Digital Signal Processing Reference
In-Depth Information
Thus (
3.2
)hasaclosedform,
x
i
,
λ
)
×
r
,
a
1
+
exp
w
a
z
r
×
b
1
exp
u
b
Z
.
θ
)
∝
∏
i
P
(
Z
|
X
;
P
C
(
z
i
|
+
(3.7)
θ
=
{
λ
,{
are parameters. They are learned from a training by maximiz-
ing the conditional likelihood in [
39
]. Once the parameters are learned, the object
class labels are inferred by maximizing posterior marginals.
w
a
},{
u
b
}}
3.3.2.2
TextonBoost
Under the CRF framework, Shotton et al. [
40
] proposed TextonBoost to learn a
discriminative model of object classes incorporating texture, layout, and context
information. Their CRF includes four types of potentials: texture-layout, color, lo-
cation, and edge.
texture
−
layout
c
olo
r
loc
ati
on
,
θ
)=
∑
i
log
P
(
Z
|
X
ψ
i
(
z
i
,
X
;
θ
ψ
)+
π
(
c
i
,
x
i
;
θ
π
)+
(
z
i
,
i
;
θ
)
edge
+
∑
(
ξ
(
z
i
,
z
j
,
g
ij
(
X
)
;
θ
ξ
)
−
log
C
(
θ
,
X
)
,
(3.8)
i
,
j
)
∈
ε
where
i
and
j
are indices of pixels,
(
i
,
j
)
∈
ε
are two neighboring pixels,
θ
=
{
θ
ψ
,
θ
π
,
θ
,
θ
ξ
}
is a normalization term.
The texture-layout potentials are provided by a boosting classifier combining
a set of discriminative features called texture-layout filters. The neighborhood of
pixel
i
is partitioned into regions by a predefined spatial kernel. Each texture-layout
v
[
r
,
t
]
(
are parameters, and
C
(
θ
,
X
)
is the number of pixels with texton
t
in region
r
. Therefore, texture-layout
filters are histograms of textons over defined spatial kernels. They capture texture,
spatial layout, and textural context. Discriminative texture-layout filters are selected
as weak classifiers and combined into a powerful classifier by Joint Boost [
41
]. Joint
Boost allows to share weak classifiers among different object classes and the learn
classifier has better generalization.
The color potentials model the color distribution of each object class using Gaus-
sian mixture models in CIELab color space.
The location potentials model the dependence between the locations of pixels
and object classes. For example, trees and sky tend to appear in the top regions of
images while roads tend to appear in the bottom regions of images.
In the edge potentials,
g
ij
measures the edge features between neighbor pixels.
A penalty is added if two neighboring pixels have different object class labels unless
there is a strong edge between them.
TextonBoost was evaluated on 21 object classes from the MSRC database and
achieved 72
i
)
.
2% overall accuracy [
40
]. The confusion matrix is shown in Fig.
3.7
.
