BS. Istanbul 2004
ns
mm?
).0005
).0007
).0007
S6E-07
S8E-10
20E-13
23E-07
21E-07
30E-06
17E-06
tric lens distortion
2ss, an additive is
inate. In order 10
jon with respect to
additive’s sign is
ctional models. In
alled RADVAR-
ANALYSIS
| free-net bundle
ctively with three
s axes. Because of
ent blunder might
e. Modern bundle
of our institute),
ave integrated and
. Strictly speaking
t object geometry.
appear when scale
m process, which
Concerning the
aled bundle results
ession input value
simulation process.
e example of the
| distributed input
int result as shown
stance input values
garding its standard
(200 simulations *
standard deviation,
on of the principal
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004
point, which spans between —0.10194mm and —0.09664mm
with reference to the standard deviation of sg, i, = 0.0007mm.
Due to a value range from 0.40561mm to 0.41106mm of the x-
direction of the principal point, 0.2% of all random values lie
outside 3c. The values of the principal point resulting inside 3o
are framed in the space of the rectangle of Figure 6.
variation of p rindpal distance (pd) vathin
200 sinzafations of G0 images (12000 values)
35.6657
35.6647 3E
.. 356642
E 35.6637
** 35.6632
35.6627
35.0622 i
35.6617 : : ; T : i
ü 2000 4000 6000 sono 10000 12000
Figure 5. Deviation of principal distance of simulation process
variation of prindpal point (pp) within
200 simulations of 60 images (12000 values)
a 0.412
0411
0410
0.409
0408
Pp-y [rm]
0.407
0406
0405
-0.103 -0.102 0.101 -0.100 -0099 -0.098 -0.097 -0.096
pp-x[mm]
Figure 6. Variation of principal point of simulation process
The distortion curve of the input values of one simulation
(hence 60 input values due to 60 images per bundle) results in
Figure 7. The variation of distortion for large radial distances
yield to +70Ojum for one simulated bundle (Fig. 8). Due to the
random modified parameters Aj, A; A; the distortion of
maximum radial distance r,,, — 26mm varies up to 80 um
regarding all simulated values (Fig. 9). Comparatively the
variation of dr’ for a radial distance of 9mm yields to 6um.
The consideration. of this effect for the affected image
coordinates seems to be significant. In particular regarding
higher deviation of radial symmetric lens distortion with respect
to the radial distance, the consideration of this variation is
essential. With regard to the distortion of the InputB value for
dr’ max) = -0.4115mm the deviation of +40um has significant
influence on the image coordinates.
4.1.2 Output values of bundle adjustments: A closer look
at the output values of the bundle adjustment with respect to the
corresponding input values of the camera parameters
demonstrates that the mean of the output values result in the
InputB value for random modification (with reference to the
example x, = -0.0993mm and Fig. 10). A generated random
input value (4) with (6)
Pim) < P(iy) (6)
on the average results in a positive value for the difference ot
output and input value, vice versa to a negative value like
illustrated in Figure 10. Ideally a straight line with a gradient of
1 would be obtained if no interacting effects would be
considered within the functional model, herein the standard
observation equations.
distortion curves of ane simulation (6fl images)
dr' (mm)
radial distance [mra]
Figure 7. Lens distortion curve of one simulation
rendom deviation of distortion curve
dr [mra]
0.40
-042
A ZEN
radial distance [nm]
Figure 8. Lens distortion for large radial distance
dr’ for radial distance mas = 26rem of 200 simulations
0 2000 4000 6000 2009 10000 12000
35 + — ———3À
dr' [rara]
-045 + x
-047
Figure 9. Variation of dr’ for r,,,, of 200 simulations
difference of bundle cutput value to input value
-D.0025
-0.002
1.0015
-0.001
0.00035
n
0.0005
0.001
0.0015
0.002
0.0025
output value minus input value [mm]
e
es
7
303
-0.10102
-0.10031
0.10013
-0.09993
0.09966
0.09936
100522
0.090017
0.0030,
0.00324
0.05859
-0.08
input value pp x [mn]
Figure 10. Differences of output and input value
