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t B5. Istanbul 2004
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004
stages are needed, apart image format and colour to grey value
conversion. Although the sand texture and colour does not offer
a well contrasted background and some grains are highly
reflective, illumination and exposure could be adjusted in such
a way as to have spheres sufficiently discriminated against the
sand.
To control the automatic tracing procedure, the user is required
to setup the parameters of the matching algorithm and to carry
out some initial manual measurements, i.e. the localization and
labelling of the position of the spheres as well as the
measurement of the approximate position of at least two
calibration targets in the first image. Position of the other
fiducials in the same image can be derived by a simple
conformal transformation, because their position in the frame
reference system is known. As initial matching location in the
following images, the same value assumed for the first image
can be used for the calibration targets; even if the camera is not
perfectly stable during the test, its displacements are very small
and approximations still hold.
Tracing the spheres along the image sequence is made up of the
following items, which are applied to each image:
sub-pixel measurement of calibration targets;
computation of image rectification parameters;
prediction of the sphere location in the next image
based on its position in the current image;
4. computation of object coordinates for all spheres by
applying the parameters.
Uu b nm
Image measurement is perform by least squares matching
(Gruen, 1985; 1996), with an affine transformation which may
compensate also for rotations and scale variations of
corresponding points. The reason for using the affine model is
that the spheres can be partially covered by sand grains, so that
allowing rotations improves the fit; besides, it happens
sometimes that a sphere is pushed away from the wall inside the
sand, so allowing a global scale variation again improves the fit.
No radiometric correction is implemented in the l.s. matching
algorithm, but mean and variances of template and patch are
equalized prior to the matching (Baltsavias, 1991).
The measurement of fiducials on the frame is performed by
template matching with a synthetic copy of the target. For the
tracing points, the template is a square window resampled
around the sphere location in the previous image; the centre of
this window is used as initial location of the patch in the second
image. This solution works fine as far as displacements are
small, as it happens at the beginning of the loading cycle, but
later the movement lead to displacements in image space larger
than the convergence radius, so that matching would fail.
Modelling as a time dependent function this displacement
would allow to predict the homologous point position on the
basis of its previous path could be computed, as shown in the
next section. Here we followed a simpler approach, which
exploits the fact that the largest component of the sphere
displacement is along vertical lines, so that other initial
positions can be set up along this direction at pre-fixed steps.
This method allows to trace all spheres along the image
Sequence, barring a little fraction which are lost in the last
stages of the loading. However, overall, this failures did not
compromise the evaluation of the displacement field. Possible
cause of failure in tracing may be the disappearing of a sphere
into the sand, disturbances introduced by reflections on the
glass or large displacements which cannot be traced with the
simple prediction model.
Since the acquisition time of each image is recorded, not only
the displacement field, but also the velocity field can be
computed.
As far image measurement accuracy is concerned, the Ls.
matching figures are about 1/20 the pixel size, resulting in
about 0.45 pm.
2.5 Results of experimental tests
The first experimental loading test concerned a sand featuring a
quite low relative density (incoherent material). In Table 3
some characteristics of this trial have been summarized, with
the indication of the number of successfully traced points in the
whole sequence.
Trial # of # of traced # of frame rate
spheres spheres images (s)
1 190 175 77 30
2 102 98 40 30
Table 3: features of experimental tests
To independently check the results, both diagrams time-
displacement of the points just below the foundation, evaluated
by photogrammetry and by the strain gauge measurement have
been compared. While it is apparent that they show the same
behaviour, a metric evaluation is not possible, because the two
methods do not determine the displacements of the same points.
Thus the measurement accuracy of tracing points has been
estimated indirectly, by comparison with the accuracy of
fiducials. By considering a few fiducials as control points and
looking at the discrepancies between estimated and known
coordinates of the remaining, an accuracy in object space of
about 15 jum has been estimated. To derive the accuracy of the
sphere, where we don't have any independent control, by
analogy we assumed that of the fiducials, reduced by the ratio
of the average values of the correlation coefficients obtained by
the l.s. matching process for both kinds of points. The estimated
value turns out to be about 18 pm, largely inferior to the
required value of 0.1 mm.
Figure 4 shows the whole displacement field, plotted with the
program GID (gid.cimne.upc.es).
In a second loading test, the device was filled with sand of
mean density. During this trial a sudden variation in load
intensity was applied to check the sensibility of the method. In
the diagram time-load reported in Figure 6, a small load
reduction (from point A to B) was followed by an increment of
20 kg applied (point C) in 5 s. At the end of this blip, it can be
seen that the original curve has been recovered. The selection of
a higher sampling rate of the sequence (30 s) permitted to
accurately follow the displacements.
Figure 5 shows another kind of visualization of the
displacement field obtained by GID software; in this case, a
mesh representation of tracing points at two different stages of
the trial is given. Apart from visualization purposes, the mesh
structure is very important as pre-processing step for the finite-
element analyses.
