3. NEURAL NETWORKS
The task facing the neural network is to perform the
multiple transformation stages of the geometric
rectification process. Firstly, a pixel's image coordinates
need to be geo-referenced into a 3-dimensional geodetic
coordinate system, from where they can be converted to
local geodetic coordinates. Subsequently, the local
ellipsoidal coordinates require projecting as grid
coordinates. This form of direct rectification produces
projection coordinates for each pixel in the image (Figure
1). This can often result in pixels being overlaid or missed
in a rectified image and therefore requires a post-
processing filter to be employed on the rectified image to
solve these problems.
E
——
put image
oordinates :
output map
coordinate:
— e
N
Figure 1
Geo-referencing Using Neural Networks
4. HYBRID NETWORKS
A hybrid network is required to learn a different mapping
function to that learnt by the stand-alone neural network.
From the exterior of a hybrid network there is no evident
change of architecture from that of a stand alone neural
network. The input and output are the same. However,
internally the architecture of the two differ significantly.
The neural network module of the hybrid network is used
to provide corrections to the estimated geo-referenced
coordinates produced from the rule-base that operates in
parallel to the neural network module. The neural network
performs a different task to that previously mentioned in
82, a different geo-referencing function is required, and
therefore a new network topology is required.
Size of Hidden Layer (processing units)
d d emm 6 8 10
s 1200
E
- 1000 + %
©
o
>
ui 800
o
£
©
9 600
©
2
2 400
©
- x
Ó 3
$= Te
oO re em 4
0 ; + + + + + + +
0 5 10 15 20 25 30 35 40 45 50
Number of Iterations
Figure 2 Hidden Layer Size Test Results
Tests were performed to decide upon the new topology
and values for the new network parameters within the
814
neural network module of the hybrid model. This included
tests for the number of hidden layer units, the learning
term and the momentum rate.
Figure 2 shows the effect of altering the number of the
hidden layer processing units. From the figure it is evident
that all five curves are highly correlated, possessing very
similar characteristics. What is apparent from the figure is
that the final result is approximately the same for all
curves independent of the number of hidden layer units.
This simple test demonstrates that a hybrid network, used
for image geo-referencing, requires fewer processing
units than a stand-alone network. This property of hybrid
networks was also concluded by Burniston (1994), for the
use of hybrid networks in speech approximation.
For geo-referencing tasks, the reduced number of hidden
layer units can be attributed to the fact that the major
rectification manoeuvres are performed by the rule-base
and not the neural network module as was the case in 82.
Other network design tests were performed using the
ERS-1 SAR image. The topology which provided the best
results, in the design phase, was subsequently kept
constant for all of the operational tests. The empirical
tests for determining values of the learning term and the
momentum rate yielded figures of 0.1 and 0.5
respectively. The design tests resulted in the network
topology as illustrated in Figure 3, with the neual network
module assembled from a single hidden layer, containing
6 hidden layer processing units.
Corrections to
rule-based
Estimates
Figure 3 Hybrid Network Topology
The final hybrid network had the same neural topology as
used for the stand-alone neural network but possessed
different values for the learning term and the momentum
rate.
4.1 Hybrid Network Geo-referencing
This section presents the results using the hybrid neural
network to determine its learning ability, its performance
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B4. Vienna 1996
