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SVM and MRF-Based Method for Accurate
Classication of Hyperspectral Images
Yuliya Tarabalka, Mathieu Fauvel, Jocelyn Chanussot, Jon Atli Benediktsson
To cite this version:
Yuliya Tarabalka, Mathieu Fauvel, Jocelyn Chanussot, Jon Atli Benediktsson. SVM and MRF-
Based Method for Accurate Classication of Hyperspectral Images. IEEE Geoscience and Remote
Sensing Letters, IEEE - Institute of Electrical and Electronics Engineers, 2010, 7 (4), pp.736-740.
�10.1109/LGRS.2010.2047711�. �hal-00578864�
736 IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 7, NO. 4, OCTOBER 2010
SVM- and MRF-Based Method for Accurate
Classification of Hyperspectral Images
Yuliya Tarabalka, Student Member, IEEE, Mathieu Fauvel, Jocelyn Chanussot, Senior Member, IEEE,and
Jón Atli Benediktsson, Fellow, IEEE
Abstract—The high number of spectral bands acquired by hy-
perspectral sensors increases the capability to distinguish phys-
ical materials and objects, presenting new challenges to image
analysis and classification. This letter presents a novel method
for accurate spectral-spatial classification of hyperspectral images.
The proposed technique consists of two steps. In the first step,
a probabilistic support vector machine pixelwise classification of
the hyperspectral image is applied. In the second step, spatial
contextual information is used for refining the classification results
obtained in the first step. This is achieved by means of a Markov
random field regularization. Experimental results are presented
for three hyperspectral airborne images and compared with those
obtained by recently proposed advanced spectral-spatial classifi-
cation techniques. The proposed method improves classification
accuracies when compared to other classification approaches.
Index Terms—Classification, hyperspectral images, Markov
random field (MRF), support vector machine (SVM).
I. INTRODUCTION
H
YPERSPECTRAL imaging sensors measure the energy
of the received light in tens or hundreds of narrow spec-
tral bands in each spatial position in the image [1]. Thus, every
pixel can be represented as a high-dimensional vector across the
wavelength dimension, called the spectrum of the material in
this pixel. Since different substances exhibit different spectral
signatures, hyperspectral imagery is a well-suited technology
for accurate image classification, which is an important task in
many application domains (monitoring and management of the
environment, precision agriculture, etc.).
Most classification methods process each pixel indepen-
dently without considering the correlations between spatially
adjacent pixels (so-called pixelwise classifiers) [2], [3]. In
Manuscript received January 25, 2010; revised March 16, 2010. Date of
publication May 18, 2010; date of current version October 13, 2010. This
work was supported in part by the Marie Curie Research Training Network
“HYPER-I-NET.”
Y. Tarabalka is with the Grenoble Images Speech Signals and Auto-
matics Laboratory (GIPSA Lab), Grenoble Institute of Technology, 38402
Grenoble, France, and also with the Faculty of Electrical and Com-
puter Engineering, University of Iceland, 107 Reykjavik, Iceland (e-mail:
yuliya.tarabalka@hyperinet.eu).
M. Fauvel is with the Modelling and Inference of Complex and Struc-
tured Stochastic Systems (MISTIS) Team, National Institute for Research in
Computer Science and Control (INRIA), 38334 Saint Ismier, France (e-mail:
Mathieu.fauvel@inrialpes.fr).
J. Chanussot is with GIPSA Lab, Grenoble Institute of Technology, 38402
Grenoble, France (e-mail: jocelyn.chanussot@gipsa-lab.grenoble-inp.fr).
J. A. Benediktsson is with the Faculty of Electrical and Computer Engineer-
ing, University of Iceland, 107 Reykjavik, Iceland (e-mail: benedikt@hi.is).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/LGRS.2010.2047711
particular, support vector machines (SVMs) have shown good
performances for classifying high-dimensional data when a
limited number of training samples are available [3], [4]. Fur-
thermore, spatial contextual information should help for an
accurate scene interpretation. Therefore, it is very important
to develop spectral-spatial classification techniques that are
capable to consider spatial dependences between pixels [5]–[8].
In general, two categories of spectral-spatial classification
methods can be distinguished. First, spatial contextual informa-
tion is exploited in the classification stage. For instance, spectral
and spatial information can be combined within a feature vector
of each pixel, and then, a pixelwise classification technique can
be applied to the obtained set of vectors [6], [9]. Another group
of methods from this category first defines the objects within
the image scene and then classifies each object [2], [5]. Second,
spatial dependences are considered in the decision rule [10].
An example is a pixelwise classification followed by spatial
regularization of the classification map.
Markov random fields (MRFs) are probabilistic models that
are commonly used to integrate spatial context into image
classification problems [7], [10], [11]. In the MRF framework,
the maximum a posteriori (MAP) decision rule is typically
formulated as the minimization of a suitable energy function
[12]. An extensive literature is available on MRF-based image
classification techniques. In particular, the research groups of
Farag [7], Bruzzone [10], and Gong [11] have investigated the
integration of the SVM technique within an MRF framework
for accurate spectral-spatial classification of remote sensing
images. All of them use SVMs to estimate class conditional
probability density functions and MRFs to estimate context-
based class priors. Farag et al. [7] have applied the mean field-
based SVM regression algorithm for density estimation, with
the purpose of hyperspectral image classification. Good classi-
fication results are reported, although no comparison with other
advanced spectral-spatial classification techniques is published.
This letter presents a novel SVM- and MRF-based
(SVMMRF) method for spectral-spatial classification of hy-
perspectral images. In the first step of the proposed method, a
probabilistic SVM pixelwise classification of the hyperspectral
image is applied. In the second step, spatial contextual informa-
tion is used for refining the classification results obtained in the
first step. This is achieved by means of the MRF regularization.
An important difference from previously proposed methods
[7], [10], [11] consists in defining and integrating the “fuzzy
no-edge/edge” function into the spatial energy function in-
volved in MRFs, aiming at preserving edges while performing
spatial regularization.
1545-598X/$26.00 © 2010 IEEE
TARABALKA et al.: SVM- AND MRF-BASED METHOD FOR CLASSIFICATION OF HYPERSPECTRAL IMAGES 737
Fig. 1. Flowchart of the proposed SVMMRF classification scheme.
The second contribution of this letter consists in the
experimental comparison of the presented approach with
other recently proposed advanced spectral-spatial classifica-
tion techniques. Experimental results are demonstrated on
three hyperspectral airborne images recorded by the Airborne
Visible/Infrared Imaging Spectrometer (AVIRIS) and the Re-
flective Optics System I maging Spectrometer (ROSIS).
The outline of this letter is as follows. In the next section,
an SVMMRF classification scheme for hyperspectral images
is presented. Experimental results are discussed in Section III.
Finally, conclusions are drawn in Section IV.
II. SVMMRF C
LASSIFICATION SCHEME
The flowchart of the proposed SVMMRF classification
method is shown in Fig. 1. At the input, a B-band hyper-
spectral image is given, which can be considered as a set
of n pixel vectors X = {x
j
∈ R
B
,j =1, 2,...,n}.LetΩ=
{ω
1
,ω
2
,...,ω
K
} be a set of information classes in the scene.
Classification consists in assigning each pixel to one of the K
classes of interest.
A. Probabilistic SVM Classification
The first step of the proposed procedure consists in per-
forming a probabilistic SVM pixelwise classification of the
hyperspectral image [4], [13]. Other probabilistic classifiers
could be used. However, SVMs are extremely well suited to
classify hyperspectral data [3]. The standard SVMs do not
provide probability estimates for the individual classes. In order
to get these estimates, pairwise coupling of binary probabilistic
estimates is applied [13], [14].
B. Computation of the Gradient
Independent of the previous step, a one-band gradient of
the hyperspectral image is computed, which is further used
for defining the f uzzy no-edge/edge function. Approaches for
defining a one-band gradient from the B-band image are ana-
lyzed in [15]. Here, we first compute horizontal, vertical, and
two diagonal gradients (corresponding to the directions 0
◦
,90
◦
,
45
◦
, and 135
◦
, respectively), using Sobel masks [16], where
each of the gradients is computed as the sum of the gradients
of every spectral channel. The resulting one-band gradient
∇(X)={ρ
j
∈ R,j =1, 2,...,n} is found as the average of
the four obtained directional gradients.
C. MRF-Based Regularization
In the final step, the regularization of the SVM classifi-
cation map is performed, using the MAP-MRF framework.
This framework is based on the interpixel class dependence
assumption, which means that a pixel belonging to a class ω
i
is
likely to have neighboring pixels belonging to the same class.
In our work, an eight-neighborhood is assumed (let N
i
be the
set of neighbors for a given pixel x
i
).
We adopt the Metropolis algorithm, based on stochastic
relaxation and annealing, for computing the MAP estimate of
the true classification map given the initial (pixelwise) classifi-
cation map [17], [18]. The considered method is based on the
Bayesian approach and aims at minimizing the global energy in
the image, by iterative minimization of local energies (defined
hereafter) associated with randomly chosen image sites, i.e.,
pixels.
Let L = {L
j
,j =1, 2,...,n} be a generic set of informa-
tion class labels for the image X. We propose to compute the
local energy of a given site associated with a pixel x
i
as
U(x
i
)=U
spectral
(x
i
)+U
spatial
(x
i
) (1)
where U
spectral
(x
i
) is the spectral energy function from the ob-
served data and U
spatial
(x
i
) is the spatial energy term computed
over the local neighborhood N
i
. We define the spectral energy
term as
U
spectral
(x
i
)=− ln{P (x
i
|L
i
)} (2)
where P (x
i
|L
i
) is estimated by pairwise coupling of probabil-
ity estimates from “one-versus-one” SVM outputs [11], [14].
For the spatial energy term, two different expressions are
investigated. We first consider the standard spatial energy ex-
pression, used, for instance, in [10], which is computed as
U
NE
spatial
(x
i
)=
x
j
∈N
i
β(1 − δ(L
i
,L
j
)) (3)
where δ(·, ·) is the Kronecker delta function (δ(a, b)=1if a =
b, and δ(a, b)=0otherwise) and β is a parameter that controls
the importance of the spatial versus spectral energy terms. The
superscript “NE” means that no edge information is taken into
account. The term U
NE
spatial
(x
i
) is proportional to the number of
neighboring pixels of x
i
assigned to one of the classes different
from L
i
. This spatial energy term is particularly suitable for
the images with large spatial structures. However, if a small
one-pixel object is present in the image, this model will favor
assigning this pixel to the class of the surrounding objects.
In order to mitigate this drawback of the previous spatial term
and to preserve small structures and edges in the classification
map, we propose to integrate the edge information into the spa-
tial energy function. The computation of an accurate edge map
for hyperspectral images is a challenging task. For instance,
it can be obtained by thresholding the gradient image {ρ
j
∈
R,j =1, 2,...,n}. For this purpose, an appropriate threshold
738 IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 7, NO. 4, OCTOBER 2010
must be chosen. Instead of computing the edge map, we pro-
pose to define the following “fuzzy no-edge/edge function”:
ε (x
j
)=1−
ρ
j
α + ρ
j
(4)
where α is a parameter controlling the approximate edge
threshold. From here, the following spatial energy function is
proposed:
U
E
spatial
(x
i
)=
x
j
∈N
i
βε(x
j
)(1 − δ(L
i
,L
j
)). (5)
The superscript “E” means that the edge information is taken
into account. In the following, we thus refer to two different
methods, namely, SVMMRF-NE and SVMMRF-E, when (3)
and (5) are used for computing the spatial energy, respectively.
We briefly summarize the considered Metropolis algorithm
for optimizing the energy function. In each iteration, an image
site (i.e., a pixel x
i
) is randomly chosen. The local energy of
the given site U(x
i
) is computed by (1). Then, a new class
label L
new
i
is randomly selected for t he site x
i
, and a new
local energy U
new
(x
i
) is computed. If the variation of the
energy ΔU = U
new
(x
i
) − U(x
i
) < 0, the new class label is
assigned to x
i
: L
i
= L
new
i
. Otherwise, the new class assign-
ment is accepted with the probability p =exp(−ΔU/T). Here,
T is a global control parameter called “temperature” [18]. The
optimization begins at a high temperature, which is gradually
lowered as the relaxation procedure proceeds. This procedure
avoids converging to local minima.
III. E
XPERIMENTAL RESULTS AND DISCUSSION
We applied the proposed SVMMRF-NE and SVMMRF-E
classification approaches to three hyperspectral airborne images
described in the following:
1) The Indian Pines image is of a vegetation area that was
recorded by the AVIRIS sensor. The image is of 145 by
145 pixels, with a spatial resolution of 20 m/pixel and
200 spectral channels. A three-band false color image and
the reference data are shown in Fig. 2. Sixteen classes
of interest are considered, which are detailed in Table II,
with a number of training and test samples for each class.
Training samples have been randomly chosen from the
reference data.
2) The Center of Pavia image was r ecorded by the ROSIS
sensor over the urban area of Pavia, Italy. It is of 900
by 300 pixels, with a spatial resolution of 1.3 m/pixel
and 102 spectral channels. The reference data contain
nine thematic classes and 56 070 labeled pixels. Thirty
samples for each class were randomly chosen from the
reference data as training samples.
3) The University of Pavia image is of an urban area, ac-
quired by the ROSIS sensor. It is of 610 by 340 pixels,
with 103 spectral channels. The reference data contain
nine classes of interest. The training and test sets are
composed of 3921 and 40 002 pixels, respectively.
More information about the images can be found in [8].
Fig. 2. Indian Pines image. (a) Three-band color composite. (b) Reference
data. (c) SVM pixelwise classification map. (d) SVMMSF + MV classification
map. (e) SVMMRF-NE classification map. (f) SVMMRF-E classification map.
In all experiments, the probabilistic one-versus-one SVM
classification with the Gaussian radial basis function (RBF)
kernel was applied. The optimal parameters C (parameter that
controls the amount of penalty during the SVM optimization
[4]) and γ (spread of the RBF kernel) were chosen by fivefold
cross validation. The temperature T was varied during the
Metropolis relaxation procedure [18]: The initial temperature
was set to T
1
=2(a relatively low value of the initial temper-
ature results in a faster execution of the algorithm). After every
10
6
(order of the number of pixels in an image) iterations, the
temperature for the next iteration (k +1) was recomputed as
T
k+1
=0.98T
k
. The optimal value of the parameter α =30
was experimentally derived (the same optimal value of α was
obtained for the three considered data sets).
Furthermore, we have investigated the performances of the
SVMMRF-NE and SVMMRF-E algorithms for different val-
ues of the context weight parameter β. Table I reports the
SVMMRF-NE and SVMMRF-E overall (percentage of cor-
rectly classified pixels) and average (mean of the percentage
of correctly classified pixels for each class) classification accu-
racies for the three considered data sets. It can be concluded
that the optimal parameter is β ∈ [1, 2] for the SVMMRF-NE
approach and β ∈ [2, 4] for the SVMMRF-E approach (for both
methods, the corresponding overall accuracies are nonsignifi-
cantly different over the given range of values). Moreover, the
TARABALKA et al.: SVM- AND MRF-BASED METHOD FOR CLASSIFICATION OF HYPERSPECTRAL IMAGES 739
TAB L E I
SVMMRF-NE
AND SVMMRF-E CLASSIFICATION ACCURACIES FOR DIFFERENT VALUES OF THE PARAMETER β
TAB L E II
N
UMBER OF LABELED SAMPLES (NUMBER OF SAMPLES) AND CLASSIFICATION ACCURACIES IN PERCENTAGE FOR THE INDIAN PINES IMAGE
methods are robust to the choice of β, and quite a wide range
of values of β leads to high classification accuracies.
1
Table II summarizes the global (overall average accuracies
and kappa coefficient [8]) and class-specific classification ac-
curacies for the Indian Pines image. In order to compare
the performances of the proposed method with other recently
proposed advanced classification techniques, we have included
results of the pixelwise SVM classifiers, the well-known ECHO
(Extraction and Classification of Homogeneous Object) spatial
classifier [5], classification using majority vote within the adap-
tive neighborhoods defined by watershed segmentation (WH +
MV) [19], as well as the results obtained using the construction
of a minimum spanning forest from the probabilistic SVM-
derived markers followed by majority voting within connected
regions (SVMMSF + MV) [8]. Fig. 2 shows some of the
corresponding classification maps. As can be seen from the
table, all the spectral-spatial approaches yield higher classifi-
cation accuracies when compared to the pixelwise method. The
proposed SVMMRF-NE and SVMMRF-E techniques give the
highest global and most of the best class-specific accuracies.
Following the results of the McNemar’s test, the SVMMRF-
NE, SVMMRF-E, and SVMMSF + MV accuracies are not sig-
nificantly different, using 5% level of significance. From Fig. 2,
it can be seen that the corresponding three classification maps
are comparable and contain more homogeneous regions, when
compared to the SVM classification map. Since the considered
1
A similar study has shown robustness of the SVMMRF-E method to the
choice of the parameter α.
TABLE III
G
LOBAL CLASSIFICATION ACCURACIES IN PERCENTAGE
FOR THE
CENTER OF PAV I A IMAGE
image contains large spatial structures and reference data do
not comprise region edges, the advantage of the SVMMRF-E
method versus the SVMMRF-NE method is not obvious here.
Table III gives the global classification accuracies for the
Center of Pavia data, where the same techniques are used for
comparison. The proposed SVMMRF-E method yields the best
classification accuracies. This image of an urban area contains
small spatial structures, such as shadows and trees. Therefore,
the inclusion of the edge information in the context-based
regularization improves the classification performances.
Table IV reports the global classification accuracies for the
University of Pavia image. For this data set, the SVMMSF +
MV classifier gives the best accuracies, and the SVMMRF-E
method outperforms the SVMMRF-NE technique in terms of
accuracies. According to the results of the McNemar’s test,
all the corresponding classification maps are significantly dif-
ferent, using 5% level of significance. From these results, the
following conclusions can be derived: 1) the advantage of the
