Skip to main content
SpringerLink
Log in

Integrability disambiguates surface recovery in two-image photometric stereo

  • Published:
International Journal of Computer Vision Aims and scope Submit manuscript

Abstract

Two images of a Lambertian surface obtained under different illumination conditions, determine the local surface normals up to two possible orientations. We show that for smooth surfaces, the local integrability constraints usually resolve the problem of deciding between the two possibilities. We also provide a complete characterization of the surfaces that remain ambiguous under given illumination conditions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • D.H. Ballard and C.M. Brown, Computer Vision. Prentice Hall: Englewood Cliffs, NH, 1982.

    Google Scholar 

  • A.M. Bruckstein, “On shape from shading methods,” Comp. Vision, Graphics Image Process. 44: 139–154, 1988.

    Google Scholar 

  • M.P. Do Carmo, Differential Geometry of Curves and Surfaces, Prentice Hall: Englewood Cliffs, NJ 1976.

    Google Scholar 

  • B.K.P. Horn, “Obtaining shape from shading information.” In P.H. Winston (ed), The Psychology of Computer Vision, pp. 115–155, McGraw-Hill: New York, 1975.

    Google Scholar 

  • B.K.P. Horn, “Understanding image intensities,” Artificial Intelligence, 8: 201–231, 1977.

    Google Scholar 

  • B.K.P. Horn, “Hill shading and the reflectance map,” Proc IEEE, (1):1981.

  • B.K.P. Horn and M.J. Brooks, “The variational approach to shape from shading,” Comp. Vision, Graphics Image Processing. 33: 174–203, 1986.

    Google Scholar 

  • K. Ikeuchi and B.K.P. Horn, “Numerical shape from shading and occluding boundaries,” Artificial Intelligence 17:141–184, 1981.

    Google Scholar 

  • K. Ikeuchi, “Determining a depth map using dual photometric stereo,” Intern Robotics Res. (1), 1987.

  • D. Marr Vision. Freeman: San Francisco, 1982.

    Google Scholar 

  • T.C. Pong, R.M. Haralick, and L.G. Shapiro, “The facet approach to shape from shading,” Proc 2nd Workshop Comp. Vision: Representation and Control, Annapolis, Maryland, April 30–May 2, 1984.

  • A. Rosenfeld and A. Kak, Digital Picture Processing, vols. 1 and 2 Academic Press: San Diego, CA, 1982.

    Google Scholar 

  • R.J. Woodham, “Photometric method for determining surface orientation from multiple images,” Optical Engineering, (1) 139–144, 1980.

  • R.J. Woodham, “Analysing images of curved surfaces,” Artificial Intelligence 17: 117–140, 1981.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Cornell University, 14853, Ithaca, NY, U.S.A.

    Ruth Onn

  2. Department of Computer Science, Technion, IIT, Haifa, Israel

    Alfred Bruckstein

Authors
  1. Ruth Onn
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alfred Bruckstein
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Onn, R., Bruckstein, A. Integrability disambiguates surface recovery in two-image photometric stereo. Int J Comput Vision 5, 105–113 (1990). https://doi.org/10.1007/BF00056773

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00056773

Keywords

Search

Navigation