ISPRS Commission III, Vol.34, Part 3A „Photogrammetric Computer Vision“, Graz, 2002
correlations between parameters. In general, the following
could be observed:
* There is high correlation between K, and K,.
* There is high correlation between x , and Py.
* There is high correlation between y p and Py.
® There is high correlation between the IOP and EOP when
using point-based self-calibration. This correlation is not
observed when using line-based self-calibration.
* The estimated A, and A; are not significantly different
from zero. This indicates that there are no affine
deformations associated with the involved camera.
Moreover, using four parameters ( x p» Yp» €, Ky) resulted ina
: 2 ; > :
variance component (O' ) that is not sienificantlv different
p 5 g y
from the variance component obtained by considering nine IOP
(x, Jp» €, Kj, Kj, Pi, P», Ay, Ay). Therefore, we concluded
that considering x p» Jp» €» Ki sufficiently models the IOP of
the involved camera.
Derived estimates of IOP using the traditional point-based and
the developed line-based self-calibration procedures are shown
in Table 1. Through visual inspection, results from both
approaches are quite comparable. Also, by comparing results
from Experiments A through D, we observe that the IOP of the
involved camera has no significant variation between
experiments. This indicates that the internal characteristics of
the camera are stable over short time periods.
Intersections of conjugate light rays have been used to compare
the IOP derived from the point-based and line-based calibration
techniques (to see if there were significant differences between
the estimated IOP). In those experiments, we used the following
to compute object coordinates:
* IOP from point-based and line-based approaches to self-
calibration.
* Image coordinate measurements of the signalised targets.
e One set of EOP
Reconstructed object spaces using the different IOP are
compared through root mean square error analysis (Table 2).
From the RMSE results in Table 2, one can see that the IOP
from the point and line-based calibration procedures are
stochastically identical.
(A)
A- 148
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LE 8.014 THE
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Tey, = ARH
4.081
AM
ZI 1
0.002 8 8.011
s i I et.
t. ena 5.553
Q4 50008 7,
0.002 j
(B)
Figure 7. Original images before (A) and re-sampled images
after (B) calibration. A dashed straight line has been
added to show the deviation from straightness before
calibration (A) and its recovery after calibration (B).
In order to evaluate the quality of the derived IOP, the images
have been re-sampled after removing various distortions (Figure
7-B). One can see that the straightness property has been
correctly restored. A quantitative measure is developed using
regression analysis applied to the measured intermediate points
along the straight lines before and after calibration (namely, the
variance component resulting from straight line fitting through
the intermediate points). These results can be seen in F igure 7-
B. The computed variance components after calibration are
significantly improved after the calibration process.
Table 1. Estimates of IOP and distortion parameter
Experiment A Point Line
o, 0.0018 0.0020
x, [mm] -0.1223 (=0.0046) | -0.1169 (+0.0016)
y, [mm] -0.0756 (0.0048) -0.0648 (+0.0016)
c [mm] 11.6042 (+0.0124) | 11.6094 (+0.0048)
K, -1.110829e-03 -1.176255e-03
Experiment B Point Line
e, 0.0018 0.0020
x, [mm] -0.1285 (+0.0042) -0.1216 (+0.0016)
y, [mm] -0.0812 (+0.0043) -0.0718 (+0.0015)
c [mm] 11.6101 (20.0103) | 11.6189 (0.0044)
K; -1.10495e-03 -1.185481e-03
Experiment C Point Line
o, 0.0017 0.0019
x, [mm] -0.1247 (40.0040) | -0.1224 (+0.0016)
y, [mm] -0.0707 (40.0042) | -0.0642 (+0.0015)
c [mm] 11.6041 (20.0118) | 11.6034 (20.0048)
K; -1.118769e-03 -1.174221e-03
Experiment D Point Line
o, 0.0018 0.0021
x, [mm] -0.1212 (#0.0044) | -0.1171 (+0.0016)
y, [mm] -0.0759 (40.0044) | -0.0711 (20.0016)
c [mm] 11.6090 (40.0114) | 11.6016 (+0.0047)
K; -1.121013e-03 -1.177155e-03
