Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 22
Introductory View of Anomalous Change Detection
Figure 13.
EX-2. (a) HACD statistic in the neighborhood of the target S1. (b)
HACD statistic in the neighborhood of the target S2.
with that of the target S1 in the reference image. Similarly, Fig. 12
(b) shows the spectral radiance of the target S2. The significant
differences between each couple of spectra in Fig. 12 prove that
the two considered targets are indeed temporal-spectral anomalies.
The HACD statistic values in the neighborhoods of the two targets are represented in Fig.13 (a) and (b). Let us note that the statistic values assigned to the pixels of S1 are very low, comparable or
less than those of the background pixels (no changes). Therefore,
such a target is expected to have very low detectability, i.e., it can
be detected with high FAR value. Conversely, Fig.13 (b) shows
that the pixels of S2 have values of the HACD statistic greater than
those of the surrounding background. This allows such a temporalspectral anomaly to be detected with low values of FAR.
The previous conclusions are confirmed by the results in Table
IV that reports the FAR corresponding to the detection of at least
one pixel of S1 and S2 attained by the HACD as well as by the
other considered algorithms.
Results in Table IV show that HACD detects S2 with FAR=8
× 10−4 which is consistent with the FAR attained by all the other
algorithms. Conversely, the FAR value for S1 (attained by HACD)
is two orders of magnitude greater than that of S2. Results also
show that the other algorithms do not yield poor performance in
detecting S2. All of them provide FAR less than 6 × 10−4.
CONCLUSIONS
Exploitation of temporal series of hyperspectral images is a relatively new discipline that has a wide variety of possible applications in fields like remote sensing, area surveillance, defense and
Table IV.
FAR for S1 and S2
ACD Algorithm
S2
SACD
6 × 10−4
2.6 × 10−3
HACD
6 × 10−2
8 × 10−4
SDACD
2 × 10−4
1 × 10−3
SDHACD
SVACD
22
S1
10−4
3 × 10−4
4 × 10−4
2 × 10−4
security, search and rescue, and so on. In this paper, we have discussed how images taken at two different times can be processed
to detect changes caused by insertion, deletion, or displacement
of small objects in the monitored scene. This problem is known in
the literature as ACD and it can be viewed as the extension, to the
multitemporal case, of the well-known anomaly detection problem
in a single image. In fact, in both cases, the hyperspectral images
are processed blindly in an unsupervised manner and without a
priori knowledge about the target spectrum.
We have formulated the ACD as a binary decision problem and
presented possible solutions based on the statistical detection theory.
Using the multivariate Gaussian model a rigorous statistical framework has been presented that explains a large class of detectors by
changing a) the decision rule (hyperbolic or elliptical), b) the observation vector model, and c) by switching from the local to the global
Gaussian model. For better clarity, we have discussed in detail four
ACD algorithms proposed in the literature (extending their decision
rule to the case of the local model assumption) and a new technique.
Specifically, we have shown how they can be easily explained within the adopted Gaussian framework. Furthermore, we have shown
that the class of detectors based on the elliptical decision rule can
be extended to the case of the multivariate EC-t distribution model.
We have also illustrated practical problems related to the application of the detectors in the real world and presented affordable
solutions. Namely, we have suggested commonly adopted methods
used to compensate pervasive radiometric changes, caused by the
different illumination/atmospheric conditions, and to mitigate the
residual geometric image coregistration errors. In particular, for
each ACD algorithm, we have shown how the expression of the
decision rule has to be modified to fit the LCRA framework used
to mitigate the RMRE .
For the ACD algorithms detailed in this paper, we have discussed and highlighted their points of strength and weakness. We
have proved that the HACD and the SACD are robust to stationary linear radiometric distortions because their decision statistics
are invariant to linear transformations operated on one or both the
multitemporal images. We have also discussed the algorithms performance under an original point of view that should make this
subject easier to understand to the many researchers who are familiar with basic anomaly detection in hyperspectral images. We
noticed that anomalous changes are indeed a subset of all the spectral anomalies in the two single HSIs. In fact, they are generated by
the anomalies, in the single HSIs, that have changed their position
(displacement) or spectrum (replacement, camouflage) from one
acquisition to the other (temporal anomalies). An ACD algorithm
can therefore be evaluated not only on the basis of its ability in
extracting a dim change from the background, but also of its ability in discriminating temporal anomalies from spectral anomalies
having the same position and spectral content in the two images
(nontemporal anomalies). Our discussion has highlighted that the
worst performing algorithm is SACD whose decision rule is not
suitable for discriminating temporal from nontemporal anomalies.
Among the other algorithms the HACD seems to be the more robust to nontemporal anomalies, even if it has poor performance
in detecting those changes caused by objects having the same position but different spectral content in the two images. We have
IEEE A&E SYSTEMS MAGAZINE
JULY 2017, Part II of II
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