In: Paparoditis N., Pierrot-Deseilligny M.. Mallet C. Tournaire O. (Eds), IAPRS. Vol. XXXVIII. Part ЗА - Saint-Mandé, France. September 1-3. 2010
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errors that are reported in tab 4.
Through these experiments, we find that over the length is long,
at least the parallax effect on the calibration.
2.5 Conclusion
In the various tests that we have performed, we have found that
the calibration of a camera through a panorama acquisition pro
cess is relatively stable and reliable. We will now compare our
method with a traditional calibration method.
3 COMPARISON WITH A TRADITIONAL METHOD
To evaluate our algorithm, we have compared it with a more tra
ditional method on the same simulated data. In this section, the
camera is calibrated with the same set of observations by a tra
ditional method by estimating the parameters R and S (respec
tively rotation and translation) for each image by using points on
the sphere as ground control points noted M. The cost function to
minimize is:
c
l
CPPA
¡PPA
fR(M-S) \
(0,0.1 ).R(M -S)J
(9)
3.1 Influence on parameters
Camera 1 Tab. 5 shows the difference between the true param
eter and the calculated parameters. There is no significant differ
ence between intrinsic parameters and distortion parameters for
the calibration of a short focal camera.
0.3
noise (
0.5
n pixel
1.0
2.0
Д f
0.04
0.07
0.16
1 „55
Д CPPA
0.09
0.14
0.27
0.95
Д ¡PPA
0.34
0.54
0.89
15.93
Д C-PPS
0.48
0.84
1.74
3.84
Д Ipps
0.92
1.6
3.15
0.54
Дpixels (image border)
0.83
1.05
1.68
34.4
Table 5: Influence of noise on the intrinsic parameters and distor
tion parameters
Tab. 6 consolidates the results obtained with our method and with
the traditional method. Our method is more accurate in the esti
mation of intrinsic parameters than the traditional method. It is
more difficult to compare the estimation of distortion parameters.
n
0.3
oise (i
0.5
n pixe
1.0
)
2.0
f
+
+
+
+
ppa
+
+
+
+
distortion
+
+
+
+
Table 6: Comparison between estimation with our method and
the traditional method. A ”+” (resp. ”-”) indicates that our
method is more (resp. less) accurate than the traditional method.
noi
0.3
se (in pix
0.5
el)
1.0
Д/
31.88
47.48
71.81
Д CPPA
1.35
2.09
3.39
Д 1 PPA
2.21
3.59
6.75
Д Cpps
2.46
4.33
11.74
Д Ipps
1.47
2.46
4.99
Дpixels (image border)
4.23
6.47
10.21
Table 7: Influence of noise on the intrinsic parameters and distor
tion parameters
Camera 2 Tab. 7 shows the difference between actual parame
ters and the estimated parameters. Note that with little noise (0.3
pixel) there is a significant error on intrinsic parameters (1% of
error on the focal). One can note in tab.8 that our method is more
accurate than the traditional method. This table is just a quali
tative summary but when you take a look on tab.7. you can see
traditional method is not very accurate to calibrate long focal!
nois
0.3
e (in p
0.5
xel)
1.0
f
+
+
+
ppa
+
+
+
distortion
+
+
+
Table 8: Comparison between estimation with our method and
traditional method. See Tab. 6 caption for an explanation.
3.2 Impact on the projection center
The main difference between a traditional calibration method and
our method is that the estimation of the position and rotation of
each image is done separately. This section discusses the differ
ence between the simulated position of the camera at (0,0,0) and
the position estimated in the calibration process.
Camera 1 The figure 8 represents the projection centres of each
image after calibration (top view). We found that w'hen increas
ing the noise, the calculated positions differ from the true posi
tion. The same behaviour can be noted for the third component
on fig. 9
-0,010 -0,005 0,000 0,005 0,010
X(m)
♦ 0,3 pixel of noise ■ 0,5 pixel of noise 1,0 pixel of noise
Figure 8: Projection center of images in plan (X,Y) after calibra
tion and noise on measures
Camera 2 The same behaviour can be observed for the short
and the long focal, but the difference between estimated position
and true position is more important (Fig. 10 and Fig. 11).
