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Figure 3. Wrong match due to different viewing angles
eliminated by the trifocal tensor test.
The disparity is recognized, and the correspondence rejected. In
some other, more malicious, cases, the parallax effect is weaker
between two simultaneous frames but became larger and larger
along the sequence, leading to a whole set of apparently good
matches in adjacent images. This suggest that a final trifocal
test may be useful in order to reject all these *moving" wrong
matches.
Finally the two trifocal filtered data are joined together leading
to a four-image block set. In the following figure the accepted
point distribution is presented.
Figure 4. Ground points distribution after the trifocal tensor
filtering. Grass presence on the image left area prevents any
reliable matching to be found.
Then the two images ahead are used to compute the essential
matrix and obtain a first reconstruction of the scene points. The
algorithm performs a test on the camera geometry: if the
reprojection errors of the ground points is worst than the a priori
expected precision (1 pixel seems to be a reasonable figure)
Space resection and space intersection are alternated until
convergence. In straight path sequences, at this stage, at least 60
- 100 points have passed all the outlier detection tests; on these
points a half pixel reprojection error on both the images is not
unusual. Along curved path, obviously the matching procedure
is hindered by the increased disparity between adjacent and
consecutive images: less matches may be tracked and the
camera geometry suffers of a poorer ground points distribution.
Nevertheless, while the solution's convergence is slower (and in
some cases may be unstable), the final reprojection errors are
similar to those of the straight road sections.
Once obtained the ground points’ coordinates, the process may .
be iterated on the back images of the sub-block.
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004
At this time the scene points coordinates and the camera pose
are referenced in a local system.
When another block is solved, through all the above mentioned
steps. using a conformal transformation estimated by using unit
quaternions for the computation of the rotations, the new block
is referenced in the first local system. The algorithm proceed in
this way until the whole sequence is processed.
The final bundle adjustment, despite possible drift of the
solution due to the linking, did not show any convergence
problem. Though independent verification of the ground
coordinates has not yet been performed, plotting suggest a
correct structure and motion reconstruction.
Matching procedure Sequence 1 Sequence 2
across | along | Across | along
Putative correspond. 785 954 710 832
Inliers after epipolar 358 581 370 573
Common pts. in 3 im. 124 137
Inliers after trifocal 86 107
S&M reconstruction Sequence 1 Sequence 2
Common pt. in 4 im. 62 80
Reproj. err. after ess.* 0.79 pix 0.65 pix
Sub-block orient. err. 4.3 cm 3.9 cm
Reproj. err. after BA.* 0.52 pix 0.51 pix
* mean value
Table 5. Mean performance of the algorithms in two different
sequence of about 100 m length (not including curved paths).
4.2 Simulations on stabilization of the solution
It 1s well known in aerial photogrammetry that long image
strips tend to drift away from the terrain, especially in
elevation, unless ground control is provided along. Since at first
sight the geometry of the MM van looks similar, we performed
a simulation to find out whether it is truly so and, in case, what
kind of improvement may be introduced by adding control
information. This may come either from maps or GIS data or by
the differential GPS code solution, whenever available (e.g.
when the ambiguity cannot yet be recovered but 4 satellites are
visible). Of course, the former solution would be the most
appealing, since no additional work would be necessary, apart
in the final block adjustment, while looking for points in the
map is always time consuming (unless they are reprojected after
an initial solution constrained only at the strip ends) and error
prone. Besides, most of the time the information from map
points is either horizontal or vertical, rather than 3D.
To this aim, starting. from a set of exterior orientation
parameters computed by the GPS solutions and a number of
suitably distributed points along the road section have been
generated and projected over the images, trying to filter out,
based on two distance thresholds, those unlikely to be visible.
By constraining the first and last image of the sequence, as we
would do using the last and first successful GPS solution before
and after the loss of lock, the RMS errors on the ground points
and on the exterior orientation elements have been computed by
variance propagation in a block adjustment. Given a
measurement accuracy of 1 pixel to image coordinates, for a
sequence of 80 images (250 m long) the RMS of the X,Y
coordinates is worse than that for elevation by almost an order
of magnitude. With an average number of 10 rays per point and
of 17 points per image, theoretical RMS are around 50 cm in
horizontal and 4 cm in elevation. Corresponding figures for
projection centres are lower, with 15 cm in horizontal and 3 cm
