International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part BI. Istanbul 2004
NE
Figure 1: The used test field for calibration. The coordi-
nates of the marks are known only approximately.
image coordinates as parameters. Five different sets of ad-
ditional calibration parameters for compensating for non-
linear distortions are used.
O no additional distortion parameters, only principal dis-
tance and principal point
additional physically motivated parameters:
A One radial-symmetric distortion parameter A1
B A; and two tangential distortion parameters By,
B» (cf. (Brown, 1966))
C Three radial-symmetric distortion parameters A,
Ag, As, two tangential distortion parameters Bj,
B3 and one affine shear parameter C
T additional modeling of distortion with Chebychev poly-
nomials with maximum degree of 3, cf. (Abraham
and Hau, 1997).
3 RESULT OF INVESTIGATIONS
3.1 Accuracy of Measurements
We first compare the precision obtainable with the different
cameras. This can be evaluated with the mean precision of
the image coordinates of the points. The automatic point
location procedure yields an individual internal estimate
for the covariance matrices for the image coordinates, and
the chosen camera model influences the residuals, thus the
estimated Go and therefore the estimated standard devia-
tion of the image coordinates. Therefore we give the mean
value of the internal estimates for the individual standard
deviations of the image coordinates corrected by the best
achievable variance factor, implicitly assuming the small-
est variance factor most realisticly reflects the achievable
measuring accuracy. In nearly all calibrations the Cheby-
chev polynomials model delivers the best c in the bundle
adjustment.
The results are shown in figure 2. The mean standard devi-
ations c5; in nearly all cases are around 0.1 pixels. The bad
results with the Terreatec web cam certainly result from the
large compression rates, whereas the standard deviation of
0.25 pixels with the large images with the Sony camera can
be explained by non-modeled distortions.
The relative accuracy (not shown in the figure) which can
be achieved can be characterized by the mean standard de-
viation related to the width w [pixel] of the image, being
the length of the larger side. Except for the web cams, a
relative precision of better than 1 : 10 000 can be reached,
indicating a high accuracy potential achievable with con-
sumer cameras.
No dependency between accuracy of mark detection and
compression ratio could be observed regarding HP, Sony
and Logitech cameras (compression ratio from 1.0 to 6.7).
The huge compression ratios of 11. 3 and 15.9 of the Ter-
ratec camera seem to have a strong influence on the accu-
racy of mark detection and as a result of that on the cali-
bration.
1 T T T T T T T T T T
1 2V 2M 3V 3MB 3MO 4V 4_1M 4M 5
Figure 2: Mean precision of image coordinates of marks
of test field: c, in pixels.
The maximal estimated distortion within an elliptic im-
age region with semi-major axis a = 97.596 of image
width and semi-major axis b = 97.5% of image height is:
Logitech: 1.8 Pixel (VGA resolution), Terratec: 2.3 Pixel
(1MB resolution), HP: 0.4 Pixel (3MB resolution), Sony:
23.7 Pixel (5M resolution, Zoom 1x), Kodak: 15.1 Pixel
(6MB resolution).
3.2 Temporal Variations of Calibration Parameters
The calibration of cameras was repeated between 3 and
7 times within a period of 4 months. We did not observe
any systematic temporal increase or decrease of calibration
parameters.
Only random variations could be observed. In the follow-
ing we show and discuss the range of change of different
parameters in the mentioned time period.
3.2.1 Temporal changes in principal distance. The
changes in principal distance c are shown in figure 3. They
again refer to the image width: (Cmax — Cmin)/W. This
Internati
Figure
From |
with v
demou
ratio i
Theref
We fin
1. For
tors. T
betwee
perfort
stable |
The zo
2. The
DCS 4
found |
or unn
tions a
than th
3. The
cipal d
4. The
variatic
(1). Re
compa
Observ
for diff
no com
322
poral c
Again |
We fin
