Graphics Reference
In-Depth Information
θ
y
+
π
θ
x
r
r
-
π
(b)
Figure 5.17
Line space in 2D. (a) Each (directed) line is uniquely represented by its distance to the
origin and the angle it makes with the
x
-axis. (b) The corresponding point in the space
of 2D lines, which is an infinite strip along the
r
-axis bounded by
±
π. (After [Levoy and
Hanrahan 96].)
(a)
The light field is a function on the space of lines. A 2D line in the plane can
be uniquely represented with two parameters:
the distance
r
to the origin and
the angle
the line makes with the
x
-axis (
Figure 5.17(a)
)
. So 2D lines are in
one-to-one correspondence with points in the infinite strip of the
r
θ
θ
-plane, with
−
π
<
θ
≤
π
(
Figure 5.17(b)
)
. This is a 2D “line space.” The pair of planes of a
light slab reduce to a pair of line segments in the 2D case; a 2D light slab consists
of all lines through each segment in the pair. Figure 5.18(a) shows the set of lines
resulting from a discrete number of parameter samples in one 2D light slab. The
points in line space (the
r
-plane) corresponding to these lines in 2D are shown
Figure 5.18(b). The distribution is not very uniform. Figure 5.18(c) and (d) shows
a collection of four different 2D light slabs, arranged to cover a square, and the
corresponding sample distribution in line space. A 3D version of this arrangement
was used to represent the light field of a small toy lion in Levoy and Hanrahan's
paper.
The storage required for the samples is proportional to the fourth power of the
number of samples in each parameter (although the parameters are not discretized
in the same way). Consequently, the storage requirements for a light field get very
large. For example, the toy-lion model light field required 402 MB. However, the
data has a fair amount of coherency and is therefore amenable to compression.
Levoy and Hanrahan used a two-stage compression algorithm. In the first stage,
the light slabs are tiled into “vectors” of data. These are then quantized into a
smaller set of representative vectors and coded using a lossy compression algo-
rithm that facilitates fast lookup of compressed vectors via a “codebook.” Each
tile thus reduces to an index known as a “codeword” into the quantized vectors in
the codebook. This stage of the compression reduces the storage requirements to
θ
