International Journal of Computer Vision

, Volume 14, Issue 3, pp 227–251

Generalization of the Lambertian model and implications for machine vision

  • Michael Oren
  • Shree K. Nayar


Lambert's model for diffuse reflection is extensively used in computational vision. It is used explicitly by methods such as shape from shading and photometric stereo, and implicitly by methods such as binocular stereo and motion detection. For several real-world objects, the Lambertian model can prove to be a very inaccurate approximation to the diffuse component. While the brightness of a Lambertian surface is independent of viewing direction, the brightness of a rough diffuse surface increases as the viewer approaches the source direction. A comprehensive model is developed that predicts reflectance from rough diffuse surfaces. The model accounts for complex geometric and radiometric phenomena such as masking, shadowing, and interreflections between points on the surface. Experiments have been conducted on real samples, such as, plaster, clay, sand, and cloth. All these surfaces demonstrate significant deviation from Lambertian behavior. The reflectance measurements obtained are in strong agreement with the reflectance predicted by the proposed model. The paper is concluded with a discussion on the implications of these results for machine vision.


diffuse reflection Lambertian model surface roughness masking shadowing interreflections diffuse reflectance model qualitative model radiance measurements image rendering reflectance maps lunar reflectance shape from shading photometric stereo binocular stereo and motion 


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Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Michael Oren
    • 1
  • Shree K. Nayar
    • 1
  1. 1.Department of Computer ScienceColumbia UniversityNew York

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