Information Technology Reference
In-Depth Information
5. If the number of inliers is greater than maximum number of inliers, maximum
iteration number is updated [41]
6. The number of iterations is increased by one, and if maximum number of itera-
tions is reached process is terminated. Otherwise, Steps 1-6 are repeated.
The maximum number of iterations,
N
, is selected sufficiently high in order to en-
sure with a probability,
p
, that at least one of the random samples of
s
points is free
from outliers. Suppose
e
is the probability that any selected data point is an outlier
(hence,
w
= 1
−
e
is the probability that it is an inlier). Then,
N
can be obtained as
[41]:
log
(1
−
p
)
N
=
e
)
s
)
.
(17)
log
(1
−
(1
−
Note that, prior to 3D motion estimation, the depth maps, which are estimated using
[38], are smoothed with a Gaussian filter of 9
x
9 kernel, in order to compensate for
the erroneously estimated depth regions.
4.3
Middle Frame Interpolation
The final step of the algorithm is the interpolation of the middle frame pixel inten-
sities, which is achieved through interpolation of the estimated 3D motion models
of foreground objects. Although the methods mentioned in this section can be used
to render multiple interpolated frames at any time instant in-between the successive
frames, for simplicity and without loss of generality, we assume that a single middle
frame is to be generated corresponding to time instant
t
1
2
. Basically,
all
3D points
on the foreground objects are rotated and translated to time instant
t
−
1
2
and then
projected to the image plane of the desired view(s) of the multi-view set. In Sect. 4.2,
the 3D motion, i.e. the rotation and translation, parameters are estimated between
the successive frames at the time instants
t
−
1and
t
.Let
R
m
and
t
m
, respectively,
represent the interpolated 3D rotation matrix and translation vector corresponding
to rigid motion of a foreground object from
t
−
1
2
. Under constant velocity
assumption of objects between successive frames, the interpolated translation vector
can be determined easily as follows:
−
1to
t
−
t
m
=
1
2
t
.
(18)
Similarly, using the angle-axis representation highlighted in Sect. 3.2, the interpo-
lated rotation
R
m
is written as:
R
m
=
R
2
,
a
,
(19)
where, as defined previously,
is the rotation angle and
a
is the rotation axis.
Using
R
m
and
t
m
, 3D coordinates of foreground objects at
t
θ
−
1 are rotated and
1
2
translated to
t
−
by the following relation:
