Photometric Stereo under Low Frequency Environment Illumination

  • Rui Huang
  • William A. P. Smith
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6454)

Abstract

The well-studied problem of photometric stereo has almost exclusively made the assumption that illumination is provided by distant point light sources. In this paper, we consider for the first time the problem of photometric shape recovery from images in which an object is illuminated by environment lighting, i.e. where the illumination is modelled as a function over the incident sphere. To tackle this difficult problem, we restrict ourselves to low frequency illumination environments in which the lighting is known and can be well modelled using spherical harmonics. Under these conditions we show that shape recovery from one or more colour images requires only the solution of a system of linear equations. For the single image case we make use of the properties of spherical harmonics under rotations. We assume homogeneous Lambertian reflectance (with possibly unknown albedo) but discuss how the method could be extended to other reflectance models. We show that our method allows accurate shape recovery under complex illumination, even when our assumptions are breached, and that accuracy increases with the number of input images.

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References

  1. 1.
    Horn, B.K.P., Brooks, M.J.: The variational approach to shape from shading. Comput. Vis. Graph. Image Process. 33, 174–208 (1986)CrossRefMATHGoogle Scholar
  2. 2.
    Woodham, R.: Photometric method for determining surface orientation from multiple images. Optical Engineerings 19, 139–144 (1980)Google Scholar
  3. 3.
    Shashua, A.: On photometric issues in 3d visual recognition from a single 2d image. International Journal of Computer Vision 21, 99–122 (1997)CrossRefGoogle Scholar
  4. 4.
    Belhumeur, P.N., Kriegman, D.J., Yuille, A.L.: The bas relief ambiguity. Int. J. Comput. Vision 35, 33–44 (1999)CrossRefGoogle Scholar
  5. 5.
    Koenderink, J.J., Doorn, A.J.V.: The generic bilinear calibration-estimation problem. International Journal of Computer Vision 23, 1573–1605 (1997)CrossRefGoogle Scholar
  6. 6.
    Yuille, W.L., Snow, D., Belhumeur, R.E., Determining, P.: generative models of objects under varying illumination: Shape and albedo from multiple images using svdand integrability. International Journal of Computer Vision 35, 203–222 (1999)CrossRefGoogle Scholar
  7. 7.
    Langer, M.S., Zucker, S.W.: Shape-from-shading on a cloudy day. J. Opt. Soc. Am. A (11), 467–478Google Scholar
  8. 8.
    Prados, E., Jindal, N., Stefano, S.S.: A non-local approach to shape from ambient shading. In: Proc. 2nd International Conference on Scale Space and Variational Methods in Computer Vision, pp. 696–708 (2009)Google Scholar
  9. 9.
    Vogiatzis, G., Favaro, P., Cipolla, R.: Using frontier points to recover shape, refectance and illumination. In: The 10th IEEE International Conference on Computer Vision (ICCV 2005), vol. 1, pp. 228–235 (2005)Google Scholar
  10. 10.
    Georghiades, A.S.: Incorporating the torrance and sparrow model of refectance in uncalibrated photometric stereo. In: ICCV, pp. 816–823 (2003)Google Scholar
  11. 11.
    Hertzmann, A., Seitz, S.: Example-based photometric stereo: Shape reconstruction with general, varying brdfs. IEEE Trans. Pattern Analysis and Machine Intelligence (PAMI) 27, 1254–1264 (2005)CrossRefGoogle Scholar
  12. 12.
    Ragheb, H., Hancock, E.R.: A probabilistic framework for specular shape from shading. Pattern Recognit. 36, 407–427 (2003)CrossRefGoogle Scholar
  13. 13.
    Basri, R., Jacobs, D.: Photometric stereo with general unknown lighting. International Journal of Computer Vision 72, 239–257 (2007)CrossRefGoogle Scholar
  14. 14.
    Kemelmacher, I., Basri, R.: 3d face reconstruction from a single image using a single reference face shape. IEEE Transactions on Pattern Analysis and Machine Intelligence 99, 1–14 (2010)Google Scholar
  15. 15.
    Green, R.: Spherical harmonic lighting: The gritty details. In: Proceedings of the Game Developers ConferenceGoogle Scholar
  16. 16.
    Frolova, D., Simakov, D., Bastri, R.: Accuracy of spherical harmonic approximations for images of lambertian objects under far and near lighting. In: Pajdla, T., Matas, J(G.) (eds.) ECCV 2004. LNCS, vol. 3021, pp. 574–587. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  17. 17.
    Ramamoorthi, R., Hanrahan, P.: On the relationship between radiance and irradiance: determining the illumination from images of a convex lambertian object. J. Opt. Soc. Am. A, 2448–2459 (2001)Google Scholar
  18. 18.
    Ma, W.-C., et al.: Rapid acquisition of specular and diffuse normal maps from polarized spherical gradient illumination. In: Proc. EGSR (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Rui Huang
    • 1
  • William A. P. Smith
    • 1
  1. 1.University of YorkUK

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