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3.3
Robust Registration
The set of 2D-to-2D point correspondences obtained in the previous stage, is easily
converted to a set of 3D-to-3D points since for every frame we have a quasi dense
3D reconstruction that is rapidly provided by Bumblebee. In the current approach,
contrary to Iterative Closest Point (ICP) based algorithms, the correspondences be-
tween the two point sets are known; hence, the main challenge that should be faced
during this stage is the fact that feature points can belong to static or moving objects
in the scene. Since the camera is moving there are no additional clues to differenti-
ate them easily. Hence, the use of a robust RANSAC-like technique is proposed to
find the best rigid transformation that maps the 3D points of frame (
n
) into their cor-
responding in frame (
n
1). The closed-form solution provided by unit quaternions
[12] is chosen to compute this 3D rigid displacement, with rotation matrix
R
and
translation vector
t
between the two sets of vertices. The proposed approach works
as follows:
Random sampling.
Repeat the following three steps
K
times (in our experiments
K
was set to 100):
+
P
n
+
1
i
P
i
(
x
,
y
,
z
)
,
1. Draw a random subsample of 3 different pairs of feature points
(
)
)
k
,
(
x
,
y
,
z
where
P
i
(
x
,
y
,
z
)
∈
P
n
,
P
n
+
1
P
n
+
1
i
(
x
,
y
,
z
)
∈
=
{
,
,
}
and
i
1
2
3
.
2. For this subsample, indexed by
k
(
k
=
1
, ....,
K
), compute the 3D rigid displace-
3
i
P
n
+
1
i
R
k
P
i
(
x
,
y
,
z
)
−
ment
D
k
=[
R
k
|
t
k
]
that minimizes the residual error
|
)
−
∑
=
1
(
x
,
y
,
z
2
. This minimization is carried out by using the closed-form solution provided
by the unit quaternion method [12].
3. For this solution
D
k
, compute the number of inliers among the entire set of pairs
of feature points according to a user defined threshold value.
t
k
|
Solution
1. Choose the best solution, i.e., the solution that has the highest number of inliers.
Let
D
q
be this solution.
2. Refine the 3D rigid displacement
by using the whole set of couples con-
sidered as inliers, instead of the corresponding 3 pairs of feature points. A sim-
ilar unit quaternion representation [2] is used to minimize:
[
R
q
|
t
q
]
#
inliers
i
=
1
P
n
+
1
|
i
(
x
,
y
,
z
)
−
∑
R
q
P
i
(
x
,
y
,
z
)
−
2
t
q
|
.
3.4
Frame Subtraction
The best 3D rigid displacement
computed above with inliers 3D feature
points is representing the camera motion. Thus, it will be used for detecting moving
regions after motion compensation. First, the whole set of 3D data points at frame
(
n
) is mapped by:
[
R
q
|
t
q
]
P
n
+
1
i
R
q
P
i
(
x
,
y
,
z
)
+
)
=
t
q
,
(1)
(
x
,
y
,
z
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