International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B6. Istanbul 2004 
  
  
Figure 1. SPOT image converted into three separated images 
2.2 Definition and verification of the training areas 
As it was later used for fuzzy logic classification, the process of 
supervised image classification will be given in brief. Selected 
land cover classes are: deciduous trees, coniferous trees, urban 
area, water, cropl and crop2. For these classes, training areas 
were pointed on the image (Figure 2.) 
  
| & PCI ImogcWorks V0.0 (VDO) »put. merged, crops 
  
  
  
  
Figure 2. Training areas shown in display window 
Since the signature separability showed that deciduous trees 
and coniferous trees are very poorly separated (low values of 
Transformed Divergence and Bhattacharrya Distance; big 
overlap between the signatures of two classes) and considering 
that this separability cannot be improved by a different channel 
combination, those classes were merged into the one single 
class: vegetation. Accepted combination of three images (with 
the biggest signature separability between the classes), in terms 
of RGB channels, was 702(red)+ 703(green) + 701(blue). 
The signature statistics gave a list of each of the classes, with 
the mean values and standard deviations for each channel for 
the class selected. These data were used later in the definition of 
the membership function. Also, the listing contained the class 
84 
correlation matrix, the covariance, inverse covariance and 
triangular inverse covariance matrices for the signature. 
In determination whether the training areas that have been 
selected are well represented, histogram was used: if the 
histogram has a single peak, then the training area is distinct 
and there is no confusion between it and another training area. 
A histogram with a bimodal distribution would indicate that 
there is an ambiguity between the current and some other class. 
2.3 Classification procedure 
In the classification process, the maximum likelihood classifier 
without NULL class was used. It assumes a normal (Gaussian) 
distribution and evaluates the variance and correlation of 
spectral response during the classification of the unknown pixel. 
In cases of overlapping areas, this method uses 'apriori' 
probabilities or a weighting factor to delineate. 
The NULL class option determines whether every pixel should 
be classified. If this option is selected, then a pixel is assigned 
to a class only if it is within the Gaussian threshold specified for 
the class. If it is not within any threshold, it is assigned to the 
NULL (0) class. 
Report about the results of the image classification contains: 
number of classified pixels, average and overall accuracy, 
statistics for the each of the classes and confusion matrix. This 
matrix gives the information how much of original training 
areas pixels was actually classified as being in the class that the 
training areas was meant to represent. If many of training areas 
pixels were classified into different classes, it is likely that the 
training areas were not so well determined. 
2.4 Result evaluation 
One way of the result evaluation was through the accuracy 
assessment. The classification results are compared to the raw 
image data and the report is created. This process is done during 
the random sample selection. The idea of the accuracy 
assessment is: point is highlighted in the sample list and 
observation was done where it is located on the image. This 
position should be compared to the class list and select the class 
that one believes it should belong. This idea was taken and 
applied in the fuzzy logic classification verification. 
3. FUZZY LOGIC CLASSIFICATION 
3.1 Matlab’s Fuzzy Logic Toolbox 
In the lack of precise mathematical model which will describe 
behaviour of the system, Fuzzy Logic Toolbox is a good 
“weapon” to solve the problem: it allows using /ogic if-then 
rules to describe the system's behaviour. 
This Toolbox is a compilation of functions built on the 
MATLAB numeric computing environment and provides 
tools for creating and editing fuzzy inference systems within the 
framework of MATLAB. 
The toolbox provides three categories of tools: 
=» command line functions, 
=» graphical interactive tools and 
=» simulink blocks and examples. 
The Fuzzy Logic Toolbox provides a number of interactive 
tools that allow accessing many of the functions through a 
graphical user interface (GUI). Fuzzy Logic Toolbox allows 
building the two types of system: 
=» Fuzzy Inference System (FIS) and 
=» Adaptive Neuro-Fuzzy Inference System (ANFIS).