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line with a winner-take-all strategy (the disparity is determined in the presence of
the lowest matching cost). The dissimilarity measure finally can be produced using
the following formula:
F
(
x
,
y
,
d
)=(1
−
ω
)
×
F
SAD
(
x
,
y
,
d
)+
ω
×
F
GRAD
(
x
,
y
,
d
)
.
(3)
3.2
Estimation of Disparity Planes
Once the disparity planes have been processed, then we may find appropriate dis-
parity planes to represent the scene structure. A robust solution is applied to esti-
mate the parameters. First of all, the horizontal slant is computed using the reliably
estimated disparities that fall in the identical line. The derivation
∂
d
∂
x
is conducted
and used to determine the horizontal slant by applying convolution with a Gaussian
kernel.
Secondly, the vertical slant is calculated using a similar way to the above ap-
proach. Thirdly, the determined slant is used to obtain a robust estimation of the
centre of the disparity pitch. The disparity map obtained according to the previous
descriptions is not good enough in terms of accuracy. A matching procedure for
each “segment to plane” assignment is used as follows:
∑
(
x
,
y
)
F
SEG
(
S
,
P
e
)=
F
(
x
,
y
,
d
)
,
(4)
∈
S
where
P
e
is a disparity plane that defines the disparity
d
. This equation is iteratively
used to find the segments with the minimum matching cost, and all the segments go
over this process.
The final stage of this segment based stereo matching is to search the solution to
the segment-to-disparity plane assignment. This in fact is a minimisation problem
that satisfies
E
(
f
)=
E
data
(
f
)+
E
smooth
(
f
)
,
(5)
where
E
data
(
f
)=
∑
s
∈
R
F
SEG
(
s
,
f
(
s
))
E
smooth
(
f
)=
(6)
∑
∀
(
s
i
,
s
j
)
∈
S
N
|
f
(
s
i
)
=
f
(
s
j
))
Ω
(
s
i
,
s
j
)
where
f
is a labeling function,
S
N
is a set of adjacent segments and
is a discon-
tinuity penalty. An optimal labeling with minimum energy is approached using the
Loopy belief propagation algorithm [22]. This optimisation is illustrated in Fig. 8,
where (a) indicates the pixel disparity map and (b) is the optimisation of (a). To
further demonstrate the performance of the colour segment based stereo approach,
we use three pairs of images for the estimation of disparity maps, which is revealed
in Fig. 9. It is observed that this proposed algorithm can effectively handle the sce-
narios that possess less clutters but fails in complex scenes.
Ω
