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In-Depth Information
from the modern advances in optical flow and stereo correspondence discussed in
the rest of the chapter.
Recent research in both optical flow and stereo correspondence has substantially
benefited from high-quality ground-truthed data sets and benchmarks hosted at
Middlebury College. Reports by Baker et al. [
27
] (on optical flow) and Scharstein
and Szeliski [
425
] (on stereo) detail the data generation and testing methodol-
ogy that is now used as a worldwide benchmark for comparing new flow and
stereo algorithms. The high-quality datasets and constantly-updated benchmarks
for hundreds of algorithms are available at
http://vision.middlebury.edu/flow/
and
Barron et al. [
31
] proposed an earlier benchmark for optical flow, now superceded
by the Middlebury database but responsible for driving much earlier research in
the field. Sun et al. [
475
] investigated the effects of several simple refinements to the
classical Horn-Schunck algorithm (such as the choice of robust penalty function, the
type of image interpolation, and theuse of amedianfilter in thewarping step) to arrive
at a set of recommendations and best practices that result in simple, competitive
optical flow algorithms. Brown et al. [
70
] gave a good survey of advances in stereo
algorithms, although many of the competitive algorithms discussed in Section
5.5
were proposed after this publication. While we didn't mention it in Section
5.3
, the
graph-cut stereomethods in Section
5.5.2
can be easily extended to estimate discrete
optical flow. In this case, the label at each pixel is multi-valued (i.e., a flow vector
(
instead of a disparity
d
).
Szeliski et al. [
485
] surveyed methods to efficiently minimize cost functions of
the form of Equation (
5.50
), including the
u
,
v
)
-expansion and loopy belief propagation
methods discussed in Section
5.5
, as well as a promising variant of belief propagation
called tree-reweighted message passing [
525
]. They also provided efficient reference
implementations for the various algorithms at
http://vision.middlebury.edu/MRF/
.
Felzenszwalb and Zabih [
139
] recently gave a good survey of dynamic programming
and graph-based techniques, with common applications to computer vision.
So far, our discussion of dense correspondence has beenmotivated almost entirely
as a 2D-to-2Dmatching problem. However, the remainder of the topic focuses on 3D
considerations, and we will see that disparity is often interpreted as an
inverse depth
map
. That is, objects that are closer to the pair of cameras have high disparities and
map requires further physical knowledge about the camera setup, whichwediscuss in
thenext chapter. Ahigh-quality optical flowfieldor disparitymap cangreatly improve
the results of other visual effects algorithms, such as matting, and is at the heart of
algorithms for converting monocular films to stereo in post-production. Conversely,
an independent estimate of depth (e.g., sparse measurements from a low-resolution
range sensor) can definitely improve the results of a dense correspondence algorithm
(see Yang et al. [
564
]).
α
22
As a simple experiment, hold a finger close to your face and alternate winking your eyes. The
relative position of your finger changes substantially compared the the position of a fixed point in
the background. If your finger is centered in front of your nose, you will also observe the double
nail illusion — that is, a violation of the monotonicity constraint.
