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What shadows reveal about object structure

  • David J. Kriegman
  • Peter N. Belhumeur
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1407)

Abstract

In a scene observed from a fixed viewpoint, the set of shadow curves in an image changes as a point light source (nearby or at infinity) assumes different locations. We show that for any finite set of point light sources illuminating an object viewed under either orthographic or perspective projection, there is an equivalence class of object shapes having the same set of shadows. Members of this equivalence class differ by a four parameter family of projective transformations, and the shadows of a transformed object are identical when the same transformation is applied to the light source locations. Under orthographic projection, this family is the generalized basrelief (GBR) transformation, and we show that the GBR transformation is the only family of transformations of an object's shape for which the complete set of imaged shadows is identical. Finally, we show that given multiple images under differing and unknown light source directions, it is possible to reconstruct an object up to these transformations from the shadows alone.

Keywords

Light Source Projective Transformation Perspective Projection Cast Shadow Point Light Source 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    E. Artin. Geometric Algebra. Interscience Publishers, Inc., New York, 1957.zbMATHGoogle Scholar
  2. 2.
    M. Baxandall. Shadows and Enlightenment. Yale University Press, New Haven, 1995.Google Scholar
  3. 3.
    P. Belhumeur, D. Kriegman, and A. Yuille. The bas-relief ambiguity. In Proc. IEEE Conf. on Comp. Vision and Patt. Recog., pages 1040–1046, 1997.Google Scholar
  4. 4.
    P. N. Belhumeur and D. J. Kriegman. What is the set of images of an object under all possible lighting conditions. In Proc. IEEE Conf. on Comp. Vision and Patt. Recog., pages 270–277, 1996.Google Scholar
  5. 5.
    P. Breton and S. Zucker. Shadows and shading flow fields. In CVPR96, pages 782–789, 1996.Google Scholar
  6. 6.
    F. Cheng and K. Thiel. Delimiting the building heights in a city from the shadow in a panchromatic spot-image. 1 test of 42 buildings. JRS, 16(3):409–415, Feb. 1995.Google Scholar
  7. 7.
    B. F. Cook. The Elgin Marbles. Harvard University Press, Cambridge, 1984.Google Scholar
  8. 8.
    L. Donati and N. Stolfi. Singularities of illuminated surfaces. Int. J. Computer Vision, 23(3):207–216, 1997.CrossRefGoogle Scholar
  9. 9.
    O. Faugeras. Stratification of 3-D vision: Projective, affine, and metric representations. J. Opt. Soc. Am. A, 12(7):465–484, 1995.Google Scholar
  10. 10.
    C. Fermuller and Y. Aloimonos. Ordinal representations of visual space. In Proc. Image Understanding Workshop, pages 897–904, 1996.Google Scholar
  11. 11.
    L. Hambrick, M. Loew, and R. Carroll, Jr. The entry-exit method of shadow boundary segmentation. PAMI, 9(5):597–607, September 1987.Google Scholar
  12. 12.
    M. Hatzitheodorou. The derivation of 3-d surface shape from shadows. In Proc. Image Understanding Workshop, pages 1012–1020, 1989.Google Scholar
  13. 13.
    A. Huertas and R. Nevatia. Detection of buildings in aerial images using shape and shadows. In Proc. Int. Joint Conf. on Art. Intell., pages 1099–1103, 1983.Google Scholar
  14. 14.
    R. Irvin and D. McKeown. Methods for exploiting the relationship between buildings and their shadows in aerial imagery. IEEE Systems, Man, and Cybernetics, 19(6):1564–1575, 1989.CrossRefGoogle Scholar
  15. 15.
    M. Kemp, editor. Leonardo On Painting. Yale University Press, New Haven, 1989.Google Scholar
  16. 16.
    M. Kemp. The Science of Art: Optical Themes in Western Art from Brunelleschi to Seurat. Yale University Press, New Haven, 1990.Google Scholar
  17. 17.
    J. Kender and E. Smith. Shape from darkness. In Int. Conf. on Computer Vision, pages 539–546, 1987.Google Scholar
  18. 18.
    J. Koenderink and A. Van Doom. Affine structure from motion. JOSA-A, 8(2):377–385, 1991.CrossRefGoogle Scholar
  19. 19.
    M. Langer and S. Zucker. What is a light source? In Proc. IEEE Conf. on Comp. Vision and Patt. Recog., pages 172–178, 1997.Google Scholar
  20. 20.
    G. Medioni. Obtaining 3-d from shadows in aerial images. In CVPR83, pages 73–76, 1983.Google Scholar
  21. 21.
    J. Mundy and A. Zisserman. Geometric invariance in computer vision. MIT Press, 1992.Google Scholar
  22. 22.
    R. Rosenholtz and J. Koenderink. Affine structure and photometry. In Proc. IEEE Conf. on Comp. Vision and Patt. Recog., pages 790–795, 1996.Google Scholar
  23. 23.
    S. Shafer and T. Kanade. Using shadows in finding surface orientation. Comp. Vision, Graphics, and Image Proces., 22(1):145–176, 1983.CrossRefGoogle Scholar
  24. 24.
    L. Shapiro, A. Zisserman, and M. Brady. 3D motion recovery via affine epipolar geometry. Int. J. Computer Vision, 16(2):147–182, October 1995.CrossRefGoogle Scholar
  25. 25.
    A. Shashua. Geometry and Photometry in 3D Visual Recognition. PhD thesis, MIT, 1992.Google Scholar
  26. 26.
    S. Ullman and R. Basri. Recognition by a linear combination of models. IEEE Trans. Pattern Anal. Mach. Intelligence, 13:992–1006, 1991.CrossRefGoogle Scholar
  27. 27.
    D. L. Waltz. Understanding line drawings of scenes with shadows. In P. Winston, editor, The Psychology of Computer Vision, pages 19–91. McGraw-Hill, New York, 1975.Google Scholar
  28. 28.
    A. Witkin. Intensity-based edge classification. In Proc. Am. Assoc. Art. Intell., pages 36–41, 1982.Google Scholar
  29. 29.
    D. Yang and J. Kender. Shape from shadows under error. In Proc. Image Understanding Workshop, pages 1083–1090, 1993.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • David J. Kriegman
    • 1
  • Peter N. Belhumeur
    • 1
  1. 1.Center for Computional Vision and ControlYale UniversityNew Haven

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