-54- 
horizontal angles) of the homologous points, considering one of 
them as the origin both on left and right sets of points. 
This verification is performed, by iteration, using all the 
selected homologous points as the origins. Only the 
homologous points that pass all the tests are accepted as precise 
homologous points. 
2.3 Registration parameter estimation 
The estimation of the six parameters of a 3D coordinate 
transformation is performed, using the homologous points 
accepted by the last step of the procedure described in the 
previous paragraph. All the points of the right scan can then be 
transferred into the reference system of the left scan using the 
well known model 
( 1 ) 
fx" 
M 
fy- \ 
A o 
Y 
= R • 
y 
+ 
Y 0 
A 
<Z 0 j 
where X, Y, Z are the coordinates of the left scan, x, y, z the 
coordinates of the point in the right scan and R is the rotation 
matrix. 
3. DATA QUALITY IMPROVEMENT 
The data acquired by laser scanner devices always has noises 
which are smaller than the tolerance of the used instruments. 
This problem is evident if one tries to create a 3D photographic 
model of the object (see figure 6). 
can be two or three times those of the adopted scanning rate. 
Each mesh contains a set of measured points. The median (m ) 
of the distances is estimated and the deviations of the single 
values are computed from their median. 
The distances which have smaller differences than the laser 
scanner accuracy are used for the estimation of the real distance 
using the mean; the other points are rejected. 
Figure 8 shows the practical effect of the removal of noise 
performed with the described procedure. 
This technique also allows the removal of any points which are 
not on the object of interest (see fig. 18). 
Figure 8. Image projection on filtered laser scanner data 
Figure 6. Image projection on original laser scanner data 
The noisy data do not allow a correct interpretation of the 
details. The noises are caused by the beam divergence: the 
measured distance is the average of the distances of the points 
of the object contained in the foot print of the laser beam. 
m-R a-r m m-r m-R 
&OSS outlier media outlier 
Figure 7. Data noise reduction 
In order to resolve this problem, a procedure based on robust 
estimation has been studied and implemented. 
The original data are subdivided into 3D meshes whose sizes 
4. LSR SOFTWARE 
In order to practically apply the previously described 
procedures, a specific software, named LSR, has been 
developed using Visual Basic language. 
Figure 9. LSR procedures 
The software runs both the data registration and the data quality 
improvement procedures and produce a final correct 3D model. 
The LRS program can perform three basic procedures: filtering 
of the original data (automatic procedure) and registration of the