along the sensor bar. The stability in the Y direction
(driven by stepping motors) is good from the begin-
ning;
e after 1 hour, the repeatability is very good, both from
geometric and radiometric points of view. A test on 4
acquired images has shown differences of less than 2
grey leveis. The geometric changes are less than 1
pixel;
e however, the (already stable) geometric results are
very bad in the X direction: discrepancies greater
than 900 um (!) can arise and their distribution is not
linear. It is impossible to use scanned images
without differential calibration. The Y co-ordinates
are much better (discrepancies < 1 pixel along the Y
grid side).
As already described in 2.2, a calibration based on bi-
linear transformation has been carried out. The calibra-
tion programme, in C++ language, takes a few seconds
to determine the 800 transformation parameters of the
100 grid meshes and the 800 parameters of the inverse
transformation, which are necessary for an automatic
on-line calibration in real time of all the image points
collimated during the restitution.
4.2 Collimation of single points
In a conventional LC-DPS the accuracy in the collimation
of single points is actually limited by the resolution of the
system, determined by the pixel size.
Let's consider a pair of photos in scale 1:S = 1:10,000
(suitable for producing a map in scale 1:2,500) acquired
at 600 dpi, that is, with a pixel size of 42 um. If the op-
erator carries out the collimation in a traditional manner,
entrusting the location of homologous points to his
stereoscopic vision he will locate for each pixel on the
left image its homologous with an accuracy - in the best
hypothesis - of + 0.5 pixel, that is 5, = +21yum.
It is well known (for ex. [1], p. 41 onwards) that, in the
case of normal taking, the r.m.s.e. of the Z co-ordinate is
given by:
H
= +S—
07 ES X (2)
where H is the flight altitude and B/H is the base ratio. In
our example, having supposed that the camera has a
focal length c = 150 mm, H is equal to 1500m and given
a 70% overlapping, B/H = 1:2. Therefore 0, = + 40 cm.
This accuracy of heights is low, if compared to that of
any analytical plotter (where 60; < H 10™ = +15cm.) and
it depends exclusively on the precision of the measure-
ment of the linear p. parallax. One should note that the
planimetric precision (o, and c,) is determined, not by
the position, but by the size of the image pixel. With the
assumed value of 40 um, the planimetric precision will
be, in the best hypothesis, of + 20 cm, which is a value
that can be considered sufficient and whose improve-
ment can be obtained only with a greater scanning den-
sity.
52
If one wishes to be certain of improving the correct loca-
tion of the homologous pixel, one can adopt the match-
ing techniques, as already described in 3.1.
4.2.1 Points of a “calibration model”. Calibration of tra-
ditional analogue or analytical plotters was carried out by
reconstructing an “artificial” calibration model, obtained
from two calibration plates of the already described type.
A similar procedure can be used for checking an LC-
DPS.
The stereo-pair consists of two identical copies of the
calibrated grid, as obtained in 4.1. As an example, by
simulating a 60% overlap, a 150mm focal length and a
1:5,000 photo scale, a "flat" model can be reconstructed
simply following the usual orientation procedures.
Three cases have been tested:
a) a rough approach: no calibration of the images, hu-
man collimation of the homologous crosses (as could
be obtained by a non expert operator using a DTP
scanner as it is and an existing LC-DPS)
b) a more accurate method: calibrated images (this also
simulates a high quality digital image, for ex. as ob-
tained by using a PS1 scanner), but human collima-
tion, to locate homologous entire pixels, is still nec-
essary
C) a computer assisted procedure: as above, but corre-
lation is obtained by using a sub-pixel matching algo-
rithm.
All crosses of the 7 columns (11 rows) of the grid model
have been measured, for a total of 77 points for each
test. The results (for case c) are summarised in the his-
tograms of fig. 6.
un
T Fd
SH
} ic
8 104 EN
5 d M
S T
9 5 : | | |
€ 7] poli
/ SM
à AN
04.
-5,00
Errors [10 H]
Figure 6 - Relative errors in X, Y,Z on a grid model
In the a), b) and c) cases the relative Z errors (AZ/H)
have the following m.s.e.:
a) 0,2 £53. 10^H b) o,2 £20. 10^H
Cc) o, 2 £06 10^H
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B1. Vienna 1996
Considerin
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4.2.2 Point
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