Computing Visibility for Triangulated Panoramas

  • Chi-Wing Fu
  • Tien-Tsin Wong
  • Pheng-Ann Heng
Part of the Eurographics book series (EUROGRAPH)


A visibility algorithm for triangulated panoramas is proposed. The algorithm can correctly resolve the visibility without making use of any depth information. It is especially useful when depth information is not available, such as in the case of real-world photographs. Based on the optical flow information and the image intensity, the panorama is subdivided into variable-sized triangles, image warping is then efficiently applied on these triangles using existing graphics hardware. The visibility problem is resolved by drawing the warped triangles in a specific order. This drawing order is derived from epipolar geometry. Using this partial drawing order, a graph can be built and topological sorting is applied on the graph to obtain the complete drawing order of all triangles. We will show that the time complexity of graph construction and topological sorting are both linear to the total number of triangles.


Optical Flow Geodesic Curve Epipolar Line Epipolar Geometry Shared Edge 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    T. Beier and S. Neely. Feature-based image metamorphosis. In Computer Graphics (SIG-GRAPH’ 92 Proceedings), volume 26, pages 35–42, July 1992.CrossRefGoogle Scholar
  2. 2.
    S. E. Chen and L. Williams. View interpolation for image synthesis. In Computer Graphics (SIGGRAPH’ 93 Proceedings), pages 279–288, 1993.Google Scholar
  3. 3.
    L. Darsa, B. C. Silva, and A. Varshney. Navigating static environments using image-space simplification and morphing. In Proceedings of the 1997 Symposium on Interactive 3D Graphics, pages 25–34, April 1997.Google Scholar
  4. 4.
    R. Hall. Illumination and Color in Computer Generated Imagery. Springer-Verlag, 1988.Google Scholar
  5. 5.
    B. Horn. Robot Vision. MIT Press, 1986.Google Scholar
  6. 6.
    S. Laveau and O. Faugeras. 3-D scene representation as a collection of images. In Proceedings of the Twelfth International Conference on Pattern Recognition (ICPR’ 94), pages 689–691, October 1994.Google Scholar
  7. 7.
    W. R. Mark and G. Bishop. Memory access patterns of occlusion-compatible 3d image warping. In Proceedings of the 1997 Siggaph/Eurographics Workshop on Graphics Hardware, pages 35–44, August 1997.Google Scholar
  8. 8.
    W. R. Mark and G. Bishop. Efficient reconstruction techniques for post-rendering 3d image warping. Technical report, University of Northern Carolina at Chapel Hill, March 1998. UNC CS#TR98-011.Google Scholar
  9. 9.
    W. R. Mark, L. McMillan, and G. Bishop. Post-rendering 3d warping. In Proceedings of the 1997 Symposium on Interactive 3D Graphics, pages 7–16, April 1997.Google Scholar
  10. 10.
    N. Max and K. Ohsaki. Rendering trees from precomputed Z-buffer views. In Eurographics Rendering Workshop 1995. Eurographics, June 1995.Google Scholar
  11. 11.
    L. McMillan. Computing visibility without depth. Technical report, University of North Carolina, October 1995. UNC Computer Science TR95-047.Google Scholar
  12. 12.
    L. McMillan. An Image-Based Approach to Three-Dimensional Computer Graphics. PhD thesis, Department of Computer Science, University of North Carolina at Chapel Hill, 1997.Google Scholar
  13. 13.
    L. McMillan and G. Bishop. Plenoptic modeling: An image-based rendering system. In Computer Graphics (SIGGRAPH’ 95 Proceedings), pages 39–46, August 1995.Google Scholar
  14. 14.
    K. Prazdny. On the information in optical flows. Computer Vision, Graphics and Image Processing, 22(9):239–259, 1983.CrossRefGoogle Scholar
  15. 15.
    F. P. Preparata and M. I. Shamos. Computational Geometry, An Introduction. Springer-Verlag, 1985.Google Scholar
  16. 16.
    S. M. Seitz and C. R. Dyer. View morphing. In Computer Graphics (SIGGRAPH’ 96 Proceedings), pages 21–30, 1996.Google Scholar
  17. 17.
    J. Shade, S. Gortler, L. He, and R. Szeliski. Layered depth images. In Computer Graphics (SIGGRAPH’ 98 Proceedings), pages 231–242, July 1998.Google Scholar

Copyright information

© Springer-Verlag/Wien 1999

Authors and Affiliations

  • Chi-Wing Fu
    • 1
  • Tien-Tsin Wong
    • 2
  • Pheng-Ann Heng
    • 1
  1. 1.The Chinese University of Hong KongChina
  2. 2.Hong Kong University of Science and TechnologyChina

Personalised recommendations