Cl PA 2003 XIX th International Symposium. 30 September - 04 October, 2003, Antalya, Turkey
significant. The a priori standard deviation was set to 1 pixel (=
0.006445 mm) for all experiments.
Focal length and principle point
Lines of three vanishing points are required for the focal length
and principle point estimation. The lines were extracted and
grouped automatically by vanishing point detection, and also
measured manually (Figure 3). The estimated parameters using
the results of each image separately were not consistent (Image
3 and 6 as an example in Table 1). Especially the difference in
the estimated focal length was considerable.
Image 3
Image 6
Image 3
Manual
Image 6
Manual
Variance fac.
1.027
0.903
1.152
0.132
d.o.f.
487
454
7
7
Max. residual
0.018 /
0.018 /
0.010 /
0.003 /
(mm / pixel)
2.8
2.8
1.6
0.4
Focal length
8.668
9.663
8.514
10.092
in mm (a)
(0.052)
(0.079)
(0.046)
(0.058)
Princip put. y
-0.200
-0.053
-0.085
0.376
in mm (a)
(0.057)
(0.067)
(0.066)
(0.076)
Table 1 : Results of camera parameters estimation using
automatically and manually extracted and labeled lines.
The location of the principle point could not be estimated in x-
direction due to the near two-point perspective of the imagery.
The precision of the parameters estimated from manual
measurements is better, although the number of lines used is
only a fraction of the number of automatically extracted lines.
The reason is found in the length of the manually extracted
lines. Therefore, hereafter only the manually extracted lines are
used for the camera calibration. This choice is also to be
preferred because it limits the assumptions of parallelism and
perpendicularity to the measured edges of the building.
The source of the inconsistency was traced by estimating the
parameters using the manual measurements of combinations of
two images. The results are shown in Table 2. Only the fit of the
combination in which image 3 is missing is of good quality; the
overall test is accepted (critical value 1.93).
Imag 3-6
Imag 3-11
Imag 6-11
Variance factor
31.01
31.63
1.435
d.o.f.
16
16
16
Max. residual (mm /
0.058 /
0.052 /
0.012 /
pixel)
8.8
8.1
1.8
Focal length in mm
9.124
9.234
10.056
(o)
(0.035)
(0.032)
(0.037)
Principle point y in
0.158
0.028
0.267
mm (o)
(0.048)
(0.046)
(0.050)
Table 2: Camera parameter estimation using the manual
measurement of combinations of images
Image 10 was now added in the estimation in order to verify the
results. In Table 3 adjustment results using the manual
measurements of three images are presented. As the critical
value is 1.8 (5% significance level) both adjustments are
accepted. Due to the 90 degree rotation around the optical axis
of image 10 the principle point x co-ordinate can also be
estimated. Note that the manual line measurements are not
suitable for estimation of lens distortion. The results in the last
column of Table 3 are the final estimates of the camera
parameters used for image orientation described in the next
section.
V
Figure 3: Manual line measurements for camera calibration
(images 3 (top) and 6)
Image 6, 10, 11
Image 6, 10, 11
Final
Variance factor
1.553
1.211
d.o.f.
26
25
Max. residual (mm
/ pixel)
0.0131/2.0
0.0100/1.6
Focal length
10.103
10.116
in mm (a)
(0.029)
(0.030)
Principle point x
-
-0.146
in mm (o)
(0.041)
Principle point y
0.222
0.220
in mm (a)
(0.047)
(0.046)
Table 3: Camera parameter estimation using the final
combination of three images
The CIPA data set was also analysed by others (Streilein et al.,
2000), (Rottensteiner et al., 2001). In the paper by Rottensteiner
the images taken with the Olympus camera are split in two
groups, one with a focal length of 8.598 mm and the other with
a focal length of 10.132 mm (balanced lens distortion).
Obviously, the setting of the zoom lens is different for the two
sets of images. The camera parameter values from (Rottensteiner
et al., 2001) derived with bundle adjustment software Orpheus,
are used as a reference. Comparison with camera parameters
provided in this set showed a good match. The lens distortion
parameter is not compared because the number and definition of
distortion parameters differs in the set determined with Orpheus.
The difference in the focal length is 3.0 times its standard