Component Analysis (VCA) (Nascimento and Bioucas-Dias, 2005), Or-
thogonal Subspace Projection (OSP) (Harsanyi and Chang, 1994), N-
FINDR (Winter, 1999) or Iterative Error Analysis (IEA) (Neville et al.,
1999), among many others (Bioucas-Dias et al., 2012); and 2) methods
that do not assume the presence of pure signatures in the image, such as
the Minimum Volume Spectral Analysis (MVSA) (Li et al., 2015), the
Simplex Identification via Split Augmented Lagrangian (SISAL), among
many others (Bioucas-Dias et al., 2012). In the recent literature, several
techniques have been developed to exploit a potentially very large
spectral library; the unmixing then amounts to choosing an optimal
subset of library endmembers to model each pixel ( Iordache et al.,
2011). Methods, such as Orthogonal Matching Pursuit (OMP) (Pati
et al., 1995), Basis Pursuit (BP) (Chen et al., 2001), Basis Pursuit De-
noising (BPDN) (Chen et al., 2001), and Iterative Spectral Mixture
Analysis (ISMA) (Rogge et al., 2007b), belong to this category.
The above mentioned techniques used a fixed number of end-
member spectra, i.e. one single endmember spectrum per endmember
class, which is simple and easy to implement. However, due to en-
vironmental, atmospheric and temporal factors, endmember variability
commonly exists in hyperspectral image data. Relevant reviews on this
topic have been provided in Somers et al. (2011) and Zare and Ho
(2014). Compared with the use of a fixed number of endmember
spectra, the use of multiple endmembers per class can provide more
accurate spectral signature representation and fractional abundance
estimation. Numerous techniques and applications have been proposed
to consider endmember variability in spectral unmixing, such as
Iterative Endmember Selection (IES) (Roth et al., 2012; Schaaf et al.,
2011). Of particular importance is the Multiple Endmember Spectral
Mixture Analysis (MESMA) techniques (Roberts et al., 1998; Somers
and Asner, 2013; Liu and Yang, 2013; Quintano et al., 2013; Fernández-
Manso et al., 2012; Delalieux et al., 2012; Thorp et al., 2013; Franke
et al., 2009; Powell et al., 2007), which use variable endmember sets to
unmix each pixel of the scene.
In recent years, several studies have revealed that hyperspectral
unmixing by using spectral information alone does not sufficiently ex-
ploit the spatial information in the scene (Shi and Wang, 2015), as the
pixels are treated as isolated entities without taking into account the
existing local correlation between them. In real hyperspectral images,
pure pixels are more likely to be present in spatially homogeneous re-
gions, and the existing spatial correlation among neighboring pixels can
be exploited. To address this important issue, several endmember ex-
traction algorithms have been designed with the goal of integrating the
spatial and the spectral information. According to the cooperative use
of spectral and spatial information, these methods can be divided into
two categories: 1) integrated spatial-spectral methods, such as the Au-
tomatic Morphological Endmember Extraction (AMEE) (Plaza et al.,
2002), Spatial-Spectral Endmember Extraction (SSEE) (Rogge et al.,
2007a), Successive Projection Algorithm (SPA) (Zhang et al., 2008),
Spatial Purity based Endmember Extraction (SPEE) (Mei et al., 2010),
the Hybrid Automatic Endmember Extraction Algorithm (HEEA) (Li
and Zhang, 2011), Spatial Adaptive Linear Unmixing Algorithm
(SALUA) (Goenaga
et al., 2013), the Unsupervised Unmixing based on
Multiscale Representation (UUMR) (Torres-Madronero and Velez-
Reyes, 2014), or the Image-based Endmember Bundle Extraction Al-
gorithm (Xu et al., 2015), among many others (Bioucas-Dias et al.,
2012); and 2) spatial preprocessing methods, which provide an (op-
tional) preprocessing step before the application of a spectral-based
endmember extraction algorithm. In this case, the output of the pre-
processing is not the final endmember set, but a set of candidate pixels
that need to be fed to an existing spectral-based endmember extraction
algorithm to obtain the final endmember set. Available methods in this
category include the Spatial Preprocessing (SPP) (Zortea and Plaza,
2009), Region-based Spatial Preprocessing (RBSPP) (Martín and Plaza,
2011), Spatial-Spectral Preprocessing (SSPP) (Martín and Plaza, 2012),
Superpixel Endmember Detection Algorithm (SEDA) (Thompson et al.,
2010), Spatial Edges and Spectral Extremes based Preprocessing
(SE
2
PP) (Lopez et al., 2013), a Fast Spatial-Spectral Preprocessing
Module (SSPM) (Kowkabi et al., 2016b), Clustering and Over-
segmentation-based Preprocessing (COPP) (Kowkabi et al., 2016a), etc.
Compared with integrated spatial-spectral methods, spatial pre-
processing methods can be flexibly included with existing spectral-
based endmember extraction methods without modifying such
methods. Also, since the number of candidate pixels is much smaller
than the number of original image pixels, the computational burden is
significantly reduced. However, a general issue with available spatial
preprocessing methods is that they generally prioritize one of the two
sources of information (spatial or spectral) when conducting the pre-
processing, which can have an important influence on the final results
as some important candidates may be lost in the preprocessing (Martín
and Plaza, 2012).
In this paper, we develop a new method for spatial preprocessing for
hyperspectral unmixing. The proposed method naturally balances the
spatial and the spectral information by means of a regional clustering
procedure that is similar to the one performed by the Simple Linear
Iterative Clustering (SLIC) (Achanta et al., 2012) method. Compared
with conventional global clustering procedures, the proposed method
presents two key differences. First, as conventional clustering algo-
rithms need to search the whole image domain to find the clusters, we
restricted the search scope to a local neighborhood around each clus-
tering center. Second, we adopted a clustering criterion that integrates
spatial and spectral information simultaneously. After the clustering
procedure, we obtain a set of clustering partitions that exhibit both
spatial correlation and spectral similarity, which are highly desirable
properties for spatial preprocessing purposes. Then we select a subset of
candidate pixels from each partition by accounting for their spectral
purity. Finally, the obtained candidate pixels are gathered together and
fed to a spectral-based endmember extraction method to obtain the
final endmember set. Our experimental results with synthetic and real
hyperspectral scenes indicate that, compared with other available
strategies for spatial preprocessing, the newly proposed method is fast
and able to consistently provide candidate pixels with higher quality
regarding their spatial and spectral information, which represents a
significant improvement over other existing methods.
The remainder of this paper is organized as follows. Section 2 pro-
vides a review of the endmember extraction methods considered in our
experiments. Section 3 describes the newly proposed method in step-by-
step fashion. Section 4 performs an extensive validation and quantita-
tive assessment of the proposed method by using both synthetic and
real hyperspectral data sets. Finally, Section 5 concludes the paper with
some remarks and hints at plausible future research.
2. Related work
The goal of our proposed spatial-spectral preprocessing strategy is to
extract spectrally pure candidates from the original image data set, thus
reducing the number of candidate endmembers and improving un-
mixing accuracy simultaneously. Considering that spectrally pure sig-
natures are more likely to appear in spatially homogeneous areas, and
that most pure candidates generally exhibit the most singular signature
in such homogeneous area, many existing methods adopted certain
homogeneous criteria to characterize spectral purity. In the AMEE
method (Plaza et al., 2002), a Morphological Eccentricity Index (MEI) is
assigned to the purest pixel (obtained by the dilation operation) in a
spatial kernel, where the MEI is calculated by using the Spectral Angle
Distance (SAD) between itself and the most highly mixed pixel (ob-
tained by the erosion operation) in the spatial kernel. In the HEEA
method (Li and Zhang, 2011), a joint Spectral Information Divergence
and Spectral Angle Mapper (SID-SAM) metric (Du et al., 2004),
X. Xu et al.
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