IEEE
JOURNAL
OF
ROBOTICS
AND
AUTOMATION, VOL.
RA-3,
NO.
4,
AUGUST
1987
323
A Versatile Camera Calibration Techniaue for
High-Accuracy 3D Machine Vision Metrology
Using Off-the-shelf TV Cameras and Lenses
ROGER
Abstract-A
new technique for three-dimensional
(3D)
camera calibra-
tion for machine vision metrology using off-the-shelf
TV
cameras and
lenses is described. The two-stage technique is aimed at efficient
computation
of
camera external position and orientation relative to
object reference coordinate system as well as the effective focal length,
radial lens distortion, and image scanning parameters. The two-stage
technique has advantage in terms of accuracy, speed, and versatility over
existing state of the art.
A
critical review of the state of the art is given in
the beginning.
A
theoretical framework is established, supported by
comprehensive proof in five appendixes, and may pave the way for future
research
on
3D
robotics vision. Test results using real data are described.
Both accuracy and speed are reported. The experimental results are
analyzed and compared with theoretical prediction. Recent effort indi-
cates that with slight modification, the two-stage calibration can be done
in real time.
I. INTRODUCTION
A.
The Importance of Versatile Camera Calibration
Technique
C
AMERA CALIBRATION in the context of three-
dimensional (3D) machine vision is the process of
determining the internal camera geometric and optical charac-
teristics (intrinsic parameters) and/or the 3D position and
orientation of the camera frame relative to a certain world
coordinate system (extrinsic parameters), for the following
purposes.
I)
Inferring
30
Information from Computer Image
Coordinates:
There are two kinds of 3D information to be
inferred. They are different mainly because of the difference
in applications.
a) The first is 3D information concerning the location of
the object, target, or feature. For simplicity, if the object is a
point feature (e.g., a point spot on a mechanical part
illuminated by a laser beam, or the corner of an electrical
component on a printed circuit board), camera calibration
provides a way of determining a ray in 3D space that the object
point must lie on, given the computer image coordinates. With
two views either taken from two cameras ,or one camera in two
locations, the position of the object point can be determined by
intersecting the two rays. Both intrinsic and extrinsic parame-
ters need to be calibrated. The applications include mechanical
Manuscript received October
18,
1985; revised September
2,
1986. A
version of this paper was presented at the 1986 IEEE International Conference
on
Computer Vision and Pattern Recognition and received the Best Paper
Award.
Heights, NY 10598.
The author
is
with the
IBM
T.
J.
Watson Research Center, Yorktown
IEEE
Log
Number 8613011.
Y.
TSAI
part dimensional measurement, automatic assembly of me-
chanical or electronics components, tracking, robot calibration
and trajectory analysis. In the above applications, the camera
calibration need be done only once.
b) The second kind is 3D information concerning the
position and orientation of moving camera (e.g., a camera
held by a robot) relative to the target world coordinate system.
The applications include robot calibration with camera-on-
robot configuration, and robot vehicle guidance.
2)
Inferring
20
Computer Image Coordinates from
30
In formation:
In model-driven inspection or assembly appli-
cations using machine vision, a hypothesis
of
the state
of
the
world can be verified or confirmed by observing if the image
coordinates of the object conform to the hypothesis. In doing
so, it is necessary to have both the intrinsic and extrinsic
camera model parameters calibrated
so
that the two-dimen-
sional (2D) image coordinate can be properly predicted given
the hypothetical 3D location of the object.
The above purposes can be best served if the following
criteria for the camera calibration are met.
I)
Autonomous:
The calibration procedure should not
require operator intervention such as giving initial guesses for
certain parameters, or choosing certain system parameters
manually.
2)
Accurate:
Many applications such as mechanical part
inspection, assembly, or robot arm calibration require an
accuracy that is one part in a few thousand of the working
range. The camera calibration technique should have the
potential of meeting such accuracy requirements. This re-
quires that the theoretical modeling of the imaging process
must be accurate (should include lens distortion and perspec-
tive rather than parallel projection).
3)
Reasonably Efficient:
The complete camera calibra-
tion procedure should not include high dimension (more than
five) nonlinear search. Since type b) application mentioned
earlier needs repeated calibration of extrinsic parameters, the
calibration approach should allow enough potential for high-
speed implementation.
4)
Versatile:
The calibration technique should operate
uniformly and autonomously for a wide range of accuracy
requirements, optical setups, and applications.
5)
Need
Only
Common Off-the-shelf Camera and
Lens:
Most camera calibration techniques developed in the
photogrammetric area require special professional cameras
and processing equipment. Such requirements prohibit full
automation and are labor-intensive and time-consuming to
0882-4967/87/0800-0323$01.00
O
1987
IEEE
