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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004
. f S sc AER" (2)
Y.yvy)zc + - exp] i— =
Flan Lax’ oy’ | of pl |
where (x, y) are image coordinates, and pis a scale factor.
An example is shown in Fig. 4. A target image of the central
part was truncated and extracted (right side) from the image
(left side).
Figure4. Extraction of a target image
When pis a small value, a zero crossing tends to appear inside a
target image according to small in-homogeneity of intensity of
a target image. On the other hand, for large value of p, the
circumference of a target image becomes blurring and the target
image can't be extracted correctly.
According to preliminary experiments, the proper value of u for
the diameter of a target image of 3-10 pixels is n 71 , j| —2 in
for the diameter of 15-30 pixels, and u =3 for the diameter of
5-20 pixels. In general most of targets were correctly measured
foru=2.
Tablel shows interior orientation parameters and standard
deviations evaluated for the five camera configurations.
Because of adjusting only in the central part of a sensor area
with little lens distortion, the value of standard deviation of Pan
exposure is the best.
3. AN EXPERIMENT ON ACCURACY CHECK
The aceuracy of interior orientation parameters by the above
five calibrations was checked.
FigureS shows a target field for the accuracy check. Twelve
scale bars (called Scale 1,2...12 hereafter) of one meter long
have been arranged squarely. The scales were made of steel.
For Scale 1, 4, 7, and 10 two retro-targets with a diameter of
15mm were applied to the ends of each bar.
For the other scales, retro-targets of 5mm in diameter were
applied. This is to compare the influence of target size.
All the scales were precisely pre-calibrated with UMM
(Universal Measuring Microscope, Leitz) The nominal
accuracy is 0.01 mm.
Three images were taken in a convergent configuration at
camera stations along the centre line of the object space. The
distance to the object space is about 1,000mm and the
convergent angle was 45degrees. The three images were
bundle-adjusted as free-network with interior orientation
parameters fixed with values shown in Tablel. For a reference
the result of self-calibration is added to the table.
Then the scale of the object space was adjusted to the Scale3
and 12. The residuals of the adjusted scale values from true
values were shown in Table2.
The size of a scale was calculated from object coordinates of
the target computed as a result of bundle adjustment, and the
result, which performed comparison with true value, was shown
in Table2.
Figure5. Test Field.
The major results obtained by the experiment are as follows.
a) The accuracy of (3) the combination of Pan exposure and
Block exposure is proved the best, and it exceeds the precision
of self-calibration.
The accuracy of measurements with 15mm targets, which were
imaged up to 40 pixels, is always degraded than the
measurements with 5mm targets.
b) The accuracy of (1) Pan exposure is the worst, since no
information of lens deformations in the fringe of the sensor.
c) The precision of (2) Close exposure is second worse to (1)
Pan exposure. Especially the cases for use of 15mm targets get
even worse. This shows that the fact the centroid of a target
images does not coincide with the true centre is strongly
influenced.
It is possible to compensate for this error by fitting an elliptic
curve to each target image. But considering additive
measurement time beside the time for the above-mentioned
processing, it may not make sense.
4. CONCLUTION
A calibration technique, which is simple and easy and produces
homogenous and high precision over the sensor area, is
discussed. Some combinations of camera configurations are
compared by an experiment using 2-D target field. As the result
the self-calibration of images taken in a combined configuration
of convergent pan exposures plus vertical close exposures
shows the best precision. By using this result, restrictions
conditions, such as camera configuration, decrease and the
range of practical use of photogrammetry can be extended.
REFERENCES
D.C.Brown, 1966, Decentering distortion of lenses,
Photogrammetric Engineering, vol32, no.3, pp.444-462.
S.Hattori and Y. Myint, 1995, Automatic Estimation of Initial
Approximations of Parameters for Bundle Adjustment, PE&RS,
Vol.61, No.7, pp.909-915
