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This chapter describes scale-invariant region detectors that are based on image operators synthesized through Genetic Programming (GP). Interesting or salient regions on an image are of considerable usefulness within a broad range of vision problems, including, but not limited to, stereo vision, object detection and recognition, image registration and content-based image retrieval. A GP-based framework is described where candidate image operators are synthesized by employing a fitness measure that promotes the detection of stable and dispersed image features, both of which are highly desirable properties. After a significant number of experimental runs, a plateau of maxima was identified within the search space that contained operators that are similar, in structure and/or functionality, to basic LoG or DoG filters. Two such operators with the simplest structure were selected and embedded within a linear scale space, thereby making scale-invariant feature detection a straightforward task. The proposed scale-invariant detectors exhibit a high performance on standard tests when compared with state-of-the-art techniques. The experimental results exhibit the ability of GP to construct highly reusable code for a well known and hard task when an appropriate optimization problem is framed.
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Preface
The publication of this book on evolutionary Image Analysis and Signal Pro-
cessing (IASP) has two main goals. The first, occasional one is to celebrate
the 10th edition of EvoIASP, the workshop which has been the only event
specifically dedicated to this topic since 1999. The second, more important
one is to give an overview of the opportunities offered by Evolutionary Com-
putation (EC) techniques to computer vision, pattern recognition, and image
and signal processing.
It is not possible to celebrate EvoIASP properly without first acknowl-
edging EvoNET, the EU-funded network of excellence, which has made it
possible for Europe to build a strong European research community on EC.
Thanks to the success of the first, pioneering event organized by EvoNET,
held in 1998 in Paris, it was possible to realize that not only was EC a fer-
tile ground for basic research but also there were several application fields to
which EC techniques could offer a valuable contribution. That was how the
idea of creating a single event, EvoWorkshops, out of a collection of workshops
dedicated to applications of EC, was born. Amongst the possible application
fields for EC, IASP was selected almost accidentally, due to the occasional
presence, within EvoNET, of less than a handful of researchers who were
interested in it. I would lie if I stated that the event was a great success since
its very start, but it was successful enough to survive healthily for a couple
of years, before reaching its present size, relevance, and popularity.
The papers selected for inclusion in this book, mostly extended ver-
sions of papers presented at EvoIASP, have no pretence of setting mile-
stones in the history of evolutionary IASP, but they do offer readers a
panoramic view of what can be currently done using EC techniques in such
applications. From this point of view, what could be seen as a defect of
thisbook,atfirstsight,canevenbecome a useful and peculiar feature.
In fact, this rather unstructured collection of papers samples the space of
Evolutionary IASP rather extensively, albeit possibly sparsely, along dif-
ferent axes. The most obvious one is related to applications in different
areas of IASP, as the book describes a wide variety of applications in which
VI Preface
EC can fruitfully be employed. However, there are less obvious ones. Amongst
these, let me mention and discuss what I believe is a very important one:
the ‘degree of involvement’ of EC in IASP applications. The book describes
applications in which EC techniques play very different roles in producing
the final results. Differently from how EC is most commonly looked upon, or
perceived, by non-EC researchers, EC techniques can actually represent more
than an external optimization tool that can be used to tune or refine param-
eters or components of a mostly pre-defined solution. In fact, EC techniques
can be embedded more intimately into IASP applications, up to situations
where the solution itself is intrinsically evolutionary. This book provides ex-
amples that are positioned at both ends of this axis. Of course, that is not
the only possible ordering criterion that can be used to create a taxonomy of
Evolutionary IASP. In a recent paper, I mentioned at least two more criteria,
perhaps the most natural ones out of many possible: EC-based, according to
the evolutionary paradigm that is used, and application-based, according to
the abstraction level of the task to which EC is applied.
Deciding the ordering criterion for the contributions in this book has been
no easy task, as they were mostly extended versions of papers that have been
presented at EvoIASP. Therefore, there is neither a pre-established logical
structure underlying their choice, nor was it possible to find any ordering
with respect to which they could appear to be uniformly distributed. Be-
cause of this, I decided not to subdivide the book into sections. Nevertheless,
an application-based ordering criterion is implicitly followed, with some addi-
tional constraints which reflect the presence of more work dealing with topics
and applications belonging to the computer vision domain. Contributions be-
longing to this larger group appear first, and are ordered according to the
abstraction level of the task they describe. In the following smaller set of con-
tributions, more general and basic tasks are tackled, which, with some exten-
sion of their context, can also find effective applications in computer vision.
An implicit secondary EC-based indexing criterion has also been followed by
trying to keep applications based on the same or similar EC paradigms close
to one another.
From the point of view of the expected audience, even if the contents of this
book are derived from a workshop that is addressed mainly to EC researchers,
this book does not specifically address any category of readers. Knowledge of
the most basic EC paradigms is given for granted, while, possibly, some more
basic detail about the specific applications is given, which may be obvious
to readers who are familiar with them. However, all authors have made their
best efforts to keep their contributions as balanced as possible for the reading
to be enjoyable for the widest possible audience. Any variations to the basic
evolutionary algorithms or application-related functions are described in de-
tails. On the other hand, details about the specific applications are usually
limited to the information that is essential for their understanding.
Preface VII
A common problem that occurs when techniques developed within a spe-
cific community are applied to a number of fields for which other well-
established communities also exist is that members of each community tend
to publicize their work within their ‘natural environment’. The result is that,
first, similar work is often described very differently, as some authors focus
mainly on applications, while others concentrate on methodology. Second,
and more important, a lack of communication occurs by which researchers
belonging to one community tend to keep a very partial view of the topics
pertaining to the other communities. As a result, on the one hand, researchers
in the application fields tend to consider basic methods to be well-established,
ready-for-use, closed tools; on the other hand, those who do basic research
often tend to consider application-related data as abstract benchmarks using
which their results can be tested, neglecting their actual meaning in the real
world. One of the most appealing features of books like this is being, in gen-
eral, more universally visible and less community-specific than, for example,
conference proceedings, besides, obviously, having a much narrower scope
than the latter. In its first 10 years, EvoIASP has, hopefully with success,
sowed the seeds for a new ‘multi-cultural’ community of researchers in evo-
lutionary IASP. I do wish this book will further contribute to the widening
of this community, both numerically and in terms of research interests, and
that we will celebrate more successes, and the 20th edition of the workshop,
10 years from now.
Parma,
January 2009 Stefano Cagnoni
Acknowledgements
This book is dedicated, in first place, to all those who made it possible for
EvoIASP to exist and survive in g ood health for 10 years (which will likely
be 11 when this book is published):
Riccardo Poli, a friend and colleague, who introduced me to Evolutionary
Computation and showed me the way into this fascinating field when w e
were still PhD students. Then, when he was already one of the most active
and influential members of the EC community, it was him who proposed
that I co-chaired the EvoIASP working group in the early years of EvoNET,
the EU-funded Network of Excellence on Evolutionary Computation;
Terry Fogarty, co-chair of the first editions of EvoIASP, but most of all a
pioneer in the field of E volutionary Computation, co-ordinator of EvoNET
as well as a friendly and hilarious companion of pleasant after-conference
chats;
Jennifer Willies, EvoNET and Evo* coordinator, as indispensable as dis-
crete support for all EvoNET events, gifted by an incredible ability to make
the best out of the budgets she has to manage, often limited and severely
constrained. Acknowledging only her professional achievements would be
more than restrictive. Just ask any EvoNET member or participant in Evo*
for more details on her availability, patience and motherly care in any of the
(infinite) situa tions where her intervention is requested, and
All those who have submitted and presented their work at EvoIASP, with
particular regards to those who, after their first participation in the work-
shop, have b een engaged in E volutionary Image Analysis and Signal Pro-
cessing and in the workshop itself. Amongst these, I would like to thank,
in particular, Evelyne Lutton, Gustavo Olague, Jean Louchet and Mengjie
Zhang, as well as all who contributed to the workshop as reviewers.
I would also like to thank very warmly all authors of the chapters included
in this book for their patience in preparing excellent extensions of their work
presented at EvoIASP, and especially for coping with my slowness in turning
their con tribution into the volume you are reading.
Contents
Evolutionary Image Analysis and Signal Processing
Texture Image Segmentation Using an Interactive
Evolutionary Approach ...................................... 3
Cynthia B. erez, Gustavo Olague, Evelyne Lutton,
Francisco Fern´andez
Detecting Scale-Invariant Regions Using Evolved Image
Operators ................................................... 21
Leonardo Trujillo, Gustavo Olague
Online Evolvable Pattern Recognition Hardware ............. 41
Kyrre Glette, Jim Torresen, Moritoshi Yasunaga
A Variant Program Structure in Tree-Based Genetic
Programming for Multiclass Object Classification ............ 55
Mengjie Zhang, Mark Johnston
Genetic Programming for Generative Learning and
Recognition of Hand-Drawn Shapes ......................... 73
Wojciech Ja´skowski, Krzysztof Krawiec, Bartosz Wieloch
Optimizing a Medical Image Analysis System Using
Mixed-Integer Evolution Strategies .......................... 91
Rui Li, Michael T.M. Emmerich, Jeroen Eggermont,
Ernst G.P. Bovenkamp, Thomas ack, Jouke Dijkstra,
Johan H.C. Reiber
Memetic Differential Evolution Frameworks in Filter
Design for Defect Detection in Paper Production ............ 113
Ferrante Neri, Ville Tirronen
XII Contents
Fast Genetic Scan Matching in Mobile Robotics ............. 133
Kristijan Lenac, Enzo Mumolo, Massimiliano Nolich
Distributed Differential Evolution for the Registration of
Satellite and Multimodal Medical Imagery................... 153
Ivanoe De Falco, Antonio Della Cioppa, Domenico Maisto,
Umberto Scafuri, Ernesto Tarantino
Euclidean Distance Fit of Conics Using Differential
Evolution .................................................... 171
Luis G. de la Fraga, Israel Vite Silva, Nareli Cruz-Cort´es
An Evolutionary FIR Filter Design Method ................. 185
Raed Abu Zitar, Ayman Al-Dmour
Author Index ................................................ 201
Subject Index ............................................... 203
List of Contributors
Raed Abu Zitar
School of Computer Science and
Engineering,
New York Institute of Technology,
Amman, Jordan
rzitar@philadelphia.edu.jo
Ayman Al-Dmour
Department of Information
Technology, Al-Hussein Bin
Talal University,
Ma´an, Jordan
d.ayman@ahu.edu.jo
Thomas ack
Natural Computing Group,
Leiden Institute of
Advanced Computer Science,
Leiden University, The Netherlands
baeck@liacs.nl
Ernst G.P. Bovenkamp
Division of Image Processing,
Department of Radiology C2S,
Leiden University Medical Center,
The Netherlands
E.G.P.Bovenkamp@lumc.nl
Nareli Cruz-Cort´es
Center for Computing Research,
National Polytechnic Institute,
Zacatenco 07738,
Mexico City, M´exico
nareli@cic.ipn.mx
Ivanoe De Falco
ICAR–CNR, Via P. Castellino 111,
80131 Naples, Italy
ivanoe.defalco@na.icar.cnr.it
Luis G. De la Fraga
Cinvestav, Department of
Computing, IPN 2508,
07360 Mexico City, M´exico
fraga@cs.cinvestav.mx
Antonio Della Cioppa
Natural Computation Lab,
DIIIE, University of Salerno,
Via Ponte don Melillo 1,
84084 Fisciano (SA), Italy
adellacioppa@unisa.it
Jouke Dijkstra
Division of Image Processing,
Department of Radiology C2S,
Leiden University Medical Center,
The Netherlands
J.Dijkstra@lumc.nl
Jeroen Eggermont
Division of Image Processing,
Department of Radiology C2S,
Leiden University Medical Center,
XIV List of Contributors
The Netherlands
J.Eggermont@lumc.nl
MichaelT.M.Emmerich
Natural Computing Group,
Leiden Institute of
Advanced Computer Science,
Leiden University, The Netherlands
emmerich@liacs.nl
Francisco Fern´andez
University of Extremadura,
Computer Science Department,
Centro Universitario de erida,
C/Sta Teresa de Jornet, 38,
06800 M´erida, Spain
fcofdez@unex.es
Kyrre Glette
University of Oslo,
Department of Informatics,
P.O. Box 1080 Blindern,
0316 Oslo, Norway
kyrrehg@ifi.uio.no
Wo jciech Ja´skowski
Institute of Computing Science,
Poznan University of Technology,
Piotrowo 2, 60965 Pozna´n, Poland
wjaskowski@cs.put.poznan.pl
Mark Johnston
School of Enginering and
Computer Science,
Victoria University of Wellington,
P.O. Box 600,
Wellington, New Zealand
mark.johnston@vuw.ac.nz
Krzysztof Krawiec
Institute of Computing Science,
Poznan University of Technology,
Piotrowo 2, 60965 Pozna´n, Poland
kkrawiec@cs.put.poznan.pl
Kristijan Lenac
A.I.B.S. Lab S.r.l.,
Via del Follatoio 12, Trieste, Italy
klenac@units.it
Rui Li
Natural Computing Group,
Leiden Institute of
Advanced Computer Science,
Leiden University, The Netherlands
ruili@liacs.nl
Evelyne Lutton
INRIA Rocquencourt,
Complex Team,
Domaine de Voluceau BP 105,
78153 Le Chesnay Cedex, France
evelyne.lutton@inria.fr
Domenico Maisto
ICAR–CNR, Via P. Castellino 111,
80131 Naples, Italy
domenico.maisto@na.icar.cnr.it
Enzo Mumolo
DEEI, University of Trieste,
Via Valerio 10,
Trieste, Italy
mumolo@units.it
Ferrante Neri
Department of Mathematical
Information Technology, Agora,
University of Jyv¨askyl¨a,
P.O. Box 35 (Agora),
FI-40014 Jyv¨askyl¨a, Finland
neferran@cc.jyu.fi
Massimiliano Nolich
DEEI, University of Trieste,
Via Valerio 10,
Trieste, Italy
mnolich@units.it
Gustavo Olague
CICESE, Research Center,
Divisi´on de F´ısica Aplicada
Centro de Investigaci´on
Cient´ıfica y de Educaci´on
Superior de Ensenada, B.C.,
Km. 107 Carretera
List of Contributors XV
Tijuana-Ensenada,
22860, Ensenada, B.C., M´exico
olague@cicese.mx
Cynthia B. P´erez
CICESE, Research Center,
Divisi´on de F´ısica Aplicada
Centro de Investigaci´on
Cient´ıfica y de Educaci´on
Superior de Ensenada, B.C.,
Km. 107 Carretera
Tijuana-Ensenada,
22860, Ensenada, B.C., M´exico
cbperez@cicese.mx
Johan H.C. Reiber
Division of Image Processing,
Department of Radiology C2S,
Leiden University Medical Center,
The Netherlands
Johan H.C. Reiber@lumc.nl
Umberto Scafuri
ICAR–CNR, Via P. Castellino 111,
80131 Naples, Italy
umberto.scafuri@na.icar.cnr.it
Ernesto Tarantino
ICAR–CNR, Via P. Castellino 111,
80131 Naples, Italy
ernesto.tarantino@
na.icar.cnr.it
Ville Tirronen
Department of Mathematical
Information Technology, Agora,
University of Jyv¨askyl¨a,
P.O. Box 35 (Agora),
FI-40014 Jyv¨askyl¨a, Finland
aleator@cc.jyu.fi
Jim Torresen
University of Oslo,
Department of Informatics,
P.O. Box 1080 Blindern,
0316 Oslo, Norway
jimtoer@ifi.uio.no
Leonardo Trujillo
CICESE, Research Center,
Divisi´on de F´ısica Aplicada
Centro de Investigaci´on
Cient´ıfica y de Educaci´on
Superior de Ensenada, B.C.,
Km. 107 Carretera
Tijuana-Ensenada,
22860, Ensenada, B.C., M´exico
trujillo@cicese.mx
Israel Vite Silva
Cinvestav,
Department of Computing,
Av. IPN 2508. 07360,
Mexico City, M´exico
ivite@
computacion.cs.cinvestav.mx
Bartosz Wieloch
Institute of Computing Science,
Poznan University of Technology,
Piotrowo 2, 60965 Pozna´n, Poland
bwieloch@cs.put.poznan.pl
Moritoshi Yasunaga
University of Tsukuba,
Graduate School of Systems and
Information Engineering,
1-1-1 Ten-ou-dai,
Tsukuba, Ibaraki, Japan
yasunaga@cs.tsukuba.ac.jp
Mengjie Zhang
School of Enginering and
Computer Science,
Victoria University of Wellington,
P.O. Box 600,
Wellington, New Zealand
mengjie.zhang@ecs.vuw.ac.nz
Evolutionary Image Analysis
and Signal Processing
Texture Image Segmentation Using an
Interactive Evolutionary Approach
Cynthia B. Pérez, Gustavo Olague, Evelyne Lutton, and Francisco Fernández
Abstract. This work presents the Interactive Evolutionary Segmentation algorithm,
I-EvoSeg, an extension of the EvoSeg algorithm [18]. The proposed approach uses
texture information as image features and identifies regions automatically using a
homogeneity criterion. Furthermore, I-EvoSeg complements the chosen texture in-
formation with direct human interaction in the evolutionary optimization process.
Interactive evolution helps to improve results by allowing the algorithm to adapt
using the new external information based on user evaluation. Texture information
is extracted from the Grey Level Co-occurrence Matrix (GLCM) using statistical
descriptors. The fitness evaluation of the I-EvoSeg algorithm is twofold: (a) Internal
fitness provided by the local and global minimum distance between regions and (b)
External fitness that depends on the expertise of the user who participates during
the evaluation process. We tested I-EvoSeg using texture images and compared it
with the standard EvoSeg algorithm. Experimental results show that the interactive
approach produces qualitatively better segmentation.
1 Introduction
Human vision is a complex process that is not yet completely understood despite
several decades of research from the standpoint of natural science and artificial
Cynthia B. Pérez and Gustavo Olague
CICESE, Research Center, División de Física Aplicada
Centro de Investigación Científica y de Educación Superior de Ensenada,
B.C., Km. 107 Carretera Tijuana-Ensenada, 22860, Ensenada, B.C., México
e-mail: cbperez@cicese.mx,olague@cicese.mx
Evelyne Lutton
INRIA Rocquencourt, Complex Team
Domaine de Voluceau BP 105
78153 Le Chesnay Cedex, France
e-mail: evelyne.lutton@inria.fr
Francisco Fernández
University of Extremadura, Computer Science Department
Centro Universitario de Merida, C/Sta Teresa de Jornet, 38. 06800 Mérida, Spain
e-mail: fcofdez@unex.es
S. Cagnoni (Ed.): Evolutionary Image Analysis and Signal Processing, SCI 213, pp. 3–19.
springerlink.com
c
Springer-Verlag Berlin Heidelberg 2009
4 C.B. Pérez et al.
intelligence. For example, the detection of a camouflaged chameleon in the desert is
a perceptual task that can be achieved by some human observer; however, this task
is more difficult for a computer system. The cause of failure is the difficulty in sep-
arating the reptile from the environmental background, a task that requires different
typesof information,e.g. surfacebrighteness,shape,colour, texture andmovements.
In computer vision, the complex cognitive process of identifying colours, shapes,
textures and automatically grouping them into separate objects within a scene is
called image segmentation, which is still an open line of research despite years of
formal inquiry.
Image segmentation is a process in which an input image is partitioned into re-
gions that are homogeneous according to some group of characteristics, e.g. texture
information. Formally, image segmentation could be defined as follows:
Definition 1. Segmentation of I is a partition P of I into a set of M regions R
m
,
m = 1,2, ..., M, such that:
1)
M
m=1
R
m
= I with R
m
R
n
= /0, m = n
2) H (R
m
)=true m
3) H (R
m
R
n
)= false R
m
and R
n
adjacent
(1)
where I is the image and H is the predicate of homogeneity. Thus, each region in a
segmented image needs to simultaneously satisfy the propertiesof homogeneityand
connectivity [1]. A region is homogeneous if all of its pixels satisfy a homogene-
ity predicate defined over one or more pixel attributes such as intensity, texture or
colour. Moreover,a region is said to be connected if a connected path exists between
any two pixels within the region. The bibliography regarding image segmentation
techniques is very extensive; therefore, we limit ourselves to a brief overview of
the subject and the reader is directed to more substantial reviews, such as [2–4], for
further information.
Segmentation methods can be classified as histogram based [5], graph based [6–
8] or region based [9], to mention but a few general categories. The first category
algorithms compute an image histogram and the regions are localized through its
peaks and valleys. Thresholding techniques can obtain good segmentation, where
images include two different regions because histograms disregard the spatial rela-
tionship of the image. Graph-based methods aim to extract the global image infor-
mation by treating the segmentation process as a graph-partitioning problem. The
region based scheme is based on the homogeneity criterion where adjacent pix-
els belong to the same region if they have similar features such as grey, colour or
texture values. This approach is used in the proposed I-EvoSeg algorithm, and is
described next. The split and merge method is widely used in this approach follow-
ing a seeded region growing technique, where a set of initial seeds along the image
are taken as input information in order to assemble the regions. The initial seeds
represent the number of possible regions to be segmented. However, the problem of
Texture Image Segmentation Using an Interactive Evolutionary Approach 5
automatically selecting the number and positions of the initial seeds is not a trivial
task because is not known a priori how many regions exist on the image and where
they are located. Hence, an optimization technique could be useful to define the
number and the location of regions in the segmented image.
Nowadays, evolutionary algorithms are known as a powerful stochastic optimiza-
tion technique and their application to image processing and computer vision has
increased mainly due to the robustness of the approach [10]. In the evolutionary
computer vision community, there are a number of works dealing with image seg-
mentation [1, 11–13]. On the other hand, Interactive Evolutionary Computation
(IEC) is a general term employed in methods of evolutionary computation that use
human evaluation. The idea of IEC is to involve a human expert during the on-line
evaluation of the evolutionary algorithm. Human evaluation is helpful when the fit-
ness criterion cannot be formulated explicitly, it is not well defined or sometimes
when it is necessary to escape a local optimum. Thus, the interactive approach al-
lows a faster convergencetowards the most promising individuals of the population.
Recent advances in IEC have initiated many attractive works, such as [11, 14–16],
where the basic goal is to allow a human user to tame and the adapt random be-
haviour of the system into a tractable problem [17].
This chapter presents a novel approach to region-based segmentation using IEC.
Our approach to image segmentation is based on analyzing texture information ex-
tracted from the Grey-Level Co-occurrence Matrix (GLCM) and combining it with
the user expertise. I-EvoSeg, the interactive evolutionary segmentation algorithm
presented in this chapter, attempts to identify how many homogeneous regions exist
in the scene while it adapts the evaluation criterion by considering user interaction
and texture statistics.
The remainder of this chapter is organized as follows. Section 2 describes the
GLCM and texture descriptors that are used for texture analysis. Section 3 intro-
duces the I-EvoSeg algorithm giving emphasis to the explanation on how interactive
evolutionwas applied to the segmentation problem. Section 4 shows the experimen-
tal results obtained using I-EvoSeg and compares them with the EvoSeg algorithm
[18]. Finally, Sect. 5 gives some concluding remarks.
2 Texture Analysis
Textureanalysis is an importantand useful area of study in computer vision; it com-
prises problems like texture classification, texture segmentation, texture synthesis
and shape from texture. A given application of texture analysis usually falls into
more than one category; our work is focused on texture classification and texture
segmentation. The difficulty of the problem can be related to the fact that real world
textures are complex to model and analyze. However, researchers agree that texture
images exhibit elementary patterns that are repeated periodically within a given re-
gion. These textures can be classified as rough or smooth textures, coarse or fine
textures and many others.
6 C.B. Pérez et al.
For instance, Hawkins [19] proposed the following texture definition: “The no-
tion of texture appears to depend upon three ingredients: (i) some local ‘order’ is
repeated over a region which is large in comparison to the order’s size, (ii) the or-
der consists in the nonrandom arrangament of elementary parts, and (iii) the parts
are roughly uniform entities having approximately the same dimensions everywhere
within the textured region”.
Historically, the most commonlyusedmethodsfor describingtextureinformation
are statistical approaches, which include first-order, second-order and higher-order
statistical methods. These methods analyze the distribution of specific image prop-
erties using every pixel contained in the image. We are interested in second-order
statistical methods, which represent the joint probability density of the intensity
values between two pixels separated by a given vector V. This information is coded
using the GLCM denoted by M
i, j
.
Formally, the GLCM M
i, j
(
π
) defines a joint probability density function
f(i, j|V,
π
),wherei and j are the grey levels of two pixels separated by a vector
V ,and
π
= V, R is the parameter set for M
i, j
(
π
). The GLCM identifies how often
pixels that define a vector V (d,
θ
) and that differ by a certain amount of intensity
value
Δ
= i j appear in a region R of a given image I
L×L
. Here, V defines the dis-
tance d and orientation
θ
between the two pixels. The direction of V can or cannot
be taken into account when computing the GLCM.
An example of GLCM is illustrated in Fig. 1, where the distance d is set as 1 and
the direction
θ
is set as 0
.
0
1
2
3
4
5
6
7
0 2 2 2 3
2 2 3 3 3
0 0 1 1 1
0 0 1 1 1
2 2 3 3 3
. . . . . . . . . . . . . . . . . .
Gray Levels
256
Gray Levels j
i
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
2 2 1 0 0 0 0 0 0 0 0
0 4 0 0 0 0 0 0 0 0 0
0 0 4 3 0 0 0 0 0 0 0
. . .0 1 2 3 4 5 6 7 8 9 10 256
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
.
.
.
. . .
0 0 0 0 0 0 0 0 0 0 0
0
0
0
0
0
0
0
0
Image
.
.
.
. . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . .
. . . . . . . . . . .
. . . . . . . . . . .
. . . . . . . . . . .
. . . . . . . . . . .
. . . . . . . . . . .
y
x
Co−occurrence Matrix
Fig. 1 GLCM example
The GLCMpresentsa problem when the numberof differentgreylevels in region
R increase, resulting in difficulty in handling or using directly due to the dimensions
of the GLCM. Fortunately, the information encoded in the GLCM can be expressed
by a varied set of statistically relevant numerical descriptors. Descriptors extracted
from M
i, j
include the following: Entropy, Homogeneity, Local Homogeneity, Con-
trast, Moments, Inverse Moments, Uniformity, Maximum Probability, Correlation
and Directivity [20, 21]. Such descriptors may be defined in the spatial domain,
such as those extracted from the GLCM, or can be extracted in other frequency
domains.
Texture Image Segmentation Using an Interactive Evolutionary Approach 7
2.1 Texture Descriptors
Texturedescriptorsare computed directly from GLCM thereby reducing the dimen-
sionality of the information that is extracted from the image I of size L×L pixels.
Extracting each descriptor effectively maps the intensity values of each pixel to a
new dimension. Texture descriptors used in the I-EvoSeg algorithm are presented
next, along with an example of its corresponding image:
- Correlation. Correlation is a measure of grey level linear dependence be-
tween the pixels at the specified positions relative to each other. Near pixels
have more correlation than far pixels.
S =
1
N
c
.
σ
x
.
σ
y
|
L1
i
L1
j
(im
x
)( j m
y
)M(i, j) |
where
m
x
=
1
N
c
i
j
iM(i, j)
m
y
=
1
N
c
i
j
jM(i, j)
σ
2
x
=
1
N
c
i
j
(im
x
)
2
M(i, j)
σ
2
y
=
1
N
c
i
j
( j m
y
)
2
M(i, j)
N
c
is the number of occurrences in M.
Correlation
Original Image
D34 D84
D15
D34D9
- Entropy.A term more commonly found in thermodynamics or statistical me-
chanics. Entropy is a measure of the level of disorder in a system. Images of
highly homogeneous scenes have a low associated entropy, while inhomoge-
neous scenes pose a high entropy measure. The GLCM entropy is obtained
with the following expression:
H = 1
1
N
c
.ln(N
c
)
L1
i
L1
j
M(i, j).ln(M(i, j)).
δ
where
δ
= 1ifM(i, j) = 0and0otherwise.
Entropy
- Local Homogeneity. This measure provides the local similarity of the im-
age data using a weight factor that gives small values for non-homogeneous
images when i = j.
G =
1
N
c
L1
i
L1
j
M(i, j)
1+(i j)
2
Local Homogeneity
- Contrast. Opposite to homogeneity. It is a measure of the difference between
intensity values of the neighbouring pixels.
C =
1