International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004
To evaluate the error of the parameters calibrated by bundle
adjustment based on multi images, we also can carry out the
experiment of simulation (the parameters of experiment are the
same as section 2.2). Differing from the simulation in section 2,
four images are gathered with the mode rotating the angle K
Oo ; - : .
every other 90", then all the data in the four images is
formulated in the uniform mathematical model. The errors of the
principal point and the focal length calibrated are shown as Fig. 8.
Only when the angle V changes, no matter what the value V
is, 71.9 and 77,9 arc cqual, the angle has little influence on
the errors of the principal point and the focal length. And
comparing Fig. 8 with Fig. 4, we can see that in the same
condition of the angle, the calibrated precision based on
multi-view is much higher than that based on single-view. (Note
that the coordinate systems of Fig.8 and Fig.4 are in the same
scale and two curves of M, and M, in fig.8 overlapped
basically with each other.
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be f
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Error
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T
0.36
20 25 30 35 40 45 50 55 60 65 70
Angle (degree)
Figure 8. The error curve of f and (x0, y0) obtained when the
angle v changed with multi-image
5. PRACTICAL DATA ANALYSIS
In practical calibrating test we use the Rollei d30 metric camera
with — known intrinsic parameters with image size
1280* 1024(pixel). Its focal length is 1510 and the principal point
is (670,492), note that the unit of the values above is pixel, and
the coordinates of principal point locates in the coordinate system
whose origin is left-top point of the image.
In calibrating experiment, four images are taken by the way of
rotating to the corner of onc building. (See Fig. (9)- (12)). First
single-view calibrations based on vanishing points to the four
images are respectively fulfilled (the results of calibration are
listed in column 2-5 of Chart 1), simultaneously, the multi-view
calibration uniting all of the four images is also done (the results
of calibration are listed in the 6^ column of Chart 1).
ET
Figure 9. The original image Figure 10. The original image
(0°) (90°)
(180°) 12/0)
As experiment is shown, in single-view calibration test, the
calibrated principal point of camera is not stable; however, the
calibrated interior parameters in multi-view calibration test are
all better than those in single-view.
Fig. 9 Fig. 10 Fig. 11 Fig. 12 Four images
f 1505.943050 1500.504439 1498.446842 1521.269439 1508.759933
633.089894 657.699167 677.716904 699.061394 665.803436
x
i
498.767641 458.748016 526.335161 493.018644 494.034017
Yo
Table 2. The result comparison with single-image and multi-image calibration
6. CONCLUSION
This paper, through a series of experiments, analyzed and
evaluated the error of interior parameters of camera calibrated
utilizing the method of vanishing point of single-view, and then
we can conclude, the error of interior parameters calibrated with
the method of vanishing point of single-view is greatly
influenced by the factors of angle view, focal length etc. Thereby,
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