Graphics Reference
In-Depth Information
the energy term (
5.3
):
E
(
D
)
=
E
data
(
D
)
+
E
smooth
(
D
)
(5.3)
The
data term E
data
in (
5.3
) encodes how well the disparity assignment fits with
the stereo pair, and often it is the sum of per-pixel data costs
C
between one
point in the reference image
R
and the supposed homologous point in the target
image
T
:
(
D
(
p
))
E
data
(
D
(
p
))
=
C
(
D
(
p
))
(5.4)
p
∈
R
enables to enforce a piecewise disparity
field
D
by modeling the interaction between each point
p
and its neighboring points
q
In (
5.3
), the
smoothness term E
smooth
(
D
)
includes points in vertical and hori-
zontal directions (typically, the four nearest neighbors of
p
on the pixel grid) while
in 1D approaches, based on Scanline Optimization (SO) or Dynamic Programming,
the smoothness term is enforced only in one direction (typically
∈
N (
p
)
. In fully global approaches,
N (
p
)
includes
only one point along a scanline). The former disparity optimization methods are
typically referred to as 2D. In general, 2D methods perform better as they enable the
enforcement of
inter
and
intra
scanline smoothness assumptions.
Unfortunately, when deploying a 2D approach, minimization of (
5.3
) turns out to
be an
N (
p
)
-hard problem. Therefore, global approaches typically rely, under partic-
ular hypotheses [
32
]on(
5.3
), on efficient energy minimization strategies typically
based on Graph Cuts (GC) or Belief Propagation (BP). However, the iterative nature
of these energy minimization strategies and their high memory footprint typically
render these approaches inappropriate for devices with limited resources such as for
our target architecture.
Nevertheless, a subclass of these algorithms that enforces disparity constraints on
1D domains by means of dynamic programming such as [
43
] or multiple scanline
optimization [
13
] represents, for the outlined target computing architecture, a viable
and effective alternative to local approaches. In particular, the semiglobal matching
algorithm [
13
] computes multiple energy terms by means of the SO technique [
29
],
independently enforcing 1D smoothness constraints along different paths (typically
8 or 16 from all directions as depicted in Fig.
5.12
for 8 paths).
The 1D energy terms independentlyminimized bymeans of the scanline optimiza-
tion approach are then summed up and the best disparity is determined by means of
the same WTA strategy adopted by local algorithms. Figure
5.13
shows, at top and
middle, the disparity maps concerned with two 1D minimizations, independently
computed along paths 0 and 5, and, at the bottom of the figure, the result of the
multiple 1D optimization computed along eight paths. Observing the figure, we can
notice that, although single scanline optimizations are not very accurate, their com-
bination by means of the method proposed in [
13
] turns out to be very effective as
can be seen, using eight paths, at the bottom of Fig.
5.12
.
NP
