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# Full text

Title
International cooperation and technology transfer
Author
Mussio, Luigi

231
In order to verify’ weather or not the flatness of the
wall is critical, the grid has been surveyed by means of
two theodolite stations (fig. 3) and the final 3D-terrain
co-ordinates of the grid points have been obtained
with an accuracy of 1/10 of mm (fig.4). 1 With the real
co-ordinates we can correct for the dX and dY relief
displacements of the grid points.
Fig. 3 - The theodolite measurement
The largest value of the deviation from plane is
dZmax=l/2mm giving a relief displacement of
dXmax=l/3mm. In figure 5 are depicted as circles the
deviations from the medium plane.
Fig. 4 - The relief displacement correction
Then an homografic transformation performed.
. a,X + a 7 Y + a,
x + dx = — - -
a 1 X + a s Y +1 (9)
y + dy = a * X+a ’ r+a >
a^X + a \$ Y + 1
The residuals of the transformations are the vector
components of the distortion. The distortion is the
difference from the real lens to the pinhole model. The
homographic transformation is a particular case of the
DLT (1) where the object space reduces to an object
plane. It has the advantage in comparison with (1) or
the self-calibration procedure, to reduce the
parameters from 11 to 8, and therefore to avoid or
reduce the problems arising with the correlation
among the coefficients.
On the left of fig. 6 the residual vectors are depicted,
overlaid to the grid, for testl. The principal point is
then computed as intersection of the straight lines
passing through the vectors giving weigh proportional
to the lenght of their module. In this manner the
vectors can be split in two components, the radial and
the tangential ones. The radial components are then
arranged accordingly to the distance from the principal
point in the graph on the right of the fig. 6. The radial
components can be interpolated by the curve (8) where
the distance ro is not arbitrary but found by least
squares interpolation. Fig. (7) shows the tangential
components.
Fig. 8 displays the three estimated characteristic
distortion curves and the calibrated Rollei curve taken
from the calibration certificate. After the
transformation (4), consisting in adding an arbitrary
linear term to the characteristic distortion, the
calibrated distortion curves have been obtained,
allowing the comparison with the certificate curve (fig.
9).
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