Graphics Reference
In-Depth Information
“snapped” to the closest representative. Vector quantization is frequently used for
compression of light field data.
PCA (principal component analysis).
In this method, all the signal vectors
over the whole region are approximated by a linear combination of a few basis
vectors. The signal vectors are replaced by their projection coefficients, which are
computed by projecting the vectors onto each basis vector. Calculations involving
signals on the region are replaced by calculations with the projection coefficients,
which can make computations involving signals more efficient. This technique
is used for compression and approximation of data in IBR and BTF rendering in
several methods described in this topic. Figure 9.18 illustrates the approach on a
surface signal.
M
p
M
0
=M
p
M
1
M
p
: Signal at point
p
M
0
: Center vector
M
i
:
i
th
basis vector
Figure 9.18
Principal Component Analysis (PCA). The set of signal vectors are shifted by the mean
(
M
0
) and the best vectors approximating the shifted vectors are selected. In this example,
only one such vector is shown. (Courtesy of Peter-Pike Sloan.)
=M
0
c
p
M
i
c
p
=M
p
M
p
: Signal at point
p
M
cp
: Cluster center vector of the cluster
C
p
M
cp
:
i
th
basis vector in the cluster
C
p
Figure 9.19
Local PCA (clustered PCA) works by grouping similar vectors into clusters, and applying
PCA on each. The cluster approximations are generally much better than an approximation
to the entire set of vectors. (Courtesy of Peter-Pike Sloan.)
