The image orientation based on free-form tie curves
consists of two steps alternately applied until the
expected accuracy is achieved.
The first step is the simultaneous adjustment of the
image orientation and the tie curves. The unknowns of
this adjustment are: the projection centres and the
rotational parameters of the images, the object co-
ordinates of the curve points, the positions of the points
along the curve and the nodes representing the tie
curves. The number of nodes remains unchanged
during this first step.
The second step is the improvement of the node
arrangement of every tie curve with significantly high
residuals by applying the curve reconstruction task as
described in section 4.1. The orientational parameters
are assumed to be constant during this step.
The refinement of a tie curve's shape during the
process of image orientation can be seen in figure 8. At
the end of this process, the shown curve is built up by a
rather high number (nine) of node points. Using even
more nodes did not improve the reconstruction of the
tie curve (second step) nor did it improve image
orientation (first step).
tie curve at the beginning
of image orientation
(every second curve point
plotted)
tie curve at the end of image orientation
(every second curve point plotted)
DET ES 3
B
Figure 8: The tie curve at the right back door at th
beginning and at the end of image orientation.
4.3 The result
The final results (see figure 9 and 10) were achieved
by twice repeating the process of image orientation and
curve reconstruction as described in section 4.2. Every
step of image orientation took among 20 (configuration
a) ) and 30 (configuration b) ) iterations; every iteration
took about seven minutes computational time on a PC-
486. The accuracies of both configurations are quite
similar: The finally adjusted tie curves fit to the oriented
e
200
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
bundles of rays with an accuracy of about 4 um or 4
pixel, respectively (see table 3 and 4).
However, inspecting the control points, reveals that the
real r.m.s error is in the order of about x35 um (2
pixels) in the image or x1.5 mm in object space.
Regarding the residual vectors of the control points, it
can be concluded that a small deformation remained in
the adjusted object points. This deformation is caused
by the weak tie information between the left and the
right side of the car, with all the tie curves available
being nearly parallel (e.g. the lower and upper
borderlines of the front and rear windows).
Adjusting the images of the left and the right side
separately results in r.m.s. errors at the control points
in the order of 20 um (1.5 pixel) or 0.8 mm in object
space. This corresponds to the uncertainty of definition
of the original object curves.
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Figure 9: Finally adjusted tie curves of configuration a)
(low bent tie curves)
No. tie No. nodes No. curve r.m.s. error
curves points in image
40 183 5529 3.8 um
Table 3: Adjustment results of configuration a)
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wi al
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Figure 10: Finally adjusted tie curves of configuration b)
(highly bent tie curves)
No. 1
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40
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