Signal Processing - September 2016 - 72

θi
θr
(a)

(b)

Figure 3. What are these? (a) and (b) show a simple snapshot of a
material, but this material is not recognizable from the photo.
y
φi
φr

Figure 6. The BRDF (bidirectional reflectance distribution function)
(a)

(b)

Figure 4. The materials [(a) satin and (b) velvet] are easily recognizable in
these images because the reflectance from multiple angles is observable in
the folds.

f (i i , z i , i v , z v ) is the ratio of radiance from a surface point in the direction
i v , z v due to incident irradiance from direction i i , z i .

guide mobile robot navigation. In architectural applications,
creating models of existing infrastructure using photography
has become an important modern tool. Adding composition
details creates a compendious scene description with surface
labeling of material composition of built structures such as
brick, limestone, stucco, wood, stone, marble, slate, granite,
and copper.

Reflectance: Functions and fields

Figure 5. Cubes of different material composition (cork, foam, aluminum,
acrylic, maple wood, granite, bakelite resin, and silicone); Architect's Cubes
Museum of Modern Art, New York. (Photo courtesy of Kristin J. Dana.)

features. For art and archeological archiving, appearance can
be integrated in three-dimensional (3-D) models so that fine
detail such as artist brushstrokes or the translucency of a marble statue can be captured for realism. In robotics, navigation
and gripping parameters depend on surface material properties. For example, robotic control variables will be different in
mud than on marble, so the ground terrain material label can
72

According to a geometric representation of light rays, a surface
point is illuminated by an incident ray oriented by polar angle
i i and azimuth angle z i as shown in Figure 6. The reflected
light is oriented along the direction i v, z v . In a mirrored surface model, the incident light ray reflects at the air-surface
boundary in a direction that is rotated 180° about the surface
normal. For nonmirrored surfaces, a typical modelling
approach is to divide reflectance into specular (mirror-like) and
diffuse components. In these reflectance models, the specular
component of the light intensity is maximal when the viewer is
at the mirror reflection direction, but then falls off according to
a parametric model as the viewer direction moves away from
the peak direction. For example, in the computer graphics
Phong reflection model [7], the intensity falls off as cos n a,
where a is the angle between the mirror reflection direction
and the observer direction and n is a parameter. A diffuse component of the reflection specified by the Lambertian model is
independent of observer direction and is proportional to cos i i,
where i i is the angle the incident light ray makes with the surface normal. The advantage of analytical models of reflectance
is the low number of parameters that can be used to describe
appearance. The disadvantage is the lack of descriptive power
of such models. For real-world surfaces, a portion of the light is
transmitted into the surface, scatters within the surface, is

IEEE SIgnal ProcESSIng MagazInE

September 2016

Table of Contents for the Digital Edition of Signal Processing - September 2016