3D graphics eBook - Course Materials Repository

OrenNayar reflectance model 89
Analysis of this phenomenon has a long history and can
be traced back almost a century. Past work has resulted
in empirical models designed to fit experimental data as
well as theoretical results derived from first principles.
Much of this work was motivated by the
non-Lambertian reflectance of the moon.
The Oren-Nayar reflectance model, developed by
Michael Oren and Shree K. Nayar in 1993 [1] , predicts
reflectance from rough diffuse surfaces for the entire
hemisphere of source and sensor directions. The model
takes into account complex physical phenomena such
as masking, shadowing and interreflections between
points on the surface facets. It can be viewed as a
generalization of Lambert’s law. Today, it is widely
used in computer graphics and animation for rendering
rough surfaces. It also has important implications for
human vision and computer vision problems, such as
shape from shading, photometric stereo, etc.
Formulation
The surface roughness model used in the
derivation of the Oren-Nayar model is the
microfacet model, proposed by Torrance
and Sparrow [2] , which assumes the surface
to be composed of long symmetric
V-cavities. Each cavity consists of two
planar facets. The roughness of the surface
is specified using a probability function for
the distribution of facet slopes. In particular,
the Gaussian distribution is often used, and
thus the variance of the Gaussian
distribution, , is a measure of the
roughness of the surfaces (ranging from 0 to
1).
In the Oren-Nayar reflectance model, each
facet is assumed to be Lambertian in
Aggregation of the reflection from rough surfaces
Diagram of surface reflection
reflectance. As shown in the image at right, given the radiance of the incoming light , the radiance of the
reflected light , according to the Oren-Nayar model, is
where
,
,