The Community for Technology Leaders
RSS Icon
Issue No.06 - November/December (2010 vol.16)
pp: 1515-1524
Ziyi Zheng , Stony Brook University
Wei Xu , Stony Brook University
Klaus Mueller , Stony Brook University
Practical volume visualization pipelines are never without compromises and errors. A delicate and often-studied component is the interpolation of off-grid samples, where aliasing can lead to misleading artifacts and blurring, potentially hiding fine details of critical importance. The verifiable visualization framework we describe aims to account for these errors directly in the volume generation stage, and we specifically target volumetric data obtained via computed tomography (CT) reconstruction. In this case the raw data are the X-ray projections obtained from the scanner and the volume data generation process is the CT algorithm. Our framework informs the CT reconstruction process of the specific filter intended for interpolation in the subsequent visualization process, and this in turn ensures an accurate interpolation there at a set tolerance. Here, we focus on fast trilinear interpolation in conjunction with an octree-type mixed resolution volume representation without T-junctions. Efficient rendering is achieved by a space-efficient and locality-optimized representation, which can straightforwardly exploit fast fixed-function pipelines on GPUs.
Direct volume rendering, computed tomography, filtered back-projection, verifiable visualization
Ziyi Zheng, Wei Xu, Klaus Mueller, "VDVR: Verifiable Volume Visualization of Projection-Based Data", IEEE Transactions on Visualization & Computer Graphics, vol.16, no. 6, pp. 1515-1524, November/December 2010, doi:10.1109/TVCG.2010.211
[1] M. Artner, T. Möller, I. Viola, M.E. Gröller, "High-Quality Volume Rendering with Resampling in the Frequency Domain," Proc. Eurographics/IEEE VGTC Symp. on Visualization, pp. 85–92, 2005.
[2] J. Beyer, M. Hadwiger, T. Möller, L. Fritz, "Smooth Mixed-Resolution GPU Volume Rendering," Proc. IEEE International Symposium on Volume and Point-Based Graphics, pp. 163–170, 2008.
[3] R. Bracewell, The Fourier Transform and its Applications, 3rd edition, McGraw-Hill, 1999.
[4] L. Condat, T. Blu, M. Unser, "Beyond Interpolation: Optimal Reconstruction by Quasi-Interpolation," Proc. IEEE. International Conference on Image Processing, pp. 33–36, 2005.
[5] C. Crassin, F. Neyret, S. Lefebvre, E. Eisemann, "GigaVoxels: Ray-Guided Streaming for Efficient and Detailed Voxel Rendering," ACM Symposium on Interactive 3D Graphics and Games, pp. 15–22, 2009.
[6] B. Csébfalvi, "An Evaluation of Prefiltered Reconstruction Schemes for Volume Rendering," IEEE Trans. on Visualization and Computer Graphics, 14 (2): 289–301, 2008.
[7] B. Csébfalvi, B. Domonkos, "Frequency-Domain Upsampling on a Body-Centered Cubic Lattice for Efficient and High-Quality Volume Rendering," Vision, Modeling, & Visualization Workshop (VMV): pp. 225–232, 2009.
[8] W. Degen, "Sharp Error Bounds for Piecewise Linear Interpolation of Planar Curves," Computing, 79 (2): 143–151, 2007.
[9] M. do Carmo, Differential Geometry of Curves and Surfaces, Prentice Hall, 1976.
[10] K. Engel, M. Hadwiger, C. Rezk-Salama, J. Kniss, Real-Time Volume Graphics. AK Peters Ltd, 2006.
[11] A. Entezari, T. Möller, "Extensions of the Zwart-Powell Box Spline for Volumetric Data Reconstruction on the Cartesian Lattice," IEEE Trans. on Visualization and Computer Graphics, 12 (5): 1337–1344, 2006.
[12] A. Entezari, T. Meng, S. Bergner, T. Möller, "A Granular Three Dimensional Multiresolution Transform," Proc. Eurographics/IEEE-VGTC Symposium on Visualization, pp. 267–274. 2006.
[13] T. Etiene, C. Scheidegger, L. Nonato, R. Kirby, C. Silva, "Verifiable Visualization for Isosurface Extraction," IEEE Trans. on Visualization and Computer Graphics, 15 (6): 1227–1234, 2009.
[14] L. Feldkamp, L. Davis, J. Kress, "Practical Cone Beam Algorithm," J. Optical. Society. America A, 1: 612–619, 1984.
[15] M. Frigo, S. Johnson, "The Design and Implementation of FFTW3," Proc. of the IEEE, 93 (2): 216–231, 2005.
[16] L. Hillebrand, R. Lapp, Y. Kyriakou, W. Kalender, "Interactive GPU-Accelerated Image Reconstruction in Cone-Beam CT," Proc. Of SPIE, vol. 7258, pp. 72582A–72582A–8, 2009.
[17] R. Kähler, M. Simon, H. Hege, "Interactive Volume Rendering of Large Sparse Data Sets using Adaptive Mesh Refinement Hierarchies," IEEE Trans. on Visualization and Computer Graphics, 9 (3): 341–351, 2003.
[18] R. Kähler, J. Wise, T. Abel, H. Hege, "GPU-Assisted Raycasting for Cosmological Adaptive Mesh Refinement Simulations," Proc. Eurographics/IEEE Workshop on Volume Graphics, pp. 103–110, 2006.
[19] R. Kirby, C. Silva, "The Need for Verifiable Visualization," IEEE Computer Graphics and Applications, 28 (5): 78–83, 2008.
[20] E. LaMar, B. Hamann, K. Joy, "Multiresolution Techniques for Interactive Texture-Based Volume Visualization," Proc. IEEE Visualization, pp. 355–361, 1999.
[21] P. La Riviere, J. Bian, P. Vargas, "Penalized-Likelihood Sinogram Restoration for Computed Tomography, IEEE Trans. on Medical Imaging, 25 (8): 1022–36, 2006.
[22] A. Li, K. Mueller, T. Ernst, "Methods for Efficient, High Quality Volume Resampling in the Frequency Domain," Proc. IEEE Visualization, pp. 3–10, 2004.
[23] P. Ljung, C. Lundström, A. Ynnerman, K. Museth, "Transfer Function Based Adaptive Decompression for Volume Rendering of Large Medical Data Sets," Proc. IEEE Volume Visualization and Graphics Symposium, pp. 25–32, 2004.
[24] P. Ljung, C. Lundström, A. Ynnerman, "Multiresolution Interblock Interpolation in Direct Volume Rendering," Euro Vis, pp. 259–266, 2006.
[25] T. Möller, R. Machiraju, K. Mueller, R. Yagel, "Evaluation and Design of Filters using a Taylor Series Expansion," IEEE Trans. On Visualization and Computer Graphics, 3 (2): 184–199, 1997.
[26] T. Malzbender, "Fourier Volume Rendering," ACM Trans. on Graphics, 12 (3): 233–250, 1993
[27] S. Marchesin, G.C, de Verdiere, "High-Quality, Semi-Analytical Volume Rendering for AMR Data," IEEE Trans. on Visualization and Computer Graphics, 15 (6): 1611–1618, 2009.
[28] S. Marschner, R. Lobb, "An Evaluation of Reconstruction Filters for Volume Rendering," Proc. IEEE Visualization, pp. 100–107, 1994.
[29] P. Rautek, B. Csébfalvi, S. Grimm, S. Bruckner, M.E. Gröller, "D2VR: High-Quality Volume Rendering of Projection-Based Volumetric Data," Eurographics/IEEE VGTC Symp on Visualization, pp. 211–218, 2006.
[30] J. Smith, P. Gossett, "A Flexible Sampling-Rate Conversion Method,' Proc. IEEE Int'l Conf. Acoustics, Speech, & Signal Proc, pp. 112–115, 1984. (Tutorial at resample).
[31] P. Suetens, Fundamentals of Medical Imaging, Cambridge University Press, 2002.
[32] P. Thevenaz, T. Blu, M. Unser, "Interpolation Revisited," IEEE Trans. on Medical Imaging, 19 (7): 739–758, 2000.
[33] M. Unser, "Sampling – 50 Years after Shannon," Proceedings of the IEEE, 88 (4): 569–587, 2000.
[34] F. Xu, K. Mueller, "GPU-Accelerated D2VR," Proc. Eurographics/IEEE VGTC Workshop on Volume Graphics, pp. 23–30, 2006.
[35] F. Xu, K. Mueller, "Real-Time 3D Computed Tomographic Reconstruction Using Commodity Graphics Hardware," Physics in Medicine and Biology, 52 (12): 3405–3419, 2007.
[36] W. Zbijewski, F. Beekman, "Efficient Monte Carlo Based Scatter Artifact Reduction in Cone-Beam Micro-CT," IEEE Trans. on Medical Imaging, 25 (7): 817–827, 2006.
25 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool