1510(pixel), and the principal point lies at the center of the image.
In Fig. 3, there A is the angle between level projection of
shooting aspect and direction of X; v is the angle between
shooting aspect and vertical direction. Assume that the standard
error of observation o0 is O.lpixel, and view the error of
parameters calibrated as error criterion.
y
Figure 3. The sketch map of simulation
1) In simulation, firstly only when the value ofangle V changes,
we observe the extent of error of the principal point and the focal
length influenced by V, Fig. 4 illustrates the error trend of the
principal point and the focal length when V ranges from
20? — 70? inthecaseof A = 45°,
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004
© 1.86
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a
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2
=
en
il
p
i
C)
|
(2
|
C
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w
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Error
«Ae dn.
2)
M
Error
c
>
=
=
0.63
0.42
0.21
0.00
20 25 30 35 40 45 50 55 60 65 70
Angle(degree)
Figure 4. The error curve of f and (x0, y0) obtained when the
angle v changed
The experiment above shows: when the angle V increases, the
error of the focal length m, becomes little, namely the
precision of f becomes high. But the three error curves trend
stable when the angle v is in the range from 40° to 70°; the
error of X, M,, becomes larger along with increasing the
angle v, and the error of Vy, M, becomes contrariwise.
Anyhow the errors of the focal length and the principal point are
profoundly influenced by the shooting angle V .
2) Only when the focal length f changes, we observe the extent of
error of the principal point and the focal length influenced by f,
Fig. 5 illustrates the error trend of the principal point and the
focal length when f ranges from 1510 — 4010 in the case
of À = v=45".
3.10
279
248
247
1.24 à Be
0.33
D.62
0.31
1510 1760 2010 2260 2510 2760 3010 3260 3510 3760 401
Focal length (pixel)
Figure 5. The error curve of f and (x0, y0) obtained when the
focus length changed
3) Finally, only when the angle A changes, we observe the extent
of error of the principal point and the focal length influenced by
A, Fig. 6 illustrates the error trend of the principal point and the
focal length when A ranges from 20° — 70° in the case
ofv = 45°.
— —
hy om
mom
/o S
-~
c
Fa
S
S
=
S
0.21
0.00
20 25 30 35 40 45 50 55 60 65 70
Angle (degree)
Figure 6. The error curve of f and (x0, y0) obtained when the
angle A changed
The experiment indicates: the angle A influences little on the
errors of the focal length and X, , but influences much on the
error of ys, from experiment (3) we can see when A439
the higher precision can be obtained. However, in practice it is
not easy to obtain the optimal shooting angle, thus the precision
of calibrated parameter based on single-view calibration is
unstable. Aiming at the shortage of this method of camera
calibration, we propose the calibrating method based on multi
orientations and multi views.
4. MULTI-VIEW CALIBRATION WITH VANISHING
POINTS
In single-view calibration utilizing vanishing points, the exterior
Internatic
orientatiot
calibratior
parameter
the accur:
error anal
and exteri
and then c
method ca
Orientatio
the other
orientatioi
of Fig. 1.
Linking
between
points:
Xv.
Xoo
Xr
V
The comp
it just lin
Therefore
adjustmen
ek.
oo