six parameters to use for the other GPS points inside the same
sample.
It is possible to show, in the topographic field, ie. in a
surrounding about 10 km, that equations (14) can be simplified
by finding a linear relationship between the (Xg ,Yc ‚Za)
coordinate system and the (X,Y,Z) cartographic coordinate
system.
Xc and Yg are the coordinates obtained from the cartographic
transformation of the @g ‚AG values of the GPS network, and
hg is the ellipsoidal height of the GPS point.
The (X, Y) cartographic system is that of the Gauss projection,
the Z coordinate is the orthometric height of the point. The
maximum errors of this approximation are of few ppm in
planimetry, also for great height differences of the ground. A
second hypothesis, which is reasonable in the topographic field
is that the geoid undulation can be modelled with a plain of the
type (Sguerso and Radicioni, 1992):
Na = No + YO 9A, (15)
One can finally write:
Y Yo PYG + qXG
xls xjl«] ^ 175 +X6 (16)
Z Zo tYg + uXg + hg
Because of the not precise absolute positioning, the coordinates
used in equation (16) are not exactly the WGS coordinates but
generic GPS coordinates (qq ,À , hg), shifted with respects to
the first, maximum values of 100-200 m for the whole
network. Nine unknowns appear in this linear equations that
can solved sharing the planimetric from the altimetric problem
or by solving the couple problem.
4. PRACTICAL EXPERIMENT
The photogrammetric method proposed in this paper,
considering the last version of the software FOTO3D (Visintini,
1993) that implements the analytical model (7), is characterized
by low cost and a kind of applicability that can be considered
almost in "real time”. It is then possible to produce and update
an economical GIS geometrical bidimensional database.
The method is highly productive since it requires just some
amateur pictures taken in the field and no kind of surveying
measurements if the georeferencing process is performed using
as control points the cartographic grid. It is only necessary to
locate (at least) two vertical signals on two different cartho-
graphic-photographic tie points.
If this is not the case, control points can be determined for
instance by GPS measurements according to what already
reported in 3.4.
The method proposed has been applied to a part of the unit n.
087044 of the Technical Mapping of the Friuli-Venezia Giulia
Italian region in scale 1:5.000, obtained by aerial
photogrammetric survey in 1977. The map projection is the
conformal Italian Gauss-Boaga which considers the
international ellipsoid oriented at Mt. Mario (Roma).
The cartographic unit has been acquired in digital form by an
Epson GT-9000 scanner having a resolution of 600 dpi (real
dimension of the pixel on the terrain 21.1 cm).
A quick analysis of the map content has put in evidence the
absence of some buildings, built later than the original flight.
For this reason some pictures of these lacking particulars (see
198
Figure 1 and 2) have been captured on the terrain by a Pentax
P30 reflex camera with an objective focal lenght of 28 mm.
Figure 1: First non-metric image of the building
to be updated in cartography
Figure 2: Second non-metric image of the building
to be updated in cartography
The image coordinates of tie and control points have been
acquired by a Calcomp Drawing Board II digitize.
Furthermore, the FOTO3D software has been applied to
georeference the cartographic unit and to determine the external
orientation parameters of some images, obtaining in this way a
digital version of the map and its updating.
Points 1, 2, 3 and 4 (see Figure 1 and 2) are the cartographic-
photogrammetric tie points used to join both methods and to fix
a weak datum to the photogrammetric survey. The approximate
values of their planimetric coordinates have been computed by
a preliminary georeference procedure, while their approximate
height has been assumed by a point where height is reported on
the map and by two vertical signals visible in the photos.
Furthermore 26 unknown points have been used. These have
been chosen with an homogeneous distribution on the image.
The obtained results seem to be particularly promising and are
summarized in the following points:
- it was possible to orient two images without any topographic
measurements;
- the numerical instability, proper of the DLT, relative to the
orientation with control points belonging to a plane, has beet
overcome with success;
- the planimetric accuracy of unknown points is characterized
by a relative accuracy of almost 4 cm: for 16 points along the
same vertical (in groups of 2) the difference of planimet
coordinates obtained is equal to 39 mm. ;
- the estimated height value for the unknown points 5
characterized by a relative accuracy of ~ 3 cm: for 16 points of
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B4. Vienna 1996
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