rt B3. Istanbul 2004
cal tensor was still
n method, whereas
error CR).
ints has to be ex-
d at least 15 points
he facade, 2 points
icade) and 2 points
imple the rigorous
uss-Helmert model
considering the in-
'essary, because for
JA’) no valid inte-
(ruppa’s equations.
e bundle block ad-
orientation (2059.7,
on-linear distortion
Jn are:
m]
focal tensor we dis-
'nthetic examples:
g algebraic and re-
on is negligible the
used and the more
ite from a common
r is more important
straints
bad and at least 10
minimum thickness
, of the camera dis-
| proper solution for
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
Radial Distortion of
Canon EOS 1Ds 20mm
207
15 «d
|
T 1
1000 2000] 3000
-5 = / i
-10
es
-15 =
Distortion [pixel]
Radial Distance [pixel]
Figure 3: Left part: The non-linear, i.e. radial , image distortion of the camera Canon EOS 1Ds with a 20 mm objective.
Right part: The second of three images of the facade used for the experiment. The 7 yellow arrows pointing up-right
mark the points used to compute the trifocal tensor for the task with known interior orientation; #1 marks the one point
on the roof significantly behind the facade by 2.5 m. The 15 blue arrows pointing up-left mark the points used to compute
the trifocal tensor for the task with unknown interior orientation.
Guided by this findings we also carried out an example
using real images taken from a facade. From this example
we see:
e ifthe interior orientation of the camera is known, then
the exterior orientation derived from the trifocal ten-
sor is sufficient to initialize a bundle block adjustment,
even in the presence of significant radial distortion
and even if the tensor is computed with the minimum
number of 7 point correspondences (since the mini-
mum thickness of the points on the facade was below
| % of the camera distance, one point significantly
away from the facade was necessary),
if the interior orientation is unknown and the tensor is
computed with at least 15 points with 4 points signif-
icantly away from the facade, reasonable approximate
values for the interior orientation can be obtained us-
ing Kruppa's equations.
Although for most of the investigated examples, the sim-
ple direct linear solution UCA") for the tensor and the
rigorous solution in the Gauss-Helmert model ('CR?) re-
turn similar results, the latter solution is the recommended
one, because for some situations the simple solution fails
to yield a usable result.
Therefore the recommended strategy for image orienta-
tion is to first estimate the trifocal tensor rigorously in the
Gauss-Helmert model, then to derive - if unknown - a com-
mon interior orientation, to extract the exterior orientation
and finally to initialize with those orientation parameters
a bundle block adjustment, which refines the orientation
by additionally modelling the non-linear image distortion.
Acknowledgment
Part of this work was supported by the Austrian Science
Fund FWF (P13901-INF).
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