Abstract
Recently the light-field and lumigraph systems have been proposed as general methods of representing the visual information present in a scene. These methods represent this information as a 4D function of light over the domain of directed lines. These systems use the intersection points of the lines on two planes to parameterize the lines in space. This paper explores the structure of the two-plane parameterization in detail. In particular we analyze the association between the geometry of the scene and subsets of the 4D data. The answers to these questions are essential to understanding the relationship between a lumigraph, and the geometry that it attempts to represent. This knowledge is potentially important for a variety of applications such as extracting shape from lumigraph data, and lumigraph compression.
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References
Jim Arvo. The irradiance jacobian for partially occluded polyhedral sources. In Computer Graphics, Annual Conference Series, 1994,pages 343–350.
Marilena Barnabei, Andrea Brini, and Gian-Carlo Rota. On the exterior calculus of invariant theory. Journal of Algebra, 96: 120–160, 1985.
R. C. Bolles, H. H. Baker, and D. H. Marimont. Epipolar-plané image analysis: An approach to determining structure from motion. IJCV, 1: 7–55, 1987.
Fredo Durand, George Drettakis, and Claude Puech. The 3d visibility complex, a new approach to the problems of accurate visibility. In 7th Eurographics Workshop on Rendering, 1996.
O. Faugeras and Q. T. Luong. A projective geometric approach to multiple image analysis. unpublished book in progress.
Ziv Gigus and Jitendra Malik. Computing the aspect graph for line drawings of polyhedral objects. IEEE Trans. PAMI, 12 (2): 113–122, 1990.
Steven Gortler, Radek Grzeszczuk, Richard Szeliski, and Michael F. Cohen. The lumigraph. In Computer Graphics, Annual Conference Series, 1996,pages 43–54.
P. Heckbert. Simulating global illumination using adaptive meshing. PhD thesis, The University of California at Berkeley, June 1991.
Mark Levoy and Pat Hanrahan. Light-field rendering. In Computer Graphics, Annual Conference Series, 1996,pages 31–42.
D. Sommerville. Analytical Geometry of Three Dimensions. Cambridge University Press, 1959.
Jorge Stolfi. Oriented Projective Geometry - A Framework for Geometric Computations. Academic Press, 1991.
Abraham Dean Stone. personal communication, ‘the graßman bunch’. 1997.
Seth J. Teller. Computing the antipenumbra of an area light source. Computer Graphics, 26 (2): 139–148, 1992.
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© 1997 Springer-Verlag/Wien
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Gu, X., Gortler, S.J., Cohen, M.F. (1997). Polyhedral Geometry and the Two-Plane Parameterization. In: Dorsey, J., Slusallek, P. (eds) Rendering Techniques ’97. EGSR 1997. Eurographics. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6858-5_1
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DOI: https://doi.org/10.1007/978-3-7091-6858-5_1
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