OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 18, Iss. 8 — Aug. 1, 2001
  • pp: 1804–1813

What shadows reveal about object structure

David J. Kriegman and Peter N. Belhumeur  »View Author Affiliations


JOSA A, Vol. 18, Issue 8, pp. 1804-1813 (2001)
http://dx.doi.org/10.1364/JOSAA.18.001804


View Full Text Article

Enhanced HTML    Acrobat PDF (318 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

In a scene observed from a fixed viewpoint, the set of shadow boundaries 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 bas-relief (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 both an object’s surface and the light source locations up to this family of transformations from the shadows alone.

© 2001 Optical Society of America

OCIS Codes
(150.0150) Machine vision : Machine vision
(150.2950) Machine vision : Illumination
(330.7310) Vision, color, and visual optics : Vision

History
Original Manuscript: May 5, 2000
Revised Manuscript: January 2, 2001
Manuscript Accepted: January 2, 2001
Published: August 1, 2001

Citation
David J. Kriegman and Peter N. Belhumeur, "What shadows reveal about object structure," J. Opt. Soc. Am. A 18, 1804-1813 (2001)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-18-8-1804


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. D.L. Waltz, “Understanding line drawings of scenes with shadows,” in The Psychology of Computer Vision,P. H. Winston, ed. (McGraw-Hill, New York, 1975), pp. 19–91.
  2. S. Shafer, T. Kanade, “Using shadows in finding surface orientation,” Comput. Vision Graph. Image Process. 22, 145–176 (1983). [CrossRef]
  3. L. N. Hambrick, M. H. Loew, R. L. Carroll, “The entry–exit method of shadow boundary segmentation,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-9, 597–607 (1987). [CrossRef]
  4. M. Hatzitheodorou, “The derivation of 3-D surface shape from shadows,” in Proceedings of the Image Understanding Workshop (Morgan Kaufmann, Los Altos, Calif., 1989), pp. 1012–1020.
  5. J. R. Kender, E. M. Smith, “Shape from darkness,” in International Conference on Computer Vision (Morgan Kaufmann, Los Altos, Calif., 1987), pp. 539–546.
  6. D. Yang, J. R. Kender, “Shape from shadows under error,” in Proceedings of the Image Understanding Workshop (Morgan Kaufmann, Los Altos, Calif., 1993), pp. 1083–1090.
  7. M. Daum, G. Dudek, “On 3-D surface reconstruction using shape from shadows,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 1998), pp. 461–468.
  8. F. Cheng, K. H. Thiel, “Delimiting the building heights in a city from the shadow in a panchromatic spot-image. 1 test of 42 buildings,” Int. J. Remote Sens. 16, 409–415 (1995). [CrossRef]
  9. A. Huertas, R. Nevatia, “Detection of buildings in aerial images using shape and shadows,” in Proceedings of the International Joint Conference on Artificial Intelligence (Morgan Kaufmann, San Francisco, Calif., 1983), pp. 1099–1103.
  10. R. B. Irvin, D. M. McKeown, “Methods for exploiting the relationship between buildings and their shadows in aerial imagery,” IEEE Trans. Syst. Man Cybern. 19, 1564–1575 (1989). [CrossRef]
  11. G. G. Medioni, “Obtaining 3-D from shadows in aerial images,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 1983), pp. 73–76.
  12. P. Belhumeur, D. Kriegman, A. Yuille, “The bas-relief ambiguity,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 1997), pp. 1040–1046.
  13. D. Kriegman, P. Belhumeur, “What shadows reveal about object structure,” in Proceedings of the European Conference on Computer Vision (Springer, Berlin, 1998), pp. 399–414.
  14. M. S. Langer, S. W. Zucker, “What is a light source?” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 1997), pp. 172–178.
  15. J. Mundy, A. Zisserman, Geometric Invariance in Computer Vision (MIT Press, Cambridge, Mass., 1992).
  16. M. Baxandall, Shadows and Enlightenment (Yale U. Press, New Haven, Conn., 1995).
  17. A. Shashua, “Geometry and photometry in 3D visual recognition,” Ph.D. thesis (Massachusetts Institute of Technology, Cambridge, Mass., 1992).
  18. O. Faugeras, Three Dimensional Computer Vision (MIT Press, Cambridge, Mass., 1993).
  19. A. Criminisi, I. Reid, A. Zisserman, “Duality, rigidity and planar parallax,” in Proceedings of the European Conference on Computer Vision (Springer, Berlin, 1998), Vol. II, pp. 846–861.
  20. J. J. Koenderink, A. J. Van Doorn, “Affine structure from motion,” J. Opt. Soc. Am. A 8, 377–385 (1991). [CrossRef] [PubMed]
  21. R. Rosenholtz, J. J. Koenderink, “Affine structure and photometry,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 1996), pp. 18–20.
  22. L. S. Shapiro, A. Zisserman, M. Brady, “3D motion recovery via affine epipolar geometry,” Int. J. Comput. Vis. 16, 147–182 (1995). [CrossRef]
  23. S. Ullman, R. Basri, “Recognition by a linear combination of models,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 992–1006 (1991). [CrossRef]
  24. O. Faugeras, “Stratification of 3-D vision: projective, affine, and metric representations,” J. Opt. Soc. Am. A 12, 465–484 (1995). [CrossRef]
  25. C. Fermuller, Y. Aloimonos, “Ordinal representations of visual space,” in Proceedings of the Image Understanding Workshop (Morgan Kaufmann, San Francisco, Calif., 1996), pp. 897–904.
  26. P. N. Belhumeur, D. J. Kriegman, A. L. Yuille, “The bas-relief ambiguity,” Int. J. Comput. Vis. 35, 33–44 (1999). [CrossRef]
  27. M. P. DoCarmo, Differential Geometry of Curves and Surfaces (Prentice-Hall, Englewood Cliffs, N.J., 1976).
  28. L. Donati, N. Stolfi, “Singularities of illuminated surfaces,” Int. J. Comput. Vision 23, 207–216 (1997). [CrossRef]
  29. E. Artin, Geometric Algebra (Interscience, New York, 1957).
  30. P. N. Belhumeur, D. J. Kriegman, “What is the set of images of an object under all possible lighting conditions,” in Proceedings of the IEEE Conference on Computer Visionand Pattern Recognition (IEEE Computer Science Press, Los Alamitos, Calif., 1996), pp. 270–277.
  31. J. Fan, L. B. Wolff, “Surface curvature and shape reconstruction from unknown multiple illumination and integrability,” Comput. Vision Image Underst. 65, 347–359 (1997). [CrossRef]
  32. P. Breton, S. W. Zucker, “Shadows and shading flow fields,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE Computer Society Press, Los Alamitos, Calif., 1996), pp. 782–789.
  33. C. Jiang, M. O. Ward, “Shadow segmentation and clas-sification in a constrained environment,” CVGIP: Graph. Models Image Process. 59, 213–225 (1994). [CrossRef]
  34. A. P. Witkin, “Intensity-based edge classification,” in Proceedings of the American Association for Artificial Intelligence (AIII Press, Menlo Park, Calif., 1982), pp. 36–41.
  35. H. von Helmholtz, Treatise on Physiological Optics (Dover, New York, 1925).
  36. J. J. Koenderink, A. J. van Doorn, “Geometry of binocular vision and a model for stereopsis,” Biol. Cybern. 21, 29–35 (1976). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited