)btained by 
tribution for 
/ and green 
3s are then 
following: 
ndas. 
ion degree 
o they are 
using the 
cultivated 
using band 
pixels are 
at even this 
the mixed 
now, green 
low + green 
2 
134.6930 
0.6757 
  
0.6612 
  
  
  
nd bandas. 
  
As table 4 shows snow+green mixed pixels can be easily 
confused with rice-field ones in bands3s and band4s. 
The spectral signatures have high std.dev values because 
the area to be classified is very wide and the class to be 
considered are only 9 (snow, green, vegetation, building, 
lake, sea, cloud, rice-field, cultivated field). The spectral 
signatures are estimated with training sites selected all 
over the region and so they express the class variability in 
such a wide region. 
8. NEW APPROACH FOR MIXED PIXELS TRATEMENT 
Since the goal is to identify the blanket of snow all over 
the Alps arc in NOAA imagery, no drastic changes in the 
number of classes and in the recorded channels are 
possible. So a good way to improve classification results 
is following a new approach. The new approach has to 
treat the mixed pixels in a different way. 
9. FUZZY APPROACH TO CLASSIFICATION 
Mixed pixels classification introduces the major problems 
which are linked to the following reasons: 
— large pixel size (1.1km x 1.1 km) and so many pixels 
are made up by two or more classes; 
— high std.dev of spectral signatures due to the high 
variability of the classes in a such a wide region. 
The complexity of the problem is double faced, because it 
comes out both from real pixel composition and from 
inaccuracy of spectral signatures. In such a context it is a 
very hard task to assign each pixel to an unique class 
having the only chance left not to classify the excessively 
uncertain pixels. 
Traditional classification assignments are total and 
absolute, that is, one pixel can be strictly assigned or not 
assigned to one class. As a classification result, each 
pixel is characterised by its belonging to a unique class 
only, mixed pixels included, and so mixed pixels cannot 
exist in the classified images, even if they are present in 
the first image. 
This approach is rigid because it allows only total 
assignment or total non-assignment and it does not allow 
partial assignments and intermediate conditions, but 
pixels having intermediate states are better described with 
class membership degrees than with the most 
representative class only. 
Fuzzy logic just corresponds to the need of describing soft 
and shading situations using membership degrees and 
things stop to be crisply described as black or white 
because they are represented in greyscale. Fuzzy 
approach to classification does not assign pixels to a 
unique class but describes them trough their membership 
degrees to all classes; all the pixels in a Fuzzy approach 
are like mixed and so they are described with their 
membership degrees. 
The result of a fuzzy classification is a multi-band image 
having many bands as classes; each band explains the 
pixels membership degrees to a class and in this way no 
assignment mistake for mixed pixels is made. 
Figure 13 illustrates a typical fuzzy classification result 
(first image is shown in figure1; only two classes are 
considered). 
  
Membership degrees 
to classe a 
AL 
0.04 0.95 1 | 
o |0.22/0.46 
  
  
  
  
  
  
and 
Membership degrees 
to glass b 
  
  
Fig. 13: Multi-band image obtained as a result from a 
fuzzy classification of the image in figure 1. Since the 
classes are two the bands are two and each band 
contains the membership degrees to one class. The sum 
of membership degrees to class a and to class b is equal 
to 1 for all the pixels. 
In a classified image each band perform membership 
degrees to one single class and so it describes the 
presence of its class in the image. 
For each pixel the sum of the membership degrees for all 
the considered classes is equal to 1; the pure pixels have 
one membership degree equal to 1 and all the other equal 
to O while the mixed pixels have all the membership 
degrees from O to 1. 
This classification approach is very powerful for the mixed 
pixels because it can treat them as really mixed and it 
does not constrain them into a unique class; these 
remarks suggests that fuzzy approach seems to be very 
apt for snow detection on NOAA images. 
Fuzzy approach is used for a new classification with all 
the five recorded channels and having the threshold 22096 
in order to deal with the classification of mixed pixels in a 
different way. 
The result of a fuzzy classification of a NOAA, image is a 
multi-band image containing nine bands, each describing 
the presence of one class. 
The pure or almost-pure pixels, that in a traditional 
classifications are assigned to a single right class, in a 
fuzzy classification have one membership degree equal to 
one or about one and all the other equal to zero or around 
zero. The mixed pixels, that in a traditional classification 
are wrongly assigned to one of the concerned classes 
only or even to an extraneous class in the fuzzy 
classification are assigned contemporarily to different 
classes with different membership degrees. 
The snow*green mixed pixels, that could be assigned in 
odd ways like clouds, building, rice-field and so on, now 
Intemational Archives of Photogrammetry and Remote Sensing. Vol. XXXII, Part 7, Budapest, 1998 333