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In-Depth Information
D
HSV
(
F
l
,
F
r
)=
(
D
V
)
2
+(
D
C
)
2
,
(24)
with
D
V
=
|
V
l
−
V
r
|
,
D
C
=
(
S
l
)
2
+(
S
r
)
2
and
−
2
S
l
S
r
cos(
θ
)
,
=
|
H
l
−
H
r
|
if
|
H
l
−
H
r
|≤
π
where
θ
2
π
−|
H
l
−
H
r
|
if
|
H
l
−
H
r
|
>
π
.
The correlation measure can now be easily extended to color images by using a
color difference measure that is suitable for the selected color space:
p
∈
B
D
m
F
l
(
p
)
,
F
r
(
p
−
d
)
,
C
c
(
F
l
,
F
r
,
d
)=
(25)
where
D
m
is defined by (23) or (24) if the HSV color space is chosen.
3.2.2
Global Approaches
In recent years, global approaches have attracted much attention in the stereo vision
community due to their excellent experimental results. These methods formulate
stereo matching in terms of an energy function, which is typically the sum of a
data term and a smoothness term, and solve the problem through various minimiza-
tion techniques. Extension to color of gray based global approaches has involved in
most cases the energy function. Alvarez and Sánchez [36] proposed a generaliza-
tion of their work presented in [20], where they applied a PDE-based method for
disparity estimation, by modifying the cost function so that to include all the three
color components. The extended set theoretic variational approach proposed in [37]
minimizes a global objective function, which is the sum of intensity differences
over the three color channels, subject to three convex constraints. Disparity range
and total variation regularization constraints proposed for gray value images remain
available. However, the Nagel-Enkelmann constraint, which involves the left stereo
image, has been extended to color images. The color evaluation study for global
approaches, addressed in [7], investigates the role of color in stereo energy func-
tions, believing also that real progress in global stereo matching can be achieved
by improving the energy function rather than by investigating on the optimization
component. Notice that for color based global approaches, the common idea is to
estimate the disparity using jointly all the three color components, which is physi-
cally plausible since disparity must be consistent across channels. The data fidelity
function that computes the color dissimilarity between a pixel
p
in one view and its
matching point
p
−
d
in the second view can be defined by
k
=1
p
∈
S
D
m
I
(
k
)
d
)
,
3
I
(
k
r
(
p
−
−
E
data
(
d
)=
(
p
)
(26)
l
