The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Voi. XXXVII. Part B5. Beijing 2008 
The model was extended by additional parameters for the 
compensation of remaining systematic errors, allowing the 
standard deviation of unit weight obtained from a spatial 
resection to be reduced to 0.1 pixels for a 14-Megapixel Kodak 
camera equipped with a Nikkor fisheye lens. Translated to 
object space, this corresponds to lateral accuracy of 1 mm at 10 
m distance. 
There are different fisheye projection geometries: Equi-distant, 
equi-solid-angle and orthographic projection (Ray, 1994; 
Backstein & Pajdla, 2002; Abraham & Forstner, 2005). The 
geometric concept is based on the dependence of the image 
radius r’ and the angle of incidence a (Figure 3). 
Experiments confirmed that the used fisheye lens complies best 
with the equi-solid-angle model. Therefore only this model will 
be described in the following. The image radius r ’ depends on 
the angle of incidence a: 
r'= 2c ■ sin 
“ where Xma= EH 
(5) 
In order to express the image observations x' and y ’ as function 
of the exterior and interior orientation as well as on the object 
point coordinates, equation (5) has to be introduced in the 
following equation, whose derivation is explained in detail in 
[Schwalbe & Schneider, 2005]: 
x'= ;c 0 ' + 
y=T 0 ' + 
\yj 
+ Ay' 
+ 1 
(6) 
The correction terms Ax ’ and Ay ’ contain additional parameters 
for the compensation of radial-symmetric (A h A 2 , A 3 ) and 
decentering (Bi, B 2 ) lens distortion (Brown, 1971) as well as 
affinity and shear of the image coordinate system (C/, C 2 ) (El- 
Hakim, 1986): 
Ax' = x' (A i r ,2 +A 2 r' 4 +A 3 r' 6 ) + Bj (r ,2 + 2x a ) + 2B 2 x' y' + C,x' + C 2 y' (7) 
Ay' = y'(A i r' 2 +A 2 r' 4 +A 3 r' 6 ) + 25,x'y' + B 2 (r a +2y a ) 
3. COMBINED BUNDLE BLOCK ADJUSTMENT 
The geometric model of fisheye lens cameras was integrated 
into a bundle adjustment software package, which was 
originally developed and implemented for a combined analysis 
of laser scanner data and central-perspective or panoramic 
image data (Schneider & Maas, 2007). 
The bundle adjustment software package supports the 
calculation as free network adjustment and handles outlier 
detection. Since different types of observations have to be 
adjusted simultaneously, it is necessary to assign adequate 
weights to the laser scanner and fisheye image observations. 
For this purpose a variance component estimation procedure 
was implemented in the adjustment. Thus, the precision 
characteristics of laser scanner and fisheye lens camera will be 
optimally utilised, and an improvement of the adjustment 
results can be achieved. Furthermore, this allows for a 
qualification of the measurements in terms of realistic accuracy 
values for fisheye lens data and laser scanner data. 
4. PRACTICAL EXPERIMENTS 
4.1 Calibration room 
In order to practically assess the presented method, multiple 
laser scans and images with a fisheye lens camera were 
acquired in a test field, which is designed for the calibration of 
fisheye lenses (Schwalbe, 2005). 
The test field is a room (4><5><3 m 3 ), where 100 signalised 
object points are distributed at the surrounding walls and at the 
ceiling in a way that they form concentric circles on the fisheye 
image (Figure 4). Object point targets are designed as black 
circles (0 10 mm) on white background with a ring code, to 
allow for an automatic target detection and identification. The 
targets are orientated in a way that they face perpendicular to 
the centre of the room. Reference coordinates were determined 
using a common photogrammetric measurement system. 
However, the coordinates are only used as approximate values 
in the bundle adjustment and to define the superordinated 
coordinate system. The XY-plane of this coordinate system is 
orientated horizontal and the Z-axis is a vertical axis. 
Figure 4. Fisheye image from the centre of the calibration room 
orthogonal to the ceiling with highlighted object point numbers 
4.2 Laser scanner data 
A terrestrial laser scanner Riegl LMS-Z420i was situated in 
each comer of the calibration room and tilted 45° vertically, in 
order to allow for the recording of points on the ceiling. 
Additionally, two scans from the centre of the room were 
recorded with a tilt angle of 90°. The laser scanner was also 
rotated 90° horizontally between both scans. 
The angular resolution of the laser scans was 0.035°, which 
corresponds to a scan point distance of 2.5 mm in 4 m distance.