Oren-Nayar Reflectance Model

Most reflectance mechanisms can be broadly classified into two categories: diffuse and specular. In computer vision and computer graphics, the diffuse component is often assumed to be Lambertian; a surface that obeys Lambert's Law appears equally bright from all viewing directions. This model for diffuse reflection was proposed by Lambert over 200 years ago and has been perhaps the most widely used reflectance model in vision and graphics.

For several real-world surfaces, however, the Lambertian model can prove to be a poor and inadequate approximation of the diffuse component. The deviation from Lambertian behavior can be significant for a variety of real materials such as concrete, plaster, sand, etc. The primary reason for this deviation is the roughness of the surface. We have developed a comprehensive model for diffuse reflectance that can be viewed as a generalization of Lambert's Law. The model is valid for a wide range of surface roughness values and takes into account complex geometrical effects such as masking, shadowing and interreflections between points on the rough surface. Extensive experiments have been conducted by the CAVE laboratory as well as other research groups to verify the accuracy of the model. Today, the Oren-Nayar model is frequently used in the creation of animations and special effects in movies. The model is available in most commercial rendering software such 3ds Max from Autodesk (formerly Discreet), Maya from Alias and Renderman from Pixar.


"Bidirectional Reflectance Distribution Function of Thoroughly Pitted Surfaces,"
J.J. Koenderink, A.J. Van Doorn, K.J. Dana and S.K. Nayar,
International Journal on Computer Vision,
Vol.31, No.2/3, pp.129-144, Apr, 1999.
[PDF] [bib] [©]

"Reflectance and Texture of Real World Surfaces,"
K.J. Dana, B. Van-Ginneken, S.K. Nayar, J.J. Koenderink,
ACM Transactions on Graphics (TOG),
Vol.18, No.1, pp.1-34, Jan, 1999.
[PDF] [bib] [©]

"Generalization of the Lambertian Model and Implications for Machine Vision,"
S.K. Nayar and M. Oren,
International Journal on Computer Vision,
Vol.14, No.3, pp.227-251, Apr, 1995.
[PDF] [bib] [©]

"Visual Appearance of Matte Surfaces,"
S.K. Nayar and M. Oren,
Vol.267, pp.1153-1156, Feb, 1995.
[PDF] [bib] [©]

"Generalization of Lambert's Reflectance Model,"
M. Oren and S.K. Nayar,
ACM 21st Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH),
pp.239-246, Jul, 1994.
[PDF] [bib] [©]

"Seeing Beyond Lambert\'s Law,"
M. Oren and S.K. Nayar,
European Conference on Computer Vision (ECCV),
Vol.B, pp.269-280, May, 1994.
[PDF] [bib] [©]

"Diffuse Reflectance from Rough Surfaces,"
M. Oren and S.K. Nayar,
IEEE Conference on Computer Vision and Pattern Recognition (CVPR),
pp.763-764, Jun, 1993.
[PDF] [bib] [©]

"Surface Reflection: Physical and Geometrical Perspectives,"
S.K. Nayar, K.Ikeuchi and T. Kanade,
IEEE Transactions on Pattern Analysis and Machine Intelligence,
Vol.13, No.7, pp.611-634, Jul, 1991.
[PDF] [bib] [©]


  Porcelain Cylinders:

Left: Camera image of two cylinders made from exactly the same material (porcelain) and illuminated from approximately 10 degrees above the camera. The right vase is much rougher than the left one resulting in a flatter appearance. Right: Synthetic image of cylinders with similar dimensions, rendered using the Oren-Nayar model (left cylinder roughness = 5 degrees, right cylinder roughness = 35 degrees).

  Roughness Causes Flatness:

The model and experiments suggest that for very high macroscopic roughness, when source and sensor directions are close to one another, all surface normals generate the same image brightness. Alternately, any object, irrespective of its three-dimensional shape, produces just a silhouette making it impossible to perceive its shape. In this picture three spheres are illuminated and viewed from the same direction. As roughness increases (left to right) the shading becomes flatter. For extreme roughness, the sphere appears like a flat disc, as observed in the case of the full moon.



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  Full Moon:

This video clip shows a Nike speculation shot created by Director Ania Hoffman and the special effects firm A52. The full moon in this clip is rendered using the Oren-Nayar model. Courtesy of A52. (With audio)



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