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GEOMETRIC CALIBRATION OF ZOOM LENSES
FOR COMPUTER VISION METROLOGY
Dr. Anthony G. Wiley, Major, U.S. Army
U.S. Army Space Programs Office
U.S.A.
Commission V
Dr. Kam W. Wong, Professor of Civil Engineering
University of Illinois at Urbana-Champaign
U.S.A.
Commission V
ABSTRACT:
Zoom lenses are used extensively in computer vision
to overcome the limited resolution provided by the
small focal planes of solid-state cameras.
Laboratory studies of zoom lenses, with a focal
range of 12.5-75 mm, showed that geometric
distortions could amount to several tens of pixels
across the focal plane, and that there were
significant changes in the distortion patterns at
the different focal settings. Changes in the
position of the principal point amounting to as much
as 90 pixels were measured. Fortunately, these
changes were found to be highly systematic over the
entire range of zoom, and were highly repeatable and
stable over time. A mathematical model was
developed to model the geometric distortions at a
fixed focal setting with an RMS error better than +
0.1 pixel. A method was devised to model the
changes in the interior geometry of zoom lenses,
with the resulting residual distortions amounting to
less than + 0.4 pixel (RMS). Laboratory results
demonstrated that three-dimensional positioning
using properly calibrated zoom lenses could improve
the accuracy as much as 200$.
KEY WORDS: Zoom lenses, geometric calibration,
computer vision, metrology.
1. INTRODUCTION
Zoom lenses have not played any significant role in
photogrammetric applications. It has been common
knowledge that major changes in both the interior
geometry and distortion characteristics occur with
changes in the focal length setting. Fryer (1986)
found that changes in radial distortions of zoom
lenses is negligible only for focal settings greater
than 50 mm. However, limiting the use of zoom
lenses to focal lengths greater than 50° mm
effectively nullify much of the advantage of the
zooming capability. In one attempt to use zoom
lenses in photogrammetric operations, Schwartz
(1989) reported on a vision system that provided
real-time calibration of the zoom lens whenever the
focal length was changed, through the use of a
super-imposed reseau grid. Extensive literature
search did not find any further quantitative data on
the changing distortion characteristics of zoom
lenses, nor any report on the use of zoom lenses for
accurate photogrammetric measurements.
On the other hand, zoom lenses are being used
extensively in machine and robot vision because of
the limited resolution capability of video cameras.
Typically, the video cameras used in vision
application have a focal plane measuring only about
9 mm x 7 mm, resulting in a very small imaging area
as compared to conventional film cameras. Zoom
lenses are needed to provide the capability to
change the focal setting on computer command so that
large areal coverage can be obtained at short focal
settings while close-up views are achieved at long
focal settings.
If geometric fidelity can be maintained on the focal
plane for the entire range of zoom, longer focal
settings will also result in higher measurement
accuracy in the three-dimensional object space.
This paper reports on the results of a study that
was aimed at developing methodologies to calibrate,
model, and correct for geometric distortions in zoom
lenses for applications in computer vision
metrology. The goal was to evaluate the geometric
stability of zoom lenses, and to develop calibration
techniques so that increase in 3-D positioning
accuracy can be achieved at longer focal settings.
2. VISION EQUIPMENTS
Experimental tests were conducted in the Vision
Research Laboratory of the U.S. Army Advanced
Construction Technology Research Laboratory at the
University of Illinois at Urbana-Champaign. An
International Robomation/Intelligence (IRI) DX/VR
vision system was used for image capture (Wong et
al, 1999).
Available for use in this study were two General
TCZ-200 interline-transfer charge-coupled device
(CCD) cameras, and two Pulnix TM80 frame-transfer
CCD cameras. All four cameras had a focal plane of
approximately 8.8 mm x 6.6 mm, which corresponds to
an aspect ratio of 4:3 for standard RS170 video
signal. The focal plane of the General cameras
consisted of 510 horizontal by 490 vertical pixels.
Each pixel has an exterior dimension of 0.017 mm(H)
x 0.013 mm (V), with only about 30$ of the surface
area being light sensitive. The focal plane of the
Pulnix TM80 cameras consisted of 800(H) x 490(V)
pixels, with nearly the entire surface area of each
pixel being light sensitive. The effective
resolution of the General cameras was 370(H) x
350(V) TV lines, whereas that of the Pulnix cameras
was 525(H) x 350(V) TV lines. Two Fujinon 12.5-75
mm, F1.2 and two Computar 12.5-75 mm, F1.8 zoom
lenses were made available for this study. Each
digital image from the vision system consisted of
512x512 pixels, with the grey level of each pixel
represented by an integer number between 0 and 255
resulting in 256 grey levels.
All program development and data processing were
performed on two monochrome DN4000 and one color
DN3000 Apollo workstations, which were part of an
Apollo network that consisted of over 75 terminals.
The high-speed, multi-window, multi-tasking
capability of the workstations provided an efficient
platform to handle the heavy computation load.
Image files were transferred between the IRI DX/VR
vision system and the Apollo workstations by means
of 5.25-inch floppy disks.
3. CONTROL FIELD
A three-dimensional control field, see Figure 1, was
established for zoom lens calibration. It consisted
of 54 round, black targets on white background.
There were ten targets of 38.1-mm diameter, eight
targets of 76.2-mm diameter, and 36 targets of
101.6-mm diameter. Each target was identified
through the use of a six-digit binary bar code
located beneath the target. A short bar represented
Figure 1. Three-dimensional control field
