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function the
lumigraph
; Levoy and Hanrahan call it the
light field
. The latter is
used here.
4
The light field is a general representation not limited to IBR, and has been used
in other areas of CG rendering (see Sections 8.2 and 10.5). In fact, a new research
field of
computational photography
[Raskar and Tumbin 09] was inspired largely
by the light field. One drawback of the light field, though, is that it requires a lot of
space—representing the light field for a scene of medium complexity can require
gigabytes of storage. To mitigate this, compression schemes were investigated in
the original papers.
5.4.1 Definition of the Light Field
As noted earlier, the plenoptic function describes the optical character of an en-
vironment by providing the radiance in every direction at each point in space, at
each wavelength of light and each instant of time. The function thus has seven
parameters; however, assuming a static scene and using a typical three-channel
color representation reduces this to a 5D function
P
where
s
and
t
are
the viewing direction parameters (
Figure 5.16(a)
). Another dimensional reduc-
tion results from assuming there is no participating medium, which means that
the radiance is constant along line segments in space. The plenoptic function thus
reduces to a radiance function of position and direction on object surfaces, which
could be stored as part of the geometric model. However, the authors wanted a
representation independent of geometry, so they instead considered the plenop-
tic function as a function on lines in space. The
light field
(lumigraph) formally
refers to this function, although the term is also used for the 5D function and other
variants. An image of the environment from an arbitrary viewpoint is a 2D slice
of this function.
The light field is represented as a large collection of samples on lines in space.
How these lines are represented is critical to the success of the representation.
Both papers use the same general approach to parametrize lines: given two fixed
planes, a line is uniquely represented by the coordinates
(
x
,
y
,
z
,
s
,
t
)
(
u
,
v
)
in one plane, and
(
in the other
(
Figure 5.16(b)
)
. Intuitively,
u
and
v
might be regarded as the
positional parameters, and
s
and
t
the directional parameters for each
s
,
t
)
(
,
)
,but
the view position can be arbitrary and neither plane is necessarily an “image”
plane. Levoy and Hanrahan refer to the collection of lines between these two
planes, limited to 0
u
v
1, as a
light slab
. A light slab is thus the set
of all lines between points in two rectangles (or general quadrilaterals) in space.
≤
u
,
v
,
s
,
t
≤
4
Although both terms refer to essentially the same thing, and the papers are considered to be
equally excellent, “light field” seems to be the name that has stuck. The term “light field” was actually
coined in a 1936 paper by Alexander Gershun, referring to what is now called the vector irradiance.
