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156. 
BUNDLE ADJUSTMENT WITH MODEL COORDINATES 
Karsten Jacobsen 
University of Hannover 
Abstract 
Model coordinates can be transformed into quasi-photo coordinates and be used in 
bundle block adjustments. Also if only analog plotters are available the advantages 
of the bundle method can be used. But some geometric information are lost by the 
creation of models. So with quasi-photo coordinates computed from model coordinates 
only the accuracy of block adjustments with independent models can be reached. In 
relation to a bundle block adjustment, the accuracy of the height can be reduced in 
using model coordinates as original information by 100%. 
Key Words: Bundle Block Adjustment, Independent Models, Model Coordinates 
1. General 
Even with the increasing number of analytical 
plotters also today not every photogrammetric 
company or governmental photogrammetric 
department is equiped with it or with comparators. 
In such a case a block adjustment must be based 
on model coordinates. A bundle block adjustment 
can be done only with photo coordinates but it is 
possible to transform model coordinates into 
quasi-photo coordinates. If this will be done, it 
is not necessary to use the method of independent 
models. So the bundle block adjustment can be 
used with the opportunity of later increase of 
accuracy if with new devices the data aquisition 
of photo coordinates will be possible. 
Based on photo coordinates model coordinates 
have been calculated and a back transformation 
to quasi photo coordinates has been done. The 
loss of accuracy caused by this has been analysed. 
This is corresponding to the loss of accuracy by 
the block adjustment with independent models 
against the bundle block adjustment if photo 
coordinates are available. All steps of computation 
and analysis have been done with the Hannover 
program system BLUH. 
2. Transformation of Model Coordinates 
into Quasi-Photo Coordinates 
The original geometric information in photo- 
grammetry are the bundle of rays from the 
projection centers over the photo points to the 
object points. Together with the inner orientation 
the measured photo coordinates are the required 
data for the reconstruction of the geometric 
situation. Model coordinates (also from analog 
plotters) are derived data. A back transformation 
from model coordinates to photo coordinates is 
not exactly possible. At first the y-parallax has 
been lost and there is no information about the 
orientation of the photos. But it is possible to 
transform neighboured models threedimensional 
together based on tie points and the projection 
centers (see figure 1). 
585 
photo 1 photo 2 photo 2 photo 3 
  
  
Fig. 1: 3-dimensional transformation of 
neighboured models 
The transformation of the points in the united 
models to a plane with a distance of the focal 
length from the projection centre will deliver 
quasi-photo coordinates (see figure 2). With 
these quasi photo coordinates the original bundle 
of rays can be reconstructed like with the original 
photo coordinates. 
  
  
  
Fig. 2: transformation from united model to 
quasi-photo coordinates 
Nevertheless there is a difference in the 
orientation oftheseartificial photos to the original 
photos. This will not influence directly the bundle 
block adjustment, but of course the adjusted