Improved texture image classification through the use of a corrosion-inspired cellular automaton
Núbia Rosa da Silva, Pieter Van der Weeën, Bernard De Baets, Odemir Martinez Bruno
IImproved texture image classification through the use of a corrosion-inspired cellularautomaton
N´ubia Rosa da Silva ∗ Pieter Van der Wee¨en † and Bernard De Baets ‡ Department of Mathematical Modeling, Statistics and Bioinformatics,Ghent University, Coupure links 653, 9000 Ghent, Belgium
Odemir M. Bruno § (Dated: September 5, 2018)In this paper, the problem of classifying synthetic and natural texture images is addressed. Totackle this problem, an innovative method is proposed that combines concepts from corrosion mod-eling and cellular automata to generate a texture descriptor. The core processes of metal (pitting)corrosion are identified and applied to texture images by incorporating the basic mechanisms ofcorrosion in the transition function of the cellular automaton. The surface morphology of the imageis analyzed before and during the application of the transition function of the cellular automaton. Ineach iteration the cumulative mass of corroded product is obtained to construct each of the attributesof the texture descriptor. In a final step, this texture descriptor is used for image classification byapplying Linear Discriminant Analysis. The method was tested on the well-known Brodatz andVistex databases. In addition, in order to verify the robustness of the method, its invariance tonoise and rotation were tested. To that end, different variants of the original two databases wereobtained through addition of noise to and rotation of the images. The results showed that themethod is effective for texture classification according to the high success rates obtained in all cases.This indicates the potential of employing methods inspired on natural phenomena in other fields. I. INTRODUCTION
The classification of texture images is an importantproblem in pattern recognition and consequently formsthe subject of many research works in this field. Tex-ture is an important image feature with a strong dis-criminative capability and is therefore widely used incomputer vision. The texture classification problem ad-dressed in this paper is a multiclass classification prob-lem and two different well-known databases are consid-ered: the Brodatz database, which contains a numberof unique textures that each form a class, and the Vis-tex database, which consists of a number of classes, eachwith several texture images belonging to it. For the Bro-datz database, ten subimages of the same size are takenfrom each texture to obtain different texture images forthe corresponding class. For each texture image of bothdatabases a feature vector, i.e. a vector of characteristics,is obtained by using a novel method introduced in this ∗ [email protected] † [email protected] ‡ [email protected] § [email protected] paper, as well as by using a number of popular meth-ods from literature. This feature vector is then employedto classify the different texture images using Linear Dis-criminant Analysis (LDA) following a stratified 10-foldcross-validation scheme. Feature vectors for image tex-ture are usually obtained from the analysis of groups ofpixels and the way this analysis is performed is used toclassify the different texture analysis methods. Five maincategories can be distinguished: structural [1–3], statisti-cal [4], model-based [5–7], spectral [8, 9], and agent-basedmethods [10–12].This paper proposes a novel method to analyze thestructural elements of textures by means of a cellularautomaton (CA) inspired by the pitting corrosion phe-nomenon, further on referred to as the Corrosion-InspiredTexture Analysis (CITA) method. The basic mechanismsbehind this detrimental reaction which occurs betweenmetals (or alloys) and their environment serve as inspira-tion to develop a CA-based model. Next, this CA-basedmodel is employed to perform texture analysis by treat-ing the image to be classified as a metal surface. TheCITA method, like real corrosion, amplifies existing dif-ferences in material and height (in this case grayscalevalue) so that the biggest contrasts in the original tex-ture image will become more pronounced and smallercontrasts will be nullified. The eroded mass of ‘metal’ by a r X i v : . [ c s . C V ] D ec the progression of pitting corrosion at each iteration isused to generate a feature vector that describes the im-age to be classified. The effectiveness of this strategy isdemonstrated on two texture data sets with natural andsynthetic textures. In addition, to verify the robustnessof the CITA method, its invariance to noise and rotationwere tested, obtaining satisfactory results.This paper is organized as follows. Section II describesthe basics behind the pitting corrosion phenomenon,while the definition of a CA as well as further explana-tion of some parts of this definition form the subject ofSection III. The CITA method is described in Section IVand the experimental setup needed to test its efficacy isexplained in Section V. Section VI presents the resultsand discussion of the study. Finally, the paper is con-cluded in Section VII. II. PITTING CORROSION
Corrosion is the disintegration of metals (and alloys)into their constituents due to reaction with the environ-ment and is one of the main causes of structural failure inindustrial systems, and poses as such an economic prob-lem [13]. Dealing with corrosion is difficult because of itscomplex nature and the involvement of many variables.Therefore, modeling and simulation could allow for pre-dicting more accurately the corrosion process in time.CA-based models are excellent candidates for modelingcorrosion due to their intrinsic simplicity and therefore,since the beginning of the new millennium, attempts arebeing made to employ these models in the field of corro-sion engineering [14–18]. Corrosion is present in a widerange of metals and environments, which points to theuniversality of this phenomenon. The latter suggests thatcorrosion does not depend on the details of the underly-ing mechanism, so that it may be modeled adequatelyusing simple models [19]. Moreover, CA-based modelsare able to capture the stochasticity of the involved elec-trochemical reactions at the mesoscopic scale [16].Pitting corrosion is a very harmful and common formof localized corrosion where all or most of the metal lossoccurs concentrated in certain areas. Upon close inspec-tion of the metal surface, pitting can be recognized by theappearance of small holes on the metal surface as shownin Figure 1.The first step in pitting corrosion is the pitinitiation which is the result of impurities or irregular-ities of the metal surface or the environment, makingperfectly polished surfaces more resistant to this typeof corrosion. From there on, the acidity inside the pitis maintained by the spatial separation of the cathodicand anodic half-reactions, which creates a potential gra-dient and electromigration of aggressive anions into thepit (see Figure 1). As pit growth progresses, differentsolution compositions develop inside the cavity and theconsequent voltage (IR) drop along the metal/electrolyteinterface illustrates that the deeper the pit, the lower thepit growth rate [17, 21, 22].
FIG. 1. Pitting corrosion: schematic representation in a metalsurface.
III. CELLULAR AUTOMATA
CAs are mathematical constructs in which the space,state and time domains are discrete as opposed to par-tial differential equations (PDE) in which these three do-mains are continuous [23, 24]. The ability of CAs togenerate a rich spectrum of sometimes complex spatio-temporal patterns from relatively simple underlying tran-sition functions has led to their successful employment inthe study of several (a)biological processes [25–30]. Mod-els based on CAs can be seen as an alternative to PDE-based models, to provide researchers with a wider rangeof modeling tools and, in some complex cases, a solutionto problems encountered with some of the more classicalmodeling methods [31, 32].In this paper, we make use of a homogeneous CA, inwhich a single transition function, constructed using acombination of knowledge on the pitting corrosion phe-nomenon and intuition, governs the dynamics of all cells.The following definition of a homogeneous 2D CA is re-lied upon.
Definition I . (Homogeneous 2D cellular automaton)A homogeneous 2D cellular automaton C can be repre-sented as C = (cid:104)T , S, s, N, Φ (cid:105) , where(i) T is a two-dimensional grid of cells c .(ii) S is a finite set of k states, with S ⊂ N .(iii) The output function s yields the state s ( c, t ) of ev-ery cell c at the t -th discrete time step.(iv) The neighborhood function N determines the neigh-boring cells of every cell c , including the cell c itself. (v) The transition function Φ yields the state s ( c, t + 1) of every cell c at the next time step, based on itsstate and that of its neighboring cells at the currenttime step. For reasons of comprehensiveness, some parts of thisdefinition will be elaborated in the remainder of this sec-tion.
A. Grid T In this paper, a finite two-dimensional grid consistingof squares is used, because it has the most straightfor-ward implementation and provides an easy way of link-ing the cells of T to the pixels of the texture images tobe classified (cfr. infra). Furthermore, an indexing of thecells of a 2D CA is introduced, which is shown in Fig-ure 2. For a square grid, it holds that i ∗ = j ∗ = (cid:112) |T | . ji ... ...... ...... ......... ............ c c c c j * - c j * c c j * c i,1 c i,j c i, j * c i * - c i * ,1 c i * , j c i * ,2 c i * , j * - c i * , j * c i * - j * FIG. 2. Ordering of the cells of a 2D CA
B. Neighborhood function N Many different neighborhoods can be defined in 2D,the two most important ones being the Moore and thevon Neumann neighborhood. The Moore neighborhoodof a cell c i,j comprises those cells that share at least avertex with c i,j (see Figure 3(a)). The von Neumannneighborhood is a more restricted neighborhood in whichonly those cells that share an edge with c i,j are consideredas neighbors (see Figure 3(b)). c i,j c i + - c i + c i + + c i - - c i - c i - + c i,j - c i,j + (a) c i + c i,j c i - c i,j - c i,j + (b) FIG. 3. Neighborhoods of a cell c i,j in a square tessellation:(a) Moore neighborhood and (b) von Neumann neighborhood C. Discrete states
Every cell c i,j has one of the k discrete states comprisedin the set S . The states of the cells c i,j of T at t = 0,i.e. s ( c i,j , T . In thispaper, the initial condition of T is determined by thegrayscale value of the different pixels of the correspondingtexture image (cfr. infra). D. Transition function Φ The transition function Φ determines the state of acell c i,j at the ( t + 1)-th time step based on the cell’scurrent state and the states of its neighboring cells. Thetransition function employed in this paper is executed ina deterministic and synchronous manner, meaning thatΦ is used to evaluate the state of every cell of T at everytime step and for all cells at the same time [33]. IV. CORROSION-INSPIRED TEXTUREANALYSIS
The CITA method proposed in this paper starts byconverting the texture image into the initial state of aCA. Thereafter, a CA-based model inspired by the pit-ting corrosion phenomenon is evaluated for a number oftime steps. The cumulative mass of corroded metal af-ter each iteration of the CA-based model is used to con-struct a feature vector for every texture image. Finally,these vectors of characteristics are used to classify theimages via LDA. In the remainder of this section, theCITA method is explained in more detail.A two-dimensional grayscale image is treated as a dis-crete object and is seen as a grid T . The dimensions of T are defined by the size of the image, where each pixelof the image is a cell of the CA. The original image isthen used to determine an initial state of the cells of theCA by converting the gray level image into a discrete ini-tial state for each cell. Thus, for the initial configuration s ( c i,j ,
0) there are 256 possible states, ranging from 0 to255. This conversion is described by s ( c i,j ,
0) = I ( i, j ) , (1)where I is the original image and I ( i, j ) represents thegray level of the pixel at the i -th row and j -th columnof the image I . In order to introduce the ideas of pittingcorrosion, the 2D grid will be regarded as a metal surfaceand the state of each cell will represent the depth of thelocal pit in the metal (i.e. along the third dimension),with state 0 meaning that there is no pit and 255 beingthe largest pit depth of the metal at t = 0. It is importantto point out that for t > s ( c ,j , t ) = s ( c ,j , t ) ,s ( c n +2 ,j , t ) = s ( c n +1 ,j , t ) ,s ( c i, , t ) = s ( c i, , t ) ,s ( c i,n +2 , t ) = s ( c i,n +1 , t ) , (2)with n the size of the original image with n × n pixels.The updated state of each cell c i,j of T at time t + 1depends on the analysis of the states of the cells in theneighborhood of c i,j at time t . In this paper, the Mooreneighborhood (see Figure 3(a)) is employed. Further-more, the CITA method makes use of a transition func-tion Φ inspired by pitting corrosion. In a first step, d i,j is calculated for every cell c i,j as the difference betweenthe state of this cell and the lowest state value within itsMoore neighborhood (see Eq. (3)): d i,j = s ( c i,j , t ) − min(˜ s ( N ( c i,j ) , t )) , (3)where ˜ s ( N ( c i,j ) , t ) is the set of states of the cells in theMoore neighborhood of c i,j .Bearing in mind the principles of pitting corrosion, alocal ‘impurity’ or minimum height difference is neededat a certain location in order to initiate or propagatepitting corrosion. For this purpose, a surface roughness parameter ν is introduced. All differences lower thanthis parameter ν are considered insignificant, i.e. notreal impurities, in order to account for the fact that noteven a polished metal surface is perfectly smooth. Thismeans that differences d i,j lower than ν will not give riseto (further) pitting. On the other hand, the larger thedifference grows, the lower the pit growth rate will be dueto the IR drop, until finally the pit growth rate becomeszero. In this paper, it is assumed that if the difference d i,j is greater than 254, the greatest possible differenceat t = 0, the corresponding pit growth rate is zero. Thismeans that only the state of those cells with a difference d i,j greater than or equal to ν and smaller than 255 areevaluated.Figures 4(a)-4(c) illustrate the selection process to de-termine whether a cell will be evaluated or not. In thisexample, ν is set to five meaning that cells c i,j whosestate differs less than five with the lowest state in itsneighborhood are considered to belong to the surface andwill not have their state changed. Figure 4(a) shows thecells belonging to a 5 × d i,j for eachof these cells calculated according to Eq. (3). Finally, inFigure 4(c) the gray cells indicate the cells that are eval-uated in that time step, because their d i,j is greater thanor equal to five and smaller than 255.
21 21 28 28 2821 27 22 21 2131 34 22 21 2122 27 22 21 2121 20 27 21 21 (a) (b) (c)
FIG. 4. Selection of cells to be updated, with ν = 5: (a) 5 × d i,j for all cells according to Eq. (3) and (c) gray cells indicatecells to be updated Under these assumptions, the transition function Φ es-tablishes the state of a cell c i,j at the ( t + 1)-th time stepaccording to s ( c i,j , t +1) = (cid:40) s ( c i,j , t ) + Q ( d i,j , γ ) , if 255 > d i,j ≥ ν,s ( c i,j , t ) , if d i,j < ν or d i,j ≥ , (4)where γ ∈ [0 ,
1] is the pitting power. This parameter γ represents the metal-specific resistance to corrosion un-der given environmental conditions, where γ = 0 standsfor completely resistant metal. Further, Q is a functionthat employs d i,j and γ to determine the level of corro-sion to be applied. In this paper, Q is defined as Q ( d i,j , γ ) = (255 − d i,j ) γ. (5)From Eq. (5), it can be seen that the function Q gives, depending on the value of γ , a non-integer output,meaning that the employed model structure is actuallya continuous CA or Coupled Map Lattice rather thana CA [34]. However, in order to keep working with aCA-based model and to not overcomplicate the model,the choice was made to limit the output of Q to integervalues (see Eq. (6)). Q ( d i,j , γ ) = (cid:98) (255 − d i,j ) γ (cid:99) , (6)where a in (cid:98) a (cid:99) denotes the floor of a .The output of the CA-based model at every time stepis the cumulative mass of corroded product. In each it-eration, after updating the state of the cells, the massthat suffered corrosion in that iteration is added to theeroded total mass from the previous iteration. Finally,this cumulative corroded mass is expressed relative to thenumber of pixels of the texture images such that textureimages with different sizes can be compared using theCITA method.Figure 5 shows some examples of initial images andthe simulated result after 90 iterations of the pitting-corrosion-inspired CA-based model. In the first columnthe original images are shown, the second column showsthe simulated output of the CA-based model in grayscale,while the third column displays the same results as thesecond column, but scaled in a color map where blue in-dicates the lowest and red the highest resulting values.After simulation, some structural details from the origi-nal image can still be retrieved in the simulated output.Regions with similar state values are mostly consideredby the model as belonging to the same local surface andtherefore tend to keep the same state value throughoutthe simulation.In a final step, the time series of cumulative mass ofcorroded metal, relative to the total number of pixels,is used as the feature vector for each texture image andclassification is performed using LDA following a strati-fied 10-fold cross-validation scheme. LDA is traditionallyused in texture analysis to find a linear combination ofattributes resulting in a good separation of the classes.The proposed method is summarized in Figure 6. Fig-ure 7 shows the feature vectors for four texture imagesfrom the Brodatz database. It can clearly be seen fromthis figure that the feature vectors from textures belong-ing to the same class are very similar on the one hand andthat these vectors are different from the feature vectorsfrom images belonging to different classes on the otherhand. V. EXPERIMENTAL SETUP
To validate the CITA method, it is employed forthe classification of the images of two classical texturedatabases, the Brodatz and Vistex databases, and the
FIG. 5. Simulation results. First column: original images.Second column: result in grayscale after application of CA-based model. Third column: result in blue-red scale afterapplication of CA-based model (see color code at the righthand side). The experiments were performed with γ = 0.05, ν = 5 and 90 iterations. results obtained by applying the CITA method are com-pared with the results obtained with several establishedmethods from literature. The remainder of this sectionincludes a short description of the employed databasesand the methods from literature used for comparison aswell as an optimization of the parameters of the CITAmethod, i.e. γ , ν and the number of iterations performedin order to obtain the most favorable results. To ensurethe CITA method is not sensitive to the parameter config-uration, Usptex, a different database than the databasesused for the validation of the method is used to performthe parameter optimization. A. Databases
Two important databases, widely used in the literatureand each with its own peculiarities, are employed for test-
Input:
Original image ( n × n ), surface roughness ν , pittingpower γ , number of iterations Output:
Class label s ( c i,j , ← original image ( I ( i, j )) Add imaginary row at top and bottomAdd imaginary column at left and right for all iterations do Apply boundary reflection on grid T : s ( c ,j , t ) = s ( c ,j , t ) s ( c n +2 ,j , t ) = s ( c n +1 ,j , t ) s ( c i, , t ) = s ( c i, , t ) s ( c i,n +2 , t ) = s ( c i,n +1 , t ) for i = 2 → n + 1 dofor j = 2 → n + 1 do d i,j ← s ( c i,j , t ) − min(˜ s ( N ( c i,j ) , t )) if ( d i,j < ν or d i,j ≥ then s ( c i,j , t + 1) ← s ( c i,j , t ) else s ( c i,j , t + 1) ← s ( c i,j , t ) + Q ( d i,j , γ ) end ifend forend for Calculate cumulative corroded mass end for
Feature vector ← cumulative corroded masses relative tonumber of pixelsDo classification via LDA FIG. 6. Pseudocode for the CITA method. ææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææææ C u m u l a ti v e m a ss FIG. 7. Feature vectors from four different texture images ofthe Brodatz database, with γ = 0.04, ν = 5 and 100 iterations.The blue and red vectors originate from class 11 images, thepurple vector from a class 24 image and the green vector froma class 78 image. ing the different methods for pattern classification: the Brodatz and Vistex databases and a third database, Usp-tex, is used to perform the parameter optimization.
1. The Brodatz database [35] contains 111 unique natural textures (and thereforealso 111 classes) with image size of 640 ×
640 pixels and256 gray levels. From each image ten subimages withsize of 200 ×
200 pixels were obtained, resulting in animage database containing 1110 images. Figure 8 showsthe complete Brodatz database and Figures 9(a) and 9(b)show for two of the original Brodatz images the ten se-lected subimages.
FIG. 8. The Brodatz database. The size of the images is640 ×
640 pixels.
2. The Vistex database [36] contains 864 images belonging to 54 texture classes.Each texture class contains 16 texture samples of 128 ×
128 pixels, each extracted from a particular texture pat-tern without overlapping (see Figure 10). The true colorRGB images are converted to grayscale intensity images,because the CITA method in its present form works onlyon grayscale images.
3. The Usptex database [37] contains 191 color images that each form a texture class(see Figure 11). Each image has a size of 512 ×
384 pixelsfrom which 12 subimages with a size of 128 ×
128 pixelsare extracted without overlapping, so that a total of 2292images is obtained. The images are again converted tograyscale images. (a) (b)
FIG. 9. (a) Two Brodatz textures with a size of 640 ×
640 pixels and (b) ten subimages with a size of 200 ×
200 pixels.FIG. 10. The Vistex database. The size of the images is128 ×
128 pixels.
B. Established methods for texture analysis
1. Fourier descriptors [38, 39] consider attributes in terms of spectral density con-sidering the texture as a Gaussian random field. TheFourier transform was calculated for each image, wherethe spectrum was divided into 64 sectors with eight ra-dial distances and eight angles. The sum of the absolutespectrum values for each sector is calculated, resulting in64 descriptors per image.
2. Gray Level Co-occurrence Matrix - GLCM [4] is based on the spatial gray level dependence matri-ces. Haralick descriptors (Contrast, Correlation, En-ergy and Homogeneity) were computed from resultingco-occurrence matrices with angles of 0 ◦ , 45 ◦ , 90 ◦ and135 ◦ , distances equal to one or two pixels and 64 graylevels in order to obtain a set of 32 descriptors for each FIG. 11. The Usptex database. The size of the images is512 ×
384 pixels. image.
3. Gray Level Difference Matrix - GLDM [40, 41] calculates the absolute gray level difference betweentwo pixels with distance h . Here, 60 descriptors were ob-tained using h = 1, 3 and 5 and the attributes contrast,angular second moment, entropy, mean, and inverse dif-ference moment from the estimated probability densityfunction.
4. Gabor filter [42–44] is a bi-dimensional Gaussian function modulated withan oriented sinusoid in a determined frequency and direc-tion. To perform the tests, 64 filters were used, composedof eight rotation filters and eight scale filters with lowestfrequency equal to 0.01 and highest frequency equal to0.4.
5. Local Binary Pattern Variance - LBPV [45] is a variation of traditional LBP [46] and is calculatedfrom the binary value of each pixel in the radius 1 neigh-borhood surrounding the central pixel, measuring the lo-cal variance.
C. Parameter Evaluation
The parameterization of the CITA method is per-formed using the Usptex database, a different databasethan the ones used for validation. This is done to ensurethat the CITA method is not susceptible to the parame-ters and therefore the same configuration can be used forclassification of textures from different databases.
1. Number of iterations
To describe each image, the cumulative mass of cor-roded metal after each iteration of the CA-based corro-sion model is used. These values constitute the vectorof characteristics that is used to discriminate each of theimages. However, finding a single number of iterationsthat gives rise to the smallest, most informative featurevector for all images of both databases is a non-trivialtask due to the variety of the type of texture images andalso because this number is dependent on the values of γ and ν . In order not to overcomplicate the problem,the choice is made to look for a single optimal number ofiterations for both databases that overall gives the bestresult for all the texture images in both databases. Thisoptimal number of iterations is nevertheless still kept de-pendent on γ and ν .
2. Surface roughness ν One of the parameters that defines the pitting corro-sion is the surface roughness ν . According to the pro-posed corrosion-based method, pixels having a difference d lower than ν (Eqs. (3) and (4)) do not suffer from theaction of the corrosion process, considering that they arepart of the local surface. However, if the neighborhoodhas a difference d greater than the permitted thresholdsurface, the center pixel will pass through a corrosion pro-cess having its value eroded according to Eqs. (4) and (5).Figure ?? shows the success rate surface, i.e. the percent-age of correctly classified texture images, for the Usptexdatabase for ν varying from 0 to 10 and and γ varyingfrom 0.01 to 0.08. The figure shows that higher values of ν lead to a lower success rate. However, when ν equals0 the obtained success rate is smaller than for ν equal to1 for almost all values of γ . Thus, a value of 1 for ν ischosen as optimal value.
3. Pitting power γ Another model parameter with a physical meaning isthe pitting power γ . This parameter is important becauseit determines the level of corrosion according to the ma-terial being eroded. However, as we are not dealing withreal metal surfaces, this parameter is not known for theimage texture analysis. Figure ?? is now studied for γ ranging from 0.01 to 0.08. It can be seen that the highestsuccess rate is obtained with γ and ν equal to 0.05 and1, respectively. For values of γ below 0.05 the rate tendsto be reduced while for values above 0.05 the rate alsotends to decrease. When looking at combined high val-ues of γ and ν the success rates drop sharply. Figure ?? shows the number of iterations to obtain the highest suc-cess rate for each of the parameter combinations. Thegraph shows that the optimal number of iterations nec-essary for γ equal to 0.05 and ν equal 1 is relatively lowin comparison to the other results. VI. RESULTS AND DISCUSSIONS
This section reports on the performance of the CITAmethod for texture analysis. Results for the classifica-tion with the proposed method are compared to the tra-ditional texture analysis methods in literature describedin Section V to evaluate the performance of the method,where the classification is performed using LDA followinga stratified 10-fold cross-validation scheme. Three sets ofexperiments were performed: firstly on the original testdatabases and afterwards on modified versions of the testdatabases to test noise and rotation invariance. All testswere performed using the optimized values for ν and γ found in the previous section and the corresponding op-timal number of iterations for that specific combinationof ν and γ , which are shown in Table I. (a)(b)FIG. 12. (a) Pitting power and surface roughness analysis forthe Usptex database with γ from 0.01 to 0.08 and ν from 0 to10. (b) Number of iterations for each parameter configurationin (a). TABLE I. Optimal parameter values.Parameter ValueNumber of iterations 158 ν γ A. Unmodified databases
Table II lists the results for the different texture anal-ysis methods for the unmodified databases. As can beseen, the CITA method achieves an excellent success rate,which outperforms all methods for the Brodatz databaseand shares the best result for the Vistex database to-gether with the GLDM method. To further test the ro-bustness of the CITA method, firstly, noise is applied tothe images and, secondly, a rotation of the images is per-formed to verify whether the performance of the CITAmethod persists under these circumstances.
TABLE II. Comparison of the CITA method with traditionaltexture analysis methods for unmodified databases.
Success rate (RMSE)Method Brodatz VistexFourier descriptors 94 ( ± ± ± ± ± ( ± ± ± ± ± ( ± ( ± B. Noise Invariance
In order to demonstrate the tolerance of the proposedmethod to noise, experiments were performed on modi-fied versions of the Brodatz and Vistex databases withaddition of noise in the form of ‘Salt & Pepper’ noise. Byapplying this type of noise to an image, black and whitepixels are randomly added to the image matrix with anintensity l which may vary from 0 to 1 and representsthe share of the image affected by the noise. The ro-bustness of the CITA method to the addition of noiseis demonstrated by performing the texture classificationon six modified databases generated from both the Bro-datz and Vistex databases. The six different databaseswere generated in both cases by adding ‘Salt & Pepper’noise with intensities l = 0 .
01, 0.05, 0.07, 0.1, 0.5 and0.7. For all different cases the CITA method is comparedwith the established methods described in Section V inorder to get an idea of how the CITA method, in com-parison with the other methods, deals with deformationof texture. Figure 13 shows samples of the modified Vis-tex databases where noise was added to the images andwhere each column shows examples of an intensity l ofnoise.The success rates for classifying the perturbated im-ages from the modified Brodatz and Vistex databases us-ing the different methods, are given in Tables III and IV,respectively. These results demonstrate the good per-formance of our method even with the addition of vari-ous intensities of noise. For all databases generated fromthe Brodatz database, the CITA method has a highersuccess rate compared to traditional methods in litera-ture. It is important to note that even with increasingnoise levels, the CITA method yields high success rates,while for all other methods the success rate declines. Forthe databases generated from the Vistex database ourmethod gives rise to the second best success rate, pre-ceded by the GLDM method, but still demonstrating itsrobustness to noise.The results in Tables III and IV are obtained with addi-tion of noise to both the training as well as the test data.Further, experiments using non-perturbated texture im-0 TABLE III. Success rates of texture classification for six databases obtained by adding different intensities l of ‘Salt & Pepper’noise to the Brodatz database. Success rate (RMSE)Method l = 0.01 l = 0.05 l = 0.07 l = 0.1 l = 0.5 l = 0.7Fourier 93 ( ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ( ± ( ± ( ± ( ± ( ± ( ± TABLE IV. Success rates of texture classification for six databases obtained by adding different intensities l of ‘Salt & Pepper’noise to the Vistex database. Success rate (RMSE)Method l = 0.01 l = 0.05 l = 0.07 l = 0.1 l = 0.5 l = 0.7Fourier 93 ( ± ± ± ± ± ± ± ± ± ± ± ± ( ± ( ± ( ± ( ± ( ± ( ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ( ± ± FIG. 13. Samples of six databases generated from the Vistexdatabase by adding ‘Salt & Pepper’ noise. Each column rep-resents an intensity of noise with l = 0.01, 0.05, 0.07, 0.1, 0.5and 0.7 from left to the right. ages for training and images with addition of noise fortesting were performed. The results are shown in Ta-bles V and VI. The success rate of the CITA method iscomparable to the other methods analyzed in both cases. It is never the worst method seen over the different in-tensities and two databases, but neither is it clearly thebest method. C. Rotation Invariance
The proposed CITA method is intrinsically rotationinvariant, so good results are expected when test areperformed with modified databases with rotated im-ages. To demonstrate the rotation invariance of theCITA method, additional versions of both the Brodatzand Vistex databases are created. Each image from thedatabases is rotated with the following angles: 0 ◦ , 45 ◦ ,90 ◦ , 135 ◦ , 180 ◦ , 225 ◦ and 270 ◦ and in this way, sevenimages are obtained from each original database image.Therefore, the new database with rotated Brodatz im-ages has 70 images per class with 111 classes in total andthe new database with rotated Vistex images has 112 im-ages per class with 54 classes in total. Figure 14 showsfor some texture images from the Brodatz database theseven rotated images obtained under the different rota-tion angles, with all images on the same row originatingfrom the same original image.Table VII shows the success rates for the classifica-tion of the texture images of the Brodatz and Vistexdatabases with rotated images. In this case, the successrates are obtained with LDA following a stratified 10-foldcross-validation scheme for the complete rotated Brodatz1 TABLE V. Success rates of classification of the texture images of the Brodatz database, with training data without additionof noise and test data with addition of noise at different intensities l of ‘Salt & Pepper’ noise. Success rate (RMSE)Method l = 0.01 l = 0.05 l = 0.07 l = 0.1 l = 0.5 l = 0.7Fourier 90 ( ± ( ± ( ± ( ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ( ± ± ± ± ± ± ± ± ( ± ± ± ± ± ( ± TABLE VI. Success rates of classification of the texture images of the Vistex database, with training data without addition ofnoise and test data with addition of noise at different intensities l of ‘Salt & Pepper’ noise. Success rate (RMSE)Method l = 0.01 l = 0.05 l = 0.07 l = 0.1 l = 0.5 l = 0.7Fourier 58 ( ± ± ± ± ± ± ± ( ± ± ± ± ± ( ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ( ± ( ± ( ± ( ± FIG. 14. Samples of rotated images from the Brodatzdatabase. Each column corresponds to a different rotationangle. From left to right: 0 ◦ , 45 ◦ , 90 ◦ , 135 ◦ , 180 ◦ , 225 ◦ and270 ◦ . and Vistex databases, where each database consists of allrotated texture images of all the original images. Thesuccess rates achieved with the CITA method are bet-ter than the success rates obtained with any of the othermethods and are comparable to the results obtained onthe unmodified databases. These experimental resultsindicate that our method has a good generalization abil- ity. Hence, the method described here has proven to beperformant also for rotated texture classification. TABLE VII. Comparison of the CITA method with tradi-tional texture analysis methods for the databases of rotatedimages.
Success rate (RMSE)Method Rotated Brodatz Rotated VistexFourier descriptors 83 ( ± ± ± ± ± ± ± ± ± ± ( ± ( ± VII. CONCLUSIONS
In this paper, a new method for texture analysisand classification was described. Combining conceptsfrom corrosion engineering, cellular automata and pat-tern recognition a texture descriptor was generated, ableto characterize an image according to the iterations ofa CA-based model drawing inspiration from the pittingcorrosion phenomenon. The developed CITA method2was used to classify the texture images of two well-knowndatabases: Brodatz and Vistex. The method was appliedto images of the original databases and the robustness ofthe method under addition of noise and rotation was in-vestigated. For this purpose, several new databases werecreated, starting from the original databases. Six newdatabases were obtained by adding ‘Salt & Pepper’ noisewith different intensities to each of the images of the testdatabases and another new database was obtained by ro-tating the images of the databases under seven angles. Inall cases, the CITA method obtained good results com-pared to the methods from literature, showing a goodgeneralization ability and proving to be performant fortexture classification.The results presented in this paper demonstrate thepotential of the CITA method. Therefore, future workshould focus on further refining the method as well asexpanding it so that it is applicable for more types of tex-ture images. This can be done by integrating measuresof corrosion frequency via a histogram of eroded pixels and measuring the velocity of corrosion by calculatingthe difference between initial and final values divided bythe number of iterations. Further, the CITA method hasto be expanded so that it can deal with RGB color im-ages as well as with dynamic textures, i.e. sequences ofimages that together form a texture.
ACKNOWLEDGMENTS
N´ubia Rosa da Silva acknowledges support fromFAPESP (The State of S˜ao Paulo Research Foundation).Pieter Van der Wee¨en was sponsored by the Fund for Sci-entific Research in Flanders (FWO). Odemir MartinezBruno gratefully acknowledges the financial support ofCNPq (National Council for Scientific and TechnologicalDevelopment, Brazil) (Grant Nos. 308449/2010-0 and473893/2010-0) and FAPESP (Grant No. 2011/01523-1). [1] R. Goyal, W. Goh, D. Mital, K. Chan, Scale and rotationinvariant texture analysis based on structural property,in: Proceedings of the 1995 IEEE IECON 21st Interna-tional Conference on Industrial Electronics, Control, andInstrumentation, volume 2, pp. 1290–1294.[2] J. Serra, Image Analysis and Mathematical Morphology,Academic Press, Inc., Orlando, FL, USA, 1983.[3] J. Zhang, T. Tan, Brief review of invariant texture anal-ysis methods, Pattern Recognition 35 (2002) 735–747.[4] R. M. Haralick, Statistical and structural approaches totexture, Proceedings of the IEEE 67 (1979) 786–804.[5] A. R. Backes, D. Casanova, O. M. Bruno, Plant leafidentification based on volumetric fractal dimension, In-ternational Journal of Pattern Recognition and ArtificialIntelligence 23 (2009) 1145–1160.[6] A. R. Backes, O. M. Bruno, A new approach to estimatefractal dimension of texture images, in: A. Elmoataz,O. Lezoray, F. Nouboud, D. Mammass (Eds.), Image andSignal Processing, volume 5099 of
Lecture Notes in Com-puter Science , Springer Berlin / Heidelberg, 2008, pp.136–143.[7] F. Cohen, Z. Fan, M. Patel, Classification of rotated andscaled textured images using Gaussian Markov randomfield models, IEEE Transactions on Pattern Analysis andMachine Intelligence 13 (1991) 192–202.[8] C. Chen, A comparative study of texture classificationusing spectral features, in: Technical report ADA109408,pp. 1074–1077.[9] X. Tang, W. Stewart, Texture classification using waveletpacket and Fourier transforms, in: OCEANS ’95.MTS/IEEE. Proceedings of Challenges of Our ChangingGlobal Environment, volume 1, pp. 387–396.[10] A. R. Backes, W. N. Gon¸calves, A. S. Martinez, O. M.Bruno, Texture analysis and classification using deter-ministic tourist walk, Pattern Recognition 43 (2010) 685–694. [11] A. R. Backes, A. S. Martinez, O. M. Bruno, Color textureanalysis and classification: an agent approach based onpartially self-avoiding deterministic walks, in: Proceed-ings of the 15th Iberoamerican Congress Conference onProgress in Pattern Recognition, Image Analysis, Com-puter Vision, and Applications, CIARP’10, Springer-Verlag, Berlin, Heidelberg, 2010, pp. 6–13.[12] M.-S. Lai, H.-C. Huang, S.-C. Chu, Image texture seg-mentation with ant colony systems, in: Proceedings ofthe First International Conference on Innovative Com-puting, Information and Control - Volume 1, ICICIC ’06,IEEE Computer Society, Washington, DC, USA, 2006,pp. 652–656.[13] P. R. Roberge, Corrosion Engineering: Principles andPractice, McGraw-Hill Professional, 2008.[14] G. Contreras, S. Goidanich, S. Maggi, C. Piccardi, M. V.Diamanti, M. P. Pedeferri, L. Lazzari, Representing lo-calized corrosion processes through cellular automata,Corrosion Reviews 29 (2011) 241–245.[15] D. di Caprio, C. Vautrin-Ul, J. Stafiej, J. Saunier,A. Chauss´e, D. F´eron, J. P. Badiali, Morphology of cor-roded surfaces: Contribution of cellular automaton mod-elling, Corrosion Science 53 (2011) 418–425.[16] S. V. Lishchuk, R. Akid, K. Worden, J. Michalski, A cel-lular automaton model for predicting intergranular cor-rosion, Corrosion Science 53 (2011) 2518–2526.[17] B. Malki, B. Baroux, Computer simulation of the corro-sion pit growth, Corrosion Science 47 (2005) 171–182.[18] R. M. Pidaparti, M. J. Palakal, L. Fang, Cellular au-tomata approach to aircraft corrosion growth, Interna-tional Journal of Artificial Intelligence Tools 14 (2005)361–369.[19] A. Valor, F. Caleyo, L. Alfonso, D. Rivas, J. M. Hallen,Stochastic modeling of pitting corrosion: A new modelfor initiation and growth of multiple corrosion pits, Cor-rosion Science 49 (2007) 559–579.3