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International Journal of Remote Sensing

ISSN: 0143-1161 (Print) 1366-5901 (Online) Journal homepage: https://www.tandfonline.com/loi/tres20

Examining region-based methods for land cover
classification using stochastic distances

R. G. Negri, L. V. Dutra, S. J. S. Sant'Anna & D. Lu

To cite this article: R. G. Negri, L. V. Dutra, S. J. S. Sant'Anna & D. Lu (2016) Examining region-
based methods for land cover classification using stochastic distances, International Journal of
Remote Sensing, 37:8, 1902-1921, DOI: 10.1080/01431161.2016.1165883

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Examining region-based methods for land cover
classification using stochastic distances
R. G. Negri a, L. V. Dutra b, S. J. S. Sant'Annab and D. Lu c

aInstituto de Ciência e Tecnologia, UNESP – Univ. Estadual Paulista, São Paulo, Brazil; bDivisão de
Processamento de Imagens, INPE – Inst. Nacional de Pesquisas Espaciais, São Paulo, Brazil; cCenter for
Global Change and Earth Observations, MSU – Michigan State University, East Lansing, MI, USA

ABSTRACT
A recent alternative to standard pixel-based classification of
remote-sensing data is region-based classification, which has
proved to be particularly useful when analysing high-resolution
imagery of complex environments, such as urban areas, or when
addressing noisy data, such as synthetic aperture radar (SAR)
images. First, following certain criteria, the imagery is decomposed
into homogeneous regions, and then each region is classified into
a class of interest. The usual method for region-based classification
involves using stochastic distances, which measure the distances
between the pixel distributions inside an unknown region and the
representative distributions of each class. The class, which is at the
minimum distance from the unknown region distribution, is
assigned to the region and this procedure is termed stochastic
minimum distance classification (SMDC). This study reports the use
of methods derived from the original SMDC, Support Vector
Machine (SVM), and graph theory, with the objective of identifying
the most robust and accurate classification methods. The equiva-
lent pixel-based versions of region-based analysed methods were
included for comparison. A case study near the Tapajós National
Forest, in Pará state, Brazil, was investigated using ALOS PALSAR
data. This study showed that methods based on the nearest
neighbour, derived from SMDC, and SVM, with a specific kernel
function, are more accurate and robust than the other analysed
methods for region-based classification. Furthermore, pixel-based
methods are not indicated to perform the classification of images
with a strong presence of noise, such as SAR images.

ARTICLE HISTORY
Received 17 March 2015
Accepted 7 March 2016

1. Introduction

The use of region-based classification methods has been increasing, particularly with
high-resolution imagery over urban areas, where pixel-based classification normally fails
because of the high heterogeneity and complexity of such environments (Liu and Xia
2010; Gigandet et al. 2005; Maillard and Alencar-Silva 2013). Herholz et al. (2014) applied
region-based classification to analyse medical imagery. Liu, Wang, and Gong (2014) used
this classification approach with light detection and ranging (lidar) data. Region-based

CONTACT R. G. Negri rogerio.negri@ict.unesp.br Instituto de Ciência e Tecnologia, UNESP – Univ. Estadual
Paulista, São José dos Campos, São Paulo, Brazil

INTERNATIONAL JOURNAL OF REMOTE SENSING, 2016
VOL. 37, NO. 8, 1902–1921
http://dx.doi.org/10.1080/01431161.2016.1165883

© 2016 Informa UK Limited, trading as Taylor & Francis Group

http://orcid.org/0000-0002-4808-2362
http://orcid.org/0000-0002-7757-039X
http://orcid.org/0000-0003-4767-5710
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classification is also especially useful for radar data, which are normally analysed using
pixel-based methods (Freitas et al. 2008; Li et al. 2012a; Li et al. 2012b; Zhang et al.
2013).

Region-based classifiers first aggregate pixels into homogeneous objects using seg-
mentation techniques and then classify the objects individually (Liu and Xia 2010).
Typically, classification is performed using a statistical distance between the representa-
tive distribution of each class of interest and the pixel distribution inside an unknown
region. As presented in Silva et al. (2011), the class at the minimum distance to the
unknown region distribution is assigned to the region and this process is known as
stochastic minimum distance classification (SMDC). A Gaussian assumption is used for
the standard statistical distance definition (Richards and Jia 2005).

Negri, Dutra, and Sant’Anna (2012a) theoretically introduced distinctive ways of using
stochastic distances for region-based classification, which have been tested with simu-
lated data. The first study to use the Bhattacharyya kernel function (Kondor and Jebara
2003) and apply Support Vector Machine (SVM) to region-based classification problems
was presented in Negri, Dutra, and Sant’Anna (2012b).

Another method that yielded good results for multispectral image classification was
proposed by Camps-Valls, Tatyana, and Zhou (2007). This method is based on graph
classification and its formalization allows for the use of kernel functions. For these
characteristics, it is possible to use the Bhattacharyya kernel function and apply the
method proposed in Camps-Valls, Tatyana, and Zhou (2007) for region-based classifica-
tion, similar to that of Negri, Dutra, and Sant’Anna (2012b).

The present work analyses the methods presented in Silva et al. (2011), Negri, Dutra,
and Sant’Anna (2012a), Negri, Dutra, and Sant’Anna (2012b), and Camps-Valls, Tatyana,
and Zhou (2007) (with the latter two methods using the Bhattacharyya kernel function)
for region-based classification. The equivalent pixel-based versions of the region-based
analysed methods were included for comparison.

In this investigation, a practical evaluation of the methods is presented for land use
and land cover (LULC) classification using ALOS PALSAR imagery in a study area near the
Tapajós National Forest in the western part of Pará state, Brazil. Two classification
scenarios with different classes were considered in this study to evaluate the analysed
methods.

2. Theoretical background

2.1. Stochastic distances

Stochastic distances were used as discrimination measures. These distances quantify the
separability of two sets of information. Probability density functions are used to model
the information distribution in each set. The separability of the sets is equivalent to the
distance between their probability functions. The Jeffries–Matusita distance (JM) is a
stochastic distance that is usually adopted in remote-sensing applications (Richards and
Jia 2005):

JMðC;DÞ ¼
ð
x2X

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
fCðx;ΘCÞ

p
�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
fDðx;ΘDÞ

ph i2
dx; (1)

INTERNATIONAL JOURNAL OF REMOTE SENSING 1903



where fC and fD are probability density functions, with parameters ΘC and ΘD; which
model the information distribution of the sets C and D; such elements belong to X.
Assuming fC and fD are Gaussian multivariate distributions, Equation (1) can be reformu-
lated as (Richards and Jia 2005)

JMðC; DÞ ¼ 2 1� e�BðC;DÞ
� �

; (2)

where Bð�; �Þ is the Bhattacharyya distance assuming the Gaussian multivariate distribu-
tion, defined by

BðC;DÞ ¼ 1
8
ðμC � μDÞT

P
C þ

P
D

2

� ��1

ðμC � μDÞ þ
1
2
ln

jPC þ
P

DjffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffijPCjj
P

Dj
p !

; (3)

where μZ and
P

Z are the mean vector and covariance matrix, respectively, estimated for

a set Z and T; j � j, and ð�Þ�1 represent the transpose, determinant, and inverse matrix
operations, respectively.

2.2. Stochastic distances and region-based classification

If I is an image defined on a support S � N
2 and X is an attribute space, IðsÞ ¼ x denotes

that a pixel s 2 S of I has an attribute vector x 2 X: The region-based classification
process consists of associating the class ωj; j ¼ 1; . . . ; c; with a region Ri � S;
i ¼ 1; . . . ; r: Ri is a set of pixels sa; a ¼ 1; . . . ;#Ri; where the attributes of sa are
obtained from I(sa) and # is the cardinality operator. In this context, the support of I is
partitioned into r disjoint regions by a segmentation process. Regions represent sets of
spatially connected pixels whose attribute vectors meet a particular uniformity criterion.
In the classification process, all pixels of the same region are assigned to a single class.

For a supervised region-based method, it is necessary to construct a set of labelled
regions D ¼ fðRi; ωjÞ 2 S� Ω : i ¼ 1; . . . ;m; j ¼ 1; . . . ; cg; where m is the number of
training regions. The notation ðRi;ωjÞ indicates that Ri is assigned to ωj:

As mentioned above, SMDC is adopted for region-based classification in Silva et al.
(2011). In this case, the pixel distribution in an unlabelled region is used to estimate a
probability distribution. This region is then associated with the class with the closest
distribution, according to an adopted stochastic distance. The class distributions are
modelled based on information from D. Formally, if we let Ri be an unlabelled region
and let MðfRi ; fωjÞ be a stochastic distance between the distributions of the attribute
vectors of the pixels in Ri and the class ωj; an assignment ðRi;ωjÞ is made when the
following rule is satisfied:

ðRi;ωjÞ , j ¼ argminMðfRi ; fωjÞ;
j ¼ 1; . . . ; c:

(4)

In Equation (4), fωj is estimated by considering the attribute vectors of the pixels of all of
the labelled regions assigned to ωj in D. Alternatives to SMDC based on simple changes
in Mð�; �Þ were derived in Negri, Dutra, and Sant’Anna (2012a).

The first proposed alternative, called the stochastic minimum averaged distance
classifier (SMADC), uses Mmeanð�; �Þ instead of Mð�; �Þ; which is defined as

1904 R. G. NEGRI ET AL.



MmeanðfRi ; fωjÞ ¼
1
tj

Xtj
l¼1

MðfRi ; fω jRlÞ; (5)

where fωjRl is the probability distribution that models the lth training region assigned to
ωj; which contains tj training regions in D.

Another alternative is the stochastic nearest neighbour classifier (SNNC), obtained by
replacing Mð�; �Þ with Mminð�; �Þ; which returns the shortest distance between Ri and one
of the training regions assigned to ωj: Mminð�; �Þ is defined as

MminðfRi ; fωjÞ ¼ minfMðfRi ; fωjRlÞ : l ¼ 1; . . . ; tjg: (6)

A third alternative is a generalization of Equation (6), which transforms Equation (4) into
a stochastic version of the k-nearest neighbour (SkNN) when Mð�; �Þ is substituted by
Mknnð�; �Þ; and is defined as

MknnðfRi ; fωjÞ ¼ e�hjðfRi Þ; (7)

where hjðfRiÞ ¼ #fðR;ωjÞ 2 VkðRiÞg; such that Vk(Ri) is the set of k training regions close
to Ri given a distance Mð�; �Þ: Formally,

VkðRiÞ ¼ fð�Rp;ωqÞ 2 D : 0<MðfRi ; f�R1Þ �
� MðfRi ; fR2Þ � � � � � MðfRi ; fRkÞ; p ¼ 1; . . . ; k; q ¼ 1; . . . ; cg: (8)

In this formalization, Rp represents a new indexing of the k nearest regions of D based
on the proximity to Ri.

2.3. Region-based classification with SVM

SVM has received great attention in recent years because of its excellent generalization
ability, its independence of data distribution, and its robustness with respect to Hughes
phenomenon (Bruzzone and Persello 2009).

The adoption of kernel functions, K : X2 ! R ; is a common strategy to improve SVM
classification performance on non-linearly separable patterns. A popular example of a

kernel function is the radial basis function (RBF) Kðxu; xυÞ ¼ e�γjjxu�xυjj2 ; γ 2 Rþ.
Another use of kernel functions is to generalize the application of SVM in problems

where patterns do not have an original vectorial representation, e.g. strings, graphs, and
sets of different cardinality. In these cases, measures of distances or similarities between
the patterns are used.

The flexibility offered by kernel functions provides a distinct way to apply the SVM to
region-based classification problems. For this purpose, we adopt a specific kernel func-
tion that considers a set of pixels (i.e. a region on an image) as a single pattern.

The given function K : X2 ! R is a kernel function if K is symmetric and conforms to
the Mercer theorem conditions (Cristianini and Shawe-Taylor 2000). However, such a
verification may not be trivial; there are alternative ways to develop such a function. For
example, the RBF model may be adopted (Schölkopf and Smola 2001):

Kðxu; xυÞ ¼ gðdðxu; xυÞÞ; (9)

INTERNATIONAL JOURNAL OF REMOTE SENSING 1905



where d : X2 ! R is a distance and g : R ! R is a strictly positive real function,
e.g. gðzÞ ¼ e�z:

Based on the model presented in Equation (9), if gð�Þ is equivalent to the negative
exponential function mentioned above and dð�; �Þ is the Bhattacharyya distance defined
in Equation (3), the following kernel function is defined:

KðRu; RυÞ ¼ e�γBðRu; RυÞ; (10)

where Ru and Rυ are sets and γ 2 Rþ is a user-adjusted parameter. Considering the sets
Ru and Rυ as regions of I, which have known attribute vectors, the use of the kernel
function in Equation (10) provides a distinct application of SVM in region-based classi-
fication. It should be noted that Equation (10) is similar to the JM stochastic distance
defined in Equation (2). The function in Equation (10) was originally proposed in Kondor
and Jebara (2003), wherein it is called a Bhattacharyya kernel. In Kim and Park (2009),
this kernel is used in artificial neural networks for signal classification. In the present
study, the Bhattacharyya kernel is used in the SVM method for region-based classifica-
tion, and this combination is denoted as SVM-BK.

2.4. Graph region-based classification

Graph classification methods are characterized by semi-supervised learning. This learn-
ing paradigm is motivated by an insufficient amount of labelled data to adequately train
the classifier. In this circumstance, the number of insufficient samples may be minimized
by increasing the training set using unlabelled data, which are abundant in most
classification problems (Zhu and Goldberg 2009).

In general, graph classification uses an affinity matrix G, which is a numerical repre-
sentation of a graph. In this matrix, the similarities between patterns are represented,
whether labelled or not. Formally, let D and ~D denote labelled and unlabelled data sets,

respectively, and let xu; xυ 2 D
S ~D represent two graph vertices. The value (weight)

associated with the edge between such vertices corresponds to a similarity measure
guυ;which is an element of G. The patterns xu and xυ tend to be associated with the
same class when the value of guυ increases.

According to Zhu and Goldberg (2009), graph methods are based on the ‘smoothness
assumption’, where the pattern labels (classes), in this case the vertices, vary smoothly
on the graph. The process of associating a class with an unlabelled vertex depends on
the similarity between other neighbour vertices in the graph.

Camps-Valls, Tatyana, and Zhou (2007) presented a graph-based method that allows
for the use of kernel functions such as those discussed for SVM. Let D ¼ D

S ~D denote a
data set composed of m and r labelled and unlabelled samples (patterns), respectively;
the affinity matrix G can be determined by

G mþrð Þ� mþrð Þ : guv ¼ e�γ xu�xvk k2 ; u; v ¼ 1; . . . ;mþ r; γ 2 Rþ: (11)

Consequently, it is verified that e�γjjxu�xυjj2 ; which corresponds to the RBF kernel, can be
substituted by the Bhattacharyya kernel function defined in (10). Under this considera-

tion, and if D is a training region set and eD is a set of unlabelled regions drawn from a
segmentation of I, as defined in Section 2.2, the method proposed in Camps-Valls,

1906 R. G. NEGRI ET AL.



Tatyana, and Zhou (2007) can address the region-based approach. This method is
denoted by GM-BK.

3. Experiments

In this section, we present practical experiments with the objective of comparing the
region-based classification methods discussed in Sections 2.2–2.4. Pixel-based equiva-
lent versions of the aforementioned region-based methods were included in the study,
which allows the comparison of the methods for both classification approaches.

For this purpose, we considered a case study using an ALOS PALSAR image over an
Amazon area. The comparison between methods was made considering the accuracy of
classifiers and accuracy of maps produced by each classification method. In addition to
the two types of accuracies considered in the analysis, two distinct classification scenar-
ios were used.

More details of the data used in the experiments are presented in Section 3.1. A
complete description of the experiment design is provided in Section 3.2. Results and
discussions are presented in Section 3.3.

3.1. Description of the data

In this section, we present practical applications of the region-based methods discussed
in Sections 2.2–2.4. For this purpose, we used a synthetic aperture radar (SAR) image
with HH, HV, and VV polarization acquired on 13 March 2009 by an ALOS PALSAR sensor
over a region near the Tapajós National Forest, Pará state, Brazil, whose location is
shown in Figure 1(a). The study image, illustrated in Figure 1(b), has 3� 3 multi-look
processing, is 860� 1229 pixels wide, has a 20 m resolution, and covers an area of
approximately 289 km2.

To perform the experiments using the region-based approach, it is necessary, first, to
segment the image to be classified. The segmentation was performed using the region-
growing method available in the Geographic Information System SPRING (Câmara et al.
1996). The segmentation parameter selection was visually performed. Figure 1(c) repre-
sents the contours of the image segmentation.

Among the LULC classes in the study area identified from a fieldwork campaign
conducted in September 2009, we considered samples of the following classes: primary
forest (PF), regeneration (RE), pasture (PS), bare soil (BS), and three types of agriculture,
denoted as Agriculture 1, 2, and 3 (A1, A2, and A3). These agricultural classes differ from
each other based on crop type or growing stage.

It is important to mention that the LULC samples identified in the study area were
initially randomly divided into two main sets designated for training the methods and
testing the classification results. The training set was intentionally defined with approxi-
mately double the number of polygons in each class compared to the test set. Unlike
traditional studies, where the sample division is performed on the basis of pixel number,
the number of polygons was considered to perform the training/test division, where
polygons (i.e. regions) were the classification objects for region-based methods, as
defined in Section 2.2. The spatial distributions of the samples for scenarios 1 and 2
are represented in Figure 1(d) and (e), respectively, where void polygons were selected

INTERNATIONAL JOURNAL OF REMOTE SENSING 1907



for training and full polygons for testing. To remove spatial correlation between the
pixels inside the training and test polygons, a resampling was performed considering a
regular grid with a lag of three pixels in both vertical and horizontal directions.

(a)

(b) (c)

(d) (e)

Location of the study area

Study image in (HH-HV-VV inten-
sity)RGB composition

Segmentation

Training and test LULC samples for
scenario 1

Training and test LULC samples for
scenario 2

Figure 1. The PALSAR image, its segmentation, and samples used in the study.

1908 R. G. NEGRI ET AL.



Additionally, Table 1 summarizes for each LULC class the number of pixels and polygons
selected for training and testing.

The considered LULC classes were organized into two classification problems, called
scenarios. The first scenario was characterized by all seven classes. However, the second
scenario was characterized by only three classes, defined by grouping PM and RE as one
class (high biomass (HB)), BS and PS as another class (low biomass (LB)), and, finally, the
three types of agriculture as a single class (agricultural areas (AA)). The groups of classes
that define each scenario are also presented in Table 1. The number of pixels and
polygons relative to scenario 2 classes was inferred by summing the relative class
numbers from scenario 1.

3.2. Experiment design

As previously mentioned, the methods presented in Sections 2.2–2.4 were compared in
terms of the accuracy of classifiers and accuracy of maps. The classification methods
used were SMDC, SMADC, SNNC, SkNN, SVM-BK, and GM-BK.

In the experiments, the generic stochastic distance M employed to formalize SMDC,
SMADC, SNNC, and SkNN on Equations (4), (5), (6), and (8), respectively, was substituted
by the JM distance (2) under the Gaussian multivariate assumption. Although a SAR
image was adopted in the case study, it is reasonable to use the Gaussian multivariate
distribution to model the data once the multi-look process had sufficiently smoothed
the speckle noise and, consequently, ‘Gaussianized’ the data; additionally, a more
appropriate distribution in terms of the SAR data is not known.

As already stated, for each region-based method analysed in this study, a correspond-
ing pixel-based classifier was considered. Specifically, the correspondence between such
methods is: for SMDC we have the Mahalanobis distance classifier (MDC) (Richards and
Jia 2005) as correspondent; similarly, for SMADC we considered the method MADC,
which changes M in Equation (5) by the Mahalanobis distance; 1NN and kNN are the
respective pixel-wise versions of SNNC and SkNN, but considering M as the Euclidean
distance instead of the JM; the correspondent of GM-BK is GM-RBF where the affinity
matrix G is defined, as in Equation (11); finally, SVM using a RBF kernel, denoted by SVM-
RBF, is the correspondent for SVM-BK.

It is worth mentioning that SVM using the RBF kernel for region-based classification,
as presented in Liu and Xia (2010), was not included in the comparisons because the
superiority of SVM-BK had already been verified in Negri, Dutra, and Sant’Anna (2012b).

Table 1. Summary of the land-cover classes and scenarios.
Training (void polygons) Test (solid polygons) Scenario/Class

LULC Types Pixels Polygons Pixels Polygons 1 2

Primary Forest 9134 10 1563 5 PF HB
Regeneration 2321 10 835 5 RE
Bare Soil 3757 11 1586 5 BS LB
Pasture 3958 10 1025 5 PS
Agriculture 1 2329 8 975 4 A1 AA
Agriculture 2 2045 8 874 4 A2
Agriculture 3 1901 8 686 3 A3

INTERNATIONAL JOURNAL OF REMOTE SENSING 1909



To address the problem of multi-class classification on SVM-BK and SVM-RBF, the one-
against-all strategy was used.

The accuracy of classifiers was computed following a repetitive training and classifi-
cation scheme using just the training samples (Section 3.1). For the first step, the
training set is randomly divided into two subsets, denoted by A and B. Subset A has
approximately 67% of all polygons from the training set and subset B has the remaining
33% of polygons. After defining these subsets, when applicable, the classifier parameter
tuning for each method is performed.

For methods for which parameters are to be set (i.e. SkNN, kNN, SVM-BK, SVM-RBF,
GM-BK, and GM-RBF), a fine-tuning procedure is performed based on a grid search
process with 10-fold cross validation, as discussed in Hsu, Chang, and Lin (2010). The
space search considered for the grid search process for each parameter/method is
shown in Table 2. This parameter adjustment process has as its objective the guarantee
that the conclusions were not impaired by results from methods with ill-tuned para-
meters. Once the best parameters are found, for those methods, the parameter tuning
process applies, and each method is trained using all of the information in subset A and
is used to classify the samples from subset B. The results from subset B classification are
assessed using the kappa agreement coefficient (Congalton and Green 2009), and the
computed measures are stored for future statistical analysis. It is worth mentioning that
for GM-BK and GM-RBF, when training or performing the grid search, the labelled data
not instantaneously in use were considered as an unlabelled set, denoted as ~D in
Section 2.4.

All steps described, from the selection of subsets A and B to the classification of the
accuracy measurement, were performed 50 times. The difference between each execu-
tion was just the choice of the distinct A and B subsets. After all 50 repetitions, the
average kappa value and its standard deviation for each method were computed. The
general classifier accuracy process is illustrated in Figure 2(a). Detailed steps on the
classifier parameter tuning are presented in Figure 2(b).

Most of the image classification results from remote-sensing applications are assessed
using an accuracy measure, such as the kappa coefficient, and a set of ground truth
information. Thus, it is estimated that the accuracy values calculated using the adopted
measure from such samples reflect the accuracy of the entire classified image, i.e. the
accuracy of the map.

However, several discussions presented in the literature (Pontius and Millones 2011)
question this classification assessment approach. As a special case, accuracy values
computed using the kappa coefficient may be influenced by the dimensions of the
ground truth class sets considered in the study, where bigger sets imply a greater

Table 2. The search space considered in the grid search for SkNN, kNN, SVM-BK, SVM-RBF, GM-BK,
and GM-RBF for parameter tuning.
Parameter Methods Search Space

C – Penalty SVM-BK, SVM-RBF {1; 10; 100; 1000}
γ – kernel flexibility SVM-BK, SVM-RBF, GM-BK, GM-RBF {0:25; 0:5; 1:0; 1:25; 2:0; 2:25}
β – graph regularization1 GM-BK, GM-RBF {0:25; 0:5; 0:75; 0:95}
κ – nearest neighbour SkNN, kNN {2; 3; 4; 5}

1Details about this regularization parameter can be found in Camps-Valls, Tatyana, and Zhou (2007).

1910 R. G. NEGRI ET AL.



influence on the accuracy values, although this behaviour is not always desired.
Unfortunately, the unavailability of ground truth class sets of the same dimension is to
be expected.

In this study, the accuracy of maps is calculated according to a particular scheme
presented in Figure 3(a). Initially, all training samples defined in Section 3.1 were used in
the training process, similar to the process discussed previously and represented in
Figure 2(b), except that all training samples were used and not just a subset. After tuning
the parameters and training, each region-based method was applied to classify the study
image based on the regions delimited by its segmentation (Figure 1(b) and (c)).
Classifications through pixel-wise methods are independent of the segmentation. Again,

(a) General process

(b) Classifier parameter tuning

Figure 2. Classifier assessment flow chart.

INTERNATIONAL JOURNAL OF REMOTE SENSING 1911



it is important to mention in this case that for GM-BK, the unlabelled set ~D is composed of
all regions delimited in the segmentation process. However, computational limitations

make impossible considering ~D in the pixel-wise approach as the set of all unlabelled
pixels once to train graph methods is necessary to store and perform matrix operations

such as inverse over matrices of (huge) dimension Dþ ~D
� �� Dþ ~D

� �
: To address this

limitation, ~D is composed of pixels sampled from the original image through a regular grid
with a lag of 25 pixels in both vertical and horizontal directions.

Once a classification result was obtained from each method, we performed the
accuracy analysis process, illustrated in Figure 3(b). This process included three repetitive
basic steps: (i) random selection of the test sample, (ii) computation of the accuracy
measures, and (iii) storage of the calculated measures. In the first step, we randomly
selected 350 pixels from each class. The reason for using 350 pixels was based on the
size of the smallest test sample, i.e. A3 (see Table 1); 350 is almost 50%. The remaining
quantity increased the possibility of generating test subsets that were at least 50%
different from each other. Next, from the defined test subset, we computed the kappa
accuracies for each classification result. The accuracies calculated were stored for future
statistical analysis. These three steps were performed 50 times.

As a final step, the averages and variances were computed from the respective 50 kappa
values stored during the accuracy analysis process. In other words, for each analysed
method there was an average performance measure and its deviation according to the
accuracies of the classifier and map. In addition to the statistical descriptive values, a
bilateral t-test was used to compare two population means (Mood and Graybill 1974).

(a) General process

(b) Accuracy analysis

Figure 3. Map assessment flow chart.

1912 R. G. NEGRI ET AL.



All processing performed were conducted on a computer with an Intel Core i5
processor and 8 GB of RAM running the Ubuntu-Linux operating system version 14.04.
The Interactive Data Language (IDL) programming language version 7.1 was used to
implement the classification methods. The algorithm SVMLight Joachims (1999) was used
to train SVM-BK and SVM-RBF.

3.3. Results and discussion

Using the data described in Section 3.1 and considering the steps specified in Section
3.2, we obtained the accuracies of the classifiers and the maps. Figure 4(a) and (b) shows
these accuracies, respectively. Furthermore, these figures simultaneously present the
performances in both scenarios 1 and 2.

As expected, very similar behaviour is observed between the accuracy of the classi-
fiers and the maps (Figure 4(a) and (b)). However, it is worth noting the opposite
performance of SNNC, SkNN, GM-BK, and SVM-BK, comparing its accuracies for classifier
and map in both scenarios 1 and 2. Such variations are introduced because of the
different training and test data sets used in each case. Furthermore, while the accuracy
of the classifiers is computed from different data sets for training and test, the accuracy

(a) Accuracy of the classifiers; error bars represent ±1 standard deviation

(b) Accuracy of the maps; error bars represent ±1 standard deviation

Figure 4. A graphical comparison between classifiers and classification accuracies.

INTERNATIONAL JOURNAL OF REMOTE SENSING 1913



of the maps comes from just one classification result. In other words, the accuracy of the
maps (single results) achieved a higher value compared to the average accuracy of the
classifiers (50 results).

Observing just the accuracy of the classifiers for scenario 1 (Figure 4(a)), it is possible
to note that all region-based methods achieved better performance compared to pixel-
based methods. A t-test to compare the accuracy of classifiers, at a 95% confidence level,
allowed us to verify the statistical equality between all region-based methods, in addi-
tion to the statistical equality between all pixel-based methods and the dominant
statistical difference between region- and pixel-based methods. We note that GM-BK
achieved lower accuracy compared with other region-based methods. Additionally, GM-
BK was statistically equivalent to SVM-RBF, where the latter had a higher accuracy value
among the observed pixel-based methods.

Conversely, with respect to the accuracy of the classifiers for scenario 2, we observed
an evident performance drop for the SMDC and SMADC methods. Furthermore, the
decrease in accuracies associated with the increase in deviations of SMADC and GM-BK,
with opposition to the increase in the accuracy of all pixel-based methods for scenario 2,
led to statistical equality between the methods. The increase of kappa values for
scenario 2 might have been influenced by the reduced quantity of classes. It is worth
noting that SNNC, SkNN, SVM-BK, and GM-BK present similar behaviours for both
scenarios 1 and 2.

The p-values for the t-tests that compare the analysed methods for scenario 1 with
respect to the accuracy of the classifiers are shown in the upper triangular matrix in
Table 3. The lower triangular matrix in Table 3 presents the corresponding p-values for
scenario 2.

Focusing the discussion on the accuracy of the maps, we can observe that the highest
accuracies for scenario 1 were obtained with classifications produced by SMDC, SNNC,
SkNN, and SVM-BK. In contrast, lower accuracies were obtained with 1NN, kNN, and
GM-RBF.

From the results of scenario 2, SNNC, SkNN, and SVM-BK were found to have similar
accuracy levels to those obtained in scenario 1; however, SMDC and SMADC showed a
lower level of performance. Even given their low performance, GM-BK achieved more
accurate values compared to those for scenario 1. Table 4 presents the p-values from a
t-test applied to compare the accuracy of the maps illustrated in Figure 4(b) for scenarios

Table 3. p-values from a bilateral t-test to compare the classifier accuracies achieved by the analysed
methods in scenarios 1 (upper triangular matrix) and 2 (lower triangular matrix).

SMDC SMADC SNNC SkNN SVM-BK GM-BK MDC MADC 1NN kNN SVM-RBF GM-RBF

SMDC 0.690 0.981 0.936 0.938 0.139 0 0 0 0 0 0
SMADC 0.305 0.728 0.748 0.759 0.245 0 0 0 0 0 0
SNNC 0.361 0.082 0.959 0.960 0.162 0 0 0 0 0 0
SkNN 0.556 0.177 0.850 0.999 0.154 0 0 0 0 0 0
SVM-BK 0.508 0.146 0.870 0.975 0.165 0 0 0 0 0 0
GM-BK 0.648 0.714 0.256 0.386 0.351 0.024 0.042 0.001 0.016 0.068 0.005
MDC 0.017 0.387 0.003 0.024 0.014 0.269 0.545 0 0.541 0.569 0.121
MADC 0.020 0.375 0.004 0.025 0.015 0.261 0.928 0 0.274 0.867 0.063
1NN 0 0.051 0 0.002 0.001 0.053 0.070 0.140 0.007 0.005 0.527
kNN 0.007 0.283 0.001 0.015 0.008 0.205 0.757 0.857 0.107 0.3d52 0.277
SVM-RBF 0.038 0.547 0.007 0.040 0.025 0.368 0.683 0.648 0.024 0.459 0.098
GM-RBF 0 0.062 0 0.002 0.001 0.058 0.116 0.180 0.915 0.170 0.052

1914 R. G. NEGRI ET AL.



1 and 2. As represented in Table 3, the upper and lower triangular matrices inside the
table contain the computed p-values for scenarios 1 and 2, respectively.

A confidence level of 95% affirms that almost all results are statistically different from
each other, except for the classifications obtained by SNNC and SkNN in scenario 1.
Adopting the same level of confidence, the scenario 2 classifications provided by SNNC
and SkNN are still statistically equal; furthermore, SMADC is statistically equal to most of
the analysed pixel-based methods.

In general, region-based methods are statistically superior to pixel-based methods.
Although a similar tendency is shown in Figure 4(b), whereas most of the pixel-based
results are different from each other in scenario 1, we have the reverse in scenario 2. It is
worth noting that 1NN achieved a lower accuracy level.

The LULC classification maps for scenarios 1 and 2, for which the accuracy of the
maps (Figure 4(b)) was computed, are illustrated in Figures 5 and 6, respectively.

With respect to the performance of region-based classification for scenario 1, there
was similarity between SMDC, SNNC, and SkNN, which yielded the highest accuracy
values. Satisfactory results were achieved by SMADC and SVM-BK. Loss of classification
precision was noted when SMADC misclassified A3, SVM-BK misclassified PS, and GM-BK
misclassified the RE and PS areas.

For pixel-based classifications, mainly as a function of the extremely noisy data, poor
results were achieved, where A1, A3, PS, and RE classes were frequently confused with
each other.

For scenario 2, the highest performances were achieved by the SNNC, SkNN, and
SVM-BK methods. Among these methods, we observed that the main divergence
occurred when SVM-BK classified the areas at the bottom of the study image. GM-BK
did not perform well the classification of LB and AA classes. As expected, because of the
data type, the pixel-based results were noisy.

Given the presented results, we can conclude that SMDC and SMADC are less robust
than SNNC, SkNN, and SVM-BK because the accuracies achieved in scenario 2 differ
considerably compared with scenario 1.

Recapping the theoretical formulation (Section 2.2), SMDC used the information from
all training samples (regions) of a given class to estimate a single statistical distribution,
which modelled the elements of this class. The classification of an unlabelled region is
made based on the most similar class distribution. It is reasonable that the more similar

Table 4. p-values from a bilateral t-test to compare the map accuracies achieved by the analysed
methods in scenarios 1 (upper triangular matrix) and 2 (lower triangular matrix) .

SMDC SMADC SNNC SkNN SVM-BK GM-BK MDC MADC 1NN kNN SVM-RBF GM-RBF

SMDC 0 0.023 0.001 0 0 0 0 0 0 0 0
SMADC 0 0 0 0.528 0 0 0 0 0 0 0
SNNC 0 0 0.221 0 0 0 0 0 0 0 0
SkNN 0 0 0.642 0 0 0 0 0 0 0 0
SVM-BK 0 0 0 0 0 0 0 0 0 0 0
GM-BK 0 0 0 0 0 0 0 0 0 0 0
MDC 0 0.300 0 0 0 0 0.424 0 0 0.367 0
MADC 0 0.090 0 0 0 0 0.596 0 0 0.065 0
1NN 0 0 0 0 0 0 0.002 0.007 0 0 0
kNN 0 0.155 0 0 0 0 0.710 0.896 0.007 0 0.428
SVM-RBF 0 0.751 0 0 0 0 0.231 0.076 0 0.124 0
GM-RBF 0 0.241 0 0 0 0 0.863 0.744 0.005 0.851 0.188

INTERNATIONAL JOURNAL OF REMOTE SENSING 1915



(a) SMDC (b) SMADC (c) SNNC

(l) GM-RBFl

(a) SMDC (b) SMADC (c) SNNC

(d) SkNNd (e) SVM-BKe (f) GM-BKf

(g) MDCg (h) MADCh (i) 1NNi

(j) kNNj (k) SVM-RBFk

Figure 5. Classification results obtained for scenario 1.

1916 R. G. NEGRI ET AL.



(a) SMDC (b) SMADC (c) SNNC

(d) SkNN (e) SVM-BK (f) GM-BK

(g) MDC (h) MADC (i) 1NN

(j) kNN (k) SVM-RBF (l) GM-RBFl)F

Figure 6. Classification results obtained for scenario 2.

INTERNATIONAL JOURNAL OF REMOTE SENSING 1917



the statistical distributions of the classes involved in the classification problem, the
greater were the chances of incorrect classification occurring. Computing the distance
between the statistical distributions of the classes in each scenario, modelled from the
training samples, while it was found that the greater distance had a value of 1:83
(between PF and BS) for the first scenario, in the second scenario, the greater value
was 0:87 (between HB and AA). Based on this fact, we can explain that the union of
classes from scenario 1, to define scenario 2, produced classes with similar statistical
distributions, which in turn decreased the robustness of the method.

A justification of the SMADC behaviour follows a similar idea. SMADC considers the
statistical distances between an unlabelled region and each training sample (region) of a
given class. After computing these distances, a ‘smoothed’ distance value was calculated
averaging all distance values previously computed for the initially considered class
(Equation (5)). This smoothing introduced possible misclassifications in scenario 2,
when the samples of each class in this scenario were most dissimilar compared to the
samples of each class in scenario 1. This fact was proved after computing intra-class
sample distances, where, whereas the highest value of 0:80 (between samples of A3) was
observed in scenario 1, the highest value in scenario 2 was 1:85 (between samples
of AA).

On the other hand, SNNC, SkNN, SVM-BK, and GM-BK methods were not affected by
this factor. The decision rule of SNNC and SkNN did not depend on the smallest
averaged stochastic distances, but on the smallest distance value found between
some training samples to the unlabelled region. Focusing on the SVM-BK method, the
weighting of training samples, defined through the Lagrangian coefficients (see
Theodoridis and Koutroumbas (2008)), to construct the decision rule, prevents problems
similar to those presented by SMDC and SMADC.

Despite the robustness of GM-BK on the analysed scenarios, i.e. without presenting
sharp drops as SMDC and SMADC, their low accuracy might have derived from their
formulation based on the ‘smoothing assumption’. This semi-supervised concept estab-
lished that the pattern labels varied smoothly on the feature space, and for this purpose,
the information from unlabelled samples was considered. This assumption may be
helpful when the quantity of samples for adequate training is insufficient, but harmful
in some cases. According to the present results, there are indications that the use of
unlabelled samples affected decision rule estimation.

Regarding the pixel-based methods, it can be observed the existence of a general
behaviour independent of the scenario and way of accuracy analysis (i.e. accuracy of the
classifier or map), most of the methods (MDC, MADC, kNN, SVMþ RBF, and GMþ RBF)
tend to present similar results. It is worth noting that the highest accuracy values are
presented by SVM, in accordance with the previous results discussed in Mountrakis, Im,
and Ogole (2011). On the other hand, lower accuracy values are associated with the 1NN
method. Such behaviour occurs in function of the decision rule of the method (assign a
class to a non-labelled pattern according to the most similar/closer labelled pattern) that
becomes inadequate for noisy data (presence of speckle).

In general, the results obtained through the pixel-based approach were overwhel-
mingly lower than those achieved with the region-based approach. Three factors that
explain the differences between these approaches are the adopted image, the pattern
type, and how such patterns are treated by the different approaches. Although multi-

1918 R. G. NEGRI ET AL.



look processing performed on the study image had minimized the speckle presence, we
could see (Figure 1(b)) that this noise was not eliminated. The high variability introduced
by this noise on the pixel’s attributes prevented pixel-based methods from performing
homogeneous classification of the targets, as illustrated in Figures 5(g)–(l) and 6(g)–(l).
On the other hand, region-based methods had higher accuracy because the classifica-
tion pattern was not a single pixel isolated from its spatial context. Furthermore, the use
of stochastic distances improved the distinction between the regions because not only
the attributes of pixels inside the region were considered, but also the variability
(texture) of such pixels. It is worth recalling that the experiment design included
procedures to decorrelate information from the training and test samples, and then
the hypothesis that the existence of correlation between samples had favoured region-
based methods was discarded.

4. Conclusion and perspectives

In this article, we investigated different image classification methods using the region-
based approach. Additionally, the pixel-based approach was included in the analysis for
comparison. A case study with respect to LULC on an Amazon area using an ALOS
PALSAR image was conducted to compare the methods. For the case study, two
classification problems were addressed: the so-called scenarios. While the first scenario
dealt with a more specific classification problem composed of seven classes, the other
scenario treated three classes, defining a grouping of classes from scenario 1. In addition
to the different scenarios, the methods were compared in two distinct assessment ways:
the accuracy of the classifiers and the accuracy of the methods. Whereas the accuracy of
the classifiers consists in examining the generalization ability of the method, through a
repetitive and distinct process of ‘training-classification’, the accuracy of the maps aims
to assess a particular classification result using the kappa coefficient, however avoiding
the fact that different quantities of test samples in different classes may influence the
accuracy values of such coefficients.

The results showed that nearest neighbour-based classifiers (SNNC and SkNN), inde-
pendent of the scenario, had better performances than minimum distance-based meth-
ods (SMDC and SMADC). Classifiers such as SNNC and SkNN are not available in any
commercial or free software; however, their implementation is simple, and they are a
good alternative for region-based methods.

The SVM method using the Bhattacharyya kernel function (SVM-BK) provided good
results for region-based classification, independent of the scenario. Conversely, SVM
with the RBF kernel function (SVM-RBF) used for pixel-based classification yielded
inferior performance. This result showed the importance of region-based classification
for problems such as the ALOS PALSAR case study discussed in this work.

Moreover, this study presented the use of the graph-based method proposed in
Camps-Valls, Tatyana, and Zhou (2007), adapted to the region-based approach using the
Bhattacharyya kernel function (GM-BK). The performance of this method in this case
study was inferior compared with that of SNNC, SkNN, and SVM using the same kernel
function.

Finally, the results indicated that the pixel-based approach was strongly influenced by
noise present in the image. Furthermore, the region-based approach could satisfactorily

INTERNATIONAL JOURNAL OF REMOTE SENSING 1919



deal with the presence of noise because of the manner in which the patterns (regions)
are compared (i.e. using stochastic distances).

Acknowledgements

The authors thank FAPESP (Grant 2014/14830-8), CAPES, and CNPq (Grant 307666/2011-5, 401528/
2012-0 and 151571/2013-9) for funding this research.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

This work was supported by the Conselho Nacional de Desenvolvimento Científico e Tecnológico
[151571/2013-9,307666/2011-5,401528/2012-0]; Coordenação de Aperfeiçoamento de Pessoal de
Nível Superior [DS]; FAPESP [2014/14830-8]

ORCID

R. G. Negri http://orcid.org/0000-0002-4808-2362
L. V. Dutra http://orcid.org/0000-0002-7757-039X
D. Lu http://orcid.org/0000-0003-4767-5710

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	Abstract
	1.  Introduction
	2.  Theoretical background
	2.1.  Stochastic distances
	2.2.  Stochastic distances and region-based classification
	2.3.  Region-based classification with SVM
	2.4.  Graph region-based classification

	3.  Experiments
	3.1.  Description of the data
	3.2.  Experiment design
	3.3.  Results and discussion

	4.  Conclusion and perspectives
	Acknowledgements
	Disclosure statement
	Funding
	References