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In this process, an estimated value is also calculated for the pixels for which reference information is available. This 
reference area, though, is not used for these estimates so that only n-1 reference areas are available for such pixels. This 
enables a cross-validation as described below. 
In the k-nearest-neighbour method for qualitative attributes, the sum of the weights is first calculated for each class of 
the qualitative attribute (Tompoo & Pekkarinen, 1997). Then the class of the qualitative attribute with the greatest 
weight sum is assigned to the pixel. 
The verification of quantitative attributes is done by the root mean square error RMSE pm 
RMSE, = (12) 
Y ix 
izl 
    
1 
n 
i=1..n verification area 
n number of verification areas 
yr measurement at verification area i 
$: k-nearest-neighbour estimate of the attribute at verification area i 
(Facakas et al. 1999). 
For the further analysis of the quantitative attributes, the root mean square error addressing the overall average of the 
sample survey to all pixels RMSE average 1S calculated 
RMSE = 
average 
(13) 
  
i-l.n reference area 
n number of verification areas 
yi measurement at the verification area 
yi estimated overall mean 
The root mean square error based on the k-nearest-neighbour estimate RMSE;m is a measure of the accuracy of the 
estimates. The comparison of the root mean square error based on the k-nearest-neighbour estimate RMSE,,, with the 
root mean square error addressing the overall average of the sample survey to all pixels RMSEaverage indicates the 
additional information gained by the k-nearest-neighbour method. This can be done with arbitrary sizes of verification 
areas, such as forest stands with data from accurate surveys. The verification and evaluation can also be done on a pixel 
level using cross validation (Facakas et al. 1999). The validation of qualitative attributes is made by measurements of 
co-occurrence. 
4.3 Results and Conclusions 
The qualitative attribute 'dominating tree species group of the area' (spruce, pine, oak, beech, other broad-leaved trees) 
and the quantitative attributes 'area proportion of a single tree species group' were studied. The visual comparison with 
the aerial photo shows great correspondence when single tree types dominate over large areas (see figure 2 and 3). Such 
dominance of single tree types does not, however, exist over large areas. In addition, in small stands mixed signatures 
predominate due to the influence of neighbouring stands. From the pixel-wise 'dominating tree species group of the 
area', the 'dominating tree species group of the stand' was calculated determining the 'dominating tree species group of 
the area' with the highest proportion within the stand. The comparison with the reference data from stands with accurate 
surveys shows that correspondence is insufficient at an overall accuracy of 47.8% (n = 23). If only stands with a size of 
two and more ha are included the overall accuracy is considerably higher (70%, n = 10). 
  
  
  
  
  
  
  
  
  
  
  
  
All verification stands, n = 23 Large stands » 2 ha, n - 10 
Oak Beech Spruce Oak Beech Spruce 
RMSE,,, |?6] 28.1 26.4 35.4 285.9 15.0 21.1 
RMSEcveragel % ] 32.7 28.1 49.2 35.8 20.5 46.3 
improvement in RMSE[%] 4.6 1.7 13.8 9.0 5.6 28.2 
  
Table 4. Evaluation of the quantitative attribute 'area proportion of a single tree species group' 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B7. Amsterdam 2000.