January 10, 2010 / Vol. 8, No. 1 / CHINESE OPTICS LETTERS 55
Study on the position and orientation measurement method
with monocular vision system
Peng Wang ( +++)
∗
, Xu Xiao ( RRR), Zimiao Zhang (ÜÜÜfff), and Changku Sun (¥¥¥)
State Key Laboratory of Precision Measuring Technology and Instruments,
Tianjin University, Tianjin 300072, China
∗
E-mail: wangpeng810@gmail.com
Received February 27, 2009
In order to estimate the position and orientation of an object with a single camera, a novel measurement
metho d based on pinhole camera model with five reference points is presented. Taking the specially
designed planar target with the monocular vision system, the projection line of the reference points is
built. According to the projection model, the coordinates of the reference points in the camera coordinate
system are estimated with the least-squares algorithm. Thus the position and orientation of the target are
worked out. Experimental result shows that the measurement precision of angle is less than 0.2
◦
, and that
of displacement is less than 0.1 mm.
OCIS co des: 150.1135, 330.4060, 150.0155.
doi: 10.3788/COL20100801.0055.
To estimate the position and orientation between two
objects is an important technique, which can be widely
applied in the fields as robot navigation
[1]
, surgery
[2]
,
human motion estimate
[3]
, and electro-optic aiming
system
[4,5]
, etc. Compared with the magnetic position
and orientation measurement method
[6,7]
, the machine
vision method which is free from the influence of the elec-
tromagnetic surroundings, is widely studied
[8−10]
. But
the method discussed in Refs. [8] and [10] uses two or
more cameras to realize the position and orientation mea-
surement. And in Ref. [9], the measurment is realized
with the assitance of a laser range-finder. In this let-
ter, a novel effective algorithm is proposed to recover the
three-dimentional (3D) position and orientation of a pla-
nar target with a single camera view. A target pattern
with five reference points is specially designed to ensure
that the target special coordinate system can be fixed
in any orientation. With the camera perspective pro-
jection model, the coordinate of the reference points in
the camera coordinate system can be estimated by con-
sidering the relationship of them on the target pattern.
The transformation matrix between the camera coordi-
nate system and target coordinate system, which is built
by the reference point coordinates, is worked out to real-
ize the position and orientation measurement.
The planar target pattern with five reference points
is designed for position and orientation estimation, as
shown in Fig. 1. The colinearity of the vector, composed
of every two reference points, is used to judge whether
the three points are in a straight line. The two points
out of the straight line are marked as No. 0, which is
closer to the line, and No. 1 (see Fig. 2). The angles
between the vector composed of No. 0 and No. 1 points
and the vectors composed of No. 0 and other points are
calculated. According to the angle size, the other refer-
ence points are marked as No. 2, No. 3, and No. 4. The
origin of the target coordinate system is the No. 0 point.
The o
t
x
t
axis is parallel to the vector composed of No. 2
and No. 4 points. The o
t
y
t
axis coincides with the vector
composed of No. 0 and No. 1 points.
The measurement method is based on the pinhole cam-
era mo del (Fig. 3). Here o
c
denotes the optical center
of the camera lens. o
c
−x
c
y
c
z
c
is the camera coordinate
system, which denotes the camera frame. uv is the CCD
image plane with the original point at the image center
of the charge coupled device (CCD) plane. o
t
−x
t
y
t
z
t
is
the target coordinate system, built by the five reference
points P
i
(i = 0, 1, ···, 4) as mentioned above. The
distance from o
c
to image plane is f , which is obtained
from camera calibration algorithms
[11,12]
. On account of
the lens radial distortion
[13]
, the undistorted coordinate
point on the image plane is I
i
= (u
i
, v
i
)
T
(i = 0, 1, ···,
4), which are different from the actual image reference
points obtained by image processing.
Considering the pinhole camera model, the coordinates
of the undistorted image reference point are I
ci
=(u
i
, v
i
,
f)
T
(i = 0, 1, ···, 4) in the camera coordinate system,
in which the projecting line of the reference point P
i
(i
= 0, 1, ···, 4) is
x
u
i
=
y
v
i
=
z
f
= t
i
. (1)
The coordinates of the reference points in the camera
coordinate system are
P
ci
=
Ã
x
ci
y
ci
z
ci
!
=
Ã
t
i
u
i
t
i
v
i
t
i
f
!
, (2)
where t
i
is the scale factor which defines the position of
P
i
.
For the relative position of the reference points P
i
in
the camera coordinate system and the target coordinate
system, t
i
can be estimated by solving
kP
ci
P
cj
k = kP
ti
P
tj
k, i = 0, 1, 2, 3, j = i + 1,
6
P
ci
P
cj
P
ck
=
6
P
ti
P
tj
P
tk
,
i = 0, 1, 2, j = i + 1, k = j + 1, (3)
1671-7694/2010/010055-04
c
° 2010 Chinese Optics Letters