correlating the sampled code with a step function 
over half the circle. This is to detect the reference 
half of the circle. The other half of the circle 
contains the 10 bit code. Reading this code is done 
in a straight forward manner by comparing the 
densities in the bit centre with a threshold density 
level. This threshold depends on the densities found 
in the binary code. 
  
  
— 
  
density (a.u.) 
  
  
  
  
   
0 180 
degree 
figure 6: sampled densities of binary coded 
identification 
The experiment showed that if the least squares 
matching procedure was successful the binary code 
could be read also, except for those cases where a 
part of the code was occluded. Note that a 
significant improvement in Signal to Noise is still 
available by better modelling the image of the 
binary code. Obviously smaller photoscales are 
allowed before one runs into detection/recognition 
and estimation problems. 
7. Bundle adjustment 
The positions of targets and reseaucrosses obtained 
through template matching are the basic input for 
the data reduction process to follow. 
The data reduction consists of two steps: 
- inner orientation; 
- bundle adjustment. 
In the inner orientation step the transformation of 
the measured positions of the targets to the system 
of the camera, represented by the imaged 
reseaucrosses is performed. 
In this step the filmdeformation is corrected for 
using the method of bilinear interpolation. The 
resulting positions of the target in the camera 
system are represented by their photocoordinates. 
228 
The photocoordinates of the targets and the 
approximate values of camera and target positions 
form the main input for the bundle adjustment step. 
The least squares bundle adjustment results in the 
3-dimensional coordinates of the targets. The 
software package BINAER used for the bundle 
adjustment allows for simultaneous solution of 
camera parameters, a so-called "on-the-job" 
calibration of the camera. 
In table 1 the results of the adjustments of the 
manual and the automatic measurements are 
generalized. Significantly more targets were 
measured manually than automatically. This is due 
to two effects: First a considerable number of 
targets were incomplete or deformed for testing 
purposes. Secondly, in contrast to the matching 
software, the operator can interpret the images that 
are incomplete and in this way he is able to 
measure most of the target images. The 
measurement of defected target images in 
combination with the resulting increase in 
redundancy leads to an increase of the estimated 
variance factor (tablel: all manual versus selection 
of manual observations). Comparing the adjustment 
of corresponding target maesurements the digital 
approach shows a reduction in estimated variance 
by a factor 1.4 (table 1: select.manual - digital). 
  
  
results # targets # target estimated degrees of 
BINAER measurements | standard deviat.| freedom 
manual 104 599 41pm 40 
select. manual | — 7) 27 35 pm 19 
digital N 227 30pm 19 
  
  
  
  
  
  
  
tabel 1: results of the bundle adjustment (8 photo- 
graphs) 
The gain in precision expected from the digital 
approach was less than anticipated. One error 
source was underestimated: the film deformation. 
Using bilinear interpolation correcting for film 
deformation errors up to 45 pm leaves errors up to 
2 pm. Furthermore it became clear that next to 
improving measurement precision the model itself 
should be improved. For instance the lens and 
camera model should be refined. The automatically 
and manually measured photo coordinates match 
with a precision of 2 pm RMS allowing an affine 
transformation between the two systems. 
Comparing this with the variance factors estimated 
in the bundle adjustment it can be concluded that