rs 
a’ Neural network | 
  
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image X betta ria 
  
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< 10. Neural ac. o V 
E 00 | 
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Figure 3 
The built-up of the neuro-fuzzy classifier 
As it can be seen the AND function was used for the 
implication. AND can be varied also: Zadeh-, algebraic, 
Zimmermann-Zysno or other type. The thematic class is 
defined in the inference phase so this is the place of 
decision: 
TC-m IPM 
«S 5) 
MN 
5. P. 
N N 
I, 
l, 
i 
j 
(9) 
where TC is the thematic class, maxc a function for 
determining the category of the maximal value. In the 
above formula the summation is the main inference step 
while the defuzzification is made by maxc. 
4. The Budapest-experiment 
There's no sense if any nice theory isn't tested on real 
data set that's also true for the neuro-fuzzy classifier. In 
the practical work it was the main topic to choose an area 
where we do have enough terrain data as well as where 
we have knowledge of the region. That was why 
Budapest has been chosen. The goal of the use of the 
neuro-fuzzy classifier is doing land cover mapping. The 
desired thematic classes are listed in the introductory 
chapter. 
Ten independent neural networks — thematic networks — 
were designed. The necessary amount of ground truth 
pixels was 2757 of which 2/3 was used for training and 
1/3 for test purposes. The selection criteria for the 
training areas were 
+ _ Size 
*  homogenity 
+  reprezentativity 
+ separability. 
(re 
2. Neural network 
y A = 
| m 
Multispectral [oai 3. Neural network 
4 JJ» +. 
ML ul 
| 
Ze 
Fuzzy | | Thematic 
decision | | map | 
making | 
The categories are as listed in chapter 1, therefore ten 
neural networks were designed. The network structure 
was 3 layers on the average with 15-8-1 neurons. The 
differences from these values were at the "difficult" 
classes like urban areas (more neuron) and at the "easy" 
classes like water (less neuron). The desired sum squared 
network error (SSE) was 0.1 that guaranteed a correct 
classification. The maximal possible number of epochs 
was 100. The independent neural networks needed 27 
iterations in average to reach the specified accuracy. 
After the training the independent networks were 
transformed into an equivalent net. The resulting network 
has 150 neurons on the first, 80 on the second and 10 
neurons on the third (output) layer. It's worth to compare 
the speed of simulation before and after the 
transformation. For the 2559 training pixels the following 
time consumption was measured: 
before the transformation 188.23 s 
after the transformation 72.83 s. 
The difference is very dramatic! While the number of 
useful” network parameters was 2420, after the 
transformation I had to store 13940. To avoid this 
memory increase the sparse matrix management was 
applied. 
The quality of the new classification method is defined by 
the usual measures: overall and average accuracy, the 
Cohen-kappa coefficient, the user’s and producer's 
accuracy. The first two qualities were 97.5 % and 96.8 96, 
while the kappa coefficient took 0.9694. The class 
describing user's and producer's accuracy is in the 
Figure 4 visualized. 
The test has proved that the thematic accuracy of the 
neuro-fuzzy method is comparable with the traditional 
mathematical statistic methods. 
5. Conclusions 
An application and development of neural network 
technique and fuzzy logic furthermore their combination 
was shown in an example of Landsat TM imagery. In the 
experiment defined thematic classes was determined for 
326 International Archives of Photogrammetry and Remote Sensing. Vol. XXXII, Part 7, Budapest, 1998 
  
land 
train 
exec 
optir 
sot 
mem 
train 
accel 
trans 
spee 
User 
Takin 
memt 
fuzzy 
achiev 
intens 
inforn 
The « 
traditi 
advan 
data a 
land u 
Refer: 
Barsi, 
Image 
Photog 
B3. pp 
Barsi, 
neural; 
No.4, | 
Brause 
Stuttga 
Cox, E 
Practiti 
Fuzzy : 
Grace, 
MATL 
Nauck, 
Netze t