Relative range camera calibration
View Patent ↗Method and system for measuring a relative position and orientation of range cameras using a movement of an object within a scene. In general, the method and system determine the relative pose between two cameras by measuring a path the movement of the object makes within a scene and calculating transformation parameters based on these measurements. These transformation parameters are used to determine the relative position of each camera with respect to a base camera. The system and method include other novel features, such as a data synchronization feature that uses a time offset between cameras to obtain the transformation parameters, and a technique that improves the robustness and accuracy of solving for the transformation parameters, and an interpolation process that interpolates between sampled points if there is no data at a particular instant in time.
1. A method of determining a relative position and orientation between a base camera and a non-base camera, comprising:
using a general-purpose computing device to perform the following:
measuring a path of a moving object with the base camera in a base coordinate frame;
measuring the object path with the non-base camera in a non-base coordinate frame;
calculating transformation parameters based on the object path by computing transformation parameters of an angle (θ) and an offset (Δx,Δy) that satisfy the equation:
(
x
1
y
1
1
)
=
[
cos
(
θ
)
-
sin
(
θ
)
Δ
x
sin
(
θ
)
cos
(
θ
)
Δ
y
0
0
1
]
(
x
2
y
2
1
)
,
where (x 1 ,y 1 ) is an (x,y) location of the moving object in a ground plane as a function of time as measured by the base camera and (x 2 ,y 2 ) is a corresponding location of the moving object as measured by the non-base camera; and
applying the transformation parameters to the object path measured by the non-base camera such that that the object path measured by the non-base camera may be expressed in the base coordinate frame.
2. The method of claim 1 , wherein the moving object is a person moving around a scene.
3. The method of claim 1 , further comprising using a time offset, Δt, to synchronize data from the base camera and the non-base camera.
4. The method of claim 1 , further comprising picking random pairs of corresponding points from a data set represented by ((x 1k *, y 1k *,x 2k *, y 2k *), where 1≦k≦n.
5. The method of claim 4 , further comprising computing the θ and (Δx,Δy) that minimize the sum of the Euclidean distances between corresponding points in (x 1k *,y 1k *,x 2k *,y 2k *), 1≦k≦n.
6. The method of claim 5 , further comprising computing the angle, θ, using:
tan
(
θ
)
=
∑
k
=
1
n
(
(
x
2
k
*
-
x
_
2
*
)
(
y
1
k
*
-
y
_
1
*
)
-
(
y
2
k
*
-
y
_
2
*
)
(
x
1
k
*
-
x
_
1
*
)
)
∑
k
=
1
n
(
(
x
1
k
*
-
x
_
1
*
)
(
x
2
k
*
-
x
_
2
*
)
+
(
y
1
k
*
-
y
_
1
*
)
(
y
2
k
*
-
y
_
2
*
)
)
where,
(
x
_
1
*
,
y
_
1
*
)
=
1
n
(
∑
k
=
1
n
x
1
k
*
,
∑
k
=
1
n
y
1
k
*
)
(
x
_
2
*
,
y
_
2
*
)
=
1
n
(
∑
k
=
1
n
x
2
k
*
,
∑
k
=
1
n
y
2
k
*
)
.
7. The method of claim 5 , further comprising computing the translation (Δx,Δy) using:
(
Δ
x
Δ
y
)
=
(
x
_
1
*
y
_
1
*
)
-
[
cos
(
θ
)
-
sin
(
θ
)
sin
(
θ
)
cos
(
θ
)
]
(
x
_
2
*
y
_
2
*
)
,
where θ and (Δx,Δy) represent a solution to the calibration problem.
8. A method for calibrating range cameras, comprising:
using a general-purpose computing device to perform the following:
capturing a path of a moving object using a base range camera and a non-base range camera;
computing transformation parameters from a first path captured by the base camera and a second path captured by the non-base camera by computing transformation parameters of an angle (θ) and an offset (Δx,Δy) that satisfy the equation:
(
x
1
y
1
1
)
=
[
cos
(
θ
)
-
sin
(
θ
)
Δ
x
sin
(
θ
)
cos
(
θ
)
Δ
y
0
0
1
]
(
x
2
y
2
1
)
,
where (x 1 ,y 1 ) is an (x,y) location of the moving object in a around plane as a function of time as measured by the base camera and (x 2 ,y 2 ) is a corresponding location of the moving object as measured by the non-base camera; and
using the transformation parameters to correlate the first and second paths such that data captured by the non-base camera can be expressed as if the data had been captured by the base camera.
9. The method of claim 8 , further comprising matching data measured by the base and non-base cameras.
10. The method of claim 8 , further comprising applying a time offset to data from at least one of the base and non-base cameras to correct for unsynchronized data between the base and non-base cameras.
11. The method of claim 9 , further comprising selecting a time value and matching points of the path as measured by the base camera at the time value with points of the path as measured by the non-base camera at the time value.