a hand-held digital video camcorder in the shaking table tests
with a two-story steel frame specimen. The displacement
results were then compared with those measured by
LVDTs
.
Wu
et al
. (2014) also made use of the single-camera video-
grammetric technique to monitor the 2D plane vibrations of a
reduced-scale frame mounted on a laboratory shaking table.
Ji and Chang (2008), Ribeiro
et al.
(2014), Busca
et al.
(2014)
and Guo and Zhu (2016) adopted more advanced components
and image processing techniques to construct unique vision-
based systems for the 2D vibration monitoring of bridges and
sound barriers.
From the aforementioned studies, we can see that us-
ing a single-camera system can normally obtain 2D in-plane
displacements in small regions. Although a monocular
videogrammetric technique was proposed by Chang and Xiao
(2009) to extract the 3D translation and rotation of a planar
target using a single image sequence, its measurement ac-
curacy is sensitive to the image orientation, and measurement
with multiple targets becomes a problem. Therefore, multiple
cameras with stereo or multi-view observations are required
to achieve 3D measurement. Chang and Ji (2007) proposed a
videogrammetric system using two commercial-grade digital
video cameras to measure the 3D structural vibration re-
sponse in the laboratory. Kienle
et al.
(2008) reported a simple
videogrammetry-based experiment involving acceleration
tracking of a fixed-free beam in vibration using three low-res-
olution
CCD
cameras. On the basis of Kienle’s research, Leifer
et al
. (2011) further analyzed and evaluated the potential
of videogrammetry-based acceleration measurements using
the same three cameras and a modal shaker. Alemdar
et al.
(2011) estimated the surface deformations and rotations of a
reinforced concrete bridge column under dynamic loading
on a shaking table using a videogrammetric system of four
cameras. An accuracy of approximately 1 mm was achieved
compared to the traditional instruments. However, few stud-
ies of 3D videogrammetric systems for monitoring complex-
condition models on a large-scale shaking table have been
reported.
As one of the major concerns for the videogrammetric
system, the performance of tracking in image sequence is
crucial to the final measurement accuracy. Normally, target
tracking in videogrammetry can be realized through shape-
based methods or intensity-based methods. The shape-based
methods use the shape information of artificial targets to
locate the target points in each frame (Ribeiro
et al.
, 2014;
Liu
et al.
, 2015). With regard to the intensity-based methods,
as the induced deformation in vibration-based applications
is relatively small in a short capturing time, template match-
ing is commonly adopted (Sutton
et al.
, 2009; Pan, 2011).
The locations of the target points in the successive frames
are determined by maximizing or minimizing the similarity/
dissimilarity measure between a local template centered at
the target position in the first frame and a deformed copy
in another frame. The common matching strategies include
correlation-like methods (Chang and Ji, 2007; Feng
et al.
,
2015), iterative optimization-based methods (Ji and Chang,
2008; Gruen, 2012), inverse compositional methods (Pan
et
al.
, 2013; Guo and Zhu, 2016) and so on. In this paper, phase
correlation is adopted to ensure the matching accuracy and
efficiency, as it is considered to be more accurate and effective
than other widely used correlation methods such as cross-cor-
relation (Heid and Kääb, 2012). A subpixel matching accuracy
is pursued as pixel-level accuracy is often inadequate in the
case of small structural vibrations. Subpixel phase correla-
tion methods can be implemented in the spatial domain or
directly in the Fourier domain (Foroosh
et al.
, 2002). In the
former case, the shift parameters are estimated by precisely
determining the main peak location after inverse Fourier
transform, such as in Foroosh
et al.
(2002), Nagashima
et al.
(2006), and Guizar-Sicairos
et al.
(2008). In the latter case, the
relative displacements were calculated by explicitly estimat-
ing the linear phase difference of the cross-spectrum, such as
in Hoge (2003) and Stone
et al.
(2001). However, most of the
existing subpixel phase correlation methods either are free of
an explicit measure to deal with aliasing, noise and other cor-
ruptions, or rely on parameter tuning to guarantee the robust-
ness. This issue leads to the sensitivity to interference factors
and the decreased performance in the practical applications
(Tong
et al.
, 2015). The interference factors tend to deteriorate
the performance of subpixel correlation for tracking in image
sequence, and thus affect the final accuracy of videogammet-
ric measurement. Therefore, it is necessary to enhance the
robustness of motion tracking especially in the presence of
various interference factors.
In this paper, an improved subpixel phase correlation
method is proposed to acquire precise and reliable displace-
ments at both multipixel and subpixel scales. The improved
method takes advantage of the idea of Stone’s method (Stone
et al.
, 2001), which considers shift estimation as a plane
fitting problem in a theoretical sense, and the main novelty
is the integration of the image gradient representation, an ef-
fective robust estimation algorithm using higher than mini-
mal subset sampling and robustness iteration operation into
the Stone’s method to further enhance the robustness and
accuracy. In addition, on the basis of the proposed phase cor-
relation method associated with other state-of-the-art image
processing algorithms, a videogrammetric system is presented
for measuring the 3D structural vibration response. The per-
formance of the improved subpixel phase correlation method
is demonstrated by comparisons in two simulated tests as
well as one static test. In addition, an empirical experiment of
monitoring of large-scale shaking table tests with a landslide
dam model is carried out to validate the feasibility and effec-
tiveness of the proposed videogrammetric system. The calcu-
lated 3D coordinates are assessed by checkpoints surveyed by
a total station, and the calculated acceleration time history is
compared with the input seismic wave and acceleration data
measured by acceleration sensors.
Proposed Subpixel Phase Correlation Method
Phase correlation is a Fourier-based matching technique,
which can be efficiently calculated by means of fast Fourier
transform (
FFT
). The theoretical basis of phase correlation is
the Fourier shift property, which states that a shift between
two images in the spatial domain will result in a linear phase
difference in the frequency domain. We assume that two im-
age functions
f
(
x,y
) and
g
(
x,y
)
that are related by shifts
x
0
and
y
0
in the row and column directions are expressed as:
g
(
x,y
) =
f
(
x
–
x
0
, y
–
y
0
). According to the Fourier shift property,
the normalized cross-power spectrum matrix is calculated by:
Q u v
F u v G u v
F u v G u v
i ux vy
,
,
,
,
,
exp
*
*
( )
=
( ) ( )
( ) ( )
=
+
(
)
{
}
0 0
(1)
where
F
(
u,v
) and
G
(
u,v
)
are the corresponding Fourier trans-
form of
f
(
x,y
) and
g
(
x,y
), and * denotes the complex conjugate.
As mentioned in Kuglin (1975), integer pixel shifts can be
estimated from the peak coordinates of the inverse Fourier
transform of the normalized cross-power spectrum matrix. As
the normalized cross-power spectrum matrix is only related
to the phase shift components of the two input images, the
phase correlation is theoretically insensitive to illumination
differences and image content.
580
September 2018
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
