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Local shape approximation from shading

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Abstract

Shading can be used as an independent cue for exact shape recovery, or it can be used as a supplementary cue for shape interpolation between features whose depths are known from other cues. Exact shape cannot be inferred from a local analysis of shading. However, for shape interpolation a crude local approximation may be sufficient. This paper explores the limits of such local approximations that are easy to compute. In particular, the shape of shading is used to approximate the surface in areas of monotonic change of intensity. This analysis is accompanied by a method for computing the direction of a single-point light source from the shading on occluding contours. A qualitative classification of shape near shading singularities is also discussed.

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References

  1. P.J. Besl and R.C. Jain, “Invariant surface characteristics for 3D object recognition in range images,”Comput. Vis., Graph., Image Process., vol. 33, pp. 33–80, 1986.

    Google Scholar 

  2. T.O. Binford, “Generalized cylinders representation,” inEncyclopedia of Artificial Intelligence S.C. Shapiro, ed., Wiley: New York, 1987, pp. 321–323.

    Google Scholar 

  3. A. Blake, A. Zisserman, and G. Knowles, “Surface descriptions from stereo and shading,” inShape from Shading, B.K.P. Horn and M.J. Brooks, eds., MIT Press: Cambridge, MA, 1989, pp. 29–52.

    Google Scholar 

  4. M.J. Brady, “Criteria for representations of shape,” inHuman and Machine Vision, J. Beck, B. Hope, and A. Rosenfeld, eds., Academic Press: New York, 1983, pp. 39–84.

    Google Scholar 

  5. M.J. Brooks and B.K.P. Horn, “Shape and source from shading,” inShape from Shading, B.K.P. Horn and M.J. Brooks, eds., MIT Press: Cambridge, MA, 1989, pp. 53–68.

    Google Scholar 

  6. H.H. Bülthoff and H.A. Mallot, “Interaction of depth modules: stereo and shading,”J. Opt. Soc. Am. vol. 5, pp. 1749–1758, 1988.

    Google Scholar 

  7. J.F. Canny, “A computational approach to edge detection,”IEEE Trans. Patt. Anal. Mach. Intell. vol. PAMI-8, pp. 679–698, 1986.

    Google Scholar 

  8. M.P. DoCarmo,Differential Geometry of Curves and Surfaces, Prentice-Hall: Englewood Cliffs, NJ, 1976.

    Google Scholar 

  9. G.J. Ettinger, “Large hierarchical object recognition using libraries of parametrized model sub-parts,” inProc. IEEE 2nd International Conference on Computer Vision, Tarpon Springs, FL, 1988, pp. 32–41.

    Google Scholar 

  10. F.P. Ferrie and M.D. Levine, “Where and why local shading analysis works,”IEEE Trans. Patt. Anal. Mach. Intell. vol. PAMI-11, pp. 198–206, 1989.

    Google Scholar 

  11. D. Forsyth and A. Zisserman, “Mutual illumination,” inProc. IEEE Conference on Computer Vision and Pattern Recognition, San Diego, CA, 1989, pp. 466–473.

  12. B.K.P. Horn,Robot Vision, MIT Press: Cambridge, MA, 1986.

    Google Scholar 

  13. B.K.P. Horn, “Height and gradient from shading,”Int. J. Comput. Vis. vol. 5, pp. 37–75, 1990.

    Google Scholar 

  14. K. Ikeuchi and B.K.P. Horn, “Numerical shape from shading and occluding boundaries,”Artif. Intell., vol. 15, pp. 141–184, 1981.

    Google Scholar 

  15. J.J. Koenderink, “What does the occluding contour tell us about solid shape?”Perception, vol. 13, pp. 321–330, 1984.

    Google Scholar 

  16. J.J. Koenderink and A.J. van Doorn, “The Internal representation of solid shape with respect to vision,”Biol. Cybernet., vol. 32, pp. 211–217, 1979.

    Google Scholar 

  17. J.J. Koenderink and A.J. van Doorn, “Photometric invariants related to solid shape,”Opt. Acta, vol. 27, pp. 981–996, 1980.

    Google Scholar 

  18. C.-H. Lee and A. Rosenfeld, “Improved methods of estimating shape from shading using the light source coordinate system,” inShape from Shading, B.K.P. Horn and M.J. Brooks, eds., MIT Press: Cambridge, MA, 1989, pp. 323–348.

    Google Scholar 

  19. E. Mingolla and J.T. Todd, “Perception of solid shape from shading,”Biol. Cybernet., vol. 53, pp. 137–151, 1986.

    Google Scholar 

  20. V.S. Nalwa, “Representation oriented piecewise c2 surfaces,” inProc. IEEE 1st International Conference on Computer Vision, 1987, pp. 40–51.

  21. S.K. Nayar, K. Ikeuchi, and T. Kanade, “Shape from interreflections,”Int. J. Comput. Vis., vol. 6, pp. 173–195, 1991.

    Google Scholar 

  22. J. Oliensis, “Uniqueness in shape from shading,”Int. J. Comput. Vis., to be published.

  23. A. Pentland, “Shape information from shading: a theory about human perception,” inProc. IEEE 2nd International Conference on Computer Vision, Tarpon Springs, FL, 1988, pp. 404–413.

    Google Scholar 

  24. A.P. Pentland, “Local shading analysis,” inFrom Pixels to Predicates, A.P. Pentland, ed., Ablex: New Jersey, 1986, pp. 40–77.

    Google Scholar 

  25. S.A. Shafer and T. Kanade, “Using shadows in finding surface orientation,”Comput. Vis., Graph., Image Process. vol. 22, pp. 145–176, 1983.

    Google Scholar 

  26. R. Szeliski, “Fast shape from shading,”Comput. Vis., Graph., Image Process., vol. 53, pp. 129–153, 1991.

    Google Scholar 

  27. J.T. Todd and F.D. Reichel, “Ordinal structure in the visual perception and cognition of smoothly curved surfaces,”Psychol. Rev., vol. 96, pp. 643–657, 1989.

    Google Scholar 

  28. B.C. Vemuri, A. Mitiche, and J.K. Aggrawal, “Curvaturebased representation of objects from range data,”Image Vis. Comput., vol. 4, pp. 107–114, 1986.

    Google Scholar 

  29. D. Weinshall, “Direct computation of qualitative 3D shape and motion invariants,”IEEE Trans. Patt. Anal. Mach. Intell., vol. PAMI-13, pp. 1236–1240, 1991.

    Google Scholar 

  30. I. Weiss, “Projective invariants of shapes,” inProc. IEEE Conference on Computer Vision and Pattern Recognition, 1988, pp. 291–297.

  31. L.B. Wolff, “A photometric invariant and shape constraints at parabolic points,” inProc. IEEE 3rd International Conference on Computer Vision, Osaka, Japan, 1990, pp. 344–349.

  32. R.J. Woodham, “Photometric method for determining surface orientation from multiple images,”Opt. Eng., vol. 19, pp. 139–144, 1980.

    Google Scholar 

  33. A.L. Yuille, “Zero crossings on lines of curvature,”Comput. Vis., Graph., Image Process., vol. 45, pp. 68–87, 1989.

    Google Scholar 

  34. Q. Zheng and R. Chellappa, “Estimation of illuminant direction, albedo, and shape from shading,”IEEE Trans. Patt. Anal. Mach. Intell., vol. PAMI-13, pp. 680–702, 1991.

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, Hebrew University of Jerusalem, 91904, Jerusalem, Israel

    Daphna Weinshall

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  1. Daphna Weinshall
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Additional information

This work was performed at the Massachusetts Institute of Technology, Center for Biological Information Processing.

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Weinshall, D. Local shape approximation from shading. J Math Imaging Vis 4, 119–138 (1994). https://doi.org/10.1007/BF01249892

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