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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B5. Beijing 2008 
about it in either case. The targets are tracked throughout the 
sequences using the process described in section 3, see results 
on Figure 3. 
Figure 3. Sample frames of the 1 st examined image sequence 
showing the 3-D test field with detected targets. 
The image coordinates resulting from target tracking are 
evaluated in three separate bundle block adjustments where the 
principal point, the focal length, and affine, tangential, and 3 rd - 
and 5 th -order radial, polynomial distortion parameters are 
introduced as unknowns. Among the estimated distortion 
parameters, only the one concerning radial, polynomial 
distortion of 3 rd degree deviates significantly from zero, 
considerably affects the sum of squared residuals, has a relevant 
influence on the image coordinates and appears to be 
reproducible. Therefore, the adjustments are repeated with this 
only term for distortion correction. Figure 4 shows a 
visualization of its impact, holding the value resulting from the 
first sequence. As may be inspected on table 1, the principal 
point results to be largely displaced from the image centre. All 
three adjustments yield similar values for its x-coordinate, the 
focal length, and the remaining distortion parameter. However, 
the principal point’s y-coordinate for the third image sequence 
differs largely from the ones for the first two, suggesting a 
strong relation to the vertical direction. For the image comers 
and at an object distance of 7.5m, the maximum variations of 
the projection centre position given on table 1 yield lateral 
deviations of object points of 27mm. Taking the whole range of 
each parameter into account, the effect increases to even 39mm. 
Finally, the stability of the interior orientation within a single 
sequence is investigated. For this purpose, separate interior 
orientations are introduced for every 100 consecutive frames of 
the first sequence. The evolution of the resulting principal point 
locations and focal lengths may also be inspected on Figure 4. 
The comparison of the fluctuation of the projection centre in the 
image coordinate system to the prevailing, slightly varying 
vertical direction during the capture of each set of 100 frames 
does not discover any relation. 
4.2 Integrated Calibration 
of Interior Orientation and Ranging System 
The image sequence gathered for the integrated calibration is 
intentionally acquired in a way that a widespread domain of 
capture conditions is covered concerning the object distance, 
integration time, angle of incidence, and position in the field of 
view. Large variations of the amplitude follow from these. 
Substantiated by the experiences described in section 2, the 
operating time, having awaited the warm-up period, is assumed 
to have no relevant influence on the measurements, and 
scattering is not present i.e. the distance between the pixel foot 
prints and the targets does not affect the range observations. 
Due to the desired variation of the exterior orientation, the field 
of control points must be designed differently from the one 
mentioned in subsection 4.1, taking into account the largely 
varying image scale and the resulting spread of imaged target 
sizes. Hence, the diameter of the target markers increases 
steadily towards the borders of the test field, allowing images 
captured close to the board to be oriented using the smaller, 
central markers, and images of smaller scales to rely on the 
outer, larger targets. Furthermore, the plane supporting the 
markers is chosen to be rather highly reflective in the near- 
infrared frequencies, which allows for shorter integration times 
and larger object distances and angles of incidence while 
avoiding the influence of motion blur to the largest extent. Due 
to restrictions of the software used for data capture, a limited 
selection of the set of potential integration times, but still a wide 
range is covered. The resulting sequence comprises 3000 
frames for the integration time of 4x4.2ms and 1000 frames for 
each of the integration times 4x2.2ms, 4x 10.2ms, and 
4x20.2ms. The calibration data thus comprises 6000 frames, 
wherefrom the amplitude data again is used for the tracking of 
targets, as described in section 3. See two samples of the 
tracking result in Figure 5. 
Image Distortion Fluctuation of the Interior Orientation 
Figure 4. Results from the first image sequence. Left: mean 
image distortion; its norm as colour coding, arrows 
pointing from distorted to according undistorted 
positions (3x enlarged). Right: interior orientations, 
determined for every 100 consecutive frames. The 
ranges of corresponding frame numbers are given 
beneath the error ellipses of the resulting principal point 
positions. The focal length is colour coded. 
[pixel] 
sequence 1 
sequence 2 
sequence 3 
Xo ± a x o 
85.175 ±.026 
84.840 ± .027 
84.785 ± .024 
Yo ± Ov0 
-53.937 ± .030 
-53.728 ± .029 
-54.992 ± .022 
f ± Of 
201.018 ± .030 
200.535 ± .035 
200.803 ± .037 
a3 ± Oa3 
-0.425 ± .001 
-0.435 ± .001 
-0.433 ± .001 
Table 1. Interior orientations and parameter values of radial, 
polynomial distortion of 3 rd degree, adjusted for the three 
investigated image sequences. 
Again, the image coordinates obtained from target tracking are 
introduced into bundle block adjustments, where the interior 
orientation and the accepted distortion parameter are treated as 
unknowns. Due to the large number of frames, the sequence is 
divided into blocks comprising 1000 frames each, yielding 
adjustments of data with common integration times. The 
resulting parameter values of the interior orientation and the 
radial distortion may be inspected on table 2. Despite the worse 
configuration following from the planarity of the test field, the 
estimated standard deviations are comparable to those presented 
on table 1. As the signal level generally grows with the 
integration time and the image noise accordingly decreases, one 
may expect an effect of the integration time on the precision of 
the given parameters. However, this cannot be verified. 
Using the parameters on table 2 in combination with the 
exterior orientations that likewise result from the bundle block 
adjustments, the projection ray of each pixel is intersected with 
the known plane of the whiteboard, providing a reference value 
for the actual range observation. As already mentioned, 
observations that point to target markers are disregarded.