264
where
r. - r n
f.
C; ~Cr
/»
(25)
are the measured distorted image coordinates of the N
control points, as derived by egde detection algorithm.
Obviously in case we consider a camera model with a
reduced set of distortion parameters, the corresponding
columns in matrix A have to be eliminated.
4. THE CALIBRATION SOFTWARE GUI
In order to make more easy and understandable the
calibration procedure from teaching and user final
point of view, we have provided the algorithm with a
Graphic User Interface. It was implemented in Matlab,
because this is a development environment best suited
for mathematical applications and it don’t requires a
specific knowledge about programming language like
Fortran, C or C++. Of course Matlab has own syntax,
anyway a complex software can be structured through
scripts readable with a common text editor, making
therefore easy to manage and modify the software
itself.
An example of the GUI is depicted in Fig. 5 showing
the DATA window, where all input parameters can be
set up, namely: CCD camera construction features
(menu Camera), number of used target planes (up to 6,
menu Target) and the calibration mode (menu Option),
listing the distortion parameters taken into account.
The user can view the results of calibration process
both in numeric form, through the PARAMETERS
window selecting the param submenu (Fig.6), and in
graphical form selecting the submenu result. The aim
of using such graphic windows should allow the user to
assess in easier way the quality and accuracy of the
calibration. 5
5. TEST AND RESULTS
In order to evaluate the overall accuracy of our method,
we have performed a calibration test using a target
plane with 48 black squares on white background, each
having lateral dimension of 50mm and horizontal and
vertical spacing of 150mm (Fig. 7). The vertices of
these squares were employed as control points.
To this aim the Canny edge detection algorithm [1] was
applied to the target squares, then the corresponding
lines were recovered from resulted edge points by
cubic splines interpolation. Finally the image coordi
nates of the vertices were determined as the points of
edge lines intersections.
For the test we used a Kodak DCS-410 professional
digital camera, employing a full-frame CCD image
measuring 1524x1012 pixels, with a lateral dimension
of CCD cells of 9pm. The target plane, located at a
distance of = 2m from the camera, was taken from dif
ferent points of view (up to 6 positions) in order to get
a larger spatial information about the perspective tran
sformations experienced by control points. Employing
an objective of 24mm the focal length was set up to
infinity and the diagfram to 11.
Considering each time a different combination of dis
tortion parameters, we have therefore performed seve
ral calibrations, which results are listed in tables 1, 2
and 3. The values of internal and distortion parameters
are reported in table 1, according to 4 calibration test
(rad2 means the estimate of both radial distortion coef
ficients). Instead, in table 2 (stdr,stdc) represent the
errors along rows (r) and columns (c) in L rc , between
image points positions, as derived by features extrac
tion procedure, and the image coordinates of same
points, as computed by the model. As both position are
affected by geometrical distortions of the camera, the
discrepancy can be regarded as an estimate of the noise
superimposed on the image. The following four para
meters (mean X w , mean Y w , std X w , std Y w ) represent
the mean and the stdev of the position errors along X w
and Y w axes in reference system X w . These values are
calculated by differences between measured 3D coor
dinates of control points and backprojected positions
on the target of corresponding image points, which
locations were corrected through the estimated camera
model. Finally, in the same way, the means and stdev
of position errors between coordinates points in the
camera reference system X c were computed, which
results are listed in table 3.
Table 1: calibration results about internal and
distortion parameters
Internal
parameters
rad + dec
rad + thin
rad2 + dec
+ thin
I'O
521.13
504.79
517.34
cp
768.25
757.54
758.51
f
23.95
23.95
23.97
s
0.99923
0.99925
0.99991
Distortion
parameters
ki
0.12650
0.12597
0.16914
h.
0
0
-0.69756
Pi
0.002332
0
0.001 S99
P2
-0.001526
0
-0.001 651
Si
0
U.ÜÜ3U53
U.000648
S2
0
-0.001948
-0.001 753
Table 2: position errors of backprojected control points
rad + dec
rad + thin
rad2 + dec + thin
std-r
0.209
0.209
0.206
std-c
0.24 7
0.248
0.244
mean X v
0.185
0.185
0.242
mean Y, r
0.232
0.232
0.322
std X*,
0.130
0.120
0.216
std Y v
0.161
0.162
0.257
