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.
818
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B4. Vienna 1996
— €
m-- | (5 um