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by the subspace segmentation approach). Let us denote intensity edge map as M I ,
occlusion region map as M O and layer edge map as M L thereafter. The motion of inten-
sity edges dominates that of their neighborhood. It is straightforward to utilize the
intensity structures of the neighborhood of the edges for detecting the layer boundaries
and inferring the occlusion relationship. The proposed post-processing procedure
given below is performed over two successive frames, but evidence could be accumu-
lated over an image sequence for a more robust segmentation.
Construct Pending Areas
For each frame, we first determine some pending areas, which should involve all
potential layer boundaries. Then, the detection of layer boundaries is carried out
on the resulting pending areas accordingly. To this end, we place a set of windows
w of size n μ n along the edges of M L . These small windows might be overlapped to
each other. Usually each window w is determined by the M O and M L without a
fixed size, i.e. it is expected to be so large that the resulting set of windows can
cover the occlusion regions M O and layer edge map M L on the current frame. In
our experiments, the minimal size n of
w is set to 10 pixels.
Match Scores
Consider the resulting pending areas
= , which contains many intensity
edges l Õ M I . The potential layer boundaries are involved in M I in terms of the
assumption (4). Thus, for each window w , we can compute the profile of every
point p , which is defined as a vector pf ( p ) by sampling the intensity derivative in
the positive and negative directions of the intensity gradient at p . This is illustrated
in Fig.2. The point profile is then normalized as,
Ww
i
pf
(
p
)
pf
(
p
)
=
.
(1)
pf
j p
(
)
j
According to the optical flow field, one can get a pair of corresponding points p
and p respectively on two successive frames. The match score is taken as the
residual error of their profiles as follows,
2
pf
(
i
)
(
p
)
pf
(
i
+
1
(
p
)
e
(
p
)
=
Exp
,
0
2
σ
where s is a reference distance and is determined empirically. When the point p is
far away from layer boundaries,
0 e should approach one, i.e. the neighborhood
of p obeys a single motion. Otherwise its neighborhood contains multiple motions.
Furthermore, we can obtain other two match scores respectively along either side
profile of the current point p , denoted as
)
pe . If point p belongs to a layer
boundary, one of these two scores should approach one while the other should
approach zero, otherwise both of them should approach one.
(
),
e
(
p
)
1
2
 
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