supervised texture classification by integration of multiple texture methods and evaluation windows

www.elsevier.com/locate/imavis

Image and Vision Computing 25 (2007) 1091–1106

Supervised texture classification by integration of multipletexture methods and evaluation windows

Miguel Angel Garcıa, Domenec Puig *

Intelligent Robotics and Computer Vision Group, Department of Computer Science and Mathematics, Rovira i Virgili University,

Avda. Paisos Catalans 26, 43007 Tarragona, Spain

Abstract

Pixel-based texture classifiers and segmenters typically combine texture feature extraction methods belonging to a same family. Eachmethod is evaluated over square windows of the same size, which is chosen experimentally. This paper proposes a pixel-based textureclassifier that integrates multiple texture feature extraction methods from different families, with each method being evaluated over multi-ple windows of different size. Experimental results show that this integration scheme leads to significantly better results than well-knownsupervised and unsupervised texture classifiers based on specific families of texture methods. A practical application to fabric defectdetection is also presented.� 2006 Elsevier B.V. All rights reserved.

Keywords: Supervised texture classification; Multiple texture methods; Multiple evaluation windows; Kullback J-divergence; MeasTex; LBP; Edge flow;JSEG; Fabric defect detection

1. Introduction

The problem of texture classification consists of identify-ing the texture patterns present in a digital image given aset of known texture patterns (models) of interest. In themost general form of the problem, in which the input imagemay contain several regions of different texture, the aim isto identify the texture pattern to which every image pixelbelongs. This will be referred to as pixel-based texture

classification.

Two examples of pixel-based texture classificationwould be the identification of tissue with a specific granu-larity in an X-ray image or the location of specific typesof soil in a satellite or aerial image. These problems donot just require the segmentation of the given image intodistinctive regions – this is the goal of unsupervised texturesegmentation algorithms (e.g. [13,17,19,27,31,34]) – but theidentification of specific regions of interest within the

0262-8856/$ - see front matter � 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.imavis.2006.05.023

* Corresponding author. Tel.: +34 977 559677; fax: +34 977 559710.E-mail addresses: [email protected] (M.A. Garcıa), dpuig@

etse.urv.es, [email protected] (D. Puig).

image. Obviously, such an identification will also lead tothe segmentation of those regions – in this respect, classifi-cation subsumes segmentation (e.g. [16]) – but it will notnecessarily lead to the segmentation of the whole image.In this scope, supervised classification algorithms (e.g.[2,23]) are generally considered to be more suitable thanunsupervised segmentation algorithms.

In order to perform pixel-based texture classification, anumber of texture measures are computed for every imagepixel by applying a predefined set of texture feature extrac-

tion methods (texture methods in short) to its neighboringpixels [28]. Usually, these neighborhoods are square win-dows centered at the considered pixel.

A wide variety of texture feature extraction methodshave been proposed in the computer vision literature (e.g.[21,24,28,30,33]). Their performance basically depends onthe type of processing they apply, the size of the neighbor-hood of pixels over which they are evaluated (window size)and the texture content. When dealing with those methods,two different issues must be addressed: (1) the determina-tion of proper window sizes for evaluating each method,and (2) how the various methods are combined in order

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1092 M.A. Garcıa, D. Puig / Image and Vision Computing 25 (2007) 1091–1106

to improve the result. These issues are further discussedbelow.

Although many studies regarding the performance ofthe different families of texture feature extraction methodshave been carried out (e.g. [6,22,28]), few have dealt withthe issue of determining optimal window sizes, and theydo it for specific texture methods (e.g., [3,8,21]). Hence,window sizes are commonly defined on an experimentalbasis, with each method being evaluated over windows ofa single size. The role played by both the shape and sizeof those windows was studied in [11], showing that texturecharacterization is much more influenced by the windowsize than by its shape, although no hints on optimal sizesare provided.

The main problem regarding the definition of proper win-dow sizes for texture feature extraction methods is that twocontradictory requirements appear when these methods areutilized for image segmentation and classification. Thus,while large windows are appropriate for texture discrimina-tion in wide areas of uniform texture, they perform poorly incontact areas among different textures. In the latter case,small windows are more adequate in order to identify thecorrect texture near the boundaries. Since the performanceof texture methods is greatly influenced by the particular tex-tures to which they are applied, it is not feasible to devise gen-eral strategies for determining window sizes that allowoptimal discrimination of arbitrary textures.

On top of the problem of selecting window sizes, no sin-gle texture method is good enough to completely character-ize and, therefore, distinguish the different textures thatmay appear in nature. Thus, several methods must be com-bined in order to obtain good classification results. The dif-ferent proposals typically combine methods that belong toa specific family (e.g. [2,5,22,24]). This combination is com-monly tailored to the particular methods that are chosen.Unfortunately, the results they obtain are likely to dependon the type of texture models to which the different propos-als are targeted.

Notwithstanding, every texture feature extractionmethod is potentially useful for texture discrimination toa larger or lesser extent. Hence, instead of trying to findout the best set of texture feature extraction methods – thisbeing a challenge that, in general, appears to be of doubtfulfeasibility in considering that there is no consensus in theliterature about which family of methods or combinationof them is the best— [10,26] show that classification ratescan be improved by integrating different families of texturemethods. The reason is that no single method is excluded apriori. Instead, all of them are considered in order toimprove the result.

This paper presents a new pixel-based texture classifierthat combines different families of texture feature extrac-tion methods, with each method being evaluated over mul-tiple windows of different size. A Bayesian scheme based onthe application of the Kullback-J divergence is proposed.Experimental results show that this technique yields signif-icantly lower classification errors and better quality seg-

mentations of the sought regions of interest than well-known classifiers and segmenters based on single familiesof texture methods evaluated over single-sized windows.

The organization of this paper is as follows. Section 2describes the evaluation of texture methods over multisizedwindows. Section 3 presents the proposed pixel-based tex-ture classifier. Section 4 shows experimental results of theintegration of widely used texture feature extraction meth-ods with the proposed technique, as well as a comparisonwith a public texture classification framework (MeasTex

[32]), the recent LBP texture classifiers [24] and two public-ly available unsupervised texture segmenters (JSEG [9] andEdge Flow [18]). A practical application of the proposedtechnique to fabric defect detection is also described. Final-ly, conclusions and further improvements are given inSection 5.

2. Evaluation of texture methods over multisized windows

Let I be a two-dimensional image of N = R · C pixelscontaining several regions of uniform texture. Let{s1, . . . ,sT} be a set of T texture models of interest. Eachmodel sk is described by a sample image Ik that containsa pattern of that texture (the algorithm can be triviallyadapted to deal with multiple sample images per texturepattern). The goal of a pixel-based texture classifier is todetermine if a pixel I (x,y) belongs to any of the T afore-mentioned texture models. If the classifier is applied toall the pixels of I, the result will be the identification (seg-mentation plus labeling) of the regions that belong to thegiven texture models.

The usual way of classifying a pixel I (x,y) based on tex-tural information consists of extracting a feature vectorfrom that pixel, F (x,y) = (f1 (x,y), . . ., fM (x,y)). Each fea-ture fi is obtained by applying a texture feature extractionmethod li that computes a value li (x,y) from the pixelscontained in a neighborhood around I (x,y). This neighbor-hood is usually a square window centered at I (x,y), whosesize is experimentally set for each method. M different tex-ture feature extraction methods are considered. The featurevector obtained in that way can then be classified by apply-ing any technique from decision theory.

One of the main problems with this approach is that, ingeneral, no optimal window size can be determined for anytexture method and application, since the outcome of thosemethods greatly depends on the texture patterns to whichthey are applied. Thus, a specific window size may allowoptimal discrimination of a particular set of texture pat-terns, but it may well be unable to distinguish other tex-tures with the same accuracy. For instance, if a windowsize allows optimal discrimination of textures with a certaingrain size, if this size is doubled, it is likely that the windowsize will also have to be doubled to maintain the same dis-crimination power.

A feasible solution to the aforementioned problem con-sists of evaluating every texture feature extraction methodli over S square windows, {w1, . . . ,wS}, with each window

M.A. Garcıa, D. Puig / Image and Vision Computing 25 (2007) 1091–1106 1093

having a different size. In this work, every window wj isconsidered to contain sj · sj pixels, with sj = 2j + 1. In thisway, every texture method li generates a feature vector Fi

with S texture features for every pixel to which the methodis applied. These features are fed into the chosen classifieralong with the feature vectors generated by other texturefeature extraction methods, if any.

Only the windows with size sj 6 2 min(x,C �1 � x,y,R � 1 � y) + 1 will be applicable to pixel I (x,y)as they will entirely fit into the image. Hence, a strip of pix-els that belong to the boundary of I will not be classified.Let W, W 6 S, be the number of windows that do entirelyfit into the image for a specific pixel I (x,y). In this case, li

generates a vector Fi (x,y) of W features: F iðx; yÞ ¼ðf 1

i ðx; yÞ; . . . ; f Wi ðx; yÞÞ.

3. Pixel-based texture classification

Given an image I and M texture feature extractionmethods, {l1, . . . ,lM}, which generate corresponding fea-ture vectors, {F1, . . . ,FM}, when FM are evaluated in theneighborhood of a certain pixel I (x,y) by using a set ofW windows of different size, {s1 · s1, . . . , sW · sW}, this sec-tion presents a technique for integrating the M feature vec-tors in order to determine whether pixel I (x,y) can beclassified into one of T given texture models {s1, . . . ,sT}.The proposed technique has five stages.

The first stage applies a supervised training scheme thatcomputes a set of frequency tables (histograms) and, basedon them, several numerical values used in the other fourstages. Each histogram models the behavior of a texturemethod evaluated over a specific window size, which isapplied to all the pixels of the sample image correspondingto one of the given texture models. From each histogram itis possible to compute the likelihood of a pixel I (x,y)according to method li, window size sj · sj and texturemodel sk. Such basic likelihood functions are denoted asPij (I (x,y)|sk). M · W · T frequency tables and, hence,basic likelihood functions are computed.

In the second stage, for each pair of texture method li andmodel sk, the W basic likelihood functions corresponding tothe different window sizes sj · sj are integrated, leading to anew subset of M · T intermediate likelihood functions,Pi (I (x,y)|sk). In the third stage, for each texture model sk,the M intermediate likelihood functions corresponding toeach texture method li are integrated in order to obtain Tfinal likelihood functions, Pi (I (x,y)|sk). In the fourth stage,the P (I (x,y)|sk) likelihood functions computed above arecombined through the Bayes rule in order to obtain the pos-terior probability that pixel I (x,y) belongs to each texturemodel sk, P (sk|I (x,y)). The texture model with maximumposterior probability is chosen.

Finally, the fifth stage performs a significance test uponthe texture model sk that yields the maximum posteriorprobability. If that probability is above a significance leveldetermined during the training stage, pixel I (x,y) is classi-fied as belonging to sk. Otherwise, it is classified as an

unknown, denoting that it is not similar enough to anyof the given texture patterns of interest. This last stagecan be omitted if all image pixels are to be classified intoone of the given models, which is what previous pixel-basedtexture classifiers and segmenters usually do.

In order to establish the computational complexity ofthe whole process, let us assume that the cost of applyinga texture method li evaluated on a window sj · sj to a singlepixel is O(1). If M is the number of integrated texturemethods, each evaluated over W different window sizes,T the number of texture patterns to be recognized and N 0

the number of pixels of the training images associated withevery pattern sk, the computational complexity of thesupervised training stage (Section 3.1) is eitherO(N 0T2WM) if the optional significance levels (Section3.5) are applied to the classifier or O(N 0TWM) otherwise.On the other hand, the computational complexity of theremaining stages of the algorithm, which aim at classifyingthe N pixels of a given test image I, is O(NTWM). In theexperiments reported in this paper (Section 4), M = 14,W = 6, T 6 8, N 0 = 216 and N 2 {216,218}. Hence,TWM 6 672, which is between two and three orders ofmagnitude lower than either N or N 0. Similarly,T2WM 6 5376 is one order of magnitude lower than N 0.Therefore, the computational complexity of the whole clas-sification algorithm in terms of asymptotic cost mostlydepends on the size of both the training pattern imagesand the final test images to be classified. In addition, thewhole algorithm is inherently parallel and can be speededup linearly in the number of processors.

The five stages of the proposed classifier are furtherdescribed below.

3.1. Supervised training stage

Let lji be a texture feature extraction method li evaluated

over a window wj of size sj · sj. When lji is applied to a pixel

I (x,y), it generates a value ljiðx; yÞ that represents a feature

of the texture pattern to which I (x,y) belongs.Every known texture model sk is associated with an image

Ik that contains an example of its pattern. For instance,Fig. 2(top) shows eight texture models belonging to the Bro-

datz album [4]. A supervised classifier conveniently trainedwith those models should distinguish them in a compleximage containing areas of different texture.

By evaluating method lji at each of the pixels contained

in Ik, it is possible to determine the probability distributionPijk associated with the feature values generated by li whenapplied to sk with a window size sj · sj. In practice, Pijk isapproximated by a frequency table (histogram) with h bins.Our experiments have shown that histograms with a lownumber of bins do not have enough discrimination power,while histograms with a large number of bins may be sosparse that do not convey sufficient information about theirunderlying probability distributions. We have finally cho-sen h = 256 bins for the histograms as this value is compu-tationally tractable and frequently used in the literature.


Notwithstanding, similar results are obtained with either128 or 512 bins.

It is assumed that the feature values computed by lji will

range in a specific real interval:

lji : Ik ! ½MIN ijk;MAX ijk� � R: ð1Þ

The basic likelihood function Pij (I (x,y)|sk) is thendefined as:

P ijðIðx; yÞjskÞ ¼ P ijkðljiðx; yÞ 2 ½MIN ijk;MAX ijk�Þ; ð2Þ

where Pij (I (x,y)|sk) is interpreted as the likelihood thatI (x,y) belongs to texture sk according to method li whenit is evaluated on a window of size sj · sj.

On top of the previous likelihood functions, five moresets of coefficients are also computed during this trainingstage: divergences KJij (sa,sb) (4), weights wijk (5) and wik

(6), prior probabilities P (sk) (8) and significance levels kk

(see Section 3.5). For the sake of clarity, those coefficientswill be defined in the following sections, right at the pointwhere they are utilized.

3.2. Integration of multiple window sizes

Given a set of M · W · T basic likelihood functionsPij (I (x,y)|sk) defined in the supervised training stage (2),the objective now is to integrate the likelihoods corre-sponding to the W window sizes, {s1 · s1, . . . , sW · sW},associated with each texture feature extraction methodand texture model: {Pi1 (I (x,y)|sk), . . . ,PiW (I (x,y)|sk)}.The result will be a set of M · T combined likelihood func-tions: Pi (I (x,y)|sk).

Due to the noisy nature of texture, the likelihood func-tions corresponding to a same texture method and patternbut different window sizes behave as random variableswhen applied to the different pixels of a same texture pat-tern. Experiments have shown that, in most cases, the jointprobability distribution of these variables is highly corre-lated with the product of their marginal distributions. Thisimplies that likelihood functions obtained by only varyingthe window size are statistically independent and, hence,provide non-redundant information that can benefit therecognition process, as the experimental results presentedin Section 4 show.

The combination of different basic likelihood functions,which can be interpreted as different sources of evidenceabout a certain ‘‘state of nature’’ [1], can be modeled as alinear opinion pool [1], which simply consists of a weightedaverage of these evidences after having been normalized:

P iðIðx; yÞjskÞ ¼XW

j¼1

wijkP ijðIðx; yÞjskÞ: ð3Þ

The weights wijk are computed during the supervisedtraining stage (Section 3.1) as follows. The Kullback J-di-

vergence [14,20], which measures the separability betweentwo probability distributions (texture models in this scope),is computed as:

KJ ijðsa; sbÞ ¼X8u;mðA� BÞ logðA=BÞ ð4Þ

with A and B being defined in our context from the prob-ability distributions determined during the supervisedtraining stage (1): A = Pija (u 2 [MINija,MAXija]) andB = Pijb (v 2 [MINijb,MAXijb]).

Each weight wijk is then defined as the normalized aver-age of the Kullback J-divergences between texture sk andthe other texture models:

wijk ¼ dijk

XW

r¼1

dirk

,dijk ¼

1

T � 1

XT

l¼1;l 6¼k

KJ ijðsl; skÞ: ð5Þ

The histograms corresponding to a texture method thatdoes not significantly change its behavior when applied todifferent texture patterns will have a large overlap. Hence,this texture method will have a low associated divergenceand will receive a low weight in the opinion pool. Con-versely, a texture method that behaves differently whenapplied to different patterns will have a large associateddivergence and weight.

3.3. Integration of multiple texture feature extraction

methods

Given a set of M · T likelihood functions Pi (I (x,y)|sk)defined in the previous stage (3), the likelihoods corre-sponding to the M texture methods associated with eachtexture model sk: {P1 (I (x,y)|sk), . . . ,PM (I (x,y)|sk) areintegrated, leading to T combined likelihood functions,P (I (x,y)|sk):

PðIðx; yÞjskÞ ¼XM

i¼1

wikP iðIðx; yÞjskÞ;

wik ¼XW

j¼1

wijk

XM

r¼1

XW

j¼1

wrjk

,: ð6Þ

The weights wjk are computed during the supervisedtraining stage (Section 3.1).

3.4. Maximum a posteriori estimation

Given a set of T likelihood functions P (I (x,y)|sk) (6), theposterior probabilities P (sk|I (x,y)) are finally computed byapplying the Bayes rule:

PðskjIðx; yÞÞ ¼PðIðx; yÞjskÞP ðskÞPTl¼1PðIðx; yÞjslÞP ðslÞ

ð7Þ

with the prior probability corresponding to each texturemodel defined during the supervised training stage (Section3.1) as:

PðskÞ ¼XM

i¼1

wik

,XM

i¼1

XT

l¼1

wil ð8Þ

T posterior probabilities are generated: {P (s1|I (x,y)), . . . ,P (sT|I (x,y))}, one per texture model. Pixel I (x,y)

Fig. 1. (Top) Test images with portions of Brodatz texture patterns. (Bottom) Test images with real outdoor scenes.

Fig. 2. Detail of texture models (sk) from both (top) the Brodatz album and (bottom) real outdoor scenes.


will likely belong to texture class sk iff P (sk|I (x,y)) >P (sj|I (x,y)), "j „ k.

3.5. Significance test

Let P (sk|I (x,y)) be the maximum posterior probability(7) corresponding to image pixel I (x,y). In order to finallyclassify I (x,y) into texture class sk, that probability must beabove a certain significance level (probability threshold) kk

computed for that texture during the supervised trainingstage (Section 3.1) as described below.

Let TP be the number of pixels I (x,y) belonging to a tex-ture pattern that are correctly classified (true positives) andFN the ones that are misclassified (false negatives). Let alsoFP be the pixels that are incorrectly classified as belongingto that particular pattern (false positives). The significancelevel is defined based on two ratios that are commonlyutilized to characterize the performance of classifiers:sensitivity, Sn = TP/(TP + FN), and specificity, Sp = TP/

(TP + FP) (notice that this definition of specificity isdifferent to the one utilized in the context of medical diagno-sis: Sp = TN/(FP + TN)). Sensitivity expresses how well theclassifier identifies pixels that belong to a given class, whilespecificity indicates how well the classifier distinguishesamong different classes.

Values of 0.95 have been experimentally determined forboth ratios in this work. These percentages aim at maxi-mizing the number of true positives while keeping a smallnumber of false positives. With values closer to one, thereis a significant increase in the number of pixels classified asunknown. Thus, areas that do not look exactly as the givenpatterns are not recognized although they are perceptuallysimilar. Hence, the classifier looses some of its generaliza-tion capabilities. On the contrary, with lower values, thenumber of unknown pixels decreases, leading to the mis-classification of pixels that do not really belong to the giventexture models. This is especially adverse for pixels belong-ing to boundary regions.

Table 1Classification rates (%) with the proposed classifier and a single texture method, by considering a single (optimal) window size per image and method (thewindow size is also shown)

Texture feature extraction method Optimal single window

Fig. 1(a) Fig. 1(b) Fig. 1(c) Fig. 1(d) Fig. 1(e) Fig. 1(f)

Laws R5R5 55.3 55.7 55.4 28.2 50.5 23.7

9 · 9 17 · 17 33 · 33 17 · 17 9 · 9 9 · 9

Laws E5L5 64.1 40.5 43.1 29.4 56.7 35.79 · 9 9 · 9 33 · 33 17 · 17 9 · 9 9 · 9

Laws E5E5 58.3 43.5 51.6 45.1 58.3 35.217 · 17 9 · 9 65 · 65 9 · 9 9 · 9 9 · 9

Laws R5S5 66.6 48.7 55.4 38.8 58.2 28.017 · 17 9 · 9 17 · 17 33 · 33 9 · 9 17 · 17

Variance 59.4 46.0 49.7 29.5 55.6 19.89 · 9 9 · 9 33 · 33 17 · 17 9 · 9 17 · 17

Skewness 37.2 35.4 43.4 9.3 23.9 25.565 · 65 33 · 33 33 · 33 9 · 9 33 · 33 9 · 9

Homogeneity (5, 45�) 7.8 11.1 10.4 48.0 61.4 67.0

33 · 33 9 · 9 33 · 33 17 · 17 9 · 9 17 · 17

Gabor (wav 4, ori 45�) 56.7 44.0 52.4 41.1 46.0 27.917 · 17 9 · 9 33 · 33 9 · 9 33 · 33 9 · 9

Gabor (wav 8, ori 0�) 56.6 44.9 52.9 50.9 46.8 29.017 · 17 9 · 9 33 · 33 9 · 9 33 · 33 9 · 9

Gabor (wav 4, ori 90�) 56.0 43.6 51.5 40.6 45.8 26.817 · 17 9 · 9 33 · 33 9 · 9 33 · 33 9 · 9

Gabor (wav 8, ori 135�) 56.2 43.1 50.2 41.3 46.1 28.517 · 17 17 · 17 33 · 33 9 · 9 33 · 33 9 · 9

Fractal 48.8 45.5 66.1 22.6 48.0 18.265 · 65 33 · 33 33 · 33 33 · 33 33 · 33 17 · 17

Wavelet Daubechies 4 49.7 44.8 43.2 24.4 66.5 60.717 · 17 17 · 17 33 · 33 33 · 33 9 · 9 9 · 9

Wavelet Haar 56.2 55.4 53.1 33.2 65.3 62.417 · 17 9 · 9 17 · 17 9 · 9 9 · 9 9 · 9

Italicized cells correspond to the experiments that produced the best classification for each test image in Fig. 1.

Table 2Classification rates (%) with the proposed classifier and a single texture method

Texture feature extraction method Multiple windows

Fig. 1(a) Fig. 1(b) Fig. 1(c) Fig. 1(d) Fig. 1(e) Fig. 1(f)

Laws R5R5 59.0 56.7 63.3 29.0 54.1 29.8Laws E5L5 65.8 42.0 49.9 29.8 59.8 31.7

Laws E5E5 56.8 51.4 53.2 63.0 70.3 52.6Laws R5S5 75.1 61.6 63.5 44.5 60.5 37.7Variance 62.2 51.8 58.8 30.5 62.7 23.6Skewness 36.9 41.1 49.1 14.5 35.4 33.8Homogeneity (5, 45�) 8.9 11.5 12.7 41.5 61.4 64.0

Gabor (wav 4, ori 45�) 68.1 54.4 59.7 64.4 57.1 42.9Gabor (wav 8, ori 0�) 69.0 53.4 60.4 65.5 58.0 49.9Gabor (wav 4, ori 90�) 70.0 54.7 61.8 64.6 56.3 41.4Gabor (wav 8, ori 135�) 69.7 54.4 59.3 64.6 56.9 42.5Fractal 51.1 53.7 67.7 25.9 44.7 23.6Wavelet Daubechies 4 55.0 51.8 54.0 25.6 61.0 58.0

Wavelet Haar 56.3 59.2 57.3 32.5 65.8 66.5

Multiple window sizes are integrated per method. Italicized cells correspond to the only experiments in which optimal single window sizes (Table 1) led tobetter classification rates than multiple sizes.


Based on those two ratios, two thresholds, kak and kb

k aredefined as follows. During the training stage, the posteriorprobabilities P (sk|Ik (x,y)) of the nk pixels that belong toIk (x,y) are calculated and sorted in ascending order. A firstthreshold ka

k is defined as the posterior probability such

that the number of sorted posterior probabilities above kak

(true positives) is TPk = nk Sn. Similarly, the posteriorprobabilities P (sk|Il (x,y)), l = 1, . . . ,T, l „ k, of the pixelsthat belong to the sample images corresponding to texturesother than sk are calculated and sorted in ascending order.


A second probability threshold kbk is defined such that the

number of new sorted posteriors above kbk (false positives)

is FPk = TPk (1 � Sp)/Sp.The significance level is finally: kk ¼ maxðka

k ; kbkÞ. If

kk ¼ kak , the classifier fulfills the desired sensitivity with a

number of false positives small enough as to also fulfillthe desired specificity. However, if kk ¼ kb

k , the classifieronly ensures the desired specificity and, hence, limits thenumber of false positives, implying that the achieved sensi-tivity is below the desired one. Hence, the significance levelfulfills the desired sensitivity whenever it does not compro-mise the desired specificity.

If P (sk|I (x,y)) > kk, pixel I (x,y) will be finally labeled asbelonging to texture class sk, otherwise it will be classifiedas an unknown.

This filtering stage can be optionally omitted in case allpixels in I have to be classified into one of the given texturemodels disregarding the actual value of the maximum pos-terior probability, for instance, in order to compare theproposed technique with previous texture classifiers andsegmenters, which do not consider the possibility of havingpixels of unknown texture. Notwithstanding, this stageshould be considered in the majority of applications, since,when dealing with complex images, only some areas willlikely belong to the sought texture patterns. Thus, not clas-sifying the remaining areas as unknowns would be concep-tually wrong.

All in all, once all pixels of the given image have beenclassified as described above, a last denoising stage isapplied over the whole labeled image in order to removevery small regions (e.g., regions containing fewer than 25pixels), which are reclassified into the texture associatedwith their largest neighboring region.

4. Experimental results

The proposed technique has been extensively evaluatedon a set of composite Brodatz images [4] [e.g.,

Table 3Classification rates (%) for the test images shown in Fig. 1, considering: (first roshown in Table 2 by using multiple evaluation window sizes; (second to fourth rdifferent MeasTex texture classifiers

Classification technique Test images

Fig. 1(a) Fig. 1(b

Proposed technique and multiple windows 92.0 89.5LBP riu2

8;1 85.4 80.6LBP riu2

16;2 83.8 81.5LBP riu2

24;3 85.9 82.5

MeasTex (Gabor, MVG) 80.3 68.5MeasTex (Gabor, 5NN) 83.7 72.9MeasTex (Markov, MVG) 80.2 66.5MeasTex (Markov, 5NN) 77.3 61.2MeasTex (Fractal, MVG) 83.0 74.2MeasTex (Fractal, 5NN) 83.7 74.8MeasTex (GLCM, MVG) 65.7 78.9

MeasTex (GLCM, 5NN) 63.5 58.5

Italicized cells highlight the best results obtained with both LBP and MeasTe

Fig. 1(top)] and real outdoor images [e.g. Fig. 1(bottom)].Fig. 2(top) shows eight Brodatz texture patterns utilizedas models for the proposed supervised classifier. Each pat-tern belongs to one of the eight texture categories proposedby Rao and Lohse [29] as representatives of the variabilityof natural textures according to human perception.Fig. 2(bottom) shows five outdoor texture patterns.

Taking relatively recent surveys into account [28,30],several widely used texture methods have been chosen tobe integrated with the proposed technique: four Laws filter

masks (R5R5, E5L5, E5E5, and R5S5) [15], two wavelet

transforms (Daubechies-4 and Haar), four Gabor filters

[25] with wavelengths (8 and 4) and orientations (0�, 45�,90�, and 135�), two first-order statistics (variance, skew-ness), a second-order statistic (homogeneity) based on co-

occurrence matrices [12] and the fractal dimension [7].In order to be able to compare the proposed technique

with the texture classifiers included in MeasTex and withLBP, the significance test described in Section 3.5 wasomitted in the first three sets of experiments. Hence, all pix-els of the given test images were classified according to theMAP estimation described in Section 3.4.

In the first set of experiments, each texture method wasevaluated over a single window size at a time (M = 1,W = 1). Six window sizes were considered in turn: {3 · 3,5 · 5, 9 · 9, 17 · 17, 33 · 33, 65 · 65}. Thus, for every testimage, texture method and window size, the classificationrate after applying the proposed classifier was obtained.

Table 1 shows the largest classification rates given byevery texture method when applied to the images shownin Fig. 1. The window sizes that led to such largest ratesare considered optimal for each method and image, andare also shown in the table. The italicized cells in the tableshow the best classification rates for each test image.

These results show that, in general, it is not feasible todetermine an a priori optimal window size for a given tex-ture feature extraction method. For example, Gabor filtersproduced optimal classification rates for window sizes

w) the proposed texture classifier, which integrates all the texture methodsows) different configurations of rotation-invariant LBP; (fifth to 12th rows)

) Fig. 1(c) Fig. 1(d) Fig. 1(e) Fig. 1(f)

93.2 79.1 77.7 73.477.5 47.0 69.4 37.984.6 42.7 52.5 51.2

83.4 44.5 46.1 48.967.6 69.2 70.6 50.670.5 67.6 68.5 55.1

67.2 58.0 58.3 35.263.8 49.9 60.6 34.270.5 43.2 51.4 41.671.1 66.9 57.3 45.670.3 48.8 53.2 25.769.7 38.9 52.2 31.8

x.

Fig. 3. Classification results corresponding to Fig. 1(b), (d), (e), and (f). (a, e, i, and m) Ground truth; (b, f, j, and n) proposed classifier (89.5%, 79.1%,77.7%, and 73%); (c, g, k, and o) best configurations of LBP: (c) LBP riu2

24;3 (82.5%), (g, k) LBP riu28;1 (47.0%, 69.4%), (o) LBP riu2

16;2 (51.2%); (d, h, l, and p) bestconfigurations of MeasTex: (d) GLCM and MVG (78.9%), (h) Gabor and MVG (69.2%), (l) Gabor and MVG (70.6%), and (p) Gabor and 5NN (55.1%).


9 · 9, 17 · 17 or 33 · 33 depending on the input image.Moreover, every test image had the maximum classificationrate with a different texture method. For instance, Gaborfilters were only optimal for Fig. 1(d). Furthermore, insome cases, the method that was most suitable for animage, performed poorly for another (e.g., Homogeneity).Hence, it is unfeasible to determine an a priori optimalfamily of texture methods.

In order to assess the benefits of integrating texture fea-tures obtained from multisized windows, the second set ofexperiments evaluated the proposed texture classifier by

applying a single texture method at a time (M = 1), witheach method being separately evaluated over six windows(W = 6) of the aforementioned sizes.

Table 2 shows the pixel classification rates obtained foreach test image in Fig. 1 and texture feature extractionmethod when multiple windows are integrated. By compar-ing Tables 1 and 2, it can be observed that the classificationrates corresponding to multiple windows are larger thanthe rates obtained with single optimal windows in themajority of experiments. Such an improvement is due tothe fact that multiple windows allow that pixels near the

Fig. 4. Qualitative study corresponding to the classification of Fig. 1(b) bycomparing the results obtained with the proposed classifier, Fig. 3(b), thebest LBP classifier, Fig. 3(c), the best MeasTex classifier, Fig. 3(d), and theaverage of the eight MeasTex classifiers: (a) classification rates for eachtexture model, (b) classification rates near boundaries for each texturemodel.

ig. 5. Qualitative study corresponding to the classification of Fig. 1(b) byomparing the results obtained with the proposed classifier, Fig. 3(b), theest LBP classifier, Fig. 3(c), the best MeasTex classifier, Fig. 3(d), and theverage of the eight MeasTex classifiers: (a) false positive rates for eachexture model, (b) number of misclassified regions for each texture model.

Fig. 6. (Top) Test images with real outdoor scenes and, (bottom)corresponding texture models.


region boundaries be classified mainly based on the smallerwindows, while pixels in the central parts of the regions canbe classified mostly based on the larger ones. The italicizedcells in Table 2 correspond to the only cases in which opti-mal single window sizes (Table 1) led to better classificationrates than multiple window sizes.

The third set of experiments evaluated the proposed pix-el-based texture classifier by integrating multiple texturefeature extraction methods computed over multiple win-dow sizes. The first row in Table 3 shows that, by integrat-ing multiple texture methods and windows, the proposedtechnique yields classification rates significantly larger thanthose obtained with single texture methods (Table 2) in allcases. The reason is that the different methods provide bothredundant and complementary information that, whenintegrated, helps identify the sought texture patterns.

Our experiments have also shown that when all theavailable methods are integrated, classification rates aregenerally larger than when only subsets of them are com-bined. The reason is that it is not feasible to determine whatmethods are most suitable for recognizing a particular setof texture patterns a priori, as methods that appear to beuseless for recognizing a specific pattern can, however, berelevant for recognizing another, as Table 1 shows. Thesame argument can be applied to the number of windowsizes that are integrated. Table 1 also shows that it is not

Fcbat

feasible to determine what window sizes are most relevantfor a particular texture method and pattern. Hence, whenonly subsets of the tested window sizes are utilized, classi-fication rates tend to be lower.

The proposed classifier has also been compared to thetexture classifiers included in MeasTex [32], a widely recog-nized texture classification framework, and to the well-known LBP texture analysis and classification methodology

Table 4Classification rates (%) for: (first row) test images shown in Fig. 6,considering the proposed texture classifier and a significance test with(Sn = 0.95, Sp = 0.95); (second to fourth rows) different configurations ofrotation-invariant LBP; (fifth to 12th rows) different configurations ofMeasTex

Classification technique Test images

Fig. 6(a) Fig. 6(b)

Proposed technique 77.8 74.4LBP riu2

8;1 74.0 67.8

LBP riu216;2 70.0 63.5

LBP riu224;3 64.9 61.4

MeasTex (Gabor, MVG) 71.2 67.5MeasTex (Gabor, 5NN) 73.2 68.3

MeasTex (Markov, MVG) 60.8 50.3MeasTex (Markov, 5NN) 61.4 48.5MeasTex (Fractal, MVG) 63.0 60.3MeasTex (Fractal, 5NN) 64.5 62.8MeasTex (GLCM, MVG) 65.7 63.2MeasTex (GLCM, 5NN) 51.1 55.9

Italicized cells highlight the best results with both LBP and MeasTex.


[24]. MeasTex provides a set of texture classifiers based onthe combination of a single family of texture methods(e.g., Gabor, Markov, Fractal, Grey-Level Co-occurrenceMatrices) and a pattern classifier (e.g., MultivariateGaussian Bayes, K-Nearest Neighbors). This frameworkis intended for the classification of entire images insteadof individual pixels. Therefore, in order to achieve pixel-based classification, MeasTex was utilized to classify everypixel of the test images given a subimage of size 33 · 33 cen-tered at that pixel – 33 · 33 is the default window size usedin MeasTex. The sample images utilized for the proposedclassifier were also used as the training dataset for MeasTex.In turn, the local binary pattern (LBP) texture analysisoperator is a gray-scale-invariant texture measure comput-

Fig. 7. Texture classification results corresponding to Fig. 6(a) and (b): (a andLBP configuration LBP riu2

8;1 : (c) 74%, (g) 67.8%; (d and h) best configurations o

ed in a local neighborhood. The experiments reported inthis paper have utilized the three rotation-invariant config-urations of LBP proposed in [24] (LBP riu2

8;1 , LBP riu216;2, and

LBP riu224;3). As the LBP methodology is intended to classify

full images, in order to achieve pixel-based classification,LBP was utilized to classify every pixel of the test imagesgiven a subimage of size 16 · 16 centered at that pixel – thissize is the one used in [24]. The sample images utilized forthe proposed classifier were also used as the training datasetfor LBP. The same denoising stage utilized for both the pro-posed technique and MeasTex was also applied to LBP.

Table 3 shows the classification rates obtained with thethree rotation-invariant configurations of LBP and theeight different combinations of texture methods and classi-fication algorithms currently supported by MeasTex. In allcases, both LBP and MeasTex produced lower classifica-tion rates than the proposed technique. In some cases,the difference in favor of the proposed technique was rathersignificant (even more than twice).

Moreover, the best MeasTex result for each test image(italicized cells in Table 3) was achieved with a different com-bination of texture method and classifier. Hence, it is unfea-sible to predict what combination is best, making that choicea critical issue. Furthermore, the performance of a specificcombination of texture family and classifier in MeasTexhas significant oscillations depending on the test image(e.g., Fractal and 5NN, GLCM and MVG). Similarly, thebest results for the images classified with LBP were notobtained with the same configurations of that technique.For instance, the best results for Fig. 1(a) and (b) wereobtained with LBP riu2

24;3, while LBP riu28;1 produced the best results

for Fig. 1(d) and (e). In contrast, the proposed classifier is farmore stable and robust because of the integration of differenttexture families and window sizes.

e) ground truth; (b and f) proposed classifier (77.8%, 74.4%); (c and g) bestf MeasTex: (d) GLCM and 5NN (73.2%), (h) Gabor and 5NN (68.3%).


Experimental results not only show that the proposedtechnique outperforms the texture classifiers in MeasTexand LBP from a quantitative standpoint, but also qualita-tively. Fig. 3 shows the classification maps correspondingto the test images shown in Fig. 1(b), (d), (e), and (f).Fig. 3(first column) shows the ground-truth classifications.Fig. 3(second column) presents the classification maps gen-erated with the proposed technique. Fig. 3(third column)shows the best results with LBP. Finally, Fig. 3(fourth col-umn) shows the best results with MeasTex according toTable 3. The rest of the results obtained with both LBPand MeasTex (not shown) are much worse qualitatively.

The black frames (16 pixels width) visible in the classifi-cation maps obtained with MeasTex correspond to pixelsthat cannot be classified as the 33 · 33 evaluation windowscentered at them do not entirely fit into the images. Thesame is applicable to the black frames (8 pixels width) ofLBP given the utilized 16 · 16 evaluation windows. Theclassification maps obtained with the proposed techniquealso have a thin black frame of unclassified pixels, althoughits width is just one pixel since the smallest evaluation win-dow that is integrated is 3 · 3.

Qualitative improvements are difficult to measure due totheir intrinsic subjective nature, rather dependent on the

Fig. 8. Test images with portions of textile fabrics. Each row represents a differ

particular application from where the textured images aredrawn. Notwithstanding, it is possible to objectively mea-sure a number of factors on the classified image that aredirectly related to the goodness of classification. In thiswork, four of those factors have been analyzed to evaluatethe qualitative benefits of the proposed technique withrespect to the texture classifiers tested from MeasTex andLBP.

The first qualitative factor measures the percentage oftrue positives for every texture model (correctly classifiedpixels for each texture model over total number of pixelsfor that texture according to the ground truth). The secondqualitative factor also measures the percentage of true pos-itives for each texture model, but only considering imagepixels that are close to boundaries among different regions.This factor conveys how well the classifier is able to differ-entiate the separation between abutting regions. The thirdqualitative factor measures the percentage of false positivesfor each texture model (number of pixels incorrectly classi-fied into a texture model over the total number of pixels inthe test image). Finally, the fourth factor measures thenumber of misclassified regions contained in the area thatevery texture model occupies in the ground truth. In a goodclassification, the area occupied by each texture pattern in

ent fabric. The middle and right columns correspond to defective samples.


the ground truth should contain a single region in the finalclassification map.

Figs. 4 and 5 summarize the results of the aforemen-tioned analysis applied to the composition depicted inFig. 1(b). In particular, the four qualitative factors men-tioned above were computed from the classification mapsobtained with the proposed technique and the eight Meas-Tex and three LBP texture classifiers included in Table 3.Four bars are displayed for each of the eight Brodatz tex-ture patterns contained in the given test image, Fig. 2(top).The first bar corresponds to the qualitative factor associat-ed with the proposed classifier. The second bar shows thequalitative factor corresponding to the LBP configurationthat produced the best classification rate for the given testimage: LBP riu2

24;3, 82.5%. The third bar shows the qualitativefactor associated with the MeasTex classifier that led to thebest classification rate for the same image: GLCM andMVG, 78.9%. Finally, the fourth bar represents the aver-age of qualitative factors computed for the eight MeasTextexture classifiers tested in the experiments.

Fig. 4(a) shows the first qualitative factor (percentage oftrue positives). The proposed technique is superior to theLBP classifiers except for texture models d32 and d5. In

Fig. 9. Segmentation results corresponding to the images in Fig. 8 by apply

addition, the classification percentages with LBP havemore fluctuations among the different models than whenthe proposed technique is applied, which is more stable.On the other hand, the proposed technique is far superiorto the texture classifiers in MeasTex for texture modelsd5 and d94, while the best texture classifier in MeasTexonly beats the proposed technique for texture d15. Moreimportantly, the average performance of MeasTex is signif-icantly below its best performance in some cases (e.g., d5,d94). This means that the choice of a specific combinationof texture family and classifier in MeasTex may have a sig-nificant impact in the final classification results.

On the other hand, qualitative results near boundaries,graphed in Fig. 4(b), emphasize the advantage of the pro-posed technique over MeasTex even more, especially ford32, d5, d94 and d3. Similarly, the proposed technique isfar superior to the best configuration of LBP for d37, whilethe latter is only slightly better than the proposed techniquefor d5.

Fig. 5(a) shows the third qualitative factor (false posi-tives for each texture model). For some of the patterns,the proposed technique produces significantly fewer errorsthan both MeasTex (d41, d32, d94, d37, and d91) and LBP

ing the proposed classifier with significance test (Sn = 0.95, Sp = 0.95).


(d32, d94, and d37). Finally, Fig. 5(b) shows the fourthqualitative factor (misclassified regions for each texturemodel). The proposed technique tends not to oversegmentregions of uniform texture. In this example, it is far superi-or both to the MeasTex texture classifiers for patterns d32,d5, d37, d91 and, especially, for d94, and to LBP for pat-terns d5, d94, d91 and especially d37.

So far, the experiments reported in this paper have beenperformed without applying the significance level testdescribed in Section 3.5, with the aim of having classifica-tion maps comparable to those obtained with MeasTexand LBP. However, the addition of this stage allows to dis-tinguish pixels that likely belong to the known texture pat-terns from those that do not. The latter pixels should beclassified as unknowns.

To study the behavior of the proposed technique whenthe significance test is included, a new set of experimentshave been conducted. Fig. 6 shows two test images contain-ing real outdoor scenes and four texture patterns of interestthat are sought in those images. The classification ratesobtained after applying the proposed texture classifierand the same LBP and MeasTex texture classifiers testedbefore are summarized in Table 4. In this case, theground-truth classification maps, Fig. 7(a) and (e), contain

Fig. 10. Segmentation results corresponding to the images in Fig. 8 by apply

pixels that are labeled as unknowns (in black). Those pixelsare discarded for the computation of classification rates.

Again, the proposed technique is the one that producesthe best quantitative results, while the performance ofMeasTex has important fluctuations depending on the cho-sen texture family and pattern classifier. Fig. 7 shows theactual classification maps obtained with both the proposedtechnique, along with the best MeasTex texture classifierfor this example (Gabor and 5NN) and the best LBPðLBP riu2

8;1 Þ. The proposed technique is able to better identifythe regions that belong to the texture patterns of interest.

The significance level test is particularly useful for a widevariety of applications whose goal is not to detect pixelsthat belong to known texture patterns, but those that donot belong to. An example is quality control of fabric pat-terns, where the aim is to identify regions in the image thatdo not correspond to any of the known fabrics. Forinstance, Fig. 8 shows three different textile fabrics. Thesecond and third columns correspond to examples withseveral fabrication defects.

Fig. 9 shows the result of applying the proposed classifiertrained with defect-free sample images similar but not thesame as those depicted in Fig. 8(left column). In this applica-tion, we assume that the texture pattern associated with each

ing LBP riu224;3, which is the best configuration of LBP for this set of images.

Fig. 11. Segmentation results corresponding to the images in Fig. 8 by applying MeasTex with Gabor and 5-NN (best combination for this example).


test image is known in advance and the goal is to seek defects.The white contours depicted in the images enclose regionswhose pixels were classified into either texture patterns differ-ent to the known pattern or as unknowns. The variousdefects are clearly detected. The little regions in the left col-umn are small enough as to be ignored.

The proposed classifier has been compared to the eightMeasTex texture classifiers and the three rotation-invariantconfigurations of LBP tested above, as well as to two unsu-pervised texture segmenters with publicly available imple-mentations: JSEG [9] and Edge Flow [18]. MeasTex andLBP were trained with the same images as the proposedtechnique.

Fig. 10 shows the best results obtained with LBP riu224;3,

which is the best configuration of LBP for this set ofimages. Fig. 11 shows the results corresponding to the com-bination of texture family and classifier that led to the max-imum classification rate with MeasTex (Gabor and5-NN). Both MeasTex and LBP were unable to identifythe location of the main defects present in the third pattern(last row). For the other two patterns, errors were partiallydetected. LBP also tends to produce false error detections.

Since JSEG and Edge Flow are not classifiers but seg-menters, they only divide an image into separate regions,without identifying them. In these experiments, the goal is

that they separate the correct portions of fabric from thedefective ones. The parameters of both segmenters weretuned to produce the best results for all the test images givenin Fig. 8. Experiments have shown that JSEG produces farbetter results than Edge Flow. Fig. 12 shows the resultsobtained with JSEG (results with Edge Flow are omittedfor space limitations). Notwithstanding, JSEG misses someimportant defects (e.g., top and middle row in Fig. 12).

All in all, these experiments show that supervised classi-fiers (proposed technique, LBP and MeasTex) outperformunsupervised segmenters (Edge Flow and JSEG) in thisscope, and that the proposed technique leads to significant-ly better results than other well-known texture classifiers,such as LBP and the more classical techniques includedin MeasTex, both quantitatively and qualitatively.

5. Conclusions and further work

This paper shows that pixel-based texture classificationcan be significantly improved by integrating texture meth-ods from multiple families, each evaluated over multisizedwindows. As an example, 14 methods from seven differentfamilies have been integrated, with each method evaluatedover six window sizes. A practical application to fabricdefect detection has also been presented.

Fig. 12. Segmentation results corresponding to the images in Fig. 8 by applying JSEG (the same optimal parameters were used for all the test images).


The proposed technique consists of an initial trainingstage that evaluates the behavior of each considered tex-ture method when applied to the given texture patternsof interest over various evaluation windows of differentsize. In a posterior classification stage, every pixel ofthe given test image is evaluated by considering all thetexture methods and window sizes. The different evalua-tions are then subsequently combined by means of a lin-ear opinion pool whose weights are obtained through aKullback J-divergence formulation. This process leadsto a final Bayesian formulation that determines the tex-ture pattern with the maximum a posteriori probability.A final significance test may be applied in order to deter-mine whether that maximum posterior is significantenough or not. In the latter case, the pixel is classifiedas an unknown.

Experimental results show that this methodology leadsto far more stable results and higher classification ratesthan traditional texture classifiers based on specific familiesof texture methods evaluated over single size windows, aswell as unsupervised texture segmenters. Comparisons towidely recognized classifiers, such as LBP and the classicaltechniques included in the MeasTex framework, as well asto unsupervised texture segmenters (Edge Flow and JSEG)

have been made. Experiments carried out upon complexsynthetic and real outdoor images show that the proposedscheme outperforms the other techniques from a quantita-tive as well as a qualitative point of view.

Further research will consist of studying whether it ispossible to determine a minimum number of texture meth-ods whose integration leads to acceptable classificationrates. The goal is to avoid the evaluation of texture meth-ods that do not significantly improve the final result given aspecific set of texture patterns of interest. We also aim atextending the proposed technique to unsupervised pixel-based classification and segmentation, by automaticallygenerating texture models from input images.

Acknowledgement

This work has been partially supported by the SpanishMinistry of Education and Science under projectDP12004-07993-C03-03.

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