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algorithm allows the analytical least squares adaptation of the 
whole set of the parcels, preserving their original shape. 
Finally, given the strict correlation and the geometrical 
interdependence existing between the fiducial points and the 
vertexes of the surveyed parcels, the proposed procedure of 
cartographic updating can be simultaneously applied to the 
rigorous adjustment of the fiducial point networks, and to the 
optimal integration of the surveyed parcels with those digitised 
from the original cadastral maps. 
This last procedure of global updating is, from the geometrical 
point of view, the most advanced and optimal one, since it 
benefits of the constraints and of the high correlation existing 
between the geometrical position of the fiducial points, and the 
cartographic location of the various parcels. 
2. THE RIGOROUS CONFORMAL ADJUSTMENT OF 
THE FIDUCIAL POLYGONS 
Every time a parcel is surveyed, in order to update or verify the 
digital archives, the Italian Cadastre rules prescribe that the 
corresponding field measurements must be recorded, processed, 
and uploaded into the centralised numerical archives, by way of 
a specific computer procedure, freely available, known as the 
"Pregeo" program. 
As outlined before, the current specifications also state that all 
the point coordinates, describing the new shape and position of 
the parcels, must be measured with respect to a local reference 
frame materialised by at least three fiducial points (fiducial 
triangle, or more (fiducial polygon), whose perimeter 
completely or almost completely contains the geometric entity 
to survey (Figure 1). 
  
  
  
  
  
Figure 1. Fiducial Point network superimposed to the cadastral 
map. Two Fiducial triangles are evidenced 
From tasks of this kind it is then possible to extract the 
reciprocal distance values existing between pairs of fiducial 
points, as determined by the actual field measurements, and to 
log them into a file. Univocal and rigorous naming standards are 
used to define the fiducial point names at a national level; this 
simplifies and makes straightforward every topological 
connection required by automated processing. 
All this specific information, available in digital form, 
represents a precious opportunity to attempt the solution of the 
first main cadastral mapping problem listed above, that is the 
rigorous re-adjustment of the fiducial point network. 
The fundamental philosophy of the proposed approach, is that it 
aims at preserving the original shape of every fiducial polygon 
(since the term "conformal"). Its geometric configuration in 
fact, has been determined by a variable set of angular and 
distance measurements, performed among the various fiducial 
points and the parcel vertexes, and results from the consequent 
internal measurements adjustment. All this furnishes an 
"invisible skeleton" to the whole fiducial polygon, giving the 
reason of its size and shape. On the contrary, decomposing the 
fiducial polygons into their sides, as required by a conventional 
least squares adjustment of the distances between fiducial 
points, might have the negative effect of destroying these 
significant internal geometrical constraints. For these reasons, 
the computation of the fiducial point network is carried out 
fitting together all the "fiducial polygons" configurations, as 
determined by the different surveyors during the time, instead of 
processing the single distances. 
The procedure that performs these transformations is based on 
the Generalised Procrustes Analysis, already employed to solve 
a classical photogrammetric problem (Crosilla, Beinat, 2002). 
Other recent geodetic applications of the Procrustes analysis are 
due to Grafarend and Awange (2000). 
Procrustes transformations are widely applied techniques for the 
shape analysis, the multifactorial analysis and for the 
multidimensional scaling problems (e.g. Borg, Groenen, 1997; 
Dryden, Mardia, 1998). They make it possible the least squares 
fit of two or more data matrices by searching a proper set of 
rotation matrices, scaling factors and translation vectors in order 
to satisfy a predefined objective function. The procedure 
consents to solve complex multidimensional problems by way 
of a rigorous sequence of simple elementary bi-dimensional or 
tri-dimensional transformation solutions. One of the major 
advantages of the proposed method is that it does not require 
any linearization of the equation system involved. As a direct 
consequence, the need for approximated values of the unknown 
parameters to be estimated is never required. 
The full process of conformal adjustment has been structured in 
two stages. In the first step, the goal is to establish the most 
probable shape, for a given fiducial triangle (or polygon), taking 
into account the variability of the different surveys of it carried 
out during the time. As a result of the data analysis performed in 
this stage it is also possible to compute an index of accuracy for 
every fiducial polygon, that can be used as a weight in the 
subsequent general adjustment. To this aim, fiducial polygons 
of the network, that were never determined directly in the field, 
or measured with poorly accurate methods or instruments, 
assume a proportionally reduced weight. The second step 
concerns the global and simultaneous adjustment of the 
representative shapes (consensus) of all the fiducial polygons. 
By the same algorithms previously used to define the most 
probable shape of every set of homologous fiducial polygons, 
the various representative polygons are linked one to the others, 
by way of their common points, in order to rigorously 
recompose the network of the fiducial points. The procedure 
individually rotates, translates, and residually scales all the 
polygons is order to obtain their reciprocal best fit condition, 
respecting the constraints imposed by an existing control 
network (e.g. GPS). This state is achieved when the sum of the 
squared residual distances between the homologous fiducial 
points, belonging to the various polygon determinations, and 
their mean position, satisfies a minimum condition. 
Finally, the definitive position of one specific fiducial point is 
obtained by averaging the coordinate definitions of the same 
point after having rotated, translated, and residually scaled in 
optimal way the different fiducial polygons that contain it. 
During the adjustment process, the vertexes of the first and 
second order of the fundamental cadastral network, and the 
vertexes of the National Geodetic network act as fixed points. In 
this way not only the adjusted network is constrained to the 
control points, letting only local adaptations among the fiducial