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PERIMETER 0.0 AREA 
Figure 6. Cluster of the polygon shapes in three-dimensional space of the scalar features area, perimeter and number of points. 
Figure 6 shows the cluster graph obtained for the same data sets using the scalar technique. This technique also shows considerable 
improvement over the Fourier descriptor method but follows closely to the results obtained for the moment method. The clusters are 
much more distinct with some overlap as would be expected. Again Table 3 shows this mathematically using the repeatability 
function. 
  
  
  
  
Perim =94.7717 
Points =6.3929 
Buildings Land Parcels 
Number of polygons analysed 537 1095 
Mean scalar values Area = 463.6964 Area =3.8695e+004 
Perim =682.1834 
Points 244.20 
  
Variance in scalar's (0?) 
Area = 9.1380e+004 
Perim =1.6348e+003 
Points =15.2103 
Area =2.8365e+009 
Perim =4.0771e+005 
Points =1.0185e+003 
  
Repeatability (30) 
Area = 906.8734 
Perim =121.2972 
Points =11.7001 
Area =159780.0 
Perim =1915.6 
Points =95.7411 
  
Distance between means for buildings and 
parcels 
  
  
Area = 38231.0 
Perim =587.4117 
Points =37.8071 
  
  
  
  
Table 3: Comparison of repeatability within feature classes and distance between classes for scalar descriptors. 
4 CONCLUSION 
As shape descriptor techniques the evidence to date is that all four techniques, namely Fourier descriptors, moment 
invariants, boundary chain code and scalar descriptors are very good features to use when dealing with particular types 
of shapes such as aircraft or alphanumeric characters. The aim of this paper was to investigate and compare their 
usefulness for shape description of general shapes on maps, for example houses, roads, parcels etc. When tested for the 
more generalised topographic shapes, Fourier descriptors do not appear to be as conclusive and successful as hoped. 
However, both the moment invariants and scalar descriptor techniques proved to be significantly more successful in 
their task. This work is part of on-going research and it is envisaged that all the above methods with their shown 
capabilities will be combined to produce the optimal results. 
ACKNOWLEDGEMENTS 
This project is supported by Enterprise Ireland’s Strategic Research Grants scheme 1998, proposal number ST/98/021. 
The Isle of Man Department of Local Government and the Environment loaned the topographic data. 
  
486 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.