[ING
3-0016, Japan -
4259, Nagatsuta-cho,
Surface Model
| is still one of the most
et, they cannot guarantee
stereo matching problem
a mapping technique for
mapping in the past. It
for application of stereo
xecuted for examine the
rapping results in linear
ancement of ANM model
roves mapping results by
"his approach is effective
ot detected satisfactorily.
G WITH ANM
matching algorithms such
mplate matching, feature-
ature points, edges and so
h is also known as optical
the stability of matching
used in combination with
xr relaxation of matching
nous approach is Dynamic
ensures unique solution by
1e system. Most of these
the assumption of smooth
onceptual model for abrupt
tion process for matching
lapping (ANM) adopted in
for the control of self-
network model, and here
lems. This approach has a
ssumption based matching
, ANM evaluates matching
pagates its influence to the
| Coincidence Enhancement
| rule for the explanation of
in extension of Hebb's rule
(Kosugi, 1993). This principle can realize by competition and
consensus process and its iterative feedback process for
activation and stability of bond strength between neurons. In
stereo matching problems, this approach is used for finding the
correspondence between sub-areas in stereo images. Figure 1
illustrates the main concepts of ANM approach.
2.2.1 Competition Process: Let the position of local sub-
areas in a pair of stereo images be xj; and y; respectively, where
suffix i and j are grid number of sub-area in images, and feature
value in each area be f(x), g(y) respectively, and the iteration
number of process be k. Then we can express the difference
evaluation function as follows.
Fa -|res «aec D
ld; ,9 2 (Ax*, Ay), Ax*, Ay »0 (2)
where dj; is the mapping or shift vector between two images, 0
is a quantity which regulates the search area size, Ax and Ay are
positive constant.
For feature values, we can use the brightness of a pixel, or a
vector sum of multiple criterions. Also image similarity
function such as cross correlation function might be used
instead of difference equation.
In competitive process, each sub-area independently searches
for the optimal mapping position where dj gives the minimum
error e; with Equation (3) according to the output of evaluation
function (1) in the condition of Equation (2), thus forming
competitive shift vectors.
e; - min(F(x;)) (3)
2.2.2 Consensus Process: The competition process
maximizes connection strength between shift vectors. On the
other hand, consensus process maximizes information of lateral
correlation, which takes into account of neighbouring matching
status, and thus is also restraining process against the
competition operation.
For effective applications of such a mechanism, we need
mapping models preferable to the object model under
consideration. For example, for a model emphasizing surface
smoothness, the continuity of shift vector needs to be
maintained. In this case, modification of mapping can make use
of median value which is obtained from all shift vectors in the
consensus area as expressed in Equation (4).
A 4
d; - median(a* | IR) (9
where median() is the function which returns median value, R is
an arbitrarily shaped consensus area around the target shift
vector.
If emphasis on bond weight of shift vector is necessary, bond
strength r; can be defined as Equation (5).
s uon
^j EP (5)
A target shift vector is updated with consideration of weight Wj
which is calculated from its bond strength with che
neighbouring shift vectors in the consensus area.
Ww. =
ij S EC (6)
R
dj'-»w,.d; (7)
For controlling the propagation of weights, also Gaussian type
functions can be used.
2.2.3 Feedback Process: Both of competition and consensus
process are repeatedly performed at local sub-area in parallel to
realize modification of mapping.
While the feature value in both processes is a very significant
factor, there are also other decisive factors. For example, sub-
area shape and size for evaluation function or search area size
have strong influence over mapping in competition process.
Similarly in consensus operation, shape and size of consensus
area or criterion for consensus affects the convergence
characteristics or mapping ability of the whole process.
Therefore these parameters need to be modified in accordance
to iteration stages. For example, the size of consensus area S, is
narrowed down with Equation (8) according to iteration number.
k
S, 2 S, exp(-25, —) (8)
where S, is the initial area size and k,,, is the maximum
iteration number.
After a series of competition and consensus process, initial
positions of shift vectors and parameters described above are
updated and feedback process is continued till iteration reaches
the predefined number or shifts of vectors are less than a preset
threshold.
Output Layer
Search
uy
(7 =
LY
Competition
Process
Correlation Unit
Unit Element
A/ (Image Pixel)
Output Layer oO[OBOOlOO OO O
Input Layer oogoooo OOo
15 + «+ Operation Processing
OOGOOOOOOQ
|]
Mapping Layer
TER, 5 A
EN fancy [9]
Figure 1. A principle of ANM
Input Layer
Correlation
nit
Addition
Element ^9
Consensus Area
2.3 Problems in ANM
Thanks to the consensus process, the continuity of stereo
matching results by typical ANM are enhanced, which also
means satisfactory processing result can be obtained when
ANM is applied to natural terrain area where parallax shifts are
smooth. On the other hand, it becomes difficult when applied to
urban area where there are abrupt changes in parallax shifts,
because building's edges tend to weaken by consensus process.
To deal with this problem, we introduce a CE process with edge
constraint or multi-clustering model approach for mapping
region.
2.4 ANM with Rectified Images
In this study, image rectification is carried out for reducing
calculation time and increasing the stability of ANM process
with epipolar geometry, which reduces the direction of mapping
to x-direction only.
Photographic coordinate uv is 2-dimensional, with the origin at
the camera's principal points of a stereo model (Figure 2).
—85—
