×

You are using an outdated browser that does not fully support the intranda viewer.
As a result, some pages may not be displayed correctly.

We recommend you use one of the following browsers:

Full text

Title
International cooperation and technology transfer
Author
Mussio, Luigi

The distortion varies with the focussing distance. A
modification in the focus distance is achieved by a
change in the principal distance, resulting in a new
lens distortion curve (Magill, 1955). But in this work
we assume that the variation of the distortion curve is
negligible. We expect moderate accuracy with non
metric cameras, and our goal is the efficiency better
than the full correctness.
2. DETERMINATION OF THE RADIAL
DISTORTION FOR NON METRIC CAMERAS
The distortion is normally assessed during the camera
calibration process. The calibrations procedures can be
subdivided in single-frame methods and multi-frame
methods. Cameras are normally calibrated in
laboratory by means of specially designed goniometers
(Petterson, 1978) or very special equipment for stellar
survey, (Fritz, 1978).
One of the main problems for non-metric cameras is
the unflatness of the film. The modélisation of the
particular deformation has been tried (Fraser, 1982).
Another problem for non-metric cameras is the
uncertainty of the interior reference system.
The here proposed procedure is suited mainly for long
focal lenses cameras in order to overcome numerical
instability. The determination of the distortion apart
from the calibration has other advantages also: a
reduction of the amount of needed control points, and
finally an improvement of the plotting accuracy.
The distortion can be regarded as the part of the
transformation that cannot be included in a linear
transformation from the object plane to the image
plane. A straight line in the object space should remain
a straight line in the image space.
3. THE RADIAL DISTORTION MODEL
The radial distortion is function of the radial distance r
from the principal point (Ziemann 1982) expressed
with odd polynomials.
3 5 7
dr = k-^r + k^r + k^r + .... (3)
This function is called characteristic curve, with an
associated characteristic principal distance c (fig. 1).
The polynome dr can be transformed getting a
variation of the principal distance from c to c+dc.
3 5 7
dr c = dr + k 0 r = k 0 r + k l r + k 2 r + k 3 r + ~(4)
The radial distortion can be set to zero dr c = 0 at a
chosen distance from principal point.
2 4 6
*0 = "(Vo +k 2 r 0 + Vo + "> (5)
c c
dc = —(dr- dr c ) = — (~Vo) = " c • k 0 ( 6 >
r 0 r 0
obtaining the so-called calibrated principal distance c*
*
c = c + dc = c(l - ) (7)
2 2
F)g. 7 The radial distortion model
The radial distortion for the tested calibrated camera, a
Rollei 6008, equipped with a Distagon 40-mm lens, is
expressed in the form (8) in the calibration certificate.
4. THE EXPERIMENT
A polyester sheet of regular grid, with 10cm interval,
has been plotted in a TA10 Wild flat-bed plotter (1.x
1. m 2 ) giving 121 points with 1/100 mm accuracy.
The sheet, hanged on a flat vertical wall, has been
photographed with a semi-metric camera Rollei 6008
at 0.8 m of distance (fig.2). The photo-scale is 1/20.
The measure of image co-ordinates has been carried
out in a TA3 Omi comparator. Three images have
been taken and measured, and they are called in this
paper testi, test2 and test3.
Fig. 2 - The layout of the test