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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
d i U) = \\xi- c jI 0=1» 2...u) 
of this process. This result indicated that the best network 
architecture had been formed. 
Where u = the number of total fuzzy rules 
c . 
J 
=the centre of Gaussian membership function. 
In comparison with the accommodation criterion value , if 
arg min(J. (j)) > k d 
(8) 
Then a new rule should be generated. 
3.3 Performance Evaluation 
The performance of a FNN model should be evaluated based 
on following requirements (Ralf Wieland et al., 2008): 
1. Accuracy: The error resulting between the calculated 
and target output values should be minimal; 
2. Generalization: The model should reduce the 
complexity of the real world using an approximation of 
the data based on fundamental knowledge; 
3. Portability: The model should be usable in different 
sites with slightly changed inputs compared to the training 
data. 
Herein, the root mean square error (RMSE) and the output 
error were considered as statistical performance evaluation 
factors. To check the utility of this DFNN model, 250 samples 
containing hyperspectral vegetation indices values and heavy 
metal stress level information were applied to neural-network 
training process. And fuzzy rules were generated as is shown in 
Figure 2. During this process, a total number of eight fuzzy 
rules were generated. Considering the significance of each rule, 
one of them was deleted. At last, this training process 
generated seven fuzzy rules. 
Fuzzy Riie Generation 
Root mean square error 
Figure 3. Root mean square error during training process based 
on 250 training samples obtained from MODIS data 
Another dataset was prepared to evaluate the accuracy and 
generalization ability of this model. It was composed of 60 
samples which were quite different from training data samples 
on crop heavy metal stress. The comparison of calculated and 
target outputs was shown in Figure 4. Three samples within 
these 60 testing samples were misclassified because their stress 
levels were distributed near the edge of two levels. According 
to the experimental result, this system achieve to an accuracy 
of 95% by a total number of seven fuzzy rules. It was 
confirmed that for crop heavy metal stress level assessment, 
this DFNN model can produce a satisfying recognition rates 
with minimal number of hidden neurons. 
Companion of calculated and target outputs 
—er 
Calculated outputs 
* Target outputs 
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Figure 4. Comparison of calculated and target outputs based 
on 60 testing samples obtained from MODIS data 
Figure 2. Generation of fuzzy rules based on 250 training 
samples obtained from MODIS data 
4. CONCLUSIONS 
This paper presents a dynamic fuzzy neural-network (DFNN) 
model and its application to the assessment of crop heavy metal 
stress levels based on MODIS data. The proposed model uses 
hyperspectral vegetation indices as input variables in order to 
Figure 3 presents the change of RMSE value during training 
procedure. The RMSE can be achieved less than 0.5 at the end