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Fig. 1
Sample segmentation results for
Mobile & Calendar
sequence. From left to right,
top row: frames 19, 21 and 23 of the original sequence, bottom row: corresponding motion
segmentation maps.
3.1
Motion Layer Correspondence Establishment
The first step of the proposed method is the estimation of a set of spatial regions
(hereafter referred to as motion layers), in which motion changes smoothly. Layer
segmentation maps for each pair of consecutive frames
F
t
−
1
and
F
t
, between which
a number of frames
F
t
−
Δ
t
1
,
F
t
−
Δ
t
2
,...,
F
t
−
Δ
t
n
t
i
<
1
,
i
= 1
,...,
n
) are to
be interpolated, are extracted by using a variant of the motion segmentation algo-
rithm by Bleyer et al. [31]. Spatial smoothness in layers is enforced by modeling
layer motion by a planar perspective mapping (i.e., eight parameter homography
model). An additional cost term for temporal coherence of motion layers is incorpo-
rated in the original cost function so as to make the layer extraction process robust
to abrupt changes in layer appearances along the temporal axis. Fig. 1 presents sam-
ple motion segmentation results for
Mobile & Calendar
sequence. Although tem-
poral coherence of motion layers is enforced explicitly, mismatches between layer
boundaries still exist due to several reasons, such as articulated object motion and
object-background appearance similarities. In addition, an object entering or exiting
the scene naturally results in addition or deletion of a layer. Therefore, as required
by the following motion parameter interpolation procedure, motion layers of con-
secutive time instants have to be linked in time.
The correspondences between the estimated motion layers at time instants
t
{
}
(0
<
Δ
1
and
t
are established by mapping the layers and their pair-wise similarity scores to a
bipartite graph. In a bipartite graph
G
=(
U
,
V
,
E
) with two disjoint sets of vertices
U
and
V
, and a set of edges
E
, every edge connects a vertex in
U
and a vertex in
V
. The set of layers corresponding to
F
t
−
1
and
F
t
are mapped to the disjoint sets
U
and
V
with vertices representing the layers and weighted edges representing the pair
−