IEEE Geoscience and Remote Sensing Magazine - September 2021 - 77

researchers have proposed spatial [33], [48], [138], [139] and
hybrid [53], [78], [93], [98], [130], [140]-[143] approaches to
BS, in addition to the purely spectral approaches. Some spatial
variants of the extended multiattribute profile and ICAbased
hybrid approaches [143] have been proposed. Using
entropy was proved to permit the selection of better bands,
which produces better classification and change detection
results. Moreover, entropy operates on a deterministic FS,
which overcomes the random nature of ICA.
Recently, a superpixel-based BS method was proposed
[99], which inherently exploits the spectral and spatial features
from an HSI and the superpixel chunklets that are
obtained. The spectrally homogeneous, spatially neighboring
pixels are denoted superpixel chunklets, which feature
higher homogeneity across land cover classes. Because
they do not use GT information, superpixel chunklets are
considered a synthetic class, and the within-class variability
is measured for each band. The extracted band correlation
and prioritization criteria are further clustered using
affinity propagation (AP) for selecting the optimal bands.
Since the superpixel approach splits an HSI into several
disjointed superpixels, it has an inherent capability to exploit
spatial features, and it can offer a better alternative to
pixel-based approaches.
OBJECTIVE FORMULATION
Formulating the objective function for BS is an essential
step. As stated, these objectives generally rely on two concurrent
strategies: 1) selecting the most informative bands
and 2) reducing the number of redundant bands. These
functions can be based on direct distance measures, derived
distance measures, and external evaluating agents
[144] (Figure 4). A theoretical survey of spectral matching
algorithms that use various distance measures can be found
in [145]. Important aspects and state-of-the-art methods
are categorized and discussed in the following.
DIRECT AND CORRELATION-BASED
DISTANCE MEASURES
For any model that targets data separation, there is a need to incorporate
measurement tools. These usually consist of some sort
of distance measure. Depending on the requirements, distance
measures can be formulated differently. Selecting suitable distance
measures is a crucial step
in BS. Since an HSI contains a
wealth of spectral information,
a variety of spectral distance
measures have been proposed
by various researchers. Direct
and correlation-based distance
measures are generally associated
with spectral information.
Popular distance measures include
the Bhattacharya distance
(BD), Jeffries-Matusita (JM)
distance, spectral angle mapper
(SAM) and its variants [145], Euclidian distance (ED),
Karhunen-Loève (KL) distance, spectral correlation angle
(SCA), Mahalanobis distance (MD), Earth mover's distance
(EMD), n-dimensional solid spectral angle (NSSA), and
dual (spectral-spatial) angle mapper. The BD [56], [64],
[121], [146]-[148] and JM [11], [49], [102], [144], [147], [149]
distances are the most popular measures for class separability
and FS.
The SAM [38] is a direct distance measure that finds
SINCE THE BS PROCESS
SHOULD SORT OUT THE
MOST DISTINCTIVE AND
INFORMATIVE BANDS, THE
BANDS THAT ARE KNOWN
TO BE UNINFORMATIVE CAN
BE REMOVED A PRIORI.
spectral dissimilarity in terms of angle ().i Keshava [58]
noted that the SAM is invariant to multiplicative scaling,
nonadditivity, and the nonmonotonicity property, making
Unsupervised
Objective Formulation
Maximize
InformationTheoretic
and
Feature
Based
Direct
Distance
Based
Spatial
Spectral
Hybrid
Minimize
FIGURE 4. Modeling the objective.
SEPTEMBER 2021 IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE
77
IEEE Geoscience and Remote Sensing Magazine - September 2021

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