DISCUSSION OF RESULTS.
To this author's delight (and relief) both the Wester-
Ebbinghaus and Brown methods for a single station
self-calibration worked with a minimum of fuss. There
were some anxious moments in the office deciding on
how it would be possible to rotate the camera while
keeping the focus point stationary, but in practice in the
laboratory it was not too difficult. Other fears of
producing 'matrix singular' conditions in the solutions
were similarly dispelled.
The result shown in Figures 1 and 2 indicate the high
degree of reliability achieved. Table 1 shows that the
root-mean-square value achieved on the images after
adjustment were all similar at approximately one-seventh
of a pixel for the Fotoman camera used. Given the
relatively small size of the targets imaged (4 to 7 pixels
in diameter), high accuracies were not anticipated.
The only real differences discernible are in the values for
the principal distance and the offsets of the principal
point. As noted earlier, uncertainties in the location of
the single station camera location directly relate to
uncertainties in the principal distance. The results of the
bundle adjustments for the additional parameters of xo, yo
and P1, P2 showed high correlation (greater than 0.85) in
each case except for the Brown method where it was not
so significant. This was a little surprising and may be
related to the higher number of images used although
further investigation may show this to be a function of
the particular set of targets used.
CONCLUSIONS AND FUTURE USES.
The photogrammetric community, especially those
working in the close range field, owe a tremendous debt
of gratitude to men like Duane Brown and Wilfried
Wester-Ebbinghaus. They pioneered many calibration
procedures and whilst this paper concentrates on the
relatively obscure topic of single station self-calibration,
their contributions to our discipline were much wider.
Is there a future for single station self-calibration? As
this paper shows, it is a technique which does work, but
it is obviously not as robust nor convenient for most
applications as is a conventional convergent self-
calibration bundle adjustment.
One could think of obscure situations where it may be
applied however. Consider a robot inside a nuclear power
station which must automatically re-focus its video
camera before taking some images of pipe-work. It is
conceivable that it could be in a confined space and by
taking several images with its camera tilted through the
range of its angular field of view, it could generate its
own self-calibrating data.
180
Perhaps other scenarios are more likely, including those
in industrial situations where cameras are fitted to
concrete plinths or bolted to frames for the taking of
images of tooling jigs. Single station self-calibration
may be used as a quality assurance event in such
situations prior to the taking of the industrial imagery.
60
$0 -] Legend
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= ee Brown Technique m c
= ---5-- . Plumbline uo
= 5
= 307
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= 20-7
= 4
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107
07
0 1 2
Radial Distance (mm)
Figure 1. Radial Distortion
3
t Legend
= —— z— Conventional Bundle "i
5 ----e--- Wester-Ebbinghaus AA
= 2:5 -----g---- Brown Technique plot
= —-o-- Plumbline aui
9—Á
ut uf ou
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EL A
= f
£45
=
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a nt
dd PE IS +" 4
03 VER A : T T
0 ] 2 3
Radial Distance (mm)
Figure 2. Decentering Distortion
ACKNOWLEDGEMENTS.
The author wishes to thank the assistance of Dr. Eric
Kniest and Ms. Kerry McIntosh during the laboratory
capture of the images and the subsequent image
processing and centroiding of the targets.
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996
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Figure 3
Brown, D.C
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Camera, R(
AFMTC-TN
Brown, D.C
: The Precis
from Photo
from Juno
Report 54, I
59-25.
Brown, D.
Calibration
Cambridge
AF19(604)-:
Brown, D.C
Symposiun
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