the large convergence angle. Therefore, point set registration,
which finds an optimal alignment between two sets of points
by means of geometric constraint and statistical information,
is alternatively employed to handle this issue. Due to strong
perspective deformation caused by the large convergence
angle and depth range, point set registration algorithms,
which are not designed for matching multiple objects, could
fail to assign the correspondences of all the control targets
and tracking targets. As a result, the control targets are manu-
ally differentiated from the tracking targets in each image in
advance, and then the non-rigid point set registration algo-
rithm preserving global and local structures (Ma
et al.
, 2016)
is adopted to match two sets of target points in each part. The
input point sets are represented as Gaussian mixture models
(
GMMs
), which is aimed at exploiting the global structures. In
addition, local features, namely shape context feature descrip-
tors, are used to assign the membership probabilities of the
mixture model. The point set registration can be considered
as a
GMM
probability density estimation problem, and the
parameters of the mixture model are solved in an expectation
maximization framework (Ma
et al.
, 2016). It is noted that the
correspondence between the stereo images determined in the
first frame hold throughout the whole image sequence.
Target Tracking
In this study, the improved subpixel phase correlation method
is performed to realize target tracking. The precise and reli-
able motion trajectory of the target points in each image
sequence is estimated. Considering that matching between
consecutive frames would induce an accumulation of errors,
the proposed phase correlation method is performed on the
first frame and the following frames. For each valid target rec-
ognized and matched through the above procedures, a region
of interest to be tracked is defined as a template around the
target’s center in the first frame. The target can be located in
the successive frames using the proposed subpixel phase cor-
relation method by calculating the shifts between templates.
As the maximum allowed displacement of phase correlation is
half the effective correlation window size, the larger displace-
ments cannot be effectively calculated. In this case, pixel-level
result of the former frame is used to provide the initial predic-
tor. The image coordinates of the center of every target points
on each image sequence can be obtained by target tracking.
3D Spatial Coordinates Calculation
After extracting, matching, and tracking the target points, the
3D spatial coordinates of the tracking points are calculated
through two photogrammetric algorithms, namely bundle
adjustment and forward intersection. As the cameras are as-
sumed to stay still during the measurement, the interior and
exterior orientation parameters remain constant at each epoch
of the image sequence. First, the exterior orientation param-
eters, including the position and orientation of the cameras,
along with the 3D spatial coordinates of the tracking points
at the first epoch, are calculated by the bundle adjustment
algorithm using the stereo images in the first frame. Using the
control points tagged with the given 3D spatial coordinates
that were previously surveyed by the total station, the final
solutions of the bundle adjustment are achieved by an itera-
tive least squares estimation process. Afterwards, the 3D spa-
tial coordinates of the tracking points at the other epochs are
estimated by a forward intersection algorithm based on the
fixed exterior orientation parameters of the stereo cameras.
Data Postprocessing and Analysis
In order to reflect the dynamic response of the structural
model, dynamic parameters at the key positions need to be
acquired based on the spatial position values calculated from
videogrammetry. However, high-frequency noise compo-
nents caused by the inherent measurement uncertainty can
significantly affect the quality of the results. An appropriate
filter should remove noise while preserving the true features of
the process. The Savitzky-Golay filter recommended in Leifer
et al.
(2011), which is an effective extension of the simple
averaging filter, is adopted in this study to smooth the video-
grammetric spatial position data. It is constructed based on
a least squares fit to each window of data by a polynomial of
fixed degree.
The filtered 3D spatial coordinates of the tracking points
are subsequently used to estimate the dynamic parameters,
including displacement, deformation, and acceleration. These
parameters, which intuitively represent the motion state of
the structural model, are the basis of the other dynamic prop-
erties such as natural frequencies, damping ratios, and mode
shapes. The displacement of a target is the difference between
the 3D spatial coordinates at a certain epoch and at the first
epoch, while deformation refers to the relative displacement
between a certain target and a reference point at each epoch.
The reference points are generally located in the rigid areas
and share the same movement with the shaking table. The
acceleration of a target can be calculated by directly twice
differentiating the filtered position data using a seven-point
numerical differentiation equation Leifer
et al.
(2011). Finally,
the performance of the videogrammetry-based positions and
accelerations are assessed by means of check points, original
waveforms, traditional sensors, etc.
Experiments
In this study, an experiment was conducted to monitor the
dynamic responses of a landslide dam under aftershocks
through large-scale shaking table tests. The deformation and
acceleration of the model dam were measured by the video-
grammetric technique.
Experimental Model and Test Process
The structural model on the shaking table was a landslide
dam with the similitude ratio of the model geometry taken as
20, and the scaling factor of density as well as acceleration
set as 1. The dam was built with the materials of 90 percent
quartz sand and 10 percent kaolin. As shown in Figure 3,
the model dam was 0.5 m in height, 0.2 m in crest length,
2.7 m in bottom length, 1 m in width (perpendicular to cross
section), and 22 degrees in slope (Shi
et al.
, 2015). The dam
was constructed within a test box and fixed on the shaking
table. For the purpose of monitoring the dynamic behavior of
the dam using videogrammetry, one side of the test box was
made of the thin tempered glass. Acceleration sensors and
other gauges were installed within the dam. According to
their positions, two acceleration sensors, namely no. 12908
and no. 12904, were chosen to validate the reliability of the
videogrammetric system. In the experiment, a Kobe wave in
the X direction with a peak ground acceleration of 0.63g was
selected as the seismic wave to input into the shaking table.
More details of the tests can be found in Shi
et al
. (2015).
Figure 3. Cross section of the landslide dam model in the
experiment.
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September 2018
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
