The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
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2. CAMERA CALIBRATION 
2.1 Calibration using a movable planar target 
The calibration target is made of a stable planar wooden board, 
sized 140 x 120 x 2.5 cm. Because of its low weight (<10 kg) it 
can be easily moved to any location suitable for calibration, 
indoor or outdoor. The layout of the present 2D target is based 
on the target used by PhotoModeler. However, the square 
layout of the original target was modified by adding two 
additional columns of markers on the left and right side (see 
Fig. 2). The four coded markers can be identified uniquely in 
images taken from arbitrary viewing directions. 
The rectangular pattern of 10 x 14 black markers (0 2cm) 
allows acquiring single images fully covered by markers. This 
facilitates measurement of the effect of lateral chromatic 
aberration (cp. Kaufmann & Ladstadter, 2005). 
For calibration purposes, images should be taken from various 
directions, viewing angles and distances. It is also 
recommended to take images with the camera rotated 90°. 
Using such an image configuration, it is possible to de-correlate 
calibration parameters from EO parameters (e.g. focal 
length/object distance and principle point/rotation angles). The 
target should not be moved during calibration in order to avoid 
deformation. 
We performed three independent calibrations, on June 25, 2007, 
on July 1, 2007, and on March 19, 2008. Series of 16 to 31 
images were taken handheld for each of the three lenses (see 
Table 1). Using daylight, it was not necessary to use a tripod 
which speeded up the whole process. Images were taken using 
the far end (oo) of the focusing ring. This is a repeatable setting, 
which corresponds more or less to an infinite object distance. 
However, this setting causes blurred images because of the 
close distance (max. 3m) of the calibration target, especially for 
the 80mm lens. A high f-number (f/27) was therefore used to 
minimize blurring. 
2.2 Calibration using a 3D test field 
Two separate calibrations were performed on August 1, 2007 
and on March 19, 2008 (on the same day as for the second 2D 
calibration) in the in-house calibration room of Vexcel Imaging 
Graz (see Fig. 3), which is routinely used for calibration of the 
UltraCamX digital aerial camera.. The size of the test field is 
approximately 8m x 2.5m x 2.5m. A total of 394 circular 
markers are glued on aluminum bars mounted on a concrete 
wall, floor and ceiling. The coordinates of all the targets have 
been determined by a geodetic survey with a precision of +/- 
0.05 mm. In contrast to the 2D calibration target, no coded 
markers exist in the test field. 
Figure 3. Calibration room of Vexcel Imaging Graz 
Images were taken from three positions (left, middle, right), 
with different viewing directions. Again, additional images 
were taken with the camera rotated 90°. Series of 15 to 35 
images were produced for each lens (see Table 2). A high f- 
number (f/27) was also used for the 3D test field. The limited 
lighting required relatively long exposure times (~0.7sec) and 
thus the use of a tripod. Because of the room dimensions, the 
maximum distance to the back wall is limited to 8m. 
2.3 Automated marker measurement 
Automated and precise measurement of circular markers 
requires an algorithm that is capable of fitting an ellipse in the 
image. Such an algorithm, described e.g. by Luhmann (1986), 
was implemented as a MATLAB function. Given a starting 
point somewhere inside the marker, the algorithm first 
determines the approximate (maximum) diameter of the ellipse, 
then performs a radial search for edges in various directions and 
finally fits an ellipse to the previously located points (see Fig. 
4). Our test results show that the center of the ellipse can be 
determined with an accuracy of at least one tenth of a pixel and 
that the algorithm also works with low contrast or noisy images. 
♦ Fitted ellipse 
Center point 
Approximation position 
+ Point measured on edge 
Rays used for edge dedection 
Figure 4. Ellipse fitting operator