ng 
or image orientation 
In this paper, image 
:al-world test object. 
ges extracted from 
nation of both, the 
sults show, that an 
e Verwertung von 
unkten basierende, 
; als Testobjekt die 
n. Mehrere rund um 
sen digitalen Bildern 
ıltanen Bestimmung 
obnisse zeigen, daß 
ı konnte. 
] was presented in 
93): The shape of a 
ompletely described 
of these nodes in 
adjusting the curve 
rays of at least two 
basic problems of 
d using line features 
ges merely by free- 
rarily chosen local 
| (alike relative 
1 free-form control 
ject curves from at 
-form control curves 
dels from computer 
nna 199¢ 
tomography (Forkert et al. 1994). The solution of the 
reconstruction task was demonstrated in 1995 with a 
car as real world test object (Forkert et al. 1995) So, 
this paper deals with the orientation of images 
exclusively based on tie curves working on the same 
car. 
2. THE TEST OBJECT 
    
Figure 1: Car image | 
Twelve images were taken from around the car using a 
P31 terrestrial metric camera with a principal distance 
of 100 mm. The camera was focused to 4m, thus 
achieving an average image scale of 1:40. The image 
format was 12 cm x 9 cm. Figure 1 shows one of the 
images; the arrangement of the photographs can be 
seen in figure 2. It was mainly chosen according to 
considerations about the depth of field. For control 
purposes, 116 points were targeted on the car surface 
using black adhesive paper dots with a diameter of 8 
mm. 
z=3m 
e £=125"" 2 
S M 
NES e Ns 
V d NS Da? 
: S 
=3 z=3m 
= a [P < (car ) #5 
SN Se 
AS £7 RO 
ke (B 2° 
? z=3m S 
[z125" 
Figure 2: Arrangement of photos 
In order to get digital images, the photographs were 
scanned with a resolution of 15 pm using a Zeiss 
PhotoScan PS1. Due to the large image format we 
obtained digital images with 50 MB each. 
The measurement of the control targets was done 
using a "digital mono comparator". The accuracy of the 
position of the targets was estimated to be about +1/2 
pixels. 
For extracting tie curves from the digital images, firstly 
a line extraction algorithm was applied to the images 
delivering rather long line segments which are likely to 
present object curves (see Forkert et al. 1995). 
Secondly, line segments from different images 
belonging to the same object curve have to be declared 
homologous. Though currently done interactively with 
the help of a graphic line editor, the assignment of 
homologous lines can possibly run automatically in 
future, at least for long line segments. 
  
  
  
  
  
  
Figure 3: Lines extracted from three images 
3. BASIC CONCEPT 
Figure 4 shows the basic concept of free-form curves in 
bundle block adjustment. We have recorded points (for 
example P from the images of the original curve in the 
way described in section 2. Note that in general it is not 
possible to find homologous edge points in different 
images. The unknown three dimensional curve point P 
corresponding to the two dimensional image point P' is 
located on its image ray running from the projection 
centre through the image point. So, a "bundle" can be 
formed by all relevant rays of an image. Now, the curve 
S can be adjusted to the bundles of rays coming from 
the images (see figure 4). 
The curve S that shall be the best possible 
reconstruction of the original is described by a series of 
cubic polynomials, each representing one curve 
segment. These curve segments are joined together at 
node points with at least the first derivations of the 
polynomials being continuous. Well-known examples 
for such "joined cubic polynomial curves" are cubic 
splines or Akima curves. 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996