Fig. 
Rapid palatal expansion appliance 
The aim of this work is to assess the volumetric 
variations relative to the palate after the active phase 
of rapid expansion and after constriction, six months 
after the removal of the appliance. 
So it's a matter of carrying out a comparative study of 
the variations of the set of teeth in three different 
moments, employing plaster casts (or other material) 
taken after each phase of the treatment using a 
tecnique that allows the maximum limitation of the 
inaccuracies in the survey of the measurements. 
Up to now the transversal diameter was measured by 
means of calipers while plaster casts were put in 
occlusion to estimate the expansion of both dental 
arches. From here aroused the search for a method of 
tridimensional surveying that could allow a more 
accurate and reliable metrical analysis. 
As a matter of fact, the analytical photogrammetry, 
starting from two castings, allows the creation of a 
"model" of the object that has the characteristic of 
being the same as the object and from which all the 
measurements of the distance and of the level 
differences between all visible points can be carried 
out. 
The points are obtained from the onward intersection, 
carried out from two points called "projection centres" 
of a pair of homologous radii relative to the same 
detail seen on two different photograms. 
The production of the model and its insertion in a 
complete reference system, whose information are 
obtained through topographical operations, can be 
realized through two operations of relative and 
absolute orientation from which it is possible to 
calculate the tridimensional values (x, y, Z) of each 
point of the model. 
One of the first problems brought about by this kind of 
study is represented precisely by the possibility of 
making the three different takings of the casts 
comparable through the creation of just one reference 
system and through the possibility of finding a 
method that starting from various points taken from 
objects with uneven shapes and no directly 
recognizable element allows a highly precise 
evaluation and the comparison of the deformations. 
    
It is necessary to underline anyway that the choise of 
photogrammetry doesn't depend exclusively on the 
advantages connected with the higher precision of the 
measurements, but also on the amount of 
information it provides, that enable the specialists to 
produce estimates which are undoubtedly more 
accurate (Vozikis, 1985). 
2. DATA ACQUISITION 
The study, then, was about six plaster casts 
respectively: three for the upper arch and three for the 
lower one, corresponing to the three different phases 
of the treatment. In particular they correspond to: 1) 
Pair C (upper arch cast n° 6 and lower arch cast n° 5) 
before the expansion orthopedical treatment; 2) Pair B 
(upper arch cast n° 4 and lower arch cast n° 3) after the 
three month expansion and contention; 3) Pair A 
(upper arch cast n° 1 and lower arch cast n° 2) after six 
months from the removal of the appliance. 
For the stereoscopical photographs the casts have been 
fixed to a bar placed inside a "cage" metrically 
predetermined using 40 points that allowed to carry 
out all the orientation operations of the casts making 
them homogeneous between them. 
The photographs have been taken with a metric 
camera terrestrial model WILD P31 with a focal lengh 
of 99.24 mm at a distance of 1.00 m from the object for 
the photographs 1-2 relative to the left side of the casts 
and for the 5-6 photographs relative to the right side, 
and of 1.70 m for the photographs 3-4 relative to the 
front view for an overall of 6 photographs (3 models) 
(fig.2). 
3. DATA PROCESSING 
Eventually a restitution of each cast was got under way 
separately so to get to the representation in scale 1:1 of 
the cast's morfology seen frontally and from both sides 
of a series of orizontal and vertical profiles each 2 mm 
(figg.3-4-5-6). The appliance used for the restitution is 
an analytical system of the WILD BC1 whose data have 
been subsequently turned in the .DXF size of AutoCad 
to allow further processing of tridimensional 
representation and modelling. 
From the restitution protocols it is already possible to 
define within which endurance margins our analysis 
was carried out with respect to the prepared survey 
conditions. 
From the table relative to the absolute orientations of 
the three models with respect to the points of the cage, 
appeared precisions in the three co-ordinates on an 
average of about 8 tenths of a millimetre (tab.1). 
The estimated taking conditions permitted to carry out 
directly on the stereoscopical models controls on the 
tridimensional changes of the palate with respect to 
the three phases of the therapy, choosing some 
elements of the set of teeth clearly identifiable and 
comparable between them in the different casts (tab.2).