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CIP A 2003 XIX 1 ' 1 International Symposium, 30 September - 04 October, 2003, Antalya, Turkey
larged prints had been somewhat cropped, the interest focused
here not on the actual values of interior orientation but rather on
the closeness of results from the three calibration approaches (it
is noted that the images were scanned in different resolutions).
Figure 1. The images of the first test.
Tablel. Results of single image calibrations
Image
1
50 mm
2
50 mm
3
35 mm
4
35 mm
5
35 mm
6
35 mm
1
45 mm
8
24 mm
Method
A
C
B
A
C
B
A
C
B
A
C
B
A
C
B
A
C
B
A
C
B
A
C
B
c (mm)
x 0 (mm)
Yo (mm)
48.84
48.80 ± 0.16
48.84 ±0.21
48.89
48.89 ±0.13
48.69 ±0.20
35.16
35.16 ±0.05
35.13 ±0.13
34.66
34.66 ± 0.05
34.63 ±0.09
36.05
36.05 ±0.12
36.16 ± 0.27
35.69
35.69 ±0.12
36.10 ±0.23
43.42
43.42 ±0.14
43.92 ±0.55
24.46
24.49 ± 0.07
24.40 ±0.17
-1.34
-2.30
-1.28 ± 0.15
-1.26 ±0.20
0.63
0.66 ±0.26
0.77 ±0.36
0.63
0.63 ± 0.06
0.52 ±0.20
0.56
-2.32 ±0.09
-2.50 ±0.12
-2.06
-2.08 ±0.12
-2.08 ±0.26
-1.31
-1.32 ±0.05
-1.33 ±0.12
-1.11
7.6 pm
7.6 pm
L5
7.1 pm
7.0 pm
1.9
8.8 pm
9.1 pm
Z9
9.4 pm
0.56 ±0.06 -1.12 ±0.05
0.56 ±0.10 -1.21 ±0.09
9.4 pm
2.6
-1.30
-1.24 ±0.26
-1.76 ± 0.58
-0.08
-0.20 ±0.20
-0.14 ±0.41
-0.12
-0.14 ±0.26
0.61 ±0.81
-0.20
-0.19 ±0.12
0.07 ± 0.24
0.62 17.4 pm
0.52 ±0.15 17.6 pm
0.75 ± 0.40 3.3
1.03
1.06 ± 0.16
1.22 ±0.28
1.28
1.19 ± 0.13
1.29 ±0.46
16.3 pm
16.5 pm
3.2
17.7 pm
16.9 pm
5.8
1.82 19.5 pm
1.79 ±0.07 19.7 pm
1.85 ±0.14 2.6
Results from all three approaches, whereby radial distortion has
been ignored, are presented in the above Table 1. It is clear that
approaches A and C give values for calibration parameters pra
ctically identical; the same holds true for the precision estimates
ct 0 (regarding approach B, it is noted that ct 0 is dimensionless as
the observations are actually weighted). Thus, it appears that in
deed these two methods are essentially equivalent. Approach B,
on the other hand, gives similar results for the first 4 images, for
which small ct 0 values are present; yet, significant deviations do
exist in some of the remaining images (for instance, differences
in c reaching 1.1%), where a 0 values are large. This could be an
indication that, since line fitting is performed as a separate step,
this method might be more sensitive to ‘noise’.
The last remark to be made here is that the precision of the un
knowns, too, appears to be considerably smaller in approach B
than in C. It is noted that in method A, where the unknowns are
finally found with no redundancy, precision estimations for the
camera parameters could also be calculated as an error propaga
tion of vanishing point standard errors, emerging from the line
fitting adjustment using Eq. (1), to the values of interior orienta
tion parameters.
3.2 Comparison of single-image and multi-image approaches
In this case, a regular grid was used to provide ample control. A
number of toy items had been placed on it to create a 3D object,
but also to provide vertical control. This structure has then been
recorded ten times using a KODAK DCS420 camera (1524x1012
pixels of size 9.2 pm) and a 28 mm lens. Thus, the performance
of single-image approaches was assessed under rather unfavour
able conditions due to the weak perspective of the narrow-angle
lens.
Six images (shown in Fig. 2) were selected for the single-image
tests, namely those whose converging lines did not intersect at
exceedingly small angles in any of the three vanishing points.
These same six images were used in the bundle adjustments.
A self-calibrating bundle solution was carried out (ignoring dis
tortion) with all six images, based on a total of 25 control points
(21 full and 4 vertical) and 60 tie points. Regarding the single
image calibrations, 3 image lines were measured in the grid X,Y
directions; more lines (7-13) were measured in the direction of
depth, to compensate for short line segments. After solution, the
values of interior orientation parameters from each approach for
