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60 2 Image formation

Di-chromatic reflection model

The Torrance and Sparrow (1967) model of reflection also forms the basis of Shafer’s (1985)
di-chromatic reflection model, which states that the apparent color of a uniform material lit
from a single source depends on the sum of two terms,

L r (ˆv r ; λ)= L i (ˆv r , ˆv i , ˆn; λ)+ L b (ˆv r , ˆv i , ˆn; λ) (2.94)
= c i (λ)m i (ˆv r , ˆv i , ˆn)+ c b (λ)m b (ˆv r , ˆv i , ˆn), (2.95)

i.e., the radiance of the light reflected at the interface, L i , and the radiance reflected at the sur-
face body, L b . Each of these, in turn, is a simple product between a relative power spectrum
c(λ), which depends only on wavelength, and a magnitude m(ˆv r , ˆv i , ˆn), which depends only
on geometry. (This model can easily be derived from a generalized version of Phong’s model
by assuming a single light source and no ambient illumination, and re-arranging terms.) The
di-chromatic model has been successfully used in computer vision to segment specular col-
ored objects with large variations in shading (Klinker 1993) and more recently has inspired
local two-color models for applications such Bayer pattern demosaicing (Bennett, Uytten-
daele, Zitnick et al. 2006).

Global illumination (ray tracing and radiosity)

The simple shading model presented thus far assumes that light rays leave the light sources,
bounce off surfaces visible to the camera, thereby changing in intensity or color, and arrive
at the camera. In reality, light sources can be shadowed by occluders and rays can bounce
multiple times around a scene while making their trip from a light source to the camera.
Two methods have traditionally been used to model such effects. If the scene is mostly
specular (the classic example being scenes made of glass objects and mirrored or highly pol-
ished balls), the preferred approach is ray tracing or path tracing (Glassner 1995; Akenine-
M¨ oller and Haines 2002; Shirley 2005), which follows individual rays from the camera across
multiple bounces towards the light sources (or vice versa). If the scene is composed mostly
of uniform albedo simple geometry illuminators and surfaces, radiosity (global illumination)
techniques are preferred (Cohen and Wallace 1993; Sillion and Puech 1994; Glassner 1995).
Combinations of the two techniques have also been developed (Wallace, Cohen, and Green-
berg 1987), as well as more general light transport techniques for simulating effects such as
the caustics cast by rippling water.
The basic ray tracing algorithm associates a light ray with each pixel in the camera im-
age and finds its intersection with the nearest surface. A primary contribution can then be
computed using the simple shading equations presented previously (e.g., Equation (2.93))
for all light sources that are visible for that surface element. (An alternative technique for
computing which surfaces are illuminated by a light source is to compute a shadow map,
or shadow buffer, i.e., a rendering of the scene from the light source’s perspective, and then
compare the depth of pixels being rendered with the map (Williams 1983; Akenine-M¨ oller
and Haines 2002).) Additional secondary rays can then be cast along the specular direction
towards other objects in the scene, keeping track of any attenuation or color change that the
specular reflection induces.
Radiosity works by associating lightness values with rectangular surface areas in the scene
(including area light sources). The amount of light interchanged between any two (mutually