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data, or data from the camera lens test,
or a determination of lens distorsion
simultaneously with the elements of the
camera internal and external orientation.
In the last case the collinearity
condition is supplemented with some
terms, taking into account the influence
of the radial and tangential distortion:
xsx.(kir?skor**kirt8)]tp.(ry? t2x,? )*2poxz2.
[5)
ze2;(k. r?-k.ri!4k.r9jeZ2pix,2rP*pao(r?422,?),
where
rsix.^ = ZA) LE, Xn X-Xo , Le = Eg
Experimental investigation
Using the advantage of single photographs
which allows a better analysis of the
influence of different factors on the
calibration accuracy, an experimental
test calibration is done. The purpose of
the investigation is to recommend the
distribution and the number of the
control points, as well as to check the
effectiveness of the sophistication of
defining the interior orientation and its
influence on the accuracy of the
calibration and of the determination of
the camera exterior orientation elements.
A test object is created. The points are
distributed in such a way that a unique
solution for the interrelated elements —
the coordinate Ys of the projection
centre and the focal length f — and for
the distortion coefficients is ensured.
The distribution of the points is shown
in Fig.2:-
17 points in the farthest plane III,
9 points in the middle plane II,
7 points in the piane nearest to the
camera station - plane I.
The coordinates of these points are
precisely determined by geodetic methods.
The photographs are taken from a
centrally located camera station using
two models of Zeiss Jena focusable
universal cameras UMK 10/1318 in the
case of a photoplane, parallel to the
planes - with ‚control ‚points of. the test
object. The image coordinates of the
photoplates points are measured on the
Zeiss Jena Stecometer stereocomparator.
To estimate the influence of the number
and distribution of the control points a
simultaneous analytical determination of
the camera station external orientation
elements and of the camera interior
orientation elements is done with and
without determining the lens distortion.
The analytical model used is based on the
collinearity condition supplemented with
terms accounting for the lens distortion
(5). A program for processing the data
from single photos is made. The
geodetically determined space coordinates
of the points are assumed correct and the
measured orientation elements are taken
as initial approximation.
1 T 4
21 2T. 24
30 NO rumes
^ 2
» 11 b
A à 28 =] 5
12 i4 17 23 IH plane
31? $33
3 2 ‚6
23 er 26
| II plane
18 19 20
I plane
Fig.2
Calculations are made in 7 different
cases of distribution and number of the
points "located in two or three of. the
planes (Fig.2).
Conclusions
The experimental and theoretical results
allow the following conclusions:
1. For pre-calibration of the camera by
single photos it is recommend to
distribut the test. object points in two
planes which are at a maximum distance
one from another but are within the range
of the camera depth brightness for the
focusing distance used. As an optimum
number it is recommended to use 6 points
in each of the two planes whose images
should lie near the edge of the photo,
parallel to the principle line.
2. The determination of the lens
distortion requires also radially located
points which are evenly distributed in
the farthest plane of the test object.
3. The differences observed in the values
of the focal length and of the