Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 17

Acito et al.

Figure 5.

EX-1. (a) ROC for the five algorithms: FAR values are in logarithmic scale. (b) AC-ROC for the five algorithms: FoDNA values are in linear scale.

the total number of anomalous objects. In practice, the nontemporal
anomalous objects are those included in the NARM, whereas all the
objects included in the NARM and in the CRM are considered as
anomalous objects (both temporal and nontemporal). The resulting
curves can be viewed as a sort of ROC conditioned to the class of
the anomalous objects. For this reason, such curves are referred to
as anomaly conditional experimental ROC (AC-ROC), hereinafter.
Notice that we can state that an algorithm has good performance
when it yields high values of FoDC with low values of FoDNA.

RESULTS AND DISCUSSION
In this subsection we show and discuss the results of the two experiments EX-1 and EX-2. Starting from EX-1, Fig. 4 shows the
test statistics obtained by applying the five ACD algorithms with
the complete processing chain including the CE and the LCRA approach. The black frames in the images correspond to the transient
introduced by the LCRA approach and, in the case of the SVACD,
by the local processing. Furthermore, a simple contrast enhancement technique has been applied to improve the visual appearance
and interpretability of the images. In the grayscale white corresponds to the highest value of the statistics.
At first glance, we see that the statistics provided by HACD, SDHACD, and SVACD have high values for most of the anomalous
changes included in the CRM of Fig. 2 (c). It seems that the abovementioned algorithms outperform SACD and SDACD in highlighting the temporal anomalous targets. Furthermore, it can be noticed
that the SACD statistic exhibits high values in correspondence of
most of the nontemporal anomalies included in the NARM. For instance, note that SACD statistic has high values for the three targets
labeled as A1, A2, and A3 which are included in the NARM. Such
targets have very low values in the statistics obtained by SDHACD,
HACD, and SVACD. This is not unexpected because of the low capability of SADC to discriminate temporal and nontemporal anomalies.
It is important to point out that in the representation of the HACD
statistic (Fig. 4 (a)) the darkest levels correspond to negative values
(more precisely, such a statistic has values ranging from -2294 to
615). Thus, we can observe that HACD provides high positive values (the brightest levels) to temporal anomalies and negative values
JULY 2017, Part II of II

to the nontemporal anomalies A1, A2, and A3. This observation can
be extended to most of the targets in the NARM and, in accordance
with the critical remarks in Subsection II-D, leads us to conclude that
HACD is robust to nontemporal anomalies. Furthermore, HACD allows most of the nontemporal anomalies to be separated from the
background pixels and not only from the temporal ones.
A more rigorous comparison of various methods can be done
by considering the ROC and the AC-ROC of Fig. 5. In deriving
such performance curves, a false alarms mitigation procedure has
been included in the processing chain that simply discards the detected objects having size greater than 20 pixels in accordance with
the maximum expected size of the objects of interest.
The ROCs of Fig. 5 (a) confirm that HACD, SDHACD, and
SVACD outperform SACD and SDACD in that they provide the
highest values of FoDC with the lowest values of FAR. The performance of the three algorithms is approximately the same in the
region of the ROCs corresponding to the highest FoDC. The ACROCs in Fig. 5 (b) confirms that HACD is the best performing
algorithm in terms of capability of discriminating temporal and
nontemporal anomalies. In fact, 100% of the temporal anomalies
are detected with FoDNA=0.0526 corresponding to 3 out of 36
nontemporal anomalous objects. The AC-ROCs for SVACD and
SDACD are very similar, whereas SDHACD outperforms the latter two algorithms. As expected the worst discrimination performance is that of SACD. The curves in Fig. 5 show that in this
experiment, HACD provides the overall best performance.
Fig. 6 (a)-(e) provide evidence of the impact of the RE and
the LCRA on the performance of the various algorithms. For each
ACD algorithm, we show the ROC and the anomalous change
(AC)-ROC obtained by adopting: a) the entire processing chain
including both the CE (as RE procedure) and the LCRA (LCRA &
CE); b) the processing chain that includes the LCRA and not the
CE (no CE); c) the processing chain that includes the CE and not
the LCRA (no LCRA).
As expected, the SACD and HACD performance does not
change when the CE is excluded from the processing chain. In
fact, as proved in Appendix II, the two algorithms are invariant
to linear transformations operated on one or both the images. The
performance of SDACD and SDHACD also does not change sig-

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