IEEE Geoscience and Remote Sensing Magazine - June 2019 - 93

This well-known problem is discussed in several textbooks and papers, including [1], [90], and [91]. If s is
unknown, we have a problem of anomaly detection;
otherwise, we have a typical MF detection problem. The
performance of each detector is evaluated using receiver operating characteristic curves. The formulas for the
anomaly detector, MF detector, and normalized MF (NMF)
detector are [86]
y AD = x T C -b 1 x ,
y MF =
y NMF =

(36)

s T C -b 1 x
,
(s C -b 1 s) 1/2

(37)

s T C -b 1 x
.
(s C s) 1/2 (x T C -b 1 x) 1/2

(38)

-1
b

the mean of the background with the library target signature. This geometrical approach explains the suitability of
MF and NMF detectors for both full-pixel and subpixel targets without the need to use different derivations or signal
models for each case. More details about this topic can be
found in [1] and [86].
As previously discussed, spectral emissivities in the
LWIR tend to be smaller than the corresponding spectral reflectance variations in the reflective region. Many target and
background materials, e.g., many paints, water, soil, road
materials, and vegetation, have spectral emissivities between 0.8 and 0.95. Furthermore, although there are spectral emissivity differences between different materials, they
are less pronounced than in the reflective region. The performances of these algorithms in real-world applications,
as well as their sensitivity to target and background model
mismatch caused by emissivity and temperature estimation
errors, are topics for future research.

PC2

If we use the whitening (or spherizing) transformation
-1/2
-1/2
xu = C b x and us = C b s, we obtain the geometrical interpretation illustrated in Figure 15. The important point here
GAS-PHASE TARGET DETECTION
is that each detector is uniquely specified by its decision
While solid materials can be identified using emissivity,
boundary or surface, which can be used to choose a detecmany chemical vapors exhibit selective absorption and
tor based on the shape of target and clutter distributions
emission in the LWIR, which can be observed when lookin the spectral measurement space. This interpretation has
ing through a vapor plume. In comparison to solid target
been used to justify the choice and success of the NMF for
detection, chemical vapors have narrow spectral features
solid-phase target detection in the VNIR-SWIR spectral rebut can consist of a large number of pixels. Additionally, ingion [86].
stead of estimating the emissivity of each pixel, processing
Because spectral emissivity is an intrinsic property of
can be done directly in the radiance domain, but the ability
natural and man-made materials, it is imperative that tarto detect a plume depends on its concentration, signature
get-detection algorithms use emissivity target libraries and
operate on emissivity data cubes.
However, detection algorithms
operating in the radiance domain
have been proposed to bypass the
0.2
NMF
emissivity retrieval problem [60],
Background Pixels
Decision
0.15
[92]. In the LWIR region, subspace
Guard Pixels
Surface
Target Pixels
models can be used to characterLibrary Signature
0.1
ize both spectral and temperatureinduced variability.
0.05
The replacement model (32),
0
which is a special case of the linear mixing model discussed in the
-0.05
"Spectral Mixture Analysis" section
and the spectral variability of target
-0.1
and background spectra, suggests
-0.15
that subpixel targets must be clustered around the line connecting
-0.2
the means of background and tarNMF
-0.25
get classes. This is illustrated in FigDecision
ure 16, which shows a scatterplot of
Surface
-0.3
background pixels, target pixels, and
-8.5
-8
-7.5
-7
-6.5
-6
-5.5
PC1
subpixel target pixels from an LWIR
scene collected by the SEBASS sensor
[60]. Careful inspection of Figure 15 FIGURE 16. The scatterplot of LWIR emissivity background and target spectra in the first two
suggests that we can use the detec- principal component spaces. Pixels at the boundary of the target array mix with background
tion algorithms (37) and (38) by re- pixels to create subpixel targets. Note that there is a significant mismatch between the inplacing s with the vector connecting scene target spectra and the library target signature. PC: principal components.
JUNE 2019

IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

IEEE Geoscience and Remote Sensing Magazine - June 2019

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