Information Technology Reference
In-Depth Information
4
Connectivity Based Stereo Correspondence
Corresponding two images of a scene involves the selection of local metric, e.g.
intensity or colour. However, image matching only based on the available local
information will not be enough. This is due to the fact that colour repetition and
redundancy exit everywhere. To reduce the effects of this uncertainty, the pixel
characteristics must be used along with additional assumptions or constraints, e.g.
continuity or smoothness. Prior knowledge of these constraints can be dominant in
the estimation of patches. For example, depth discontinuities (edges or connective
parts of inhomogeneous regions) will be determined if and only if smoothness is
enforced. This also brings an interesting question, “has a shape anything to with
the stereo correspondence”? The answer is yes. In fact, if we know where to find a
shape, then the segmentation and correspondence of the associated image areas will
be achieved without any problem, and vice versa. Unfortunately, this kind of prior
knowledge is unavailable in all the time.
To effectively solve this problem, Ogale and Aloimonos [23] treat the disparity
map of a real scene as a piecewise continuous function, where the images are de-
scribed with the minimum possible number of pieces (segmentations). This piece-
wise continuous function is approximated by piecewise consistency. The role of
shape in establishing correspondence is also discussed in their report. Particularly,
the relation of the image correspondence and the segmentation is un-separated. The
authors also emphasize on the geometric effects that were raised regarding the cor-
respondence of a horizontally slanted surface. This is because the uniqueness con-
straint used to find the one-to-one correspondence does not hold in the presence of
horizontally slanted surfaces and hence one against many matches will be observed.
The proposed algorithm presented in [23] is summarised as follows, given that
the two images has shifts
∈{
σ
1
,
1
,...,
σ
k
}
:
Step 1: Shift the left image
I
L
horizontally by
σ
σ
x
σ
x
and then generate a new image
I
L
. Then match
I
L
with
I
R
.
Step 2: Investigate the closeness of the pixel (
x
,
y
) and its vertical neighbor
(
x
,
y
1).
Step 3: Build up connected components using the vertical connections from
Step 2.
Step 4: Determine the weights of the connected components.
Step 5: If the connected components surrounding the image pixel cause larger
shifts, then the estimated left/right disparity maps must be updated by taking into
account the uniqueness constraint.
One simple scanline algorithm was used to deal with the horizontal slant that leads
to the violation of the uniqueness constraint in the correspondence. Assume that we
have a pair of scanlines
I
L
(
x
) and
I
R
(
x
). Horizontal disparities
−
L
(
x
) are assigned
to the left scanline within RANGLE OF [
1
,
2
], and
R
(
x
) to the right scanline
with the range [
−
2
. The left scanline consists of the functions
m
L
(
x
) and
d
L
(
x
) and the right scanline has the functions
m
R
(
x
) and
d
R
(
x
). Two image points
x
L
and
x
R
must satisfy the following formula:
−
1
,
