Digital Signal Processing Reference
In-Depth Information
Fig. 2.1
The relationship of signal and noise subspaces
Fig. 2.2
Problems in the first
principal component with
larger projection (The solid
region (dark blue) and dot
region (blue) have the same
direction)
R
Larger
projection
value
≠
Better
matched
Principal
Component
Vector
G
dark blue
B
blue
the signal is the span of
.
Figure
2.1
shows the relationship of signal and noise subspaces for the skin objects.
In order to segment the desired object, the most frequent approaches perform the
so-called principal color segmentation [
23
-
27
]. First, we can obtain the sampled co-
variance matrix followed by an eigen-decomposition to obtain
v
1
, the eigenvector,
which is corresponding to the largest eigenvalue. With the principal component vec-
tor at hand, we then project all the color vectors of image pixels to the principal
component vector
v
1
. Finally, the object segmentation can be achieved by choosing
the pixels, which have the largest projections with a proper threshold. The threshold
method of the principal value technique is widely adopted for many optimization
applications. However, there are two problems that arise in use of the first principal
color component for color object segmentation. Figure
2.2
shows the fact that the
larger the projection, it implies the better match of color. From the viewpoint of
{
v
1
}
and the noise subspaces become the span of
{
v
2
,
v
3
}
