VISUALIZATION OF 3D GRAY-TONE IMAGES - Fundamentals of Three-Dimensional Digital Image Processing - page 221

(a) Diffuse reflection

Incident light is reflected with equal intensity in all directions. This kind of
reflection is called diffuse reflection .

(a-1) Irradiation by parallel rays : When a light source is located infinitely far
away like the sun, all rays radiated from the source are regarded as parallel.
In this case, the intensity of the reflected light is given by

I = kI i cos α

(7.7)

where
I i = intensity of incident light,
I = intensity of reflected light,
α angle between the normal of a surface and the direction of the incident
light at a point P (= incident angle),
k = reflectance (index of reflection) of a surface in diffuse reflection.

(a-2) Irradiation from a point source : If a light source Q is at a definite dis-
tance from an object and its physical size is small enough compared to an
object, the source is regarded as a point source . Then, the intensity of the
reflected light I is given by

I = kI q cos α/r 2 , (7.8)

where
I q = amount of luminous intensity of a light source Q (= brightness of
a light source),
I = intensity of the reflected light at a point P,
α = angle between the surface normal and the direction of a light source
PQ,
k = reflectance (reflection index) of a surface in diffuse reflection,
r = distance between a point P and light source Q.

(b) Specular reflection

Specular reflection is intuitively known as a phenomenon that reflected light
from a surface is concentrated in a particular direction. This is observed typ-
ically in the reflection by an ideal mirror. The well-known law of the incident
and reflected light holds here. That is, the angle of incidence is equal to the
angle of reflection (Fig. 7.8 ( b )). Actually reflected light expands to some ex-
tent around the direction of the specular reflection. We will introduce here a
typical model by Eq. 7.9 (Fig. 7.8 ( c ))

I = I i k α cos n δ, (7.9)

where