which prominent subpixel Fourier-based correlation methods
and successful tracking methods in videogrammetry are used
for comparison. Second, the results of the relative displace-
ment and acceleration in the large-scale shaking table tests are
presented and analyzed. The performance of the videogram-
metric measurement is quantitatively assessed by several
checkpoints. In addition, the stability of the control points
and the effect of the smoothing filter are investigated. In order
to validate the effectiveness of the proposed videogrammet-
ric system, the acceleration measurement is evaluated by
comparison with the input seismic wave based on reference
points and acceleration sensors at similar positions.
Performance of the Proposed Subpixel Phase Correlation Method
The performance of the proposed subpixel phase correlation
method is investigated by implementing two simulated tests
and a static test with known ground truths.
Simulated Tests
In the simulated tests, image pairs with known subpixel shifts
were generated through low-pass filtering and downsampling,
following the approach described in Stone
et al.
(2001). We
started by introducing an integer shift
S
to the basis images
and downsampled both the original and shifted images by a
factor of
M
in each dimension through bicubic interpolation.
A 2D Gaussian filter was applied prior to downsampling to
suppress the amount of aliasing. The proposed method was
compared with five representative subpixel phase correlation
methods: Foroosh’s method (Foroosh
et al.
, 2002), the peak
evaluation formula (
PEF
) (Nagashima
et al.
, 2006), UCC (Gui-
zar-Sicairos
et al.
, 2008), Hoge’s method (Hoge, 2003), Stone’s
method (Stone
et al.
, 2001), and another frequency-based
method known as cross-correlation operated in the frequency
domain on orientation images (CCF-O) (Heid and Kääb, 2012).
The raised-cosine window was applied for all the methods to
reduce the influence of edge effects.
In the first simulated test, the same image dataset gener-
ated in Tong
et al.
(2015) was used. The integer shift
S
ranged
from −5 to 5 pixels by a step of 1 pixel without consideration
of null displacement in each dimension, and the downsam-
pling factor
M
was set as 10. In addition, Gaussian noise was
added with the normalized variance of noise
Vn
varying from
0 to 0.05 in steps of 0.005. For each level of
Vn
, 300 simulated
image pairs were generated. The correlation errors of the dif-
ferent methods were computed using the ground truth as
e e e
x y
= +
(
)
2 2
, where
e
x
,
e
y
corresponds to the error in each
direction. The mean value
µ
and the root mean square (RMS)
of the correlation error vector were served as evaluation
metrics, and were calculated over all 300 image pairs as a
function of
Vn
.
The corresponding results of the different subpixel meth-
ods in terms of
µ
and RMS as a function of
Vn
are depicted
in Figure 5. It can be seen that Hoge’s method is the most
sensitive to noise and obtain the worst results. Therefore, the
results of Hoge’s method are truncated for a better visualiza-
tion in Figure 5. It is obvious that the propose method show
the best performance with the smallest
μ
and RMS of the
correlation error, which validate the robustness of the propose
method to interference factors. Even though UCC and CCF-O
methods provide worse estimates in the noise-free case, they
achieve second-best and stable results in the case of high-lev-
el noise. The reason could be UCC only uses a small neigh-
borhood for the final subpixel estimation, and CCF-O uses
the gradient orientations. It is found that the errors of Stone’s
method and Hoge’s method obviously increase with the grow-
ing noise variance, which indicate that the effect of frequency
masking operation depends on the parameter selection, while
the improved method reduce the effect of this issue. The re-
sults of Hoge’s method are truncated for a better visualization.
In the second simulated test, the first frames of the left and
right image sequences were selected as the basis images. The
integer shift S ranged from 1 to 5 pixels with a step of 1 pixel
in both directions, and the downsampling factor M was set
as 5, so that the final relative shifts were [0.2, 0.4, 0.6, 0.8,
1]. Therefore, 50 synthetic image pairs in total were formed.
Three types of correlation window size, namely 32 × 32, 64 ×
64, and 128 × 128 pixels, were considered, which generated
2106, 425, and 60 windows for each image pair, respectively.
Except for the above six comparative methods, four variants
of Stone’s method with different additional measure, namely
Stone’s method with gradient representation (Stone_GR),
Stone’s method with phase filtering (Stone_PF), Stone’s
method with robust estimation (Stone_RE) and Stone’s
method with robustness iteration (Stone_RI), were considered
to highlight the effect of each individual part. The RMS of the
absolute error vector between the estimates and the ground
truth calculated over all the correlation windows, as well as
the mean standard deviation (MeanStd) of the estimates in
each image pair in the row and column directions are used as
evaluation metrics.
Table 1 shows the comparison results in terms of RMS and
MeanStd. As can be seen, the proposed method consistently
yields the best results in all cases and greatly enhances the
performance of the original Stone’s method. The PEF and
Hoge’s methods form the second-best group according to
the overall performance. All the four variants achieve bet-
ter results compared to the original Stone’s method, which
Figure 5. (a) Mean value, and (b) RMS of the correlation error for the different methods as a function of Vn. The results of
Hoge’s method are truncated for a better visualization.
586
September 2018
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
