Generalizing Lambert's Law for smooth surfaces

  • Lawrence B. Wolff
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1065)


One of the most common assumptions for recovering object features in computer vision and rendering objects in computer graphics is that diffuse reflection from materials is Lambertian. This paper shows that there is significant deviation from Lambertian behavior in diffuse reflection from smooth surfaces not predicted by existing reflectance models, having an important bearing on any computer vision technique that may utilize reflectance models including shape-from-shading and binocular stereo. Contrary to prediction by Lambert's Law, diffuse reflection from smooth surfaces is significantly viewpoint dependent, and there are prominent diffuse reflection maxima effects occurring on objects when incident point source illumination is greater than 50‡ relative to viewing including the range from 90‡ to 180‡ where the light source is behind the object with respect to viewing. Presented here is a diffuse reflectance model, derived from first physical principles, utilizing results of radiative transfer theory for subsurface multiple scattering together with Fresnel attenuation and Snell refraction at a smooth air-dielectric surface boundary. A number of experimental results are presented demonstrating striking deviation from Lambertian behavior predicted by the proposed diffuse reflectance model.


Diffuse Reflection Dielectric Surface Reflectance Model Single Scattering Albedo Photometric Stereo 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Lawrence B. Wolff
    • 1
  1. 1.Computer Vision Laboratory, Department of Computer ScienceThe Johns Hopkins UniversityBaltimore

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