“Fast volume rendering using a shear-warp factorization of the viewing transformation” by Lacroute and Levoy

  • ©Philippe Lacroute and Marc Levoy

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Title:

    Fast volume rendering using a shear-warp factorization of the viewing transformation

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Abstract:


    Several existing volume rendering algorithms operate by factoring the viewing transformation into a 3D shear parallel to the data slices, a projection to form an intermediate but distorted image, and a 2D warp to form an undistorted final image. We extend this class of algorithms in three ways. First, we describe a new object-order rendering algorithm based on the factorization that is significantly faster than published algorithms with minimal loss of image quality. Shear-warp factorizations have the property that rows of voxels in the volume are aligned with rows of pixels in the intermediate image. We use this fact to construct a scanline-based algorithm that traverses the volume and the intermediate image in synchrony, taking advantage of the spatial coherence present in both. We use spatial data structures based on run-length encoding for both the volume and the intermediate image. Our implementation running on an SGI Indigo workstation renders a 2563 voxel medical data set in one second. Our second extension is a shear-warp factorization for perspective viewing transformations, and we show how our rendering algorithm can support this extension. Third, we introduce a data structure for encoding spatial coherence in unclassified volumes (i.e. scalar fields with no precomputed opacity). When combined with our shear-warp rendering algorithm this data structure allows us to classify and render a 2563 voxel volume in three seconds. The method extends to support mixed volumes and geometry and is parallelizable.

References:


    1. Cameron, G. G. and P. E. Undrill. Rendering volumetric medical image data on a SIMD-architecture computer. In Proceedings of the Third Eurographics Workshop on Ren-dering, 135-145, Bristol, UK, May 1992.
    2. Crow, Franklin C. Summed-area tables for texture map-ping. Proceedings of SIGGRAPH ’84. Computer Graphics, 18(3):207-212, July 1984.
    3. Danskin, John and Pat Hanrahan. Fast algorithms for volume ray tracing. In 1992 Workshop on Volume Visualization,91- 98, Boston, MA, October 1992.
    4. Drebin, Robert A., Loren Carpenter and Pat Hanrahan. Vol-ume rendering. Proceedings of SIGGRAPH ’88. Computer Graphics, 22(4):65-74, August 1988.
    5. Glassner, Andrew S. Multidimensional sum tables. In Graphics Gems, 376-381. Academic Press, New York, 1990.
    6. Glassner, Andrew S. Normal coding. In Graphics Gems, 257-264. Academic Press, New York, 1990.
    7. Hanrahan, Pat. Three-pass affine transforms for volume ren-dering. Computer Graphics, 24(5):71-77, November 1990.
    8. Laur, David and Pat Hanrahan. Hierarchical splatting: A progressive refinement algorithm for volume render-ing. Proceedings of SIGGRAPH ’91. Computer Graphics, 25(4):285-288, July 1991.
    9. Levoy, Marc. Display of surfaces from volume data. IEEE Computer Graphics & Applications, 8(3):29-37, May 1988.
    10. Levoy, Marc. Volume rendering by adaptive refinement. The Visual Computer, 6(1):2-7, February 1990.
    11. Levoy, Marc and Ross Whitaker. Gaze-directed volume ren-dering. Computer Graphics, 24(2):217-223, March 1990.
    12. Levoy, Marc. Efficient ray tracing of volume data. ACM Transactions on Graphics, 9(3):245-261, July 1990.
    13. Meagher, Donald J. Efficient synthetic image generation of arbitrary 3-D objects. In Proceeding of the IEEE Confer-ence on Pattern Recognition and Image Processing, 473- 478, 1982.
    14. Novins, Kevin L., Fran~ cois X. Sillion, and Donald P. Green-berg. An efficient method for volume rendering using perspective projection. Computer Graphics, 24(5):95-102, November 1990.
    15. Porter, Thomas and Tom Duff. Compositing digital im-ages. Proceedings of SIGGRAPH ’84. Computer Graphics, 18(3):253-259, July 1984.
    16. Sakas, Georgios and Matthias Gerth. Sampling and anti-aliasing of discrete 3-D volume density textures. In Proceed-ings of Eurographics ‘91,87-102, Vienna, Austria, Septem-ber 1991.
    17. Schr~ oder, Peter and Gordon Stoll. Data parallel volume ren-dering as line drawing. In Proceedings of the 1992 Workshop on Volume Visualization,25-32, Boston, October 1992.
    18. Subramanian, K. R. and Donald S. Fussell. Applying space subdivision techniques to volume rendering. In Proceedings of Visualization ’90, 150-159, San Francisco, California, Oc-tober 1990.
    19. V~ ezina, Guy, Peter A. Fletcher, and Philip K. Robertson. Volume rendering on the MasPar MP-1. In 1992 Workshop on Volume Visualization,3-8, Boston, October 1992.
    20. Westover, Lee. Footprint evaluation for volume render-ing. Proceedings of SIGGRAPH ’90. Computer Graphics, 24(4):367-376, August 1990.
    21. Wilhelms, Jane and Allen Van Gelder. Octrees for faster isosurface generation. Computer Graphics, 24(5):57-62, November 1990.
    22. Yagel, Roni and Arie Kaufman. Template-based volume viewing. In Eurographics 92, C-153-167, Cambridge, UK, September 1992.
    23. Zuiderveld, Karel J., Anton H.J. Koning, and Max A. Viergever. Acceleration of ray-casting using 3D distance transforms. In Proceedings of Visualization in Biomedical Computing 1992, 324-335, Chapel Hill, North Carolina, Oc-tober 1992.


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