In: Wagner W., Székely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Voi. XXXVIII, Part 7B 
397 
6x 2 = P,(r 2 +2x 2 ) + 2P 2 xy 
Sy 2 =2P 1 xy + P 2 (r 2 +2y 2 ) 
A third distortion element, specific to digital cameras 
accounting for scale distortion of pixel sizes in the x and y 
direction is also incorporated 
5x 3 = Bix + B 2 y 
(5) 
The final mathematical model is a result of adding Eqs. 3 and 4 
and 5 to the right hand side of Eq. 
x f m n (X-X c ) + m 12 (Y-Y c ) + m 13 (Z~Z c ) 
Xp ~ [_ m 31 (X - X c ) + m 32 (Y - Y c ) + m 33 (Z - Z c ) 
+ 8xj + 5x 2 + 8x 3 
y-y P 
f m 21 (X - X c ) + m 22 (Y - Y c ) + m 23 (Z - Z c ) 
|_m 31 (X - X c ) + m 32 (Y - Y c ) + m 33 (Z - Z c ) 
•f 8yj +• 8y2 
(6) 
EDC CAL/VAL LAB SIZE 
Figure 1. Layout of the calibration lab and the calibration cage 
2.2 Experimental set-up for cage based self calibration 
The camera calibration facility is located at the ETSGS’s Earth 
Resources Observation and Science (EROS) Data Center in 
Sioux Falls, South Dakota. Fig. 1 shows the position of the 
calibration cage, with respect to the room. Also shown are some 
of the positions for locating the cameras. The cage consists of 
three parallel panels. Each panel has a number of circular retro- 
reflective targets (dots), and a few coded targets (Fig 2a). The 
coded targets are so referred because the pattern of the 
placement of the individual circular dots that make up these 
targets is unique (Fig. 2b). Each coded target has five dots that 
are positioned in the same relative orientation as the red lines 
shown in Fig. 2(b). The intersection of the red lines is taken as 
the centre of the coded target. 
For the calibration procedure, the camera lens is always 
focussed at infinity. The choice of the distance of the camera 
from the front panel of the cage depends on the focal length of 
the camera, and the depth of focus that has been selected. Once 
the camera-cage distance is fixed, three angular positions from 
the centre of the front panel of the cage are selected. The 
angular positions are selected keeping in mind the optimal 
angles for convergent photography, and the limitations imposed 
by the dimensions of the calibration room. Ideally, the angular 
positions will be close to what is shown in Fig 1. Once the 
images are captured, they are processed using software called 
Australis (Fraser, 2001). Australis uses a free network method 
of bundle adjustment. It recognizes the patterns in the coded 
targets and calculates their centre. 
(a) 3D Calibration cage 
Coded 
target 
centre 
D 
(b) Coded target (c) Circular target 
Figure 2. (a) Image of the calibration cage, with three panels (b) 
the pattern in a coded target and (c) the individual circular 
target