. Is referred to 
the Procrustes 
the x and y 
greater than 6 
rent technique 
ates a better 
he Procrustes 
o observe that 
ors, Procrustes 
1al to zero for 
this case, the 
ution, without 
applying the 
wy between 2 
ithm, the root 
r the classical 
0 centimetres. 
random error 
t of the whole 
or. Finally, if 
1e differences 
le for the two 
the root mean 
f fixed points 
points for the 
n 1, first, the 
'ordinates and 
lgorithm (see 
veen the true 
a traditional 
oper symbol). 
> error is only 
ie Procrustes 
ues, while the 
20-30 cm. 
s 
  
  
onditions 
  
X COORDINATE DIFFERENCES 
WO aon oto po 
[mj 
Point ID 
  
  
Y COORDINATE DIFFERENCES 
T $^. et # a in A 
Point iD 
  
  
  
Figure 7. Residuals for mixed systematic and random error 
conditions (Procrustes €, traditional ) 
The graphs of Figure 7 refer to the case in which systematic and 
random errors are both present; in this case, a generally 
significant better result is evidenced when applying the 
Procrustes method with respect to the traditional one. It is worth 
of mention the fact that the residuals are perfectly comparable 
with the applied random error values, emphasising in this way 
the capability of the Procrustes algorithm to compensate the 
systematic component also in the case in which it is 
superimposed to the random errors. 
  
X COORDINATE DIFFERENCES 
{m} 
fel ee / 
Point ID 
  
  
Y COORDINATE DIFFERENCES 
v Te INR 
Im] 
Point ID 
  
  
  
Figure 8. Residuals for pure random error conditions 
(Procrustes ®, traditional ) 
The above graphs (Figure 8) consider the case in which only the 
random errors are present: the results are generally similar. 
As the previous results show, the Procrustes technique seems 
very powerful in the presence of systematic errors, and can be 
used also in the case in which only random errors are present: 
this is true if and only if the fixed points adequately cover the 
network taken into account. 
S. A NUMERICAL EXPERIMENT ON A REAL CASE 
The Udine branch of the Italian *Dipartimento del Territorio* 
made available the coordinates values and the description of the 
fiducial points surveyed since 1990 in the North-West part of 
the Udine municipality. The network is constituted by 64 
fiducial points, covering an area of almost 2.8 km”; the number 
of total polygons used for the various surveys is equal to 205 
(see Figure 9, and Figure 10). The initial experimental phase 
consisted in the GPS measurement of 18 fiducial point 
positions. Of these points, 9 were considered like fixed points, 
and homogeneously distributed over the entire network, while 
the remaining 9 have been used to control the results. 
  
  
  
  
  
Figure 9. Spread of the 205 adjacent, partially or totally 
overlapping fiducial polygons composing the real network.