Digital Signal Processing Reference
In-Depth Information
Fig. 3.6
A graphical representation of CRF. Reproduced from [
39
]
The regional features
P
R
represent local geometric relationships between objects.
They avoid impossible combinations of neighboring objects such as “ground is
above sky” and also encourage the segmentation results to be spatially smooth.
A collection of regional features are learned from the training data. Let
r
be the
index of regions and
a
be the index of the different regional features within each
region, and
j
be the index of image patches within in region
r
.
P
R
is defined as
exp
r
,
a
f
r
,
a
w
a
z
r
P
R
(
Z
,
f
)
∝
.
(3.3)
f
=
{
f
r
,
a
}
are binary hidden regional variables.
f
r
,
a
=
0
,
1 indicating the feature
a
in
region
r
exists or not.
w
a
=[
α
a
is a bias term.
w
a
,
j
connects
f
r
,
a
with
z
r
,
j
and specifies preferences for the possible label value of
z
r
,
j
.
z
r
w
a
,
1
,...,
w
a
,
J
,
α
a
]
are parameters and
=[
,...,
,
]
=
z
r
,
1
z
r
,
J
1
.
P
R
is high of
z
r
matches
w
a
and
f
r
,
a
1or
z
r
does not
=
match
w
a
and
f
r
,
a
0.
The global feature
P
G
is defined over the whole image,
exp
g
b
u
b
Z
b
P
G
(
Z
,
g
)
∝
.
(3.4)
b
is the index of the global label patterns, which are encoded in the parameters
{
u
b
}
.
g
=
{
are the binary hidden global variables.
Both hidden variables
f
and
g
can be marginalized, leading to
g
b
}
a
1
exp
w
a
z
r
,
(
)
∝
+
P
R
Z
(3.5)
r
,
)
∝
b
1
exp
u
b
Z
.
P
G
(
Z
+
(3.6)
