distance 
on 2 for 
nts and 
general 
'riment. 
Fourier 
nty, the 
parcels) 
d scalar 
ows the 
two sets 
cription 
= 0 and 
ent was 
> can be 
' fourier 
(4), (b): 
lised for 
  
  
  
  
  
  
  
  
  
  
Buildings Land Parcels 
Number of polygons analysed 537 1095 
Mean FD values FD(2) = 0.0422 FD(2) =0.0489 
FD(3) =0.0795 FD(3) = 0.0672 
FD(4) = 0.0416 FD(4) = 0.0279 
Variance in FD's (o?) FD(2) 70.0073 FD(2) =0.0088 
FD(3) =0.0067 FD(3) = 0.0030 
FD(4) = 0.0049 FD(4) = 0.0016 
Repeatability (36) FD(2) =0.2562 FD(2) =0.2814 
FD(3) = 0.2457 FD(3) = 0.1644 
FD(4) = 0.2100 FD(4) = 0.1200 
Distance between means for buildings and parcels FD(2) =0.0067 
FD(3) = 0.0123 
FD(4) = 0.0137 
  
  
Laura Keyes 
Table 1: Comparison of repeatability within feature classes and distance between classes for Fourier descriptors. 
Table 1 shows the measurements for the sample of building and land parcels. The repeatability of the measurements of 
the class, represented as 3 times the standard deviation, is sizeably larger than the distance between the mean values for 
the two classes. 
  
IM(2) 
IM(1) 
Figure 5. Clustering of the polygon shapes in three dimensional space of the feature IM(1), IM(2) and IM(3). 
Producing the same style of graphical and mathematically output for the moment invariants technique, Figure 5 and 
Table 2,there is a considerable improvement in shape recognition of general shapes on maps over the Fourier descriptor 
method. Although overlap exits (also seen by the human eye) good classification occurs. In table 2 it can be seen that 
unlike the Fourier descriptors, the distance between the mean values is smaller than the repeatability for buildings and 
close to the repeatability for the land parcels. 
  
  
  
  
MI(2) =1.5450e-013 
MI(3) =2.2317e-022 
Buildings Land Parcels 
Number of polygons analysed 537 1095 
Mean MI values MI(1) = 6.56112e-004 MI(1) = 0.0750 
MI(2) =1.8363e-007 MI(2) 20.0021 
MI(3) =6.5318e-012 MI(3) =9.7574e-005 
Variance in MI's (0^) MI(1) = 2.5518e-007 MI(1) =0.0059 
MI(2) =1.2250e-005 
MI(3) =4.1673e-008 
  
Repeatability (30) 
MI(1) = 0.0015 
MI(2) =1.1792e-006 
MI(3) =4.4818e-011 
MI(1) = 0.2295 
MI(2) =0.0106 
MI(3) =6.1242e-004 
  
Distance between means for buildings and 
parcels 
  
  
MI(1) 2 0.0743 
MI(2) 20.0021 
MI(3) =9.7574e-005 
  
  
  
Table 2: Comparison of repeatability within feature classes and distance between classes for moment invariants. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 
485