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In-Depth Information
Several implementations of the FW algorithm, and its variants, suited for FPGA
were proposed in the literature with different degrees of algorithmic complexity and
hence with different resources used. Some recent representative approaches in this
field are [
17
,
39
,
50
]. In Sect.
5.6
, we report experimental results concerned with
our implementation of the FW algorithm on the constrained hardware architecture
previously outlined.
5.5.1.2 Local Algorithms Based on Adapting Weights and Constrained
Supports
Although the FW approach is widely used in many practical applications, it is clearly
outperformed by more recent local approaches based on cost aggregation techniques
that aggregate costs according to weights assigned by examining the image content
[
15
,
19
,
23
,
36
,
46
]. In these approaches, differently by the simple average score
computed by FW, the overall score is given by a weighted sum/average of the costs
computedwithin each support window [
18
]. The key idea behind this strategy consists
of weighting each cost according to its
relevance
with respect to the point under
examination (i.e., the central points of the supports).
Many methodologies to assign weights have been proposed in the literature and
an effective rationale is that inspired by bilateral filtering [
26
,
34
] applied to the
stereo matching by the AW (Adaptive Weights) algorithm [
46
]. That is, points with
similar
intensity with respect to the central point should be more influential in the
weighted sum. Moreover, points
closer
to the central point should also be more
relevant according to [
46
]. This strategy is similar to the weight computation strategy
used by bilateral filtering and, in stereo, weights are often computed within the
support window of reference and target images (this strategy is often referred to as
joint
or
symmetric
). In the strategy based on segmentation [
35
], the original bilateral
filtering weight computation was relaxed by removing the proximity constraint.
Afirst optimization [
15
,
23
] consists of asymmetrically computingweights, exam-
ining only the image points belonging to the reference image. Although this strategy
significantly reduces weight computation by a factor of
d
max
, the number of opera-
tions required for cost aggregation is always proportional to
M
1)
and may exceed the resources available in the target FPGA. However, simplified yet
effective strategies based on the computation of weights and/or costs and/or overall
weighted costs only in sampled points may help to further reduce the number of
elementary operations per point, maintaining high accuracy. These approaches also
exploit massively incremental calculation schemes for cost computation, similar to
those outlined for FW. An approach that efficiently computes weights, on a sparse
regular grid, and aggregated costs on a block basis, by means of [
21
], is the Fast
Bilateral Stereo (FBS) algorithm [
19
]. This approach represents a link between the
traditional fixed window approach and AW. Figure
5.10
shows for the Tsukuba stereo
pair, the results obtained by FW, AW, and FBS. Compared to AW, FBS obtains equiv-
alent results with a fraction (about 10%) of operationsmaking it suitable for hardware
×
N
×
(
d
max
+
