IEEE Geoscience and Remote Sensing Magazine - June 2019 - 148

stationary objects that have spectrum changes between
images, such as in the case of camouflage, concealment,
and deception [49].
In the literature, approaches such as chronochrome [45]
and covariance equalization [46] are classical algorithms
for ACD. They investigate a linear prediction of posttime
data using the statistics of both pretime and posttime data
sets to discover and highlight the anomalous changed pixels
against the unchanged background. In greater detail, in [45],
the authors compute the covariance matrices of the spectral
signatures at times t 1 and t 2 and the cross-temporal covariance matrix. Then, they compute the chronochrome prediction error between the real signatures at t 2 and the ones predicted using the chronochrome. The prediction error is then
used in the Reed-Xiaoli (RX)
anomaly detector to identify
changes. In [46], the authors
ANOTHER SIGNIFICANT
consider a covariance-equalization implementation that
PROBLEM OF HS IMAGES IS
is meant to be more robust to
DATA REDUNDANCY.
registration errors. They exploit an ACD approach based
on the assumption that the
mean spectral signature of the target is known. They also use
a combination of chronochrome and matched filtering. In
[47], three iterative clustering methods, that is, class-conditional covariance equalization (QCE), bitemporal QCE, and
wavelength-dependent segmentation, were applied to detect
human-caused changes in VNIR and thermal-IR HS images.
The results prove that the use of a spatially adaptive detector greatly enhanced ACD performance in the target CD in
terms of false alarm reduction.
Some techniques focused on modeling data variables
from different perspectives have recently been proposed.
For instance, in [48], the anomalous changes in HS images were modeled and detected according to elliptically
contoured distributions. This is motivated by the fact that,
because the problem is the detection of anomalous changes (which are rare), there is a high probability that these
changes are represented in the tail of the statistical distribution. Therefore, elliptically contoured distributions may
be more suitably compared with Gaussian distribution. In
[50], the change residual image is computed based on slow
feature analysis (SFA), and changes are detected with the
RX anomaly detector. SFA is used to compute the change
residual image in which the unchanged areas and large areas affected by changes show small values. This makes the
problem of ACD a classical anomaly-detection problem,
which is solved using the RX algorithm.
In [51], a cluster kernel RX algorithm is presented that
clusters the background samples while using the cluster
centers for anomaly detection. The clustering step is used to
cluster the background pixels, which are then replaced with
the corresponding cluster centers. The RX is subsequently
applied to the new samples, reducing the computation load.
An improved ACD approach that exploits a model-based
148

method is proposed in [52]. It is extended for use on both
relatively calibrated and uncalibrated HS images and applied to airborne HS images. In [64], the authors propose a
subspace-based CD method using undesired class information as prior knowledge. A subspace distance was computed
to determine that the anomalous pixels have changed when
compared with the background subspace.
Recently, a tutorial on the ACD problem in HS images
within a theoretical Gaussian framework was presented
[49]. This tutorial addresses several solutions based on
the statistical detection theory by formulating the ACD as
a binary decision problem. Using the multivariate Gaussian model, it presents a rigorous statistical framework to
explain the detectors by changing 1) the decision rule (hyperbolic or elliptical), 2) the observation vector model, and
3) the local or global Gaussian model. Some other useful
theoretical information is provided, including the presentation of a freely available validation data set. A comprehensive experimental comparison is also carried out to
show the performance of different ACD algorithms. In the
literature, there are also some other works focused mainly
on the detection of specific changes by addressing specific
issues, for example, eliminating image parallax errors [54],
registration errors [53], [56], vegetation and illumination
changes [55], and diurnal and seasonal variations [57].
BINARY CHANGE DETECTION
Binary CD is one of the typical and popular CD applications of recent decades. Its objective is to detect and separate the change and no-change classes in the considered
multitemporal images. Accordingly, from the spectral point
of view, pixels with significant spectral variations between
the considered dates have higher probability to be changed
and vice versa. A common way to identify binary information based on comparison operators, such as CVA, is to
construct the compressed change magnitude information
t as in (3). Other methods focus on the construction of
binary representations based on similarity measures, such
as the spectral angle mapper (SAM) [77] or spectral information divergence [78]. Therefore, it is possible to use approaches similar to those developed for binary CD in MS
because the full dimensionality of data is compressed into
one magnitude feature space. However, the information
redundancy in the adjacent bands might affect the change
magnitude and, thus, the binary CD performance, so the
selection of the most informative band subsets is crucial,
as pointed out in [28]. Based on the magnitude image, it is
possible to model the specific statistical distribution of the
two classes (e.g., by Gaussian mixture [41] or Rayleigh-Rice
mixture [79]) under the Bayesian framework and then use
thresholding techniques to generate the CD map. In [41]
and [79], the statistical distribution parameters are estimated using the expectation maximization (EM) algorithm.
Another major group of classical binary CD methods
in HS images is designed based on the features extracted
by using data transformation techniques. The original
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

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IEEE Geoscience and Remote Sensing Magazine - June 2019

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