Graphics Reference
In-Depth Information
e
−
|
I
(
x
,
y
)
−
I
(
x
−
1
,
y
)
|
W
LR
(
x
,
y
)
=
(5.1)
σ
with
I
(
x
,
y
)
and
I
(
x
−
1
,
y
)
the pixel intensity at coordinate
(
x
,
y
)
and
(
x
−
1
,
y
)
,
respectively, in the reference image and
an appropriate empirically determined
constant value. The aggregated cost computed along the same horizontal scanline
and direction, from left to right in the considered example, is then computed according
to:
σ
C
LR
W
LR
C
LR
(
x
,
y
,
d
)
=
C
(
x
,
y
,
d
)
+
(
x
−
1
,
y
)
·
(
x
−
1
,
y
,
d
)
(5.2)
This strategy, applied to both horizontal directions depicted in Fig.
5.11
and along
both vertical directions on horizontally aggregated costs, efficiently enables to adap-
tively perform cost aggregation on unconstrained 2D support windows. More pre-
cisely, cost aggregation is initially independently performed along horizontal scan-
lines (from left to right (LR) and right to left (RL)). Then, a similar approach is applied
along vertical directions (from top to bottom (NS) and bottom to top (SN)) to the
summed aggregated matching cost computed along horizontal paths. In practice, in
this method, the support window implicitly consists of the entire image. Although
this strategy requires us to store the entire image and matching costs, a simplification
of the original approach restricted to a subset of scanlines (e.g., from left to right,
from right to left, and from top to bottom) is certainly feasible for the constrained
our hardware friendly implementation of the Permeability algorithm based on two
single directions. Another implementation suited to FPGAs was proposed in [
1
].
Finally, a different and effective algorithm that, similarly to the previous method,
does not explicitly define a fixed support window was proposed in [
45
]. In this
approach, the matching costs are aggregated using as weights the minimum intensity
distance between any two points in the reference image. These weights are stored
in a tree structure and, to this aim, a MST (Minimum Spanning Tree ) containing a
number of nodes equal to the number of image points is created. This enables to very
efficiently and in constant time obtain for each point the aggregated weighted cost
computed on the whole image. Nevertheless, although this method is very fast and
effective on traditional CPU or GPU architectures, in its original formulation, it, due
to the memory footprint required to store the MST, seems inappropriate to a target
computing architecture without being provided with external memory devices, such
as DDR memory.
5.5.2 Global and Semiglobal Approaches
Although local algorithms described so far yield excellent results, they are often out-
performed by approaches that explicitly enforce a smoothness term on the resulting
disparity map. These methods solve the correspondence problem in terms of a pixel-
labeling assignment of disparities, determining the disparity field
D
that minimizes
