Laura Keyes 
  
Recognition and classification of the resulting scalar values, to describe a shape, can be evaluated through the distance 
between the vectors in the n-dimensional space in the same way as the classification method described in section 2 for 
the Fourier descriptor and moment invariants techniques. 
3 RESULTS 
In this section a sample of the results produced by the application of the Fourier descriptor, moment invariants and 
scalar descriptor techniques are presented to evaluate and compare their usefulness in shape discrimination of general 
topographic features. Evaluation of the BCC method is not presented in this work as this is still an on-going experiment. 
Figure 3 plots the average values, obtained for five categories of objects from the sample maps (using the Fourier 
descriptor method in this example). This shows that in order to classify shapes with any degree of certainty, the 
variation within classes must be less than that between classes. 
  
0.06 
rp 994 4— 
as e Parcel 
Railway 
| - 
0.04 s 
FD(3) 0.03 FD(2) 
Figure 3. Average values of five sample classes 
To compare the three shape recognition techniques used, several sample shapes from the map (buildings and parcels) 
were used as test images. Figures 4a, 4b, 5 and 7 show plots for the Fourier descriptor, moment invariants and scalar 
descriptor techniques respectively for a small representative sample of buildings and land parcels. Each plot shows the 
degree to which the two sets of objects cluster in three-dimensional space. As can be seen in Figure 4(a), these two sets 
are not distinct. The evidence therefore indicates that normalised FD's are not very good for use in shape description 
where the data sets are of a very general shape. Note, that due to normalisation the first two terms, FD(0) — 0 and 
FD(1)= 1 are redundant in comparison. However, because the polygons are of a known scale the experiment was 
conducted using a Fourier descriptor technique that is not normalised for scale, that is, FD(1) # 1 and therefore can be 
used as a comparison. The resulting clusters (figure 4(b)) are much more significant indicating that using fourier 
descriptors without scale normalisation gives an improvement in object discrimination. 
   
FI 09 FOR) 
Figure 4, (a): Clustering of the polygon shapes in three-dimensional space of the features FD(2), FD(3) and FD(4), (b): 
Clustering of the polygon shapes in three-dimensional space of the features FD(1), FD(2) and FD(3), not normalised for 
scale. 
  
484 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.