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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004
whether the effect is stationary with respect to time, the
measurements were carried out at 4 different epochs. Figure 6
shows the observations for one epoch. A Fourier analysis of the
signal was carried out, which shows a high peak at the period
near Z (Figure 6). The analysis of the other epochs shows that
the camera is not stable over time. The instability of the camera
causes different amplitudes and periods of the observations.
Figure 7 shows the observations and the power spectrum of
another epoch. These experiences indicate that the camera has a
periodic oscillation.
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4.2. Camera Calibration
Camera calibration was performed by the mentioned sensor
model using additional parameters. For the analysis of the
additional parameters (to find the most influential parameters
and those which are stable under the given network condition)
we added step by step each parameter to the previous stage of
the model and used the correlations for stability checking.
Comparing the additional parameters of different images, we
found the image and block-invariant parameters. We will report
the result of calibration in the following sections for the last
stage.
4.2.1. SpheroCam
The camera calibration was performed using a testfield. We
established a testfield with 96 circular targets at our institute and
used it for the calibration of the SpheroCam. The testfield was
measured with a Theodolite with mean precision of 0.3, 0.3, 0.1
mm for the three coordinate axes (X, Y, Z). The camera
calibration was performed by the additional parameters
mentioned in chapter 3. To model the tumbling error 6
parameters were used. The a posteriori variance of unit weight
is 0.59 pixel (4.7 microns) after self-calibration. Figure 8 shows
the residuals of the image point observations in the image space
for this case. A comparison of the computed tumbling
parameters of different images shows that none of the tumbling
parameters is block-invariant. To see the effect of tumbling
parameters, a camera calibration was performed with the same
condition but without tumbling parameters. In this case the a
posteriori variance of unit weight is 1.37 pixels (10.9 microns).
4.2.2. EYESCAN
For EYESCAN, we got the image and field observations from
Mr. Schneider, TU Dresden. TU's testfield consists of more
than 200 control points and the mean precision of control points
is 0.2, 0.3, 0.1 mm for the three coordinate axes (X, Y, Z). The
camera calibration was performed with the same model and the
additional parameters as mentioned in chapter 3. To model the
tumbling error of this camera 3 parameters were used. The a
posteriori computed variance of unit weight is 0.33 pixel (2.6
microns) Figure 9 shows the residuals of the image point
observations in the image space. A comparison of the computed
tumbling parameters of different images shows that 2 of 3
tumbling parameters are block-invariant. In the case that
tumbling parameters were not used the a posteriori computed
variance of unit weight is 1.30 pixels (10.4 microns).
4.3. Block Adjustment with Accuracy Test
An accuracy test was performed for EYESCAN by block
triangulation using 5 camera stations and by defining 151 check
and 3 control points. Considering the result of camera
calibration for different images, totally 8 parameters were used
as unknown block-invariant, 1 parameter as priori known
parameter (camera constant) and 6 parameters as image-
invariant parameters. Table 2 shows the summary of the results
of adjustment without the modeling of the tumbling. The RMS
errors of check points compared with the standard deviations
are too large. The reason is that the mathematical model is not
complete and cannot interpret the physical behavior of the
dynamic camera system. To complete the mathematical model,
tumbling parameters were added and the accuracy test was
performed. In this case, 8 parameters were used as unknown
block-invariant, 4 parameters as a priori known parameters
(camera constant and 3 tumbling parameters), and 6 parameters
as image-invariant parameters. The summary of the results of
adjustment is in the Table 3. Figures 10 and 11 show the object
space residuals for checkpoints in depth axes (X and Y) and
lateral axis (Z). The RMS errors of check points, compared with
standard deviations, are reasonable and shows the effect the
tumbling parameters in the modeling. However, the systematic
patterns of the residuals have not been completely removed, but
the size of the errors is significantly reduced. The remained
systematic errors may come from non-modeled mechanical
errors of the camera.
For the accuracy test, similar to the conventional close range
—-
photogrammetry (frame CDD cameras), 3 control points were
