Digital Signal Processing Reference
In-Depth Information
prohibitively expensive alternative is to start the computation with a disparity space
already discretized to sub-pixel accuracy.
Foreground objects in the scene occlude different parts of the background
when seen from the two camera perspectives. Consequently disparities cannot be
computed for these occluded areas of the image due to missing stereo correspon-
dences. This is visible in Fig.
1
by the halos around the foreground objects. It is
often desirable to exclude these areas and areas with low confidence from the
disparity map and optionally process them with sophisticated hole filling algorithms.
Identification of these areas is performed with a
left/right check
, where the disparity
maps for the left and right perspective are computed and only matching depth
information from both perspectives to a 3D world point is allowed. With respect to
the camera-to-camera projection in a rectified stereo pair the constraint for a valid
disparity in the base image can be formulated as
D
b
|
D
b
(
,
)
−
(
e
mb
(
,
D
b
(
,
))
,
)
|≤
δ
if
x
y
D
m
x
x
y
y
D
b
,
check
(
x
,
y
)=
(3)
invalid
otherwise
with
D
b
and
D
m
are the disparity maps from the base and match perspective,
respectively.
Further post-processing of the disparity map can be performed using basic
median filtering to remove single outliers, peak removal and sophisticated whole
filling algorithms, such as surface fitting. However, without a dense, highly accurate
initial disparity map, post-processing will not provide reliable disparities.
2.3
Algorithm Example: Semi-global Matching
As a specific example disparity estimation based on the highly relevant and
Simultaneously, SGM will be used as a case study for implementations on FPGA
and GPU.
The matching costs
C
(step 1) are calculated from the rank transform of
thebaseandmatchimage
R
b
and
R
m
with absolute difference comparison:
(
x
,
y
,
d
)
R
b
(
.
C
(
p
,
d
)=
p
x
,
p
y
)
−
R
m
(
p
x
−
d
,
p
y
)
(4)
T
the pixel location in the left image. The rank transform is defined
as the number of pixels
p
in a square
M
It is
p
=[
p
x
,
p
y
]
×
M
neighborhood
A
(
p
)
of the center pixel
p
with a luminous intensity
I
less than
I
(
p
)
p
∈
)
.
p
)
<
R
(
p
)=
A
(
p
)
|
I
(
I
(
p
(5)
