IEEE Geoscience and Remote Sensing Magazine - June 2016 - 81

and transformed image using the Harris corner detector and
SURF. As clouds do not possess strong edges, the number of
detected feature points using the Harris corner detector is
far lower than that of the SURF detector. Furthermore, the
repeatability of the SURF detector is higher than the corner
detector for the same amount of scaling and rotation.
REMOTE SENSING FEATURES
In remote sensing, hand-crafted features exploiting the
characteristics of the input data are widely used for image classification [42], involving the generation of a large
number of features that capture the discriminating cues
in the data. The user makes an educated guess about the
most appropriate features. Unlike the popular computer vision feature-extraction techniques given previously, remote
sensing features use their inherent spectral and spatial
characteristics to identify discriminating cues of the input
data. They are not learning based but are derived empirically from the input data and achieve good results in certain applications.
Heinle et al. [43] proposed a 12-dimensional feature
vector that captures color, edge, and texture information
of a sky/cloud image, which is quite popular in cloud
classification. The raw intensity values of RGB aerial images have also been used as input features [44]. In satellite imagery, the normalized difference vegetation index
is used in association with the raw pixel intensity values
for monitoring land cover, road structures, and so on [45].
In high-resolution aerial images, neighboring pixels are
considered for the generation of feature vectors, which
results in the creation of, e.g., 3 # 3, 15 # 15, and 21
# 21 pixel neighborhoods. Furthermore, to encode the
textural features of the input images, Gabor- and edgebased texture filters are used, e.g., for aerial imagery [46]
or landscape image segmentation [47]. Recently, we have
used a modified set of Schmid filters for the task of cloud
classification [48].
DIMENSIONALITY REDUCTION
Remote sensing data are high-dimensional in nature.
Therefore, it is advisable to reduce the inherent dimensionality of the data considerably while capturing sufficient information in the reduced subspace for further data
processing. In this section, we discuss several popular DR
techniques and point to relevant remote sensing applications. A more detailed review of various DR techniques can
be found in [49].
Broadly speaking, DR techniques can be classified as either linear or nonlinear. Linear DR methods represent the
original data in a lower-dimensional subspace by a linear
transformation, while nonlinear methods consider the
nonlinear relationship between the original data and the
features. This article focuses on linear DR techniques because of their lower computational complexity and simple
geometric interpretation. A brief overview of the different
techniques is provided in Table 2, and a detailed treatment
june 2016

ieee Geoscience and remote sensing magazine

TABLE 2. A SUMMARY OF LINEAR DR TEcHNIqUES.
TEcHNIqUES

MAxIMIzED OBjEcTIVES

SUpERVISED

cONVEx

Pca

data variance

Yes

Likelihood function of
underlying distribution
parameters

Lda

Between-class variability
over within-class variability

Yes

nca

stochastic variant of the
leave one out score

Yes

of the various methods can be found in [50]. We denote the
data as X = 6x 1 | x 2 | ... | x n@ ! R N # n, where each x i d R N
represents a vectorized data point, N denotes the data dimensionality, and n is the data size. The corresponding
features are denoted as Z = 6z 1 | z 2 | ... | z n@ ! R K # n, where
each z i ! R K is the feature representation of xi, and K denotes the feature dimensionality.
Principal component analysis (PCA) is one of the most
common and widely used DR techniques, which projects
the N-dimensional data X onto a lower K-dimensional (i.e.,
K # N) feature space as Z by maximizing the captured data
variance or, equivalently, minimizing the reconstruction
error. PCA can be represented as
Z = U T X,

(1)

where U d R N # K is formed by the principal components
that are orthonormal and can be obtained from the eigenvalue decomposition of the data covariance matrix.
The objective function is convex, thus convergence and
global optimality are guaranteed. In the field of remote
sensing, PCA is often used to reduce the number of
bands in multispectral and hyperspectral data, and it is
also widely used for change detection in forest fires and
land-cover studies. Munyati [51] used PCA as a changedetection technique in inland wetland systems using
Landsat images, observing that most of the variance was
captured in the near-infrared reflectance. Subsequently,
the image composite obtained from the principal axes
was used in change detection.
Factor analysis (FA) is based on the assumption that the
input data X can be explained by a set of underlying factors.
These factors are relatively independent of each other and
are used to approximately describe the original data. The
input data X can be expressed as a linear combination of
K factors with small independent errors E:
X=

/ Fi Z i + E,

(2)

i= 1

where " Fi ,Ki = 1 d R N are the different derived factors, and Zi
denotes the ith row of the feature matrix Z. The error matrix E explains the variance that cannot be expressed by any
of the underlying factors. The factors " Fi ,Ki = 1 can be found
by maximizing the likelihood function of the underlying
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