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2.2 Photometric image formation 57

Figure 2.16 This close-up of a statue shows both diffuse (smooth shading) and specular (shiny highlight) reflec-
tion, as well as darkening in the grooves and creases due to reduced light visibility and interreflections. (Photo
courtesy of the Caltech Vision Lab, http://www.vision.caltech.edu/archive.html.)

through empirical observation (Ward 1992; Westin, Arvo, and Torrance 1992; Dana, van Gin-
neken, Nayar et al. 1999; Dorsey, Rushmeier, and Sillion 2007; Weyrich, Lawrence, Lensch
6
et al. 2008). Typical BRDFs can often be split into their diffuse and specular components,
as described below.

Diffuse reflection
The diffuse component (also known as Lambertian or matte reflection) scatters light uni-
formly in all directions and is the phenomenon we most normally associate with shading,
e.g., the smooth (non-shiny) variation of intensity with surface normal that is seen when ob-
serving a statue (Figure 2.16). Diffuse reflection also often imparts a strong body color to
the light since it is caused by selective absorption and re-emission of light inside the object’s
material (Shafer 1985; Glassner 1995).
While light is scattered uniformly in all directions, i.e., the BRDF is constant,

f d (ˆv i , ˆv r , ˆn; λ)= f d (λ), (2.86)

the amount of light depends on the angle between the incident light direction and the surface
normal θ i . This is because the surface area exposed to a given amount of light becomes larger
at oblique angles, becoming completely self-shadowed as the outgoing surface normal points
away from the light (Figure 2.17a). (Think about how you orient yourself towards the sun or
fireplace to get maximum warmth and how a flashlight projected obliquely against a wall is
less bright than one pointing directly at it.) The shading equation for diffuse reflection can
thus be written as

+ +
L d (ˆv r ; λ)= L i (λ)f d (λ) cos θ i = L i (λ)f d (λ)[ˆv i · ˆn] , (2.87)
i i
6 See http://www1.cs.columbia.edu/CAVE/software/curet/ for a database of some empirically sampled BRDFs.