Contextual and Hierarchical Classification of Satellite Images Based on Cellular Automata

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 53, NO. 2, FEBRUARY 2015 795

Contextual and Hierarchical Classification ofSatellite Images Based on Cellular Automata

Moisés Espínola, José A. Piedra-Fernández, Rosa Ayala, Luis Iribarne, and James Z. Wang

Abstract—Satellite image classification is an important tech-nique used in remote sensing for the computerized analysis andpattern recognition of satellite data, which facilitates the auto-mated interpretation of a large amount of information. Today,there exist many types of classification algorithms, such as paral-lelepiped and minimum distance classifiers, but it is still necessaryto improve their performance in terms of accuracy rate. On theother hand, over the last few decades, cellular automata havebeen used in remote sensing to implement processes related tosimulations. Although there is little previous research of cellularautomata related to satellite image classification, they offer manyadvantages that can improve the results of classical classificationalgorithms. This paper discusses the development of a new classi-fication algorithm based on cellular automata which not only im-proves the classification accuracy rate in satellite images by usingcontextual techniques but also offers a hierarchical classification ofpixels divided into levels of membership degree to each class andincludes a spatial edge detection method of classes in the satelliteimage.

Index Terms—Cellular automata, image classification, patternrecognition, remote sensing.

I. INTRODUCTION

R EMOTE sensing has been used in countless environmen-tal applications with the aim of solving and improving all

sorts of problems: soil quality studies, water resource research,meteorology simulations, and environmental protection, amongothers [14]. To solve all of these problems, one must collect andprocess huge amounts of satellite data, which creates one ofthe most difficult problems facing remote sensing [8]. Amongall of the techniques used in remote sensing to help analystexperts interpret the data gathered, classification algorithms arethe most useful and promising. These classification algorithmsfor satellite images group together image pixels into a finitenumber of classes, which helps in interpreting a great deal ofdata contained in the spectral bands [44]. When applying aclassification algorithm to a satellite image, the data obtained

Manuscript received February 4, 2013; revised June 17, 2013, November 18,2013, April 2, 2014, and May 11, 2014; accepted May 21, 2014. This work wassupported by the EU European Regional Development Fund and the SpanishMinistry of Economy and Competitiveness (MINECO) under Project TIN2010-15588, by the Andalusian Regional Government (Spain) under Project P10-TIC-6114, and by the CEiA3 and CEIMAR consortia. The work of J. Z. Wangwas supported by the National Science Foundation under Grant 1027854.

M. Espínola, J. A. Piedra-Fernández, R. Ayala, and L. Iribarne are with theDepartment of Informatics, University of Almería, 04120 Almería, Spain.

J. Z. Wang is with the College of Information Sciences and Technology, ThePennsylvania State University, University Park, PA 16802 USA.

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TGRS.2014.2328634

by the satellite sensors as digital levels are changed into acategorical scale that is easily interpreted by analyst experts.The resulting classified image is a thematic map of the originalsatellite image, and pixels belonging to the same class sharesimilar spectral characteristics.

The results provided by classification algorithms of satelliteimages have many political, social, and environmental appli-cations. These results are very important for any problem thatrequires the use of geographic information systems (GIS) forcritical information, such as calculating the growth of urbanland in cities in a given time interval, monitoring environmen-tal quality after natural disasters, creating Global PositioningSystem maps automatically, preventing natural disasters likefires from spreading, avoid snow avalanches, evaluating riskmanagement of natural resources, or studying climate changeevolution in risk areas. Classification algorithms are the basis ofGIS, and for that, it is very important to provide optimal resultsnot only in the classification accuracy rate obtained but also inthe amount of useful information offered after the classificationprocess. Therefore, if the classification process is improved byreducing the error margin in the labeling of each pixel and byincreasing the amount of useful information offered, the GISperformance could also be improved because a very importantfeature for the correct behavior of a GIS is the correct identifica-tion of each pixel with its corresponding class. There are manyclassification algorithms of satellite images, and the use of aparticular one depends on the analyst expert’s knowledge aboutthe study zone. However, most classical algorithms presentthree major problems.

First, although there are a large number of satellite imageclassification algorithms, it is still necessary to improve theirperformance in terms of accuracy rate [26]. In general, classi-fication algorithms work acceptably well if the spectral prop-erties of the pixels determine the classes well enough or if theimages are not noisy. However, if there are some classes witha high degree of heterogeneity grouping pixels with differentcharacteristics that may belong to several classes (uncertainpixels) or the images are altered with a Gaussian impulse-type noise (noisy pixels), the resulting image may have manytiny areas (often a pixel) that are misclassified. All of theseproblems cause a loss of classification accuracy rate. To solvethese problems, we can apply contextual postclassification al-gorithms that use contextual data in addition to spectral data.Several contextual postclassification algorithms use averagevalues or texture description to improve the spectral classi-fication. However, such approaches generally require the useof three algorithms: a preclassification algorithm to eliminatenoisy pixels, a classification algorithm, and a postclassification

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796 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 53, NO. 2, FEBRUARY 2015

algorithm to improve the classification of uncertain pixels.Grouping the three algorithms into one could improve theclassification accuracy rate based on spectral–contextual data.

A second problem in regard to the current classification algo-rithms of satellite images is that the results are too rigid becauseeach pixel is labeled in its corresponding class regardless of itsmembership degree. Only the fuzzy classification algorithmsprovide such information, not the classical ones. It wouldbe helpful if we use an algorithm that offers a hierarchicalclassification divided into levels of quality that analyst expertscould use to determine which pixels are closer to their classesand which are more distant in the feature space in order to detectthe doubtful pixels.

Third, in some studies, it would be desirable to obtain addi-tional information such as edge detection from the classificationprocess. It may also be desirable to locate the satellite imagepixels that cause the most problems in the classification process.It is therefore important to customize the classification processto obtain the largest number of possible results.

This paper reports on the development of an algo-rithm based on cellular automata (ACA), which solvesthe three problems described, providing improved spectral–contextual results divided into levels of membership degree foreach class. This allows the analyst experts to have as much in-formation as possible to improve the subsequent interpretationof the results. Thus, ACA optimizes the functionality of anyGIS that uses spectral–contextual results because it improvesthe classification results of satellite images. Cellular automatahave been widely used by the scientific community to simulatethe behavior of complex systems [45] and, in the field of remotesensing, to implement simulation of environmental and weatherprocesses in satellite images [30], but they have been used verylittle to implement classification algorithms of satellite images[9], [46].

The rest of this paper is structured as follows. Section IIdescribes the classification problems of satellite images inclassical algorithms. Section III describes the mathematicaldescription of cellular automata and their applications in remotesensing simulation processes. In Section IV, this paper focuseson the use of cellular automata to classify satellite images(ACA), improving the characteristics and solving the problemsof the classical classification algorithms. Section V describesthe experimental features, and Section VI describes the resultsof the work. Finally, Section VII shows some conclusion andfuture work.

II. PROBLEMS OF CLASSICAL

CLASSIFICATION ALGORITHMS

Classification algorithms of satellite images can be dividedinto two main categories: supervised and unsupervised algo-rithms [47]. The use of supervised or unsupervised algorithmsin the classification process depends on the analyst expert’sknowledge of the satellite image study area [4], [41]. De-spite the large number of classification algorithms of satel-lite images, all algorithms have limitations that prevent themfrom being fully reliable in terms of classification accuracyrate [38]. These limitations are increased when some classes

Fig. 1. (a) Parallelepiped. (b) Minimum distance.

have a high degree of heterogeneity because it complicatesthe grouping of pixels with different characteristics that maybelong to several classes (uncertain pixels) or when the imagesare altered with a Gaussian impulse-type noise (noisy pixels),causing the resulting image to have lots of tiny areas (oftena pixel) which are misclassified. In this paper, we focus onsolving the classification problems of two classical supervisedclassification algorithms of satellite images: parallelepiped andminimum distance. Fig. 1 shows a graphical representation ofthe classification process with these two classical supervisedalgorithms from the viewpoint of feature space and taking intoaccount three different classes in the satellite image.

The parallelepiped algorithm assigns pixel x to class A if itsSV (spectral values) are included in the domain area of thatclass in the different N bands while considering their centroidvalue and dispersion range, as shown in the following formula:

CV A,n −DRA,n ≤ SVx,n ≤ CV A,n +DRA,n (1)

whereCV A,n centroid value of class A in band n;DRA,n dispersion range of class A in band n;SVx,n spectral value of pixel x in band n;n = 1, 2, . . . , N bands of the satellite image.The parallelepiped algorithm has the disadvantage that some

pixels may be unclassified after the process because their digitalvalues are not within a range of any class (as you can see inFig. 1). It can also happen that a pixel is wrongly classified intoseveral classes.

The minimum distance algorithm assigns pixel x to classA with which there is less spectral Euclidean distance withrespect to its centroid taking into account the different N bandsinvolved in the classification process, as shown in the followingformula:

dx,A =

√√√√Nbands∑n=1

(SVx,n − CV A,n)2 (2)

wheredx,A distance between pixel x and class A;SVx,n spectral value of pixel x in band n;CV A,n centroid value of class A in band n;n = 1, 2, . . . , N bands of the satellite image.Once all of the distances between the pixel and the classes

have been calculated, the algorithm assigns the pixel to the

ESPÍNOLA et al.: CLASSIFICATION OF SATELLITE IMAGES BASED ON CELLULAR AUTOMATA 797

nearest class using the following formula:

class(x) = {A|dx,A = minimum}. (3)

The minimum distance algorithm has the disadvantage ofbeing prone to commission errors (assigning a pixel to a wrongclass) because the variance of each one of the classes is notconsidered in the classification process.

If we add some classes with a high degree of heterogeneityand the presence of Gaussian impulse-type noise in the satelliteimages, the classification accuracy rate obtained by these classi-cal supervised classification algorithms decreases considerably.

Most of these disadvantages can be overcome with the use ofcellular automata that use contextual data taking into accountnot only the pixel’s spectral values but also its surroundingpixels. This paper presents some research on how these twosupervised classification algorithms (parallelepiped and mini-mum distance) can be improved using techniques of cellularautomata modifying the mathematical formulas shown in thissection.

III. CELLULAR AUTOMATA

A cellular automaton is a mathematical model which consistsof a set of cells usually distributed in a matrix form [28]. Inrecent years, cellular automata have become a powerful toolapplied in remote sensing especially to implement any kindof simulation process in satellite images. From a mathematicalpoint of view, a cellular automaton is a set of six components,as shown in the following expression:

CA = (d, r,Q,#, V, f) (4)

whered|d > 0 spatial dimension of the cellular automaton. The

position of each cell is shown by a vector of Zd.Given d = 1, it is a 1-D cellular automaton withcells position in Z; given d = 2, it is a bidimen-sional cellular automaton with cells position inZ × Z; given d = 3, it is a tridimensional cellularautomaton with cells position in Z × Z × Z, andso on;

r index that shows the neighborhood dimension, i.e.,how many neighbors interact with each cell of thecellular automaton;

Q set of states per cell. The set of states is finite,equal for all of the cells of the cellular automa-ton, and it cannot be changed during the cellularautomaton application process.

# state called quiescent. This state shows inactivityin the cells of the cellular automaton, and it is oftenused as the initial state of the cells.

V neighborhood vector which has r different el-ements from Zd. The most common types ofneighborhood in a cellular automaton are 4 neigh-bors (von Neumann neighborhood), 8 neighbors(Moore neighborhood), and 24 neighbors (ex-tended Moore neighborhood). Fig. 2 shows themost common types of neighborhood that we can

Fig. 2. (a) Von Neumann neighborhood. (b) Moore neighborhood. (c) Ex-tended Moore neighborhood.

find in a regular cellular automata. The neighbor-hood vector V is a subset of Zd, as shown in thefollowing expression:

V ⊂ (Zd)r; (5)

f cellular automaton transition function. It takes asinput arguments the states of the current cell andits neighborhood and returns a new state for thecurrent cell. The transition function f uses a setof rules that specifies the changes of the cellularautomaton cell states, and it is applied to each cellthrough a finite number of iterations, as shown inthe following expression:

f : Qr+1 → Q

qi(t) = f (qi−r(t− 1), qi−r+1(t− 1), . . . , qi+r(t− 1)) (6)

where qi(t) is the state of cell i at time t. Thechanges in cell states of the cellular automatonoccur in discrete time form. In each iteration, thewhole cells stored in Zd are checked, and the rulesare applied through the transition function f toeach cell taking into account the neighborhood Vto change its state Q to its corresponding state.

When we work with satellite images, we usually considereach pixel of the image as a cell of a bidimensional cellularautomaton (d = 2), we normally use the Moore neighborhood(r = 8), we assign to each cell a defined set of states to performthe corresponding simulation (Q = q1, q2, . . . , qn), and we ap-ply the different rules (R = r1, r2, . . . , rm) in each iteration ithrough the transition function f .

Therefore, cellular automata have an evolution process be-cause the cells are always changing their states through thedifferent iterations [50]. From this point of view, cellular au-tomata have become a powerful tool to simulate environmentalprocesses in satellite images.

Cellular automata have been widely used for environmentalsimulations and models like simulating snow-cover dynamics[33] or snow avalanches [3], modeling vegetation system dy-namics [6] or land use dynamics [32], simulating lava flows[49], simulating forest fire spread for the prediction of disasters[27], [40], and modeling species competition and evolution [13].

There is also cellular automata research related to urbanand complex social phenomena simulations: a system for theunderstanding of urban growth [12], an advanced urban mesh


generation model in urban design [11], a model of vehiculartraffic in a city [2], and a traffic noise control system [43].

As far as medicine is concerned, we can find the creationof a cellular-automata-based model for therapies against HIVinfection [48], a model that simulates how people are infectedby a periodic plague [19], the detecting of Vibrio cholerae byindirect measurement of climate and infectious disease [35],and a model for simulating cancer growth [25].

Cellular automata have been applied not only to implementsimulation processes but also to sort out a wide range ofproblems of different types: new cryptographic systems basedon the cellular automata approach [17], [24], new modularillumination systems [7], new image processing techniques likeimage enhancement (noise reduction filters) and edge detectionwith cellular automata [42], and new texture characterizationsystems in images [31].

However, in the ambit of satellite image classification, thereis little previous research [37], [39] related to cellular automatadespite the many advantages they can offer, like getting con-textual techniques or a hierarchical classification using someproperties of cellular automata, such as the use of iterations.

In the next section, we propose a new application of cellularautomata: a novel supervised classification algorithm based oncellular automata which not only improves the classificationaccuracy rate but also gives us information on the membershipdegree of each pixel to its class through a hierarchical classifi-cation divided into levels of reliability.

IV. CLASSIFICATION WITH CELLULAR AUTOMATA

This paper presents a new methodology for implementing asupervised classification algorithm of satellite images (ACA)[20]–[23] that classifies the image pixels based on both spectraland contextual data of each pixel, and it also provides hier-archical classification results divided into hierarchical levelsof membership degree to each class. Thus, ACA improvesthe results obtained by other classical supervised classificationalgorithms as described in current literature.

ACA is a supervised classification algorithm, implementedwith Visual C++ and Erdas Imagine Toolkit, based on a multi-state cellular automaton that allows analyst experts to introducenew states and rules to the cellular automaton in order tocustomize as much as possible the classification process ofsatellite images. In this sense, there is also research related tocellular automata combined with artificial neural networks thatdefine the rules with a higher degree of objectivity [34], [36].We must take into account the following associations between acellular automaton and the basic elements of a generic processof supervised classification of satellite images.

1) Each pixel of the satellite image corresponds to a partic-ular cell of the cellular automata grid.

2) Each different class of the supervised classification pro-cess is represented by a particular state of the cellularautomaton.

3) The neighborhood of each cell may consist of the 4surrounding pixels (von Neumann neighborhood), the8 nearest cells (Moore neighborhood), or even the 24

surrounding pixels (extended Moore neighborhood) inorder to customize the final classification process.

4) The transition function f must correctly classify eachpixel of the image based on the features of the current celland its neighborhood, using mixed spectral and contex-tual data to improve the results obtained by the classicalsupervised classification algorithms.

The analyst expert of satellite images must establish thedesired behavior of ACA through the states and rule definitionof the cellular automaton to adjust to the classification processin order to customize the final classification process. In thispaper, we have implemented a version of ACA (ACA v1.0)whose main goals are the following.

• Objective #1. Improve the classification accuracy rateobtained by the classical parallelepiped and minimumdistance supervised classification algorithms by means ofcontextual information to avoid misclassifying the uncer-tain or noisy pixels. ACA must classify the problematicpixels, taking into account not only their spectral data(ambiguous for uncertain pixels, wrong for noisy pix-els) but also their neighbor’s contextual data in order toimprove the final classification accuracy rate. With thisobjective, ACA must merge the following three techniquesinto one algorithm: preclassification process (noisy pixelelimination), supervised classification process, and post-classification process (uncertain pixel refinement).

• Objective #2. Obtain a hierarchical classification dividedinto hierarchical layers of membership degree to eachclass. ACA must classify only those pixels which arewithin a maximum spectral distance in the featured spacewith regard to the center of their corresponding class, andsuch distance must increase in each iteration. Thus, ACAwill get a hierarchical classification divided into hierarchi-cal layers of membership degree to each class, where thefirst layers offer more reliability than the last ones becausethe pixels of the first layers are closer spectrally to theirclasses, and consequently, they have a higher membershipdegree. These results can be very useful for the subsequentinterpretation of the results made by the analyst experts.Moreover, this objective helps the first one because theuncertain and noisy pixels, usually further from the centerof their classes, must be classified in the last iterations ofthe cellular automaton and they use, as neighbors, pixelsthat are very likely to be classified in previous iterations, sothey offer more reliability in terms of membership degreeto their classes, improving the total accuracy rate of theoptimized classification process.

• Objective #3. Get a detailed list of the uncertain and noisypixels, which can be useful if the classification processfails even when using contextual techniques, and get alist of those pixels that determine the spatial edges of theimage classes, comparing the class of each pixel with theclasses of its neighbors through the cellular automatonrules. In this way, it is easy to determine the spatial edgesof the image classes because, if the class of a pixel isdifferent from some of the classes of its neighbors, thispixel is a spatial edge of its class in the image. Conversely,


if the class of a pixel is the same as all of the classesof its neighbors, this pixel is called focus to differentiatefrom edge pixels. Therefore, we can analyze the resultsfrom two different perspectives: spectral level (uncertainand noisy pixels) and spatial level (edge and focus pixels).This second choice, spatial level, is of interest because thespatial edge detection of classes is also a problem in thescope of remote sensing.

ACA is based on the parallelepiped and minimum distancesupervised classifiers. The cellular automaton selects the re-sults of one classification algorithm and subsequently appliesthe rules of its transition function f . In each iteration of thecellular automaton, the permitted spectral radius distance ofsearch in the feature space (called threshold) increases. In thefirst iterations, ACA classifies the pixels whose distance withrespect to their class is very low. In the next iterations, thethreshold increases again so that the majority of image pixelsare classified. The uncertain and noisy pixels are classified inthe last iterations. The transition function f takes into accountthe inputs in order to apply the cellular automaton rules.

1) Possible classes offered by the selected supervised al-gorithm (parallelepiped or minimum distance): class setof current pixel (maybe one class or several classesfor uncertain pixels that are near two or more classes).The spectral classification classes are given by a paral-lelepiped or minimum distance algorithm modified withcellular automata techniques.

2) Neighborhood states: states of current pixel neighbor-hood. This neighborhood can be von Neumann, Moore,or extended Moore type. The cellular automaton neigh-borhood is chosen by the user before undergoing theclassification process in order to customize the resultsobtained as much as possible.

3) Cellular automaton iteration: the iteration of the cellularautomaton that specifies the current quality level of theclassification process.

A. Mathematical Definition of ACA

ACA is based on a multistate cellular automaton, and eachcell of the grid has three independent and different states,namely, class, quality, and type, which correspond to the threeobjectives outlined. The first state, class, corresponds to theclass in which each pixel of the satellite image is classifiedby using not only its spectral values but also contextual data.This state allows us to improve the classification accuracyrate (objective #1 of ACA v.1.0). The second state, quality,indicates the iteration number of the cellular automaton inwhich each image pixel is classified. This state allows usto obtain the hierarchical classification based on hierarchicallevels of membership degree to each class (objective #2 of ACAv.1.0). The third state, type, provides additional information andcorresponds to the pixel type: uncertain, noisy, edge, or focus.This state allows us to get a detailed list of uncertain, noisy,and class edge pixels (objective #3 of ACA v.1.0). These threestates of the cellular automaton can take the following values.

1) State #1. [class] = spectralClass (defined by the train-ing group) or emptyClass (pixels that have not beenclassified yet).

2) State #2. [quality] = 1..numIterations (iteration of thecellular automaton that determines the hierarchical layersof membership degree to each class; the first iterations aremore reliable in terms of classification accuracy rate thanthe final ones).

3) State #3. [type] = uncertain (doubtful pixels), noisy(noisy pixels), edge (spatial border pixels of classes), andfocus (pixels that are not uncertain, noisy, or edge).

State #1 [class] can take any spectral class previously definedin the training group by the analyst expert or empty class(quiescent state) for pixels not classified yet. Therefore, in thefirst iteration of the cellular automaton, all cells have emptyclass in this state. State #2 [quality] takes the value of thecellular automaton iteration where the pixel is classified, avalue between 1 and the maximum number of iterations. Thisinformation enables us to know in which iteration each pixel isclassified, which allows us to calculate the membership degreeto its class, as shown in the following formula:

mdx,A =iterationA,finish − iterationx,classified(A)

iterationA,finish(7)

wheremdx,A membership degree of pixel x to

class A;iterationA,finish iteration in which all of the pixels of

class A have been classified;iterationx,classified(A) iteration in which pixel x has been

classified into class A.State #3 [type] can take the type of pixel: uncertain, noisy,

edge, or focus. The cellular automaton rules that achieve thethree ACA objectives are the following.

1) Rule #1. If the number of spectralClass is 0 because thecurrent pixel has wrong spectral values:[class][quality][type] =

{majority class of the neighborhood, iteration, noisy}.2) Rule #2. If the number of spectralClass is 1 and all

of the neighborhood class states are emptyClass or thesame as current pixel then:[class][quality][type] =

{spectralClass, iteration, focus}.3) Rule #3. If the number of spectralClass is 1 and any

neighborhood class state is different from current pixelclass then:[class][quality][type] =

{spectralClass, iteration, edge}.4) Rule #4. If the number of spectralClass is bigger than

1 then:[class][quality][type] =

{majority class of the neighborhood among thedubious classes, iteration, uncertain}.

Each rule identifies one of the four types of pixels of state #3:rule #1 for the noisy pixels, rule #2 for the focus type, rule #3for the edge type, and rule #4 for the uncertain pixels. By meansof rules #1 and #4, ACA improves the classification accuracy


rate obtained through contextual techniques (objective #1), andby means of rules #2 and #3, ACA gets a list of geographical-spatial focus and edges in the satellite image (objective #3).Through the iterative behavior of the cellular automaton, ACAoffers a hierarchical classification divided into layers of mem-bership degree for each class (objective #2). Moreover, the firstrule is characterized by an error in the classification process, sothe potential number of spectral classes is zero. In the secondand third rules, the first condition is the same: the numberof spectral classes obtained in the supervised classification(through the modified parallelepiped or minimum distance al-gorithm) is equal to 1. Therefore, we are dealing with pixelswhich we can definitely classify (focus or edge certain pixels).This condition changes in the fourth rule because uncertainpixels are known for belonging to several classes.

The cellular automaton of ACA can be expressed mathemati-cally, following the nomenclature of expressions (4)–(6), by thefollowing expression:

ACA=(d, r,Q,#, V, f)

=(2×N,{4|8|24} , [qclass, qquality, qtype], [∅, ∅, ∅],V,f)(8)

where— d = 2×N : spatial dimension of the ACA cellular auto-

maton is 2, so cells are distributed in a matrix form.However, as each pixel of the image has a total of Nvalues stored (one for each satellite image band), we areactually working on a d = 2×N dimension;

— r = {4|8|24}: neighborhood dimension may consist ofthe 4, 8, or 24 surrounding pixels in order to customizethe final classification process;

— Q = [qclass, qquality, qtype]: set of states per cell is formedby all sets of values that can take each of the three states,as shown in the following expression:

[qclass, qquality, qtype]

= [{emptyClass|spectralClass},{1| . . . |numIterations},{focus|edge|uncertain|noisy}] ; (9)

— # = [∅, ∅, ∅]: quiescent state, or initial value, is ∅ for thethree states;

— V : neighborhood vector is configurable to 4, 8, or 24surrounding neighbors of each one of the cells in allof the working dimensions, as shown in the followingexpression:

V ⊂ (Z2×N ){4|8|24}

; (10)

— f : transition function applies the four rules to each one ofthe cells along the different iterations in order to changetheir states taking into account the neighborhood chosen,as shown in the following expression:

f : Q{4|8|24}+1 → Q. (11)

TABLE IMAIN ACA ALGORITHM PSEUDOCODE

TABLE IISPECTRAL ACA ALGORITHM PSEUDOCODE

B. Main, Spectral, and Contextual ACA Algorithms

ACA consists of three algorithms: main, spectral, and con-textual. The main ACA algorithm executes the iterations ofthe cellular automaton. In each iteration, we first make aspectral classification of all of the pixels not classified yet inthe satellite image, and subsequently, we make a contextualclassification for pixels that have been classified in the currentiteration in order to improve the results provided by the spectralclassification. The threshold increases its value in each iterationof the classification process. Table I shows the main ACAalgorithm that follows the nomenclature of all of the formulasand expressions seen before.

The spectral ACA algorithm is based on classical supervisedalgorithms (parallelepiped and minimum distance) improvedby means of cellular automata techniques dividing the clas-sification process into several iterations through the thresholdincreasing. This division entails a hierarchical classification ofdifferent layers with a different level of reliability, each one interms of membership degree to each class. In this part of thealgorithm, we achieve objective #2 of ACA. Table II shows thespectral ACA algorithm that follows the nomenclature of all ofthe formulas and expressions seen before.


TABLE IIICONTEXTUAL ACA ALGORITHM PSEUDOCODE

In the function hierarchicalClass(), ACA uses a classicalsupervised algorithm modified by means of cellular automata.In the case of the parallelepiped algorithm, ACA uses thefollowing formula modified from the formula (1):

CV A,n −DRthrA,n ≤ SVj,n ≤ CV A,n +DRthr

A,n (12)

where the modified argument from formula (1) is the following:1) DRthr

A,n: dispersion range of class A in band n at iterationi of the classification process. This value is increased ineach iteration taking into account thr.

For the minimum distance algorithm, ACA uses the follow-ing formula modified from formula (3):

CA.Qj,class = {A, ∀A|dj,A ≤ thr}. (13)

ACA modifies the behavior of these classical classificationalgorithms by means of formulas (12) and (13), adjusting theirbehavior to the number of iterations of the cellular automatonthrough the parameter thr.

The contextual ACA algorithm applies the four rules of thecellular automaton. The other two objectives are achieved inthis part of the algorithm. On the one hand, ACA improvesthe classification accuracy rate obtained through contextualtechniques (objective #1 of ACA) by applying rules #1 and#4 (for noisy and uncertain pixels). On the other hand, ACAdefines the pixel type in the following order: noisy, focus,edge, or uncertain (objective #3 of ACA). Table III shows thecontextual ACA algorithm that follows the nomenclature of allof the formulas and expressions seen before.

The function classesEqual() checks whether the classof the current cell is the same as the classes of itsneighborhood, the function majorityneighborhood() ob-tains the majority neighborhood class, and the functionmajorityneighborhoodClass() obtains the majority neigh-borhood class among the dubious classes.

Fig. 3. General ACA architecture.

C. General ACA Architecture

The ACA architecture is composed of 1) the classificationwith cellular automata (ACA) and 2) the calculation of quality(classification accuracy rate), as shown in Fig. 3.

1) Classification with cellular automata (ACA). ACA haseight parameters as input arguments and produces asingle output: the classified image. Of the eight inputparameters, two are related to the original image: theimage loading function, which loads the satellite image(image.img = SV ), and the class sample loading func-tion, which loads the samples of each class selected by theanalyst experts (samples.sig = {CV ,DR}). With thesetwo components, ACA is prepared to make a supervisedclassification, although it is based on the results previ-ously obtained by a modified classical supervised classi-fication algorithm (parallelepiped or minimum distance)through the threshold (thr). ACA changes the behaviorof these classifiers by using a cellular automaton, addingthe following parameters to the supervised classificationprocess: states (CA.Q), rules, neighborhood (CA.r),and iterations (CA.nIter). The user can configure theneighborhood and iteration parameters of the cellular au-tomaton before carrying out the classification process inorder to adjust the cellular automata behavior to the studyarea and customize the final results of the classificationprocess.

2) Calculation of quality. This algorithm takes two param-eters as input arguments: the classified image throughACA (classified image = CA.Q) and the classifiedimage through an expert field work (expert classifiedimage). As a result, this algorithm produces the confusionmatrix between these two images, it shows an index ofthe accuracy rate in the cellular automaton classificationprocess, and it provides a list of wrongly classified pixelsthat relates the class to which it really belongs (expertfield work) to the class where it has been classified (ACAclassification results).


TABLE IVADVANTAGES AND DISADVANTAGES OF PARALLELEPIPED

AND MINIMUM DISTANCE

Fig. 4. (a) ACA parallelepiped. (b) ACA minimum distance.

D. ACA Improvements in Classical Algorithms

In Section II of this paper, we discussed the most commonclassification problems that exist in the parallelepiped andminimum distance supervised algorithms. The advantages anddisadvantages of these classical classification algorithms aresummarized in Table IV.

By using cellular automata, all of these disadvantages areeliminated. In the parallelepiped algorithm, all of the unclas-sified pixels disappear because the dispersion range increasesat each iteration of the cellular automaton until all image pixelsare classified, and the uncertain pixels disappear because it usescontextual information like neighborhood of each pixel if itcan belong to several classes. Furthermore, in the case of theminimum distance algorithm, the uncertain pixels misclassifiedby commission errors are greatly reduced with the contextualclassification, and thus, the variance is deemed to take intoaccount the neighboring pixels. Fig. 4 shows a graphical rep-resentation of the classification process of ACA parallelepipedand ACA minimum distance algorithms in three iterations.

V. EXPERIMENTAL FEATURES

ACA was tested under the framework of the Soleres Project:“a spatiotemporal environmental management information sys-tem based on neural networks, agents and software compo-nents.” The experiments were carried out on three seven-bandmultispectral Landsat TM satellite images for Níjar, west ElEjido, and east El Ejido, three regions in Almería (southeastSpain). Fig. 5 shows the satellite images of Níjar, west El Ejido,and east El Ejido (bands 3, 2, and 1) with the 400 × 400 window(total of 160 000 pixels) used to test ACA performance, at a30 × 30 m spatial resolution.

Fig. 5. (a) Areas of study in Almería, Spain (April 2003). (b) Níjar. (c) WestEl Ejido. (d) East El Ejido.

Fig. 6. Vegetation areas of the southeast of Spain. Níjar (red square) and ElEjido (blue squares).

Vegetation and soil in southeast Spain are extremely diverse,complicating verification of any classification algorithm, asshown in previous Soleres Project experiments [5]. Fig. 6 showsthe six main vegetation areas in southeast Spain [15], [16] withthe areas of study marked by the squares.

Specifically, the Níjar and El Ejido regions are characterizedby vegetation areas 1 and 3 and can be classified into six


TABLE VCLASS DESCRIPTION OF NÍJAR AND EL EJIDO

Fig. 7. Feature space plot of west El Ejido (bands 2–7).

classes, some of them highly diverse. Above all, El Ejido ischaracterized by the presence of an enormous number of green-houses. There are so many greenhouses in El Ejido that theycan be seen from the International Space Station in outer space,even in satellite images with low spatial resolution. Níjar alsohas greenhouses but fewer of them. Pixel classification in the“greenhouse” class is very complicated because this class is soextremely diversified, and feature spaces in its pixels may havea wide spectral range due to the different construction materialsused, like plastic or polycarbonate. Therefore, classic classifi-cation algorithms fail with this type of pixels [1], [10]. Theseregions are also characterized by the presence of the “built-upand disturbed area” class, which is also very diverse, becauseit groups pixels with different characteristics, such as buildingsand soil. The classic classification algorithms therefore fail inthis class as well. Níjar and El Ejido are also characterizedby moderately diversified classes, like “continuous pasture,”“scattered scrub with rock,” and “wetlands and open water.”Finally, Níjar and El Ejido are characterized by the presenceof the “paved road” class, with low-level diversity, as shownin Table V.

Summarizing, Níjar and El Ejido are characterized by onevery highly diverse class, one highly diverse class, three mod-erately diverse classes, and one less diverse class. Many classesare spectrally too close, as shown in Fig. 7, with the followingcolor code: C1 (blue), C2 (white), C3 (green), C4 (light brown),C5 (dark brown), and C6 (gray).

TABLE VICHARACTERISTICS OF NÍJAR, WEST EL EJIDO, AND EAST EL EJIDO

However, the satellite images of El Ejido are more difficultto classify than Níjar because there are more greenhouses in ElEjido than in Níjar, and the greenhouses are the class with themost diversity. In addition, east El Ejido has a higher concen-tration of greenhouses than west El Ejido. Specifically, Níjarhas 18% greenhouses, west El Ejido has 55%, and east El Ejidohas 71%. To further complicate classification in El Ejido, 1%noise and 2% noise were artificially added to west and east ElEjido satellite images, respectively. The noise was random andentered before ACA was applied. These percentages were cho-sen because, when the image pixels are noisy, the percentageof this type of pixels is usually very low, so there was no pointin making the percentage any higher. However, ACA greatlyimproves this type of pixels because the cellular automatonrules take the average of the noisy pixel neighbor into accountand almost always classifies it correctly. Therefore, as noiseincreases, the ACA improvement percentage is higher becauseclassic algorithms always make many mistakes in labeling thistype of pixels.

With these three images, we established three levels ofclassification difficulty: Níjar (low), west El Ejido (medium),and east El Ejido (high), in order to compare ACA performancewith different levels of classification complexity. Table VIsummarizes the characteristics of the three satellite images.

VI. RESULTS

The application of ACA to these three satellite images aimsto achieve the objectives described in Section IV: to improvethe classification accuracy rate using contextual techniques(objective #1), to construct a hierarchical classification basedon the degree of class membership (objective #2), and to detectedge, uncertain, and noisy pixels (objective #3).

A. Objective #1: Improve the Classification Accuracy RateUsing Contextual Techniques

As discussed in the previous section, the highly diversifiedfeatures of the study areas complicate their classification, andtherefore, classification algorithm accuracy rates are disap-pointing. However, ACA accuracy is better than other super-vised classification algorithm rates since the surrounding pixelsare used as the neighborhood of the transition function f inthe classification of each pixel. These image pixel relationshipsprovide an optimized contextual classification that improves thefinal results in uncertain and noisy pixels.

ACA improves the performance of classical parallelepipedand minimum distance algorithms. In the first iterations ofthe cellular automaton, there are only well-classified pixelsin the confusion matrix because the threshold is very low, somost of the pixels classified in these first iterations are in thetraining set. If the algorithm continues to run, there is a point


TABLE VIIACCURACY RATE AND COMPUTATIONAL COMPLEXITY OF CLASSIFICATION ALGORITHMS (WHERE n IS THE NUMBER

OF TRAINING INSTANCES, m IS THE NUMBER OF ATTRIBUTES, AND i IS THE NUMBER OF CA ITERATIONS)

at which all of the pixels in low and moderate diversity classeshave already been classified (C1, C3, C5, and C6), and fromthat point on, only some pixels in the high diversity classesremain unclassified (C2 and C4). This occurs at approximatelyiteration 40 during classification of the three satellite images.During the following 60 iterations, ACA refines the classifi-cation to further improve the results, correctly classifying themost difficult pixels: uncertain pixels in classes C2 and C4and noisy pixels. By iteration 100, all image pixels have beenclassified. Therefore, ACA has solved one of the main problemsof classic parallelepiped algorithm since, by using cellularautomata, there are no unclassified pixels at the end becausethe threshold increases with each iteration. Moreover, ACA hasgrouped the preclassification (noise reduction), classification,and postclassification (uncertain pixel refinement) processes.The use of cellular automata not only improves the performanceof the classic algorithms but also its classification accuracy rate:the ACA parallelepiped algorithm improves the accuracy rateof the classical parallelepiped algorithm (by 4.82% in Níjar,8.10% in west El Ejido, and 15.73% in east El Ejido), and theACA minimum distance algorithm improves the accuracy rateof the classical minimum distance algorithm (by 3.31% in Níjar,3.92% in west El Ejido, and 9.71% in east El Ejido).

In a comparison of the ACA accuracy rate with five otherwidely used classification algorithms (C4.5, multilayer percep-tron, Naive Bayes, k-NN, and RBF network), ACA is observedto provide better results. A field image of each study areamade by expert ecologists was used to calculate the accuracyrate of algorithms. All algorithms were evaluated using ten-fold cross-validation. Table VII shows the accuracy rates ofthese classification algorithms for the classification of the threeimages and their computational complexity.

Comparison of the satellite images of Níjar (low classifica-tion complexity) shows that the C4.5 and multilayer percep-tron algorithms outperform the ACA parallelepiped algorithmaccuracy rate by 5.52% and 1.47%, respectively. However, al-though the C4.5 and multilayer perceptron algorithms are moreaccurate than ACA in satellite images with low classificationcomplexity, they do not offer the additional information thatthe ACA does: hierarchical classification and edge detection.Thus, even with these accuracy rates, it is still better to useACA instead of C4.5 and multilayer perceptron if more in-formation is desired from the classification process. The ACAparallelepiped algorithm improves the accuracy rate of ACAminimum distance algorithm by 0.79%, and the ACA minimumdistance algorithm is 0.49% more accurate than Naive Bayes,2.41% better than k-NN with k = 3, and 3.22% better thanRBF network. This satellite image is the one with the lowest

Fig. 8. Accuracy rate of classification algorithms. (a) Níjar. (b) West El Ejido.(c) East El Ejido.

ACA scores, and therefore, two algorithms have better accuracyrates.

Comparison of the satellite images of west El Ejido (mediumclassification complexity) shows that only the C4.5 algorithmoutperforms the accuracy rate of ACA parallelepiped algorithmby 3.39%. The ACA parallelepiped algorithm improves the ac-curacy rate of multilayer perceptron by 1.72%, but the accuracyrate of multilayer perceptron is better than the accuracy rateof ACA minimum distance algorithm. However, the accuracyrate of ACA minimum distance algorithm is 1.53% better thanthe Naive Bayes, 3.08% better than k-NN with k = 3, and3.79% better than the RBF network. This satellite image showshow the ACA accuracy rate is better than the other algorithms,except C4.5.

Comparison of the east El Ejido satellite images (highclassification complexity) shows that the ACA parallelepipedalgorithm outperforms all of the other algorithms. The accuracyrate of ACA parallelepiped algorithm is 1.91% better thanC4.5, 5.28% better than multilayer perceptron, 9.44% betterthan Naive Bayes, 10.81% better than k-NN with k = 3, and12.53% better than RBF network. This satellite image is theone in which ACA scores are the highest because ACA providesbetter results with satellite images that have a large number ofuncertain pixels belonging to highly diverse classes, images inwhich the other classification algorithms often fail.

Regarding the computational cost, ACA is moderately com-plex because it is not as fast as k-NN, Naive Bayes, or mul-tilayer perceptron but neither is it as slow as C4.5 and RBFnetwork.

Fig. 8 shows how the accuracy rates of the classificationalgorithms used in the three satellite images evolve. It may


be seen that the ACA parallelepiped and minimum distancealgorithm accuracy rates perform better than the others sincethe ACA accuracy rate decreases more slowly as classificationcomplexity increases.

B. Objective #2: Construct a Hierarchical ClassificationBased on Degree of Class Membership

ACA produces a hierarchical classification divided into lay-ers by degree of membership in each class based on spectralproximity of the pixels to their class within the feature space.In each iteration of the cellular automaton, ACA classifiesimage pixels farthest from the center of their correspondingclass as indicated by the threshold. The range of membershipdistance permitted in each class increases with every iteration.The pixels spectrally closest to the classes are classified in thefirst iteration. The furthest pixels are classified in the followingiterations. Therefore, pixels classified in a given iteration aremore reliable in terms of classification accuracy rate thanthose classified in the following iteration and so on. Finally,the uncertain pixels are classified by contextual classificationtechniques, based on neighboring pixels correctly classifiedin previous iterations. Fig. 9 shows the classification in thethree satellite images after 100 iterations of the ACA minimumdistance algorithm with the following color code: C1 (blue), C2(white), C3 (green), C4 (light brown), C5 (dark brown), and C6(gray). The ACA parallelepiped algorithm classifications aresimilar.

Most pixels are observed to be classified in the first 40 iter-ations, and the following refine the classification and optimizeresults using contextual techniques. As shown, in iteration 40,the satellite images of El Ejido have a higher percentage ofunclassified pixels than the satellite image of Níjar because thenumber of greenhouse pixels is much larger. In the remaining60 iterations, the classification is improved using contextualtechniques to classify the uncertain and noisy pixels. Theseresults display where the most difficult pixels (uncertain andnoisy) in the satellite image are.

C. Objective #3: Edge, Uncertain, and Noisy Pixel Detection

ACA assigns not only the class (state #1) and iterationnumber to each pixel when it is classified (state #2) but also thepixel type: uncertain, noisy, focus, or edge (state #3). This thirdstate provides the expert analysts with more information fromthe classification process, enabling them to arrive at specificconclusions for each class.

Analysis of noisy pixels is important because they contributeto the improvement of the classification accuracy rate. Thenoise entered in west (1% noise) and east El Ejido (2% noise)is random, and therefore, the noisy pixels are randomly dis-tributed throughout the satellite images. The number of randompixels in each class is weighted by the sizes of the classes, andconsequently, the classes that have a higher percentage of totalpixels in each image also have a higher percentage of noisypixels. The noise introduced in each class in east El Ejido is notalways double the noise in each class in west El Ejido becausethe two images have different numbers of pixels in each class.

Fig. 9. ACA minimum distance classification process. (a) Níjar. (b) West ElEjido. (c) East El Ejido.

TABLE VIIICORRECTLY CLASSIFIED NOISY PIXELS (WEST AND EAST EL EJIDO)

It is important to highlight the percentage of well-classifiednoisy pixels because they raise the classification accuracy rate.Table VIII shows the well-classified noisy pixels in west andeast El Ejido found with the ACA parallelepiped (ACA P) andACA minimum distance (ACA MD) by class.


TABLE IXWELL-CLASSIFIED UNCERTAIN PIXELS OF NÍJAR, WEST EL EJIDO, AND EAST EL EJIDO

TABLE XEDGE AND FOCUS PIXELS OF NÍJAR, WEST EL EJIDO, AND EAST EL EJIDO

The classes with the highest percentages of well-classifiednoisy pixels are C2 and C4 because there are more pixelsin them than in the rest of the classes in the satellite image.In west El Ejido, the ACA parallelepiped algorithm correctlyclassified 0.831% of the noisy pixels, and the ACA minimumdistance algorithm correctly classified 0.803% of noisy pixelsout of a total 1%. In east El Ejido, the ACA parallelepipedalgorithm correctly classified 1.635% noisy pixels, and theACA minimum distance algorithm correctly classified 1.612%noisy pixels out of a total 2%. In both satellite images, thepercentage of well-classified noisy pixels is quite high.

Analysis of uncertain pixels allows the expert analysts tospecify the contribution of each class to the improvement inthe classification accuracy rate, which is based primarily onrefining classification of this type of pixels. The uncertain pixelsmay be either misclassified or well classified. The misclassifieduncertain pixels in each class are equal to the sum of allvalues outside the main diagonal in the corresponding row ofthe confusion matrix. The misclassified uncertain pixels aresubtracted from the total number of uncertain pixels to find thenumber of well-classified uncertain pixels in each class. Thesepixels show the improvement of ACA over classical algorithms.Table IX shows the uncertain pixels in Níjar, west El Ejido, andeast El Ejido properly classified by the ACA parallelepiped andACA minimum distance by class.

C2 and C4 are again the classes with the highest percentagesof well-classified uncertain pixels, but unlike the previous case,it is not because there are more such pixels in the satellite imagebut because these two classes are the most diversified. In theclasses with low and moderate diversities, the uncertain pixelsoften appear at the space edges, and so, their neighbors may beof any of several different classes, and ACA fails. However,in the more diversified classes, uncertain pixels may appearin places where they are surrounded by other pixels of thesame class, and therefore, ACA classifies them successfully.Classes C2 and C4 coincide precisely with the two classes thatwe had previously established as highly diverse, and a greatmany iterations are required to classify all of their pixels. In

fact, the results of objective #1 showed that the last 60 ACAparallelepiped iterations were aimed solely at improving theclassification of these two classes, whose pixels are furthestaway from the centers of their spectral classes. The other classeshave a very low percentage of well-classified uncertain pixels(below 1%), except C1 in west El Ejido and east El Ejido, soACA barely improved the classification accuracy rate in theseclasses. Therefore, ACA improved the classification accuracyrate mainly due to uncertain pixel refinement in classes C2and C4, which are highly diversified and classic classificationalgorithms fail. Although some percentages in Níjar are lowerthan in the other images, its accuracy rate is higher because thesatellite image has fewer uncertain pixels.

The analysis of focus and edge pixels allows the expertanalysts to establish the spatial distribution of the classesthroughout the satellite image. Table X shows the edge andfocus pixels in Níjar, west El Ejido, and east El Ejido foundwith ACA parallelepiped and ACA minimum distance by class.

Class C1 has the highest percentage of edge pixels in Níjarand the lowest percentage in west El Ejido and east El Ejido.This is because, in Níjar, little ponds of water occupy a singlepixel surrounded by pixels of other classes. In west El Ejido andeast El Ejido, the regions of water are larger than in Níjar andspatially distributed in the ellipse (wetlands and open water).Class C3 has a high percentage of edge pixels in all threesatellite images since the vegetation in the study areas is dis-tributed in many small groups of pixels, and therefore, most ofthese pixels are borders (continuous pasture). Class C6 has thehighest percentage of edge pixels of almost all of the satelliteimages, which indicates that the pixels in this class are ratherelongated (paved road) and spatially distributed in the images.

VII. CONCLUSION AND FUTURE WORK

In conclusion, the results with ACA are very satisfying fromseveral points of view. Cellular automata have been validatedas a technique that improves the results of satellite imageclassification, successfully achieving the three objectives set.


First, the ACA classification accuracy rate was very highin satellite images with low, medium, and high classificationcomplexities. Compared to other classifiers (C4.5, multilayerperceptron, Naive Bayes, k-NN, and RBF network), the ACAaccuracy rate was higher than most on low and medium com-plexity images and better than any of the rest on highly com-plicated satellite images. Furthermore, the more complicatedclassification is, the greater the improvement in the successrate compared to the other algorithms. ACA improves clas-sification precisely in satellite images with great difficultiesand very diversified classes with many uncertain and noisypixels. Therefore, although ACA can be used for any typeof satellite image, its performance is especially good in themore complicated ones. ACA achieves this objective by usingthe contextual information provided by the cellular automatonneighborhood, allowing it to make a mixed spectral–contextualclassification. This process was improved because ACA couldmake use of a neighborhood of uncertain and noisy pixelsclassified in previous iterations and, therefore, pixels closer tospectral classes. This process enables classification of uncertainand noisy pixels to a higher degree of certainty. ACA notonly improved the accuracy rate of classic parallelepiped andminimum distance algorithms but also the performance of theclassic algorithms by solving the disadvantages described inSection II of this paper. In the ACA parallelepiped algorithmclassification results, there are no unclassified pixels becausethe threshold is raised in each iteration until all pixels havebeen classified, and no pixels are identified in more than oneclass because uncertain pixels are refined by contextual infor-mation. Moreover, in the ACA minimum distance algorithmclassification results, commission errors are reduced by usingcontextual information, and although the variance is not takeninto account in the ACA classification process, it is simulatedfor uncertain and noisy classes by the neighborhood functions.Thus, ACA optimizes the general functionality of any GIS thatuses it because it improves the classification results of satelliteimages. A very important feature in the proper behavior of aGIS is correct identification of each pixel with its correspondingclass. Therefore, with respect to improvement in the accuracyrate, the results with low- and moderate-complexity satelliteimages are very good, and with highly complex satellite images,they are excellent.

Second, ACA hierarchical classification is based on thedegree of class membership layers, each layer correspondingto a cellular automaton iteration. Throughout ACA execution,the class spectral radius increases with each iteration. The firstiterations provide the most reliable layers because these layerscontain the pixels spectrally closest to the centers of theirclasses, some even correspond to the set of samples selected bythe expert analyst. As the cellular automaton iterations are run,spectral distance increases, and as a result, the classified pixelsare less reliable in terms of classification accuracy becausethey are further from the center of their corresponding classes.Finally, the uncertain pixels are classified in the last iterationswith the assistance of contextual information. They requirecontextual information to count the classes of the neighboringpixels, already classified in previous iterations and, therefore,more reliable in terms of classification accuracy, and thus

improve the final result. Using this method, ACA simulates apseudofuzzy classification in which the degree of class mem-bership of each pixel is indicated by the iteration in which ithas been classified, so it is very high in the first iteration but isconsiderably lower in the last iterations. Therefore, presentingthe results of the classification process by iterations provides theexpert analyst with extra information about each pixel, who candetermine the degree of class membership of each pixel. We canalso determine how diversified the classes are since all pixels inless diversified classes are classified in the first 40 iterations,and the uncertain pixels belonging to highly diversified classesare classified in the following 60 iterations. The longer it takesall of the uncertain pixels in a class to be classified, the morediversified that class is.

Third, the algorithm also provides spatial edge detection ofclasses in the satellite image, which can be rather useful in laterinterpretation and analysis of the results, as well as a list ofuncertain and noisy pixels, so experts can detect them easily.Analysis of uncertain and noisy pixels shows the contribution ofclasses to the improvement in classification accuracy rate, whilethe analysis of focus and edge pixels determines the spatialdistribution of the pixels for each class in the image.

As a final advantage of using cellular automata for satel-lite image classification, we have concluded that they allowexpert analysts to configure a personalized classification ofeach particular satellite image in each specific study area, bymodifying only some of the properties of cellular automata:neighborhood, number of iterations, rules, and states. It istherefore a novel application of cellular automata which opensthe way to additional research.

As future work, we would like to develop a new version ofACA with a different configuration of states and rules of thecellular automaton to customize the classification process (i.e.,develop a fuzzy ACA classification algorithm adding fuzzyrules and states to the cellular automata). It would also beof interest to create a new version of ACA to determine thenumber of classes of the image directly without knowing thembefore the classification process. Finally, we would like to adda new level of classification to ACA: textural classification(based on textures). Thus, we would have two different levels ofclassification: pixel level (spectral and contextual information)and regional level (textural data).

ACKNOWLEDGMENT

The authors would like to thank the anonymous reviewers forthe constructive comments.

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Moisés Espínola received the B.S. and M.S. degreesin computer science from the University of Almería,Almería, Spain, in 2002 and 2005, respectively. Heis currently working toward the Ph.D. degree at theUniversity of Almeria, Almeria, Spain, where hisresearch work is focused on remote sensing, imageprocessing, and cellular automata.

In 2007, he joined the Applied Computing Group,and he worked in several national and internationalresearch projects. He is mainly involved in the clas-sification of satellite images using algorithms based

on cellular automata. His other major research interests include soft computingand computer graphics applied in the field of psychology and education.


José A. Piedra-Fernández received the B.S. degreein computer science and the M.S. and Ph.D. degreesfrom the University of Almería, Almería, Spain, in2001, 2003, and 2005, respectively.

He is an Assistant Professor with the Universityof Almería. He visited the College of InformationSciences and Technology, The Pennsylvania StateUniversity, University Park, PA, USA, in 2008–2009.He has designed hybrid systems applied to remotesensing problems. His main research interests in-clude image processing, soft computing, and image

retrieval.

Rosa Ayala received the B.S. and M.S. degrees incomputer science from the University of Granada,Granada, Spain, and the Ph.D. degree in computerscience from the University of Almería, Almería,Spain.

From 1992 to 1998, she was a Researcher withthe Foundation for Agricultural Research in theProvince of Almería (FIAPA). She worked in sev-eral national and international research projects ondistributed simulation and geographic informationsystems (GIS). She became an Associate Professor

with the University of Almería in 2000. In 2007, she joined the AppliedComputing Group. Her research interests include satellite classification, GIS,and cellular automata.

Luis Iribarne received the B.S. and M.S. degreesin computer science from the University of Granada,Granada, Spain, and the Ph.D. degree in computerscience from the University of Almería, Almería,Spain.

From 1991 to 1993, he was a Lecturer with theUniversity of Granada and collaborated as an IT Ser-vice Analyst with the University of Almería. Since1993, he has been a Lecturer with the AdvancedCollege of Engineering, University of Almería. From1993 to 1999, he worked in several national and

international research projects on distributed simulation and geographic infor-mation systems. He has been the coordinator of several projects founded by theSpanish Ministry of Science and Technology. In 2007, he founded the AppliedComputing Group. His research interests include software engineering, model-driven engineering, ontology-driven engineering, component-based softwaredevelopment, modeling, and simulation.

James Z. Wang received the Bachelor’s degreein mathematics and computer science (summacum laude) from the University of Minnesota,Minneapolis, MN, USA, and the M.S. degree inmathematics, the M.S. degree in computer science,and the Ph.D. degree in medical information sciencesfrom Stanford University, Stanford, CA, USA.

He has been a faculty member with ThePennsylvania State University, University Park, PA,USA, since 2000, where he is a Professor with theCollege of Information Sciences and Technology. In

2008, he served as the Lead Guest Editor of the IEEE TRANSACTIONS ON

PATTERN ANALYSIS AND MACHINE INTELLIGENCE Special Section on Real-world Image Annotation and Retrieval. He was also a Visiting Professor withthe Robotics Institute, Carnegie Mellon University, Pittsburgh, PA, USA, in2007–2008 and a Program Manager with the National Science Foundation in2011–2012. His main research interests are automatic image tagging, imageretrieval, computational aesthetics, and computerized analysis of paintings.

Dr. Wang was a recipient of a U.S. National Science Foundation CareerAward and the endowed PNC Technologies Career Development Professorship.

Contextual and Hierarchical Classification of Satellite Images Based on Cellular Automata

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