交互选取感兴趣特征。定义能量函数度量当前传输函数作用下感兴趣特征可见性分布与目标可见性分布的差异,利用最速梯度下降法自动优化传输函数设计,最终实现感兴趣特征的有效展示。该方法利用体数据播放器按序绘制预分类特征,无需用户对初始体数据具有丰富的先验知识,且提供了传输函数自动优化设计方案,避免了复杂而耗时的体数据分类过程,使体数据特征的探索与分析过程更加自动化,具有较强的实用性。
本文旨在研究高效的体数据绘制方法与自动的体数据分类技术,以简化复杂而耗时的传输函数设计过程,提升体数据可视化与分析效率。大量的实验结果对比与用户反馈信息亦验证了本文算法的高效性与实用性。
Volume visualization can expressively display internal features of interest inside the volume and greatly helps users in data analysis. It is widely used in a large number of important fields, including medicine, climate, geology and scientific simulation.
The transfer function has proven as an effective tool for volume classification, and it defines a mapping from original data properties and their derived properties to optical contributions, such as color and opacity. Unfortunately, it is often a time-consuming and trial-and-error task to specify an effective transfer function for desired feature classification, and this largely influences the efficiency of volume classification and hampers the expansive applications of volume visualization.
This paper focuses on the research of high-efficiency volume rendering techniques and automatic volume classification methods, to improve volume visualization efficiency. Maximum intensity projection (MIP) and maximum intensity difference accumulation (MIDA) are two popular rendering techniques for efficient volume visualization, without the complex design of transfer functions. However, the visual perception of MIP rendered images is poor, because the visible features lack depth compensation and local shape description. MIDA is able to provide spatial and occlusion context information for maximum intensity features, while features of interest located behind the maximum intensity features would contribute little to the final rendering. As automatic design of transfer function is another effective way for high-efficiency volume visualization, the requirement of domain knowledge makes feature classification still a complex task. In this paper, we propose three novel techniques to enhance the efficiency of volume visualization.
A novel maximum intensity projection method is proposed to enhance shape and depth perception of the internal maximum intensity features, without a sophisticated or time-consuming transfer function specification. We first employ the gradient-based shading to improve shape perception of structures in MIP. As the shading result may be over the maximum intensity of the display device, a tone mapping technique is used to reduce the intensity of the rendered image while preserving the original local contrast. To enhance depth perception of rendered images, local illumination coefficients are updated according to the depth of boundary features and depth-based color cues are applied. A two-threshold region growing scheme is also designed to perform a focus and context operation to further highlight features of interest.
We also propose occluded feature exploration methods for high-efficiency volume visualization. A novel ray casting algorithm to reveal occluded features for MIDA is firstly introduced. During the ray casting procedure, a low-pass filter is used to remove noises of the sampled values along the ray, and the features behind the position of the current maximum intensity can be located accurately. Then, we adjust the current maximum intensity according to the depth information of the occluded features. Finally, the accumulated color and opacity value can be adaptively modulated with the maximum intensity difference, which is the difference between the modified current maximum intensity and the current sampled value. As a result, features occluded in MIDA can be effectively displayed in the rendered image. Inspired by MIDA, another novel feature exploration method is proposed to achieve the better visibility of internal features based on simple initial transfer functions, in which an adaptive volume rendering integral modification is conducted when the accumulated opacity is approaching to overflow. Therefore, the structures located behind thick non-transparent regions would contribute to the corresponding pixel, and have more influence on the final rendered image. Furthermore, several binary functions are introduced to classify features, and improve the integral modification for feature enhancements.
In order to simplify volume classification and improve the efficiency of volume visualization, we propose an automatic volumetric feature exploration system. We firstly identify different interval features by means of a spatial pre-classification method. Then, volume player is introduced to browse the internal features according to their corresponding intensity values, which makes the complex process of volume exploration easy to understand and simple to operate. For further enhancing the visual perception of the features selected by users, traditional visibility estimation is extended to feature visibility calculation, to better quantify the contribution of each feature in the final rendering result. To minimize the difference between the current feature visibility distribution and the desired visibility distribution, the steepest gradient descent method is employed to achieve the effective opacity vector. Without the requirements of prior knowledge and complex design of transfer functions, the proposed system exhibits an intuitive and automatic tool for volume visualization and feature exploration.
The research of this paper can achieve high efficiency of volume visualization, without specifying complex transfer functions. Experiments with several volume data sets and user studies demonstrate the effectiveness and application value of the proposed volume visualization methods.
传输函数是实现体数据分类的有效手段,即对体数据内部特征映射不同的光学属性,进而获取感兴趣特征的有效展示,这直接决定了体数据可视化的有效性。然而,定义一个能够有效展示体数据内部特征的传输函数是一个复杂而耗时的过程,制约了体数据可视化效率的提升,妨碍了体数据可视化在各个领域的拓展与应用。
本文旨在研究高效的体数据绘制方法和自动的体数据分类方法,其目的均是避免复杂的传输函数设计过程,提升体数据可视化效率。经典的最大密度投影法和最大标量差累积法是当前流行的高效体绘制方法,无需调节复杂的传输函数,即可获得感兴趣特征的有效展示。然而,最大密度投影法绘制结果中最大密度特征的视觉感知效果不佳,容易引起视觉歧义,而最大标量差累积法则无法完整展现视线方向上的重要特征。传输函数的自动优化是当前体数据分类领域的研究热点,但是需要用户对初始数据具有丰富的先验知识,交互地指定感兴趣的特征,对于那些对初始数据认识不足的用户来说,这仍然是一个反复尝试、复杂而耗时的过程,存在一定的局限性。针对上述问题,本文从绘制和分类两个角度出发,对上述算法进行改进,进一步提升了体数据特征的可视化与分析效率。
本文提出了一种视觉感知增强的最大密度投影法,以梯度模为衡量标准,查找最大密度特征的最佳法向,利用经典的光照模型对最大密度特征做光照处理,获得形状感知增强的最大密度特征图像。引入图像处理领域的色调映射技术增强局部特征的对比度。利用最佳法向特征的深度自适应更新光照系数,并且采用HSV颜色模型对其进行颜色映射,增强最大密度特征的深度感知。最后提出一种双阈值的区域增长策略,能够准确地提取感兴趣区域,突出地展示感兴趣的最大密度特征信息。该方法无需传输函数作用,即可获得最大密度特征的增强展示,提升了用户探索与分析体数据的效率。
本文亦提出了隐藏特征展示的体数据可视化方法。在最大标量差累积法的基础上,动态更新当前最大标量值,使得隐藏于当前最大标量值之后的特征能够有效展示于绘制结果中。进而提出一种有效展示隐藏特征的直接体绘制方法,在不透明度的累加值到达临界状态时,动态计算调整系数,降低可见特征在绘制结果图像中的贡献,使得隐藏特征能够展示于结果图像中。进一步定义了方便用户选取感兴趣特征的二值函数,增强感兴趣特征在绘制结果中的展示。该类方法在初始的线性传输函数作用下,即可完整地展示体数据内部的特征信息,方便用户快速地获取与分析体数据内部特征。
为简化体数据分类过程,本文提出一种体数据特征自动分析与可视化技术。对初始体数据做基于空间相似性的预分类,进而提供一种直观的体数据播放器交互手段,帮助用户交互选取感兴趣特征。定义能量函数度量当前传输函数作用下感兴趣特征可见性分布与目标可见性分布的差异,利用最速梯度下降法自动优化传输函数设计,最终实现感兴趣特征的有效展示。该方法利用体数据播放器按序绘制预分类特征,无需用户对初始体数据具有丰富的先验知识,且提供了传输函数自动优化设计方案,避免了复杂而耗时的体数据分类过程,使体数据特征的探索与分析过程更加自动化,具有较强的实用性。
本文旨在研究高效的体数据绘制方法与自动的体数据分类技术,以简化复杂而耗时的传输函数设计过程,提升体数据可视化与分析效率。大量的实验结果对比与用户反馈信息亦验证了本文算法的高效性与实用性。
Volume visualization can expressively display internal features of interest inside the volume and greatly helps users in data analysis. It is widely used in a large number of important fields, including medicine, climate, geology and scientific simulation.
The transfer function has proven as an effective tool for volume classification, and it defines a mapping from original data properties and their derived properties to optical contributions, such as color and opacity. Unfortunately, it is often a time-consuming and trial-and-error task to specify an effective transfer function for desired feature classification, and this largely influences the efficiency of volume classification and hampers the expansive applications of volume visualization.
This paper focuses on the research of high-efficiency volume rendering techniques and automatic volume classification methods, to improve volume visualization efficiency. Maximum intensity projection (MIP) and maximum intensity difference accumulation (MIDA) are two popular rendering techniques for efficient volume visualization, without the complex design of transfer functions. However, the visual perception of MIP rendered images is poor, because the visible features lack depth compensation and local shape description. MIDA is able to provide spatial and occlusion context information for maximum intensity features, while features of interest located behind the maximum intensity features would contribute little to the final rendering. As automatic design of transfer function is another effective way for high-efficiency volume visualization, the requirement of domain knowledge makes feature classification still a complex task. In this paper, we propose three novel techniques to enhance the efficiency of volume visualization.
A novel maximum intensity projection method is proposed to enhance shape and depth perception of the internal maximum intensity features, without a sophisticated or time-consuming transfer function specification. We first employ the gradient-based shading to improve shape perception of structures in MIP. As the shading result may be over the maximum intensity of the display device, a tone mapping technique is used to reduce the intensity of the rendered image while preserving the original local contrast. To enhance depth perception of rendered images, local illumination coefficients are updated according to the depth of boundary features and depth-based color cues are applied. A two-threshold region growing scheme is also designed to perform a focus and context operation to further highlight features of interest.
We also propose occluded feature exploration methods for high-efficiency volume visualization. A novel ray casting algorithm to reveal occluded features for MIDA is firstly introduced. During the ray casting procedure, a low-pass filter is used to remove noises of the sampled values along the ray, and the features behind the position of the current maximum intensity can be located accurately. Then, we adjust the current maximum intensity according to the depth information of the occluded features. Finally, the accumulated color and opacity value can be adaptively modulated with the maximum intensity difference, which is the difference between the modified current maximum intensity and the current sampled value. As a result, features occluded in MIDA can be effectively displayed in the rendered image. Inspired by MIDA, another novel feature exploration method is proposed to achieve the better visibility of internal features based on simple initial transfer functions, in which an adaptive volume rendering integral modification is conducted when the accumulated opacity is approaching to overflow. Therefore, the structures located behind thick non-transparent regions would contribute to the corresponding pixel, and have more influence on the final rendered image. Furthermore, several binary functions are introduced to classify features, and improve the integral modification for feature enhancements.
In order to simplify volume classification and improve the efficiency of volume visualization, we propose an automatic volumetric feature exploration system. We firstly identify different interval features by means of a spatial pre-classification method. Then, volume player is introduced to browse the internal features according to their corresponding intensity values, which makes the complex process of volume exploration easy to understand and simple to operate. For further enhancing the visual perception of the features selected by users, traditional visibility estimation is extended to feature visibility calculation, to better quantify the contribution of each feature in the final rendering result. To minimize the difference between the current feature visibility distribution and the desired visibility distribution, the steepest gradient descent method is employed to achieve the effective opacity vector. Without the requirements of prior knowledge and complex design of transfer functions, the proposed system exhibits an intuitive and automatic tool for volume visualization and feature exploration.
The research of this paper can achieve high efficiency of volume visualization, without specifying complex transfer functions. Experiments with several volume data sets and user studies demonstrate the effectiveness and application value of the proposed volume visualization methods.
引文
[1]石教英,蔡文立(译).科学计算可视化算法与系统[M].科学出版社,2011.
[2]彭群生,鲍虎军,金小刚.计算机真实感图形的算法基础[M].科学出版社,1999.
[3]唐泽圣等.三维数据场可视化[M].清华大学出版社,1999.
[4]Jinman K, Weidong C, Dagan F. Dual-Modality PET-CT Visualization using Real-Time Volume Rendering and Image Fusion with Interactive 3D Segmentation of Anatomical Structures[C]. Engineering in Medicine and Biology Society,2005. IEEE-EMBS 2005.27th Annual International Conference of the,2005.2005:642-645.
[5]Prassni J S, Ropinski T, Hinrichs K. Uncertainty-Aware Guided Volume Segmentation[J]. Visualization and Computer Graphics, IEEE Transactions on.2010, 16(6):1358-1365.
[6]陈为,Sakas Georgios,彭群生.手动式电磁定位及图像导航的短径癌症放射治疗系统[J].计算机辅助设计与图形学学报.2002,14(9)：870-876.
[7]彭艺,陈莉.医学可视化中利用形状特征设计传递函数[J].计算机辅助设计与图形学学报.2011,23(1)：78-84.
[8]梁荣华,李诚,吴福理,等.面向医学数据的分层剥离体绘制算法[J].计算机辅助设计与图形学学报.2009,21(10)：1381-1386.
[9]Kadlec B J, Tufo H M, Dorn G A. Knowledge-Assisted Visualization and Segmentation of Geologic Features[J]. Computer Graphics and Applications, IEEE. 2010,30(1):30-39.
[10]Patel D, Bruckner S, Viola I, et al. Seismic volume visualization for horizon extraction[C]. Pacific Visualization Symposium (PacificVis),2010 IEEE,2010.2010: 73-80.
[11]刘少华,肖克炎,王新海.地质三维属性建模及其可视化[J].地质通报.2010,29(10)：1554-1557.
[12]张挺,卢德唐,李道伦,等.基于软硬数据的多点地质统计法在图像统计信 息重构中的应用研究[J].计算机研究与发展.2010,47(1)：43-52.
[13]Hlawatsch M, Leube P, Nowak W, et al. Flow Radar Glyphs—Static Visualization of Unsteady Flow with Uncertainty[J]. Visualization and Computer Graphics, IEEE Transactions on.2011,17(12):1949-1958.
[14]Gao Y, Fei Y, Zheng T, et al. Visualization of 3D spatial data sets applied in radar imaging[C]. Microwave and Millimeter Wave Technology,2008. ICMMT 2008. International Conference on,2008.2008:2059-2062.
[15]侯焕,韩雷,林忠宇.VTK技术在雷达图像可视化中的研究与应用[J].现代电子技术.2010,33(6)：122-124.
[16]张志强,刘黎平,王红艳.三维可视化技术在雷达三维组网产品显示中的运用[J].气象科技.2010,38(5)：605-608.
[17]Hanqi G, He X, Xiaoru Y. Multi-dimensional transfer function design based on flexible dimension projection embedded in parallel coordinates[C]. Pacific Visualization Symposium (PacificVis),2011 IEEE,2011.2011:19-26.
[18]Tompkins G H, Kornreich D E, Parker R Y, et al. Dynamic radiation dose visualization in discrete-event nuclear facility simulation models[C]. Simulation Conference,2004. Proceedings of the 2004 Winter,2004.2004:1541-1547.
[19]Duke D, Carr H, Knoll A, et al. Visualizing Nuclear Scission through a Multifield Extension of Topological Analysis[J]. Visualization and Computer Graphics, IEEE Transactions on.2012,18(12):2033-2040.
[20]Max N. Optical models for direct volume rendering[J]. Visualization and Computer Graphics, IEEE Transactions on.1995,1(2):99-108.
[21]Kruger J, Westermann R. Acceleration techniques for GPU-based volume rendering[C]. Visualization,2003. VIS 2003. IEEE,2003.2003:287-292.
[22]Schreiner S, Jr. Galloway R L. A fast maximum-intensity projection algorithm for generating magnetic resonance angiograms[J]. Medical Imaging, IEEE Transactions on.1993,12(1):50-57.
[23]Bruckner S, Groller M E. Instant Volume Visualization using Maximum Intensity Difference Accumulation [J]. Computer Graphics Forum.2009,28(3):775-782.
[24]Marchesin S, Dischler J M, Mongenet C. Per-Pixel Opacity Modulation for Feature Enhancement in Volume Rendering[J]. Visualization and Computer Graphics, IEEE Transactions on.2010,16(4):560-570.
[25]Yingcai W, Huamin Q. Interactive Transfer Function Design Based on Editing Direct Volume Rendered Images[J]. Visualization and Computer Graphics, IEEE Transactions on.2007,13(5):1027-1040.
[26]Hanqi G, Ningyu M, Xiaoru Y. WYSIWYG (What You See is What You Get) Volume Visualization[J]. Visualization and Computer Graphics, IEEE Transactions on. 2011,17(12):2106-2114.
[27]Kniss J, Kindlmann G, Hansen C. Interactive volume rendering using multi-dimensional transfer functions and direct manipulation widgets[C]. Visualization, 2001. VIS'01. Proceedings,2001.2001:255-562.
[28]Kniss J, Kindlmann G, Hansen C. Multidimensional transfer functions for interactive volume rendering[J]. Visualization and Computer Graphics, IEEE Transactions on.2002,8(3):270-285.
[29]Kindlmann G, Whitaker R, Tasdizen T, et al. Curvature-based transfer functions for direct volume rendering:methods and applications[C]. Visualization,2003. VIS 2003. IEEE,2003.2003:513-520.
[30]Prassni J S, Ropinski T, Mensmann J, et al. Shape-based transfer functions for volume visualization[C]. Pacific Visualization Symposium (PacificVis),2010 IEEE, 2010.2010:9-16.
[31]Correa C, Kwan-Liu M. Size-based Transfer Functions:A New Volume Exploration Technique[J]. Visualization and Computer Graphics, IEEE Transactions on.2008,14(6):1380-1387.
[32]Caban J J, Rheingans P. Texture-based Transfer Functions for Direct Volume Rendering[J]. Visualization and Computer Graphics, IEEE Transactions on.2008, 14(6):1364-1371.
[33]Yunhai W, Wei C, Jian Z, et al. Efficient Volume Exploration Using the Gaussian Mixture Model[J]. Visualization and Computer Graphics, IEEE Transactions on.2011, 17(11):1560-1573.
[34]Maciejewski R, Insoo W, Wei C, et al. Structuring Feature Space:A Non-Parametric Method for Volumetric Transfer Function Generation[J]. Visualization and Computer Graphics, IEEE Transactions on.2009,15(6):1473-1480.
[35]Correa C D, Kwan-Liu M. Visibility Histograms and Visibility-Driven Transfer Functions[J]. Visualization and Computer Graphics, IEEE Transactions on.2011, 17(2):192-204.
[36]Correa C D, Kwan-Liu M. Visibility-driven transfer functions[C]. Visualization Symposium,2009. PacificVis'09. IEEE Pacific,2009.2009:177-184.
[37]Lorensen W E, Cline H E. Marching Cubes:A High Resolution 3D Surface Construction Algorithm[Z].1987:4,163-169.
[38]Westover L. Footprint evaluation for volume rendering[J]. Computer Graphics. 1990,4(24):367-376.
[39]Lacroute P, Levoy M. Fast Volume Rendering Using a Shear-Warp Factorization of the Viewing Transformation[Z].1994,451-458.
[40]Kniss J, Premoze S, Hansen C, et al. A model for volume lighting and modeling[J]. Visualization and Computer Graphics, IEEE Transactions on.2003,9(2): 150-162.
[41]Jian-Feng Z. GPU-based direct volume rendering with advanced illumination and Deep Attenuation Shadows[C]. Computer-Aided Design and Computer Graphics,2009. CAD/Graphics'09.11th IEEE International Conference on,2009.2009:536-539.
[42]Sato Y, Shiraga N, Nakajima S, et al. LMIP:Local Maximum Intensity Projection: Comparison of Visualization Methods Using Abdominal CT Angiograpy[J]. Journal of Computer Assisted Tomography.1998,6(22):912-917.
[43]Diaz J, Vazquez P. Depth-enhanced maximum intensity projection[Z].2010, 93-100.
[44]Gibson S, Beardsley P, Ruml W, et al. Design Galleries:A general approach to setting parameters for computer graphics and animation[C]. In Proceedings of SIGGRAPH97,1997.1997:389-400.
[45]Jankun-Kelly T J, Kwan-Liu M. A spreadsheet interface for visualization exploration[C]. Visualization 2000. Proceedings,2000.2000:69-76.
[46]Ropinski T, Prassni J S, Steinicke F, et al. Stroke-based transfer function design[C]. IEEE/EG International Symposium on Volume and Point-Based Graphics, 2008.2008:41-48.
[47]Roettger S, Bauer M, Stamminger M. Spatialized Transfer Functions[C]. EUROGRAPHICS-IEEE VGTC Symposium on Visualization,2005.2005:271-278.
[48]Sereda P, Bartroli A V, Serlie I W O, et al. Visualization of boundaries in volumetric data sets using LH histograms[J]. Visualization and Computer Graphics, IEEE Transactions on.2006,12(2):208-218.
[49]Yunhai W, Wei C, Guihua S, et al. Volume exploration using ellipsoidal Gaussian transfer functions[C]. Pacific Visualization Symposium (PacificVis),2010 IEEE,2010. 2010:25-32.
[50]Sereda P, Bartroli A V, Gerritsen F A. Automating transfer function design for volume rendering using hierarchical clustering of material boundaries[C]. Eurographics/IEEE VGTC Symposium on Visualization (EuroVis),2006.2006: 243-250.
[51]Nguyen B P. Automatic Transfer Function Design for Volumetric Data Visualization using Clustering on LH Space[C]. in proceedings of Computer Graphics International 2011 (CGI 2011), Ottawa, Ontario, Canada,2011. Ottawa, Ontario, Canada:2011:1-10.
[52]Bordoloi U D, Shen H W. View selection for volume rendering[C]. Visualization, 2005. VIS 05. IEEE,2005.2005:487-494.
[53]Wang Y, Zhang J, Chen W, et al. Efficient opacity specification based on feature visibilities in direct volume rendering[J]. Computer Graphics Forum.2011,30(7): 2117-2126.
[54]Ruiz M, Bardera A, Boada I, et al. Automatic Transfer Functions Based on Informational Divergence[J]. Visualization and Computer Graphics, IEEE Transactions on.2011,17(12):1932-1941.
[55]Keppel E. Approximating Complex Surfaces by Triangulation of Contour Lines[J]. IBM Journal of Research and Development.1975,1(19):2-11.
[56]Herman G T, Liu H K. Three-dimensional display of human organs from Computed Tomograms[J]. Computer Graphics and Images Processing.1979,1(9): 1-21.
[57]Schlegel P, Makhinya M, Pajarola R. Extinction-Based Shading and Illumination in GPU Volume Ray-Casting[J]. Visualization and Computer Graphics, IEEE Transactions on.2011,17(12):1795-1802.
[58]Hernell F, Ljung P, Ynnerman A. Local Ambient Occlusion in Direct Volume Rendering[J]. Visualization and Computer Graphics, IEEE Transactions on.2010, 16(4):548-559.
[59]Glassner A. Situation normal [Gourand and Phong shading][J]. Computer Graphics and Applications, IEEE.1997,17(2):83-87.
[60]Behrens U, Ratering R. Adding shadows to a texture-based volume renderer[C]. Volume Visualization,1998. IEEE Symposium on,1998.1998:39-46.
[61]Heidrich W, Mccool M, Stevens J. Interactive maximum projection volume rendering[C]. Visualization,1995. Visualization'95. Proceedings., IEEE Conference on,1995.1995:11-18,433.
[62]Bruckner S, Grimm S, Kanitsar A, et al. Illustrative Context-Preserving Exploration of Volume Data[J]. Visualization and Computer Graphics, IEEE Transactions on.2006,12(6):1559-1569.
[63]Fout N, Ma K. Fuzzy Volume Rendering[J]. Visualization and Computer Graphics, IEEE Transactions on.2012,18(12):2335-2344.
[64]Svakhine N, Ebert D S, Stredney D. Illustration motifs for effective medical volume illustration[J]. Computer Graphics and Applications, IEEE.2005,25(3): 31-39.
[65]Zou Q, Kwoh C K, Ng W S. Interactive surgical planning using context based volume visualization techniques[C]. Medical Imaging and Augmented Reality,2001. Proceedings. International Workshop on,2001.2001:21-25.
[66]Ebert D, Rheingans P. Volume illustration:non-photorealistic rendering of volume models[C]. Visualization 2000. Proceedings,2000.2000:195-202.
[67]Rheingans P, Ebert D. Volume illustration:nonphotorealistic rendering of volume models [J]. Visualization and Computer Graphics, IEEE Transactions on.2001,7(3): 253-264.
[68]Falk M, Weiskopf D. Output-Sensitive 3D Line Integral Convolution[J]. Visualization and Computer Graphics, IEEE Transactions on.2008,14(4):820-834.
[69]Bruckner S, Groller M E. Enhancing Depth-Perception with Flexible Volumetric Halos[J]. Visualization and Computer Graphics, IEEE Transactions on.2007,13(6): 1344-1351.
[70]Svakhine N A, Ebert D S. Interactive volume illustration and feature halos[C]. Computer Graphics and Applications,2003. Proceedings.11th Pacific Conference on, 2003.2003:347-354.
[71]Yubo T, Hai L, Feng D, et al. Opacity Volume Based Halo Generation for Enhancing Depth Perception[C]. Computer-Aided Design and Computer Graphics (CAD/Graphics),2011 12th International Conference on,2011.2011:418-422.
[72]He T, Hong L, Kaufman A, et al. Generation of transfer functions with stochastic search techniques[C]. Proceedings of the 7th conference on Visualization'96,1996. 1996:227-234.
[73]Wang Y, Zhang J, Lehmann D J, et al. Automating Transfer Function Design with Valley Cell-Based Clustering of 2D Density Plots[J]. Computer Graphics Forum.2012, 31(3pt4):1295-1304.
[74]Haidacher M, Patel D, Bruckner S, et al. Volume visualization based on statistical transfer-function spaces[C]. Pacific Visualization Symposium (PacificVis),2010 IEEE, 2010.2010:17-24.
[75]Lum E B, Ma K L. Lighting transfer functions using gradient aligned sampling[C]. Visualization,2004. IEEE,2004.2004:289-296.
[76]Bruckner S, Moller T. Isosurface Similarity Maps[J]. Computer Graphics Forum. 2010,29(3):773-782.
[77]Haidacher M, Bruckner S, Groller M E. Volume Analysis Using Multimodal Surface Similarity[J]. Visualization and Computer Graphics, IEEE Transactions on. 2011,17(12):1969-1978.
[78]Lundstrom C, Ljung P, Ynnerman A. Local Histograms for Design of Transfer Functions in Direct Volume Rendering[J]. Visualization and Computer Graphics, IEEE Transactions on.2006,12(6):1570-1579.
[79]Lindholm S, Ljung P, Lundstro X, et al. Spatial Conditioning of Transfer Functions Using Local Material Distributions[J]. Visualization and Computer Graphics, IEEE Transactions on.2010,16(6):1301-1310.
[80]Tzeng F Y, Lum E B, Ma K L. An intelligent system approach to higher-dimensional classification of volume data[J]. Visualization and Computer Graphics, IEEE Transactions on.2005,11(3):273-284.
[81]Moura Pinto F, Freitas C M D S. Design of multi-dimensional transfer functions using dimensional reduction[C]. Proceedings of the 9th Joint Eurographics/IEEE VGTC conference on Visualization,2007.2007:131-138.
[82]Zhao X, Kaufman A E. Multi-dimensional Reduction and Transfer Function Design using Parallel Coordinates[C]. IEEE/EG International Symposium on Volume Graphics,2010.2010:69-76.
[83]Viola I, Kanitsar A, Groller M E. Importance-driven volume rendering[C]. Visualization,2004. IEEE,2004.2004:139-145.
[84]Drago F, Myszkowski K, Annen T, et al. Adaptive Logarithmic Mapping For Displaying High Contrast Scenes[J]. Computer Graphics Forum.2003(22):419-426.
[2]彭群生,鲍虎军,金小刚.计算机真实感图形的算法基础[M].科学出版社,1999.
[3]唐泽圣等.三维数据场可视化[M].清华大学出版社,1999.
[4]Jinman K, Weidong C, Dagan F. Dual-Modality PET-CT Visualization using Real-Time Volume Rendering and Image Fusion with Interactive 3D Segmentation of Anatomical Structures[C]. Engineering in Medicine and Biology Society,2005. IEEE-EMBS 2005.27th Annual International Conference of the,2005.2005:642-645.
[5]Prassni J S, Ropinski T, Hinrichs K. Uncertainty-Aware Guided Volume Segmentation[J]. Visualization and Computer Graphics, IEEE Transactions on.2010, 16(6):1358-1365.
[6]陈为,Sakas Georgios,彭群生.手动式电磁定位及图像导航的短径癌症放射治疗系统[J].计算机辅助设计与图形学学报.2002,14(9)：870-876.
[7]彭艺,陈莉.医学可视化中利用形状特征设计传递函数[J].计算机辅助设计与图形学学报.2011,23(1)：78-84.
[8]梁荣华,李诚,吴福理,等.面向医学数据的分层剥离体绘制算法[J].计算机辅助设计与图形学学报.2009,21(10)：1381-1386.
[9]Kadlec B J, Tufo H M, Dorn G A. Knowledge-Assisted Visualization and Segmentation of Geologic Features[J]. Computer Graphics and Applications, IEEE. 2010,30(1):30-39.
[10]Patel D, Bruckner S, Viola I, et al. Seismic volume visualization for horizon extraction[C]. Pacific Visualization Symposium (PacificVis),2010 IEEE,2010.2010: 73-80.
[11]刘少华,肖克炎,王新海.地质三维属性建模及其可视化[J].地质通报.2010,29(10)：1554-1557.
[12]张挺,卢德唐,李道伦,等.基于软硬数据的多点地质统计法在图像统计信 息重构中的应用研究[J].计算机研究与发展.2010,47(1)：43-52.
[13]Hlawatsch M, Leube P, Nowak W, et al. Flow Radar Glyphs—Static Visualization of Unsteady Flow with Uncertainty[J]. Visualization and Computer Graphics, IEEE Transactions on.2011,17(12):1949-1958.
[14]Gao Y, Fei Y, Zheng T, et al. Visualization of 3D spatial data sets applied in radar imaging[C]. Microwave and Millimeter Wave Technology,2008. ICMMT 2008. International Conference on,2008.2008:2059-2062.
[15]侯焕,韩雷,林忠宇.VTK技术在雷达图像可视化中的研究与应用[J].现代电子技术.2010,33(6)：122-124.
[16]张志强,刘黎平,王红艳.三维可视化技术在雷达三维组网产品显示中的运用[J].气象科技.2010,38(5)：605-608.
[17]Hanqi G, He X, Xiaoru Y. Multi-dimensional transfer function design based on flexible dimension projection embedded in parallel coordinates[C]. Pacific Visualization Symposium (PacificVis),2011 IEEE,2011.2011:19-26.
[18]Tompkins G H, Kornreich D E, Parker R Y, et al. Dynamic radiation dose visualization in discrete-event nuclear facility simulation models[C]. Simulation Conference,2004. Proceedings of the 2004 Winter,2004.2004:1541-1547.
[19]Duke D, Carr H, Knoll A, et al. Visualizing Nuclear Scission through a Multifield Extension of Topological Analysis[J]. Visualization and Computer Graphics, IEEE Transactions on.2012,18(12):2033-2040.
[20]Max N. Optical models for direct volume rendering[J]. Visualization and Computer Graphics, IEEE Transactions on.1995,1(2):99-108.
[21]Kruger J, Westermann R. Acceleration techniques for GPU-based volume rendering[C]. Visualization,2003. VIS 2003. IEEE,2003.2003:287-292.
[22]Schreiner S, Jr. Galloway R L. A fast maximum-intensity projection algorithm for generating magnetic resonance angiograms[J]. Medical Imaging, IEEE Transactions on.1993,12(1):50-57.
[23]Bruckner S, Groller M E. Instant Volume Visualization using Maximum Intensity Difference Accumulation [J]. Computer Graphics Forum.2009,28(3):775-782.
[24]Marchesin S, Dischler J M, Mongenet C. Per-Pixel Opacity Modulation for Feature Enhancement in Volume Rendering[J]. Visualization and Computer Graphics, IEEE Transactions on.2010,16(4):560-570.
[25]Yingcai W, Huamin Q. Interactive Transfer Function Design Based on Editing Direct Volume Rendered Images[J]. Visualization and Computer Graphics, IEEE Transactions on.2007,13(5):1027-1040.
[26]Hanqi G, Ningyu M, Xiaoru Y. WYSIWYG (What You See is What You Get) Volume Visualization[J]. Visualization and Computer Graphics, IEEE Transactions on. 2011,17(12):2106-2114.
[27]Kniss J, Kindlmann G, Hansen C. Interactive volume rendering using multi-dimensional transfer functions and direct manipulation widgets[C]. Visualization, 2001. VIS'01. Proceedings,2001.2001:255-562.
[28]Kniss J, Kindlmann G, Hansen C. Multidimensional transfer functions for interactive volume rendering[J]. Visualization and Computer Graphics, IEEE Transactions on.2002,8(3):270-285.
[29]Kindlmann G, Whitaker R, Tasdizen T, et al. Curvature-based transfer functions for direct volume rendering:methods and applications[C]. Visualization,2003. VIS 2003. IEEE,2003.2003:513-520.
[30]Prassni J S, Ropinski T, Mensmann J, et al. Shape-based transfer functions for volume visualization[C]. Pacific Visualization Symposium (PacificVis),2010 IEEE, 2010.2010:9-16.
[31]Correa C, Kwan-Liu M. Size-based Transfer Functions:A New Volume Exploration Technique[J]. Visualization and Computer Graphics, IEEE Transactions on.2008,14(6):1380-1387.
[32]Caban J J, Rheingans P. Texture-based Transfer Functions for Direct Volume Rendering[J]. Visualization and Computer Graphics, IEEE Transactions on.2008, 14(6):1364-1371.
[33]Yunhai W, Wei C, Jian Z, et al. Efficient Volume Exploration Using the Gaussian Mixture Model[J]. Visualization and Computer Graphics, IEEE Transactions on.2011, 17(11):1560-1573.
[34]Maciejewski R, Insoo W, Wei C, et al. Structuring Feature Space:A Non-Parametric Method for Volumetric Transfer Function Generation[J]. Visualization and Computer Graphics, IEEE Transactions on.2009,15(6):1473-1480.
[35]Correa C D, Kwan-Liu M. Visibility Histograms and Visibility-Driven Transfer Functions[J]. Visualization and Computer Graphics, IEEE Transactions on.2011, 17(2):192-204.
[36]Correa C D, Kwan-Liu M. Visibility-driven transfer functions[C]. Visualization Symposium,2009. PacificVis'09. IEEE Pacific,2009.2009:177-184.
[37]Lorensen W E, Cline H E. Marching Cubes:A High Resolution 3D Surface Construction Algorithm[Z].1987:4,163-169.
[38]Westover L. Footprint evaluation for volume rendering[J]. Computer Graphics. 1990,4(24):367-376.
[39]Lacroute P, Levoy M. Fast Volume Rendering Using a Shear-Warp Factorization of the Viewing Transformation[Z].1994,451-458.
[40]Kniss J, Premoze S, Hansen C, et al. A model for volume lighting and modeling[J]. Visualization and Computer Graphics, IEEE Transactions on.2003,9(2): 150-162.
[41]Jian-Feng Z. GPU-based direct volume rendering with advanced illumination and Deep Attenuation Shadows[C]. Computer-Aided Design and Computer Graphics,2009. CAD/Graphics'09.11th IEEE International Conference on,2009.2009:536-539.
[42]Sato Y, Shiraga N, Nakajima S, et al. LMIP:Local Maximum Intensity Projection: Comparison of Visualization Methods Using Abdominal CT Angiograpy[J]. Journal of Computer Assisted Tomography.1998,6(22):912-917.
[43]Diaz J, Vazquez P. Depth-enhanced maximum intensity projection[Z].2010, 93-100.
[44]Gibson S, Beardsley P, Ruml W, et al. Design Galleries:A general approach to setting parameters for computer graphics and animation[C]. In Proceedings of SIGGRAPH97,1997.1997:389-400.
[45]Jankun-Kelly T J, Kwan-Liu M. A spreadsheet interface for visualization exploration[C]. Visualization 2000. Proceedings,2000.2000:69-76.
[46]Ropinski T, Prassni J S, Steinicke F, et al. Stroke-based transfer function design[C]. IEEE/EG International Symposium on Volume and Point-Based Graphics, 2008.2008:41-48.
[47]Roettger S, Bauer M, Stamminger M. Spatialized Transfer Functions[C]. EUROGRAPHICS-IEEE VGTC Symposium on Visualization,2005.2005:271-278.
[48]Sereda P, Bartroli A V, Serlie I W O, et al. Visualization of boundaries in volumetric data sets using LH histograms[J]. Visualization and Computer Graphics, IEEE Transactions on.2006,12(2):208-218.
[49]Yunhai W, Wei C, Guihua S, et al. Volume exploration using ellipsoidal Gaussian transfer functions[C]. Pacific Visualization Symposium (PacificVis),2010 IEEE,2010. 2010:25-32.
[50]Sereda P, Bartroli A V, Gerritsen F A. Automating transfer function design for volume rendering using hierarchical clustering of material boundaries[C]. Eurographics/IEEE VGTC Symposium on Visualization (EuroVis),2006.2006: 243-250.
[51]Nguyen B P. Automatic Transfer Function Design for Volumetric Data Visualization using Clustering on LH Space[C]. in proceedings of Computer Graphics International 2011 (CGI 2011), Ottawa, Ontario, Canada,2011. Ottawa, Ontario, Canada:2011:1-10.
[52]Bordoloi U D, Shen H W. View selection for volume rendering[C]. Visualization, 2005. VIS 05. IEEE,2005.2005:487-494.
[53]Wang Y, Zhang J, Chen W, et al. Efficient opacity specification based on feature visibilities in direct volume rendering[J]. Computer Graphics Forum.2011,30(7): 2117-2126.
[54]Ruiz M, Bardera A, Boada I, et al. Automatic Transfer Functions Based on Informational Divergence[J]. Visualization and Computer Graphics, IEEE Transactions on.2011,17(12):1932-1941.
[55]Keppel E. Approximating Complex Surfaces by Triangulation of Contour Lines[J]. IBM Journal of Research and Development.1975,1(19):2-11.
[56]Herman G T, Liu H K. Three-dimensional display of human organs from Computed Tomograms[J]. Computer Graphics and Images Processing.1979,1(9): 1-21.
[57]Schlegel P, Makhinya M, Pajarola R. Extinction-Based Shading and Illumination in GPU Volume Ray-Casting[J]. Visualization and Computer Graphics, IEEE Transactions on.2011,17(12):1795-1802.
[58]Hernell F, Ljung P, Ynnerman A. Local Ambient Occlusion in Direct Volume Rendering[J]. Visualization and Computer Graphics, IEEE Transactions on.2010, 16(4):548-559.
[59]Glassner A. Situation normal [Gourand and Phong shading][J]. Computer Graphics and Applications, IEEE.1997,17(2):83-87.
[60]Behrens U, Ratering R. Adding shadows to a texture-based volume renderer[C]. Volume Visualization,1998. IEEE Symposium on,1998.1998:39-46.
[61]Heidrich W, Mccool M, Stevens J. Interactive maximum projection volume rendering[C]. Visualization,1995. Visualization'95. Proceedings., IEEE Conference on,1995.1995:11-18,433.
[62]Bruckner S, Grimm S, Kanitsar A, et al. Illustrative Context-Preserving Exploration of Volume Data[J]. Visualization and Computer Graphics, IEEE Transactions on.2006,12(6):1559-1569.
[63]Fout N, Ma K. Fuzzy Volume Rendering[J]. Visualization and Computer Graphics, IEEE Transactions on.2012,18(12):2335-2344.
[64]Svakhine N, Ebert D S, Stredney D. Illustration motifs for effective medical volume illustration[J]. Computer Graphics and Applications, IEEE.2005,25(3): 31-39.
[65]Zou Q, Kwoh C K, Ng W S. Interactive surgical planning using context based volume visualization techniques[C]. Medical Imaging and Augmented Reality,2001. Proceedings. International Workshop on,2001.2001:21-25.
[66]Ebert D, Rheingans P. Volume illustration:non-photorealistic rendering of volume models[C]. Visualization 2000. Proceedings,2000.2000:195-202.
[67]Rheingans P, Ebert D. Volume illustration:nonphotorealistic rendering of volume models [J]. Visualization and Computer Graphics, IEEE Transactions on.2001,7(3): 253-264.
[68]Falk M, Weiskopf D. Output-Sensitive 3D Line Integral Convolution[J]. Visualization and Computer Graphics, IEEE Transactions on.2008,14(4):820-834.
[69]Bruckner S, Groller M E. Enhancing Depth-Perception with Flexible Volumetric Halos[J]. Visualization and Computer Graphics, IEEE Transactions on.2007,13(6): 1344-1351.
[70]Svakhine N A, Ebert D S. Interactive volume illustration and feature halos[C]. Computer Graphics and Applications,2003. Proceedings.11th Pacific Conference on, 2003.2003:347-354.
[71]Yubo T, Hai L, Feng D, et al. Opacity Volume Based Halo Generation for Enhancing Depth Perception[C]. Computer-Aided Design and Computer Graphics (CAD/Graphics),2011 12th International Conference on,2011.2011:418-422.
[72]He T, Hong L, Kaufman A, et al. Generation of transfer functions with stochastic search techniques[C]. Proceedings of the 7th conference on Visualization'96,1996. 1996:227-234.
[73]Wang Y, Zhang J, Lehmann D J, et al. Automating Transfer Function Design with Valley Cell-Based Clustering of 2D Density Plots[J]. Computer Graphics Forum.2012, 31(3pt4):1295-1304.
[74]Haidacher M, Patel D, Bruckner S, et al. Volume visualization based on statistical transfer-function spaces[C]. Pacific Visualization Symposium (PacificVis),2010 IEEE, 2010.2010:17-24.
[75]Lum E B, Ma K L. Lighting transfer functions using gradient aligned sampling[C]. Visualization,2004. IEEE,2004.2004:289-296.
[76]Bruckner S, Moller T. Isosurface Similarity Maps[J]. Computer Graphics Forum. 2010,29(3):773-782.
[77]Haidacher M, Bruckner S, Groller M E. Volume Analysis Using Multimodal Surface Similarity[J]. Visualization and Computer Graphics, IEEE Transactions on. 2011,17(12):1969-1978.
[78]Lundstrom C, Ljung P, Ynnerman A. Local Histograms for Design of Transfer Functions in Direct Volume Rendering[J]. Visualization and Computer Graphics, IEEE Transactions on.2006,12(6):1570-1579.
[79]Lindholm S, Ljung P, Lundstro X, et al. Spatial Conditioning of Transfer Functions Using Local Material Distributions[J]. Visualization and Computer Graphics, IEEE Transactions on.2010,16(6):1301-1310.
[80]Tzeng F Y, Lum E B, Ma K L. An intelligent system approach to higher-dimensional classification of volume data[J]. Visualization and Computer Graphics, IEEE Transactions on.2005,11(3):273-284.
[81]Moura Pinto F, Freitas C M D S. Design of multi-dimensional transfer functions using dimensional reduction[C]. Proceedings of the 9th Joint Eurographics/IEEE VGTC conference on Visualization,2007.2007:131-138.
[82]Zhao X, Kaufman A E. Multi-dimensional Reduction and Transfer Function Design using Parallel Coordinates[C]. IEEE/EG International Symposium on Volume Graphics,2010.2010:69-76.
[83]Viola I, Kanitsar A, Groller M E. Importance-driven volume rendering[C]. Visualization,2004. IEEE,2004.2004:139-145.
[84]Drago F, Myszkowski K, Annen T, et al. Adaptive Logarithmic Mapping For Displaying High Contrast Scenes[J]. Computer Graphics Forum.2003(22):419-426.