Number of Hidden Layer Units 
  
Geo-referencing Error (m) 
o 
o 
  
0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000 
Number of Iterations 
Figure 10 Geo-referencing Error against number of 
iterations for different Hybrid Network Topologies 
  
  
No of Hidden Hybrid Network 
Units mean (m) std dev (m) 
6 59 37 
10 62 6.9 
20 71 12.1 
  
Table4 Statistics of the Learning Curves 
in Figure 10 
The results in Table 4 using 20, closely resemble the 
results for the same test using the stand-alone neural 
network in Table 3, however, the stand-alone neural 
network does not achieve the levels of precision achieved 
by the hybrid network (ie. 59 m using 6 units) 
irrespective of the number of iterations and number of 
hidden layer processing units used in training. 
Unfortunately, the hardware used in this work restricted 
the exploitation of the parallel structure of the neural 
network and hybrid network algorithms. The total time 
taken to geo-reference the complete ERS-1 SAR image 
(8000 x 8000 pixels) was approximately 3 hr 30 mins. The 
time taken to geo-reference the complete image, and the 
geo-referencing precision of the hybrid network, are 
compared to those of the Platform Trajectory Model rule 
base and to those of the stand-alone neural network in 
the following section. 
6. SUMMARY 
The paper has analysed the functionality of a Platform 
Trajectory Model approach (82) a neural network 
approach (83) and a hybrid network approach (84) for 
image geo-referencing. The results of this latter approach 
have shown that a hybrid network can achieve better 
precisions, while at the same time, remove a significant 
proportion of the unmodelled, undetected systematic 
errors which exist when  geo-referencing earth 
observation imagery using neural networks. 
Figure 11 illustrates the relationships when comparing the 
geo-referencing precisions and times taken to geo- 
reference the complete image using the three 
approaches; the Platform Trajectory Model, the stand- 
alone neural network and the hybrid network. It must be 
borne in mind that it takes more time to train the network 
than it does to use it. 
300 
  
250 L Platform Trajectory Model 
200 + 
150 L Stand-alone Neural Network 
100 + * 
50 + 
Hybrid Network 
  
  
  
Typical Geo-referencing Precision (m) 
i + i : i : — 
0 2000 4000 6000 8000 10000 12000 13000 
Time taken to Geo-reference 8000 x 8000 pixel image (seconds) 
Figure 11 Comparison of Geo-referencing 
Techniques 
The tests presented in this paper were not designed to 
provide an optimised geo-referencing tool for the 
geometric rectification of earth observation imagery. The 
tests were performed to analyse the behaviour of an 
integrated rule base / neural network processing model. 
Similar network architectures, to those presented, may be 
used in any area of image processing where there is the 
requirement for improving the function mapping ability of 
a neural network. 
7. ACKNOWLEDGEMENTS 
The authors would like to acknowledge the support of the 
United Kingdom Science and Engineering Research 
Council (SERC, subsequently EPSRC). 
8. REFERENCES 
Bengio, Y, De Mori, R, Flammia, G and Kompe, R, 
1992, Global Optimisation of a Neural Network-Hidden 
Markov Model Hybrid, IEEE Transactions on Neural 
Networks, Vol 3, No 2, March 1992. 
Burniston, J D, 1994, Integrated Neural Network/Rule- 
Based Architecture for | Continuous Function 
Approximation, PhD Thesis, Department of Electrical and 
Electronic Engineering, The University of Nottingham. 
Dumville, M., 1995. Geo-referencing Earth Observation 
Imagery. PhD Thesis, The Univeristy of Nottingham. 
Putter E, 1993, An Ecological Application of SAR 
Imagery, MSc Thesis, Department of Geography, The 
University of Nottingham. 
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International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B4. Vienna 1996 
— € 
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