International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part BI. Istanbul 2004
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Figure 4: Maximum normalized distance in principal point. The distances are normalized with the image width. From left
to right: Logitech camera (1), Terratec camera (2), HP camera with vga and 3MB resolution (3), Sony camera with VGA
and 5MB resolution with 4 different zoom values (4), Kodak DCS 460 without demounting of lens (5S), with demounting
of lens (SU).
4. Big differences in distortion changes regarding different
zooms settings of the Sony camera could not be observed.
3.3 Changing Resolution
Nearly all cameras offer the possibility to change resolu-
tion. Therefore it might be possible to transfer the calibra-
tion of one resolution to another, as two different resolution
only differ by resampling. So principal distance, principal
point and distortion just needed to be scaled up or down.
This is straight forward if aspect of width and height re-
mains the same which is often the case.
We found this possibility depends on the camera. It works
fine for the Sony camera, there the differences between one
set of calibration parameters and the scaled parameters of
another resolution are in the order of the temporal changes.
Recalculating calibration parameters does not work for the
HP camera: We found differences between calibrated and
rescaled coordinates of the principal point, probably as not
the same pixels on the chip in the different resolutions is
chosen. Therefore each resolution requires its own cali-
bration of the principal point.
3.4 Effect of Zoom
We investigate the relation between nominal focal length
and calibrated principal distance and the change of distor-
tion as a function of zoom factor. We studied this with the
Sony camera.
Today every camera stores the nominal focal length in the
header of each image, using the so-called EXIF-format.
We studied the relation between this nominal value and the
calibrated principal distance, in order to find in how far
the nominal value can replace the principal distance. Fig-
ure 6 shows a strong linearity between c and nominal focal
length f. However, the RMS-error of 12.7 pixel is sig-
nificantly larger than the accuracy of the calibrated princi-
pal distance which for 1 Mega-pixel resolution has a mean
value of o.=0.7 pixel. So for precise measurements the
camera needs to be calibrated at the used zoom factor.
Distortion varies extremely with zoom factor, cf. figure 7.
At zoom factor 1x where the principal distance is stable
(see figure 3) the distortion is maximal. The distortion pa-
rameter A; decreases nearly monotonically with a increas-
ing zoom factor.
The distance of the principal point from the image center
increases heavily with the zoom factor, even worse: there
is no linear behavior, which at least in this case would not
allow linear interpolation.
3500 = T 1 T T
30001 RMS= 12.707163
2500r f(x)» 86.937703 x + -13.778193
2000}
1500
1000+
1 A L
7 9.1 11.813.9 16.5 19.21.23.425.5 28 30.1322 35
focal length [mm]
500
Figure 6: principal distance of Sony DSC V1 at differ-
ent optical and digital zoom levels (30.1-35 mm is digital
zoom), used distortion: A1, Bj, B3. Resolution: VGA
images.
3.5 Influence of Focus
Changing focus changes the principal distance, though to a
much smaller amount than zooming. We studied the effect
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