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where
S
is the image support and
D
m
is the color difference function that mea-
sures the distance between two points in the color space. It is defined by (23) or (24)
as in the gray level case.
The second major approach to incorporate color information in global stereo
methods is to use a segmentation algorithm that decomposes the image into homo-
geneous color regions [18, 38, 39]. Disparity smoothness constraint is then enforced
inside each color segment, assuming that discontinuities only occur on the bound-
aries of homogeneous color segments. The use of color segmentation makes global
stereo algorithms capable of handling large untextured regions, estimating precise
depth boundaries and propagating disparity information to occluded regions. The
comparative study conducted in [4] shows that these algorithms, based in general
on graph cuts and belief propagation, are among the best performing. However,
these methods require precise color segmentation that is very difficult when dealing
with highly textured images.
⊂
N
4
Comparisons and Discussion
The previous survey on color based stereo methods has indicated that color informa-
tion improves the estimation of binocular disparity to recover the three-dimensional
scene structure from two-dimensional images. In addition, we have noticed that a
large variety of color spaces exists, which raises the question which color system to
use to solve the stereo matching problem. In this section, we will give some insights
about the suitability of a color space for this application. From an intuitive point of
view, a color system should exhibit perceptual uniformity, meaning that distances
within the color space should model human perceptual color differences. Moreover,
to achieve robust and discriminative image matching, color invariance is another
important criterion. Indeed, stereo images are taken from different viewpoints and
may be subject to photometric variations. The RGB color system is not perceptual
uniform and depends on the imaging conditions and viewing direction. Therefore,
RGB is not suitable for matching images taken under illumination variations. The
luminance-chrominance systems are very close to human perception and are ex-
pected to achieve good performances. The color space I
1
I
2
I
3
can also offer suitable
color features for stereo matching. The components I
2
and I
3
are invariant to the
intensity variations and so systematic errors between the left and right images can
be reduced. Moreover, since the color components of this system are statistically
independent, color information can be fully used in the matching process.
To argue the above analysis, we made a comparison of two stereo algorithms
which are among the most efficient in the literature: the convex variational approach
based on the total variation (TV) regularization [37] and the global optimization al-
gorithm (GC) of Kolmogorov and Zabih [40] based on graph-cuts. Four different
color models RGB, Luv, Lab, I
1
I
2
I
3
are evaluated along with the gray level image
representation and three stereo pairs taken from the Middlebury Database are con-
sidered (see Fig. 4). These stereo pairs have complex scene structures, wide disparity
ranges and large occluded regions. As ground truth fields are available, results are
