wavelet based

80 IEEE TRANSACTIONS ON INFORMATION TECHNOLOGY IN BIOMEDICINE, VOL. 16, NO. 1, JANUARY 2012

Wavelet-Based Energy Features for GlaucomatousImage Classification

Sumeet Dua, Senior Member, IEEE, U. Rajendra Acharya, Pradeep Chowriappa, Member, IEEE, and S. Vinitha Sree

Abstract—Texture features within images are actively pursuedfor accurate and efficient glaucoma classification. Energy distri-bution over wavelet subbands is applied to find these importanttexture features. In this paper, we investigate the discriminatory po-tential of wavelet features obtained from the daubechies (db3), sym-lets (sym3), and biorthogonal (bio3.3, bio3.5, and bio3.7) waveletfilters. We propose a novel technique to extract energy signaturesobtained using 2-D discrete wavelet transform, and subject thesesignatures to different feature ranking and feature selection strate-gies. We have gauged the effectiveness of the resultant ranked andselected subsets of features using a support vector machine, se-quential minimal optimization, random forest, and naı̈ve Bayesclassification strategies. We observed an accuracy of around 93%using tenfold cross validations to demonstrate the effectiveness ofthese methods.

Index Terms—Biomedical optical imaging, data mining, featureextraction, glaucoma, image texture, wavelet transforms.

I. INTRODUCTION

G LAUCOMA is the second leading cause of peripheralblindness worldwide and results in the neurodegenera-

tion of the optic nerve. As the revitalization of the degener-ated optic nerve fibers is not viable medically, glaucoma oftengoes undetected in its patients until later stages. The prevalentmodel estimates that approximately 11.1 million patients world-wide will suffer from glaucoma induced bilateral blindness in2020 [1]. Furthermore, in countries, like India, it is estimatedthat approximately 11.2 million people over the age of 40 suf-fer from glaucoma [2]. It is believed that these numbers can becurtailed with effective detection and treatment options.

In light of the diagnostic challenge at hand, recent advancesin biomedical imaging offer effective quantitative imaging al-ternatives for the detection and management of glaucoma.Several imaging modalities and their enhancements, includingoptical coherence tomography [3] and multifocal electroretino-graph (mfERG) [4], are prominent techniques employed to

Manuscript received April 12, 2011; revised July 19, 2011; acceptedNovember 6, 2011. Date of publication November 18, 2011; date of currentversion February 3, 2012.

S. Dua and P. Chowriappa are with the Computer Science Program, LouisianaTech University, Ruston, LA 71272 USA (e-mail: [email protected];[email protected]).

U. Rajendra Acharya is with the Department of Electronics and Com-munications Engineering, Ngee Ann Polytechnic, Singapore 599489 (e-mail:[email protected]).

V. Sree S is with the School of Mechanical & Aerospace Engineering,Nanyang Technological University, Singapore 639798 (e-mail: [email protected]).

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

Digital Object Identifier 10.1109/TITB.2011.2176540

quantitatively analyze structural and functional abnormalitiesin the eye both to observe variability and to quantify the pro-gression of the disease objectively [5].

Automated clinical decision support systems (CDSSs) in oph-thalmology, such as CASNET/glaucoma [6], [7], are designedto create effective decision support systems for the identificationof disease pathology in human eyes. These CDSSs have usedglaucoma as a predominant case study for decades. Such CDSSsare based on retinal image analysis techniques that are used toextract structural, contextual, or textural features from retinalimages to effectively distinguish between normal and diseasedsamples.

Retinal image analysis techniques rely on computational tech-niques to make qualitative assessments of the eye more repro-ducible and objective. The goal of using such methods is toreduce the variability that may arise between different clini-cians tracking the progression of structural characteristics in theeye. In CDSS, features extracted from the images are catego-rized as either structural features or texture features. Commonlycategorized structural features include disk area, disk diameter,rim area, cup area, cup diameter, cup-to-disk ratio, and topo-logical features extracted from the image [8]. Proper orthogonaldecomposition (POD) is an example of a technique that usesstructural features to identify glaucomatous progression [9].In POD, pixel-level information is used to gauge significantchanges across samples that are location or region specific. Themeasurement of texture features, on the other hand, is roughlydefined as the spatial variation of pixel intensity (gray-scale val-ues) across the image. Textural features are, thus, not boundto specific locations on the image. Several feature extractiontechniques, including spectral techniques, are available to minetexture features. The use of texture features and higher orderspectra (HOS) features were proposed by [10] for glaucomatousimage classification. The readers may refer to [10] and [11] foran introductory summary of the various supervised classificationtechniques used to detect glaucoma. Although the texture-basedtechniques have been proven successful, it is still a challenge togenerate features that retrieve generalized structural and texturalfeatures from retinal images.

Texture features using wavelet transforms (WTs) in imageprocessing are often employed [12] to overcome the general-ization of features. In WT, the image is represented in terms ofthe frequency of content of local regions over a range of scales.This representation provides a framework for the analysis ofimage features, which are independent in size and can often becharacterized by their frequency domain properties.

The use of wavelet-Fourier analysis (WFA) for the character-ization of neuroanatomic disruption in glaucoma was proposed

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DUA et al.: WAVELET-BASED ENERGY FEATURES FOR GLAUCOMATOUS IMAGE CLASSIFICATION 81

by [12] and has achieved considerable success. WFA is usedas a mathematical model to analyze and parameterize the tem-poral, superior nasal, inferior, and temporal (TSNIT) shapes.In this approach, discrete wavelet transform (DWT) using afourth-order symlets wavelet is used to extract features and an-alyze discontinuities and abrupt changes contained in signals.DWT is a multiscale analysis method, in which analysis can beperformed on various scales. Each level of the transformationprovides an analysis of the source image at a different resolution,resulting in its independent approximation and detailed coeffi-cients. In the WFA, the fast Fourier transform (FFT) is appliedto the detailed coefficients. The resultant Fourier amplitudes arecombined with the normalized approximation coefficients ofthe DWT to create a set of features. Though providing valuableinsight into the analysis of images using mathematical general-ization techniques with DWT and FFT, it is yet uncertain whichDWT features need to be extracted to represent an image that isas discriminative as possible in the transform domain.

In image processing, it is also common practice to usethe wavelet energy of each wavelet subband by implement-ing wavelet packet-based texture classification [13] to gauge thediscriminatory potential of the texture features obtained fromthe image [14]. The goal of this study is, thus, to automaticallyclassify normal eye images and diseased glaucoma eye imagesbased on the distribution of average texture features obtainedfrom three prominent wavelet families. Hence, our objective isto evaluate and select prominent features for enhanced speci-ficity and sensitivity of glaucomatous image classification.

In this paper, we quantitatively examine the effectiveness ofdifferent wavelet filters on a set of curated glaucomatous imagesby employing the standard 2-D-DWT. We propose to use threewell-known wavelet filters, the daubechies (db3), the symlets(sym3), and the biorthogonal (bio3.3, bio3.5, and bio3.7) fil-ters [15]. We calculate the averages of the detailed horizontaland vertical coefficients and wavelet energy signature from thedetailed vertical coefficients. We subject the extracted featuresto a myriad of feature ranking and feature selection schemes todetermine the best combination of features to maximize inter-class similarity and aid in the convergence of classifiers, suchas the support vector machine (SVM), sequential minimal op-timization (SMO), random forest, and naı̈ve Bayes techniques.The paper is organized in the following way. Section II con-tains an explanation of the dataset used in this paper. Section IIIcontains a detailed description of the methodology adopted forthis research, including the feature preprocessing, feature rank-ing, and feature selection schemes that we chose. Section IVcontains a description of the classifiers and classifier parametersemployed for our experiments. Section V includes an interpre-tation of results obtained using the proposed method. Finally,the paper concludes with Section VI.

II. DATASET

The retinal images used for this study were collected fromthe Kasturba Medical College, Manipal, India (http://www.manipal.edu). The doctors in the ophthalmology department ofthe hospital manually curated the images based on the quality

Fig. 1. Typical fundus images (a) normal (b) glaucoma. In glaucoma, thepressure within the eye’s vitreous chamber rises and compromises the bloodvessels of the optic nerve head, leading to eventual permanent loss of axons ofthe vital ganglion cells.

and usability of samples. The ethics committee, consisting ofsenior doctors, approved the use of the images for this research.All the images were taken with a resolution of 560 × 720 pixelsand stored in lossless JPEG format [10]. The dataset contains60 fundus images: 30 normal and 30 open angle glaucomatousimages from 20 to 70 year-old subjects. The fundus camera, amicroscope, and a light source were used to acquire the retinalimages to diagnose diseases. Fig. 1(a) and (b) presents typicalnormal and glaucoma fundus images, respectively.

III. METHODOLOGY

The images in the dataset were subjected to standard his-togram equalization [16]. The objective of applying histogramequalization was twofold: to assign the intensity values of pix-els in the input image, such that the output image contained auniform distribution of intensities, and to increase the dynamicrange of the histogram of an image. The following detailed pro-cedure was then employed as the feature extraction procedureon all the images before proceeding to the feature ranking andfeature selection schemes.

A. Discrete Wavelet Transform-Based Features

The DWT captures both the spatial and frequency informa-tions of a signal. DWT analyzes the image by decomposing itinto a coarse approximation via low-pass filtering and into de-tail information via high-pass filtering. Such decomposition isperformed recursively on low-pass approximation coefficientsobtained at each level, until the necessary iterations are reached.

Let each image be represented as a p × q gray-scale matrixI[i,j], where each element of the matrix represents the gray-scale intensity of one pixel of the image. Each nonborder pixelhas eight adjacent neighboring pixel intensities. These eightneighbors can be used to traverse the matrix. The resultant 2-D-DWT coefficients are the same irrespective of whether the matrixis traversed right-to-left or left-to-right. Hence, it is sufficientthat we consider four decomposition directions correspondingto 0◦ (horizontal, Dh), 45◦ (diagonal, Dd), 90◦ (vertical, Dv), and135◦ (diagonal, Dd) orientations. The decomposition structurefor one level is illustrated in Fig. 2. In this figure, I is the image,g[n] and h[n] are the low-pass and high-pass filters, respectively,and A is the approximation coefficient. In this study, the resultsfrom level 1 are found to yield significant features.

As is evident from Fig. 2, the first level of decompositionresults in four coefficient matrices, namely, A1, Dh1, Dv1, and


Fig. 2. 2-D-DWT decomposition: 2ds1 indicates that rows are down sampledby two and columns by one. 1ds2 indicates that rows are down sampled by oneand columns by two. The “×” operator indicates convolution operation.

Dd1. Since the number of elements in these matrices is high,and since we only need a single number as a representative fea-ture, we employed averaging methods to determine such single-valued features. The definitions of the three features that weredetermined using the DWT coefficients are in order. Equations(1) and (2) determine the averages of the corresponding inten-sity values, whereas (3) is an averaging of the energy of theintensity values.

Average Dh1 =1

p × q

∑

x={p}

∑

y={q}|Dh1(x, y)| (1)

Average Dv1 =1

p × q

∑

x={p}

∑

y={q}|Dv1(x, y)| (2)

Energy =1

p2 × q2

∑

x={p}

∑

y={q}(Dv1(x, y))2 (3)

B. Preprocessing of Features

As shown in Table I, 14 features can be found among theNormal and Glaucomatous image samples. Their correspondingdistribution across these samples is also shown in the table. Itshould be noted that the features that exhibited p values <0.0001were chosen for analysis.

C. Normalization of Features

Each of the 14 features is subject to z-score normalization[17]. In the process of z-score normalization, a sample (vector)consisting of 14 features is converted to zero mean and unitvariance. The mean and standard deviation of the input vectorare computed as follows:

ynew =yold − mean

std(4)

where yold is the original value, ynew is the new value, and themean and std are the mean and standard deviation of the originaldata range, respectively. Fig. 3(a) and (b) shows the z-scorednormalized distribution for each of the features across the 30Glaucoma and 30 normal samples used in this study.

TABLE IWAVELET FEATURES AND CORRESPONDING P -VALUES

D. Feature Ranking

Feature ranking is a preprocessing step that precedes classifi-cation. In this paper, we focus on using filter-based approaches torank the features based on their discriminatory potential acrosssamples. Since our objective is to estimate the effectiveness ofthe wavelet features, our analysis consists of four widely usedfeature ranking schemes. These include chi squared ([χ2 ]) [18],gain ratio [19], information gain [20] feature evaluation tech-niques, and relief feature ranking schemes [21] that are basedon an extensive ranking algorithm. Each of these algorithms isdetailed as follows.

1) Chi-Squared (χ2) Feature Evaluation: In this method,the value of a feature is estimated by computing the value ofits χ2 statistic. The compuation of the χ2 statistic is tied to thedistribution of values that the feature possesses with respect tothe class label [18]. This feature evaluation technique is dividedinto two phases. In the first phase, each feature is sorted ac-cording to a significance level (sigLevel). Set at a sigLevel of0.5, the features are discretized into random intervals. The χ2

value is then computed for every pair of adjacent intervals of thefeature. Next, interval pairs of lowest χ2 value are merged in aprocess that terminates when the χ2 value exceeds the previousset sigLevel.

Phase two of the feature evaluation is considered to be a finetuning of the process performed in phase one. Once the mergingof feature intervals is carried out independently, a consistencycheck is performed for the second phase. Any inconsistency inthe merging of feature i does not pass the previously determinedsigLevel(i) for that feature, may not be considered a poten-tially significant feature, and is discouraged for future merging.


Fig. 3. Distribution of the 14 normalized wavelet features across (a) 30 glaucoma samples. (b) 30 normal samples in the dataset.

In this way, the features are ranked according to the level ofsignificance.

2) Gain Ratio and Information Gain Feature Evaluation: Inthis paper, we have utilized both information gain and gain ratio-based methods to rank features [19], [20]. For these techniques,the expected information needed to classify a sample in a datasetS with m classes is given by

I(S) = −m∑

i=1

pi log2(pi) (5)

where pi is the probability that an arbitrary sample belongs toclass Ci and is estimated by Si /S.

The entropy or expected information of a feature A having vdistinct values is given as

E(A) = −m∑

i=1

I(S)(s1i + s2i + · · · smi)

s. (6)

The information that would be gained by spliting the dataseton attribute A is gathered using the following relation:

Info Gain(A) = I(S) − E(A). (7)

The normalization of information gain using a constant calledSplitInfo for each feature is obtained as follows:

SplitInfoA (S) = −v∑

i=1

(|Si ||S|

)log2

(|Si ||S|

). (8)

The aforementioned SplitInfo for a feature represents the in-formation generated by splitting training set S into v partitionscorresponding to v outcomes of a test on feature A

Thus, Gain Ratio is defined as

Gain Ratio(A) =InfoGain(A)

SplitInfoA (S). (9)

The feature with the highest gain ratio is selected as the featurebased on which the training set is split.

3) Relief Feature Ranking: The relief algorithm was firstproposed by [21] as a feature selection approach and is based oninstance-based learning. The relief algorithm uses a relevancyparameter τ , which acts as a threshold that ranges between (0 <τ < 1) and is used to gauge the statistical relevancy of a featureto the target concept, or the class to which a sample belongs.

Relief uses two measures “near hit” and “near miss” to de-scribe the proximity of an instance to a subset of instances thatbelong to a class. An instance is a near hit of X if it belongs toa close neighborhood of X and to the same class as X . Simi-larly, an instance is considered a near miss if it belongs to theproximity of X but also belongs to a different class than X .

This algorithm chooses a triplet of samples that include the<instance X , its Near Hit, and its Near Miss>, where the nearhit and near miss are chosen using the Euclidean distance. Oncethe near hit and near miss are determined, a feature weight vectorW is updated using the following:

Wi = Wi − diff(xi, nearhiti)2 + diff(xi, nearmissi

)2 . (10)

A relevance vector R is determined using every sample triplet.This relevance vector R is derived from the weight vector W ,and is used to depict the relevance of each feature using thefollowing:

R =(

1m

)W. (11)

The features in this paper are ranked based on increasing orderof relevance R.

E. Feature Selection

To select a subset of relevant features, we subject the given setof features to the consistency subset evaluation (CSE) strategy.CSE finds the combinations of features that have values thatdivide the data into subsets containing a strong single class ma-jority, i.e., high-class consistency. This consistency as a measurewas first presented by [22] as follows:

Consistencys = 1 −∑J

i=0 |Di | − |Mi |N

(12)

where s is a feature subset, J is the number of distinct combina-tions of feature values for s, |Di | is the number of occurrencesof the ith feature value combination, |Mi | is the cardinality ofthe majority class for the ith feature value combination, and Nis the number of instances in the dataset.

To use the CSE, the dataset is discretized with numeric at-tributes using forward selection search, which produces a listof ranked attributes. The rank of the attribute is determined


TABLE IICLASSIFIERS USED TO VALIDATE THE FEATURES

according to its overall contribution to the consistency of theattribute set. The various feature subset selection schemes fol-lowed in this paper are part of the WEKA [23] suite and includethe best first, random search, genetic search, and greedy step-wise approaches.

Best First: The best first search strategy implementation isbased on the beam search algorithm [24]. The rudiments of thisalgorithm are based on the standard hill climbing approach withbacktracking to determine the best fit of a subset of features.

Random Search: In the random search approach, an exhaus-tive list of random feature combinations are generated andtested. The subset of features that generates the best accuracyis chosen as the subset of features that best represents the inputset.

Genetic Search: The genetic search technique was proposedin [25], and utilizes neural network feature ranking. This al-gorithm entails several iterations of the evaluation of a featuresubset and includes training a neural network and computing itscost and accuracy.

Greedy Stepwise: Greedy stepwise subset evaluation is per-formed using the greedy forward or backward search throughthe feature space.

IV. CLASSIFIER SETTINGS

We performed the validation of the ranked features and fea-ture subsets using the standard C-SVC implementation of SVM,SMO, random forest, and naı̈ve Bayes (as shown in Table II)[26]–[28]. The SVM employs the radial basis function with apredetermined value of gamma set at 0.28. John C. Platt’s SMOalgorithm is used to train the SVM [27]. The implementation ofSMO is performed using both the polynomial kernel with theexponential set to 2.5, and the Pearson VII function-based uni-versal kernel, each having parameters omega and sigma, whichare both set at 0.1. The number of trees in the random forestalgorithm is set at 10. The naı̈ve Bayes classifier is set to usea kernal function to estimate the distribution of the data, ratherthan assuming that the data follow a normal distribution. Theclassifier settings are determined based on repeated trials on thetraining set, until a classification accuracy of 100% is obtainedon the training set.

V. EXPERIMENTAL RESULTS

The following section provides a detailed description of theresults obtained from our feature ranking and feature selectionexperiments.

A. Feature Ranking and Feature Selection

Table III provides a snapshot of the results obtained from boththe feature ranking and feature selection schemes described inthe methodology section. The ranking algorithms include χ2 ,gain ratio, info gain, and the relief algorithm. Table III alsoshows the ranks of the features selected using four consistencysubset evaluation strategies, best first, random search, geneticsearch, and greedy search. The cells of the table highlighted withthe symbol “�” depict the selected features, and the number ofeach highlighted cell depicts the ranking of each of the featuresobtained.

B. Classification

Once the features are subject to both categories of featureranking and/or feature selection, we perform both the tenfoldcross validation and the 60:40 slip tests. Both tests are carriedout on the entire 60-sample dataset. In the tenfold cross valida-tion method, the dataset is split into ten parts. During the firstiteration, nine parts are used for training and the remaining partis used for testing. This procedure is carried out ten times usinga different part for testing in each iteration. The results obtainedfrom the ten iterations are then averaged to obtain an overallaccuracy. The 60:40 split test provides the accuracy of the clas-sification obtained when 60% of the total number of samplesfrom the dataset are chosen randomly. The classifier is testedagainst the remaining 40% of the samples that constitute thetest set. Table IV provides the results obtained using the tenfoldcross validation. Table V contains the results obtained using the60:40 split test.

From Table IV, it is evident that the highest accuracy ob-tained is 93.33% using the tenfold cross-validation method. Inthe case of 60:40 split up, all classifiers except the random for-est classifier presented the highest accuracy of 95.83%. It canbe seen from Tables IV and V that the use of feature rankingand CSE techniques had very little impact on the accuracy ob-tained using LibSVM, SMO, naı̈ve Bayes with the exceptionof the random forest classifier. However, it is possible to obtainthe highest accuracy using fewer features in CSE. For exam-ple, Table IV shows that the SMO_(2) classifier gives 93.33%accuracy using just two features selected by the best first andgreedy stepwise strategies in the CSE method. These featuresare db3-Dh1_Average_l1_Norm and rbio3.3-cD_Energy (seeTable I). Therefore, these features can be considered highlydiscriminatory. The consistency of results indicates that thesefeatures perform consistently independent to the classifier. Wecan conclude that the CSE feature selection method does helpin obtaining the highest accuracy using fewer features, therebysimplifying the implementation of the technique.

For further validation, we conducted a sensitivity and speci-ficity analysis of 42 training samples belonging to classes


TABLE IIIFEATURE RANKING

TABLE IVCLASSIFICATION ACCURACIES OBTAINED USING TENFOLD CROSS VALIDATION

TABLE VCLASSIFICATION ACCURACIES OBTAINED USING THE 60:40 SPLIT TEST

TABLE VISENSITIVITY AND SPECIFICITY ANALYSIS USING INDEPENDENT TEST SET:

ACC: ACCURACY; SN: SENSITIVITY; SP: SPECIFICITY

glaucoma and normal, each consisting of 21 samples. In thisstudy, the features were not subject to any feature ranking orfeature selection technique. The test set consisted of 18 samples.Nine samples belonged to the class glaucoma, and the other nine

TABLE VIIOVERALL ACCURACIES OF INDIVIDUAL WAVELET FEATURES USING TENFOLD

CROSS VALIDATION

samples belonged to the class normal. Table VI shows the resultsobtained for each of the five classifiers.

Nayak et al. [30] used structural features such as cup-to-disc(c/d) ratio, the ratio of the distance between the optic disc center


TABLE VIIICOMPARISON OF ACCURACIES USING FIVEFOLD CROSS VALIDATION

and optic nerve head to diameter of the optic disc, and the ratioof blood vessels area in inferior–superior side to area of bloodvessel in the nasal-temporal side as features in a neural net-work. Their technique detected glaucoma with a sensitivity andspecificity of 100% and 80%, respectively. This result impliesthat although the system can detect all subjects with glaucomaaccurately, it can detect only 80% of the normal subjects as nor-mal. In our proposed technique using texture features based onwavelets, we were obtained a higher accuracy of over 93.33%.

Finally, we compare our results with those obtained usingHOS and texture features [10]. The training samples and the testsample identifiers are mapped with those used in [10] to enable adirect comparision of accuracy. To establish a baseline analysisof the features used in this study, we gauge the reliability ofindividual wavelet features by performing standard sensitivityand specificity analysis on the independent training and test setsused in [10]. The classifiers used for this analysis are described inTable II. We carried out a tenfold cross validation of independentwavelet features on the entire set, consisting of 60 samples. Theresults of this experimentation are shown in Table VII. It canbe seen that the SMO_(2) classifier performs consistently wellusing any wavelet-based feature. Table VIII contains the resultsobtained using fivefold cross validation. From Table VIII, it canbe observed that our features outperform the LibSVM, SMO,and Naı̈ve Bayes classifiers. However, the results obtained usingthe random forest classifier is almost at par with the resultsobtained in [10].

When the optic nerve is damaged by glaucoma, most of theindividual fibers in the nerve are lost, and the optic nerve be-comes excavated. As glaucoma progresses, more optic nervetissue is lost and the optic cup grows [31]. These changes makethe fundus images obtained from glaucoma patients differentfrom those obtained from normal subjects. We believe that thefeatures selected and evaluated in this study adequately capturethese subtle differences in the fundus images and, thus, helpthe classifiers to detect normal and glaucoma cases with highaccuracy.

VI. CONCLUSION

This study illustrates the dependence between features ex-tracted using three wavelet filters that have been subjected to var-ious feature ranking and feature selection methods. The rankedsubsets of selected features have been fed to a set of classificationalgorithms to gauge the effectiveness of these features. From theaccuracies obtained and contrasted, we can conclude that the en-ergy obtained from the detailed coefficients can be used to distin-

guish between normal and glaucomatous images with very highaccuracy. As observed the db3-Dh1_Average_l1_Norm and therbio3.3-cD_Energy features are highly discriminatory. Further-more, from Table IV that both LibSVM_(1) and SMO_(2)present the highest accuracy of 93.33%.

REFERENCES

[1] R. Varma et al., “Disease progression and the need for neuroprotectionin glaucoma management,” Am. J. Manage Care, vol. 14, pp. S15–S19,2008.

[2] R. George, R. S. Ve, and L. Vijaya, “Glaucoma in India: Estimated burdenof disease,” J. Glaucoma, vol. 19, pp. 391–397, Aug. 2010.

[3] K. R. Sung et al., “Imaging of the retinal nerve fiber layer with spectraldomain optical coherence tomography for glaucoma diagnosis,” Br. J.Ophthalmol., 2010.

[4] J. M. Miquel-Jimenez et al., “Glaucoma detection by wavelet-based anal-ysis of the global flash multifocal electroretinogram,” Med. Eng. Phys.,vol. 32, pp. 617–622, 2010.

[5] B. Brown, “Structural and functional imaging of the retina: New waysto diagnose and assess retinal disease,” Clin. Exp. Optometry, vol. 91,pp. 504–514, 2008.

[6] S. Weiss, C. A. Kulikowski, and A. Safir, “Glaucoma consultation bycomputer,” Comp. Biol. Med., vol. 8, pp. 24–40, 1978.

[7] S. Weiss et al., “A model-based method for computer-aided medicaldecision-making,” Artif. Intell., vol. 11, pp. 145–172, 1978.

[8] R. O. Duncan et al., “Retinotopic organization of primary visual cortexin glaucoma: A method for comparing cortical function with damage tothe optic disk,” Invest. Ophthalmol. Vis. Sci., vol. 48, pp. 733–744, Feb.2007.

[9] M. Balasubramanian et al., “Clinical evaluation of the proper orthagonaldecomposition framework for detecting glaucomatous changes in humansubjects,” Invest. Ophthalmol. Vis. Sci., vol. 51, pp. 264–271, 2010.

[10] U. R. Acharya, S. Dua, X. Du, V. S. Sree, and C. K. Chua, “Automateddiagnosis of glaucoma using texture and higher order spectra features,”IEEE Trans. Inf. Technol. Biomed., vol. 15, no. 3, pp. 449–455, May 2011.

[11] S. Dua, U. R. Acharya, and E. Y. K. Ng, Computational Analysis of theHuman Eye With Applications. World Scientific Press, 2011.

[12] E. A. Essock, Y. Zheng, and P. Gunvant, “Analysis of GDx-VCC polarime-try data by wavelet-Fourier analysis across glaucoma stages,” Invest.Ophthalmol. Vis. Sci., vol. 46, pp. 2838–2847, Aug. 2005.

[13] K. Huang and S. Aviyente, “Wavelet feature selection for image classifi-cation,” IEEE Trans. Image Process., vol. 17, no. 9, pp. 1709–1720, Sep.2008.

[14] A. Arivazhagan and L. Ganesan, “Texture classification using wavelettransform,” Pattern Recog. Lett., vol. 24, pp. 1513–1521, 2003.

[15] I. Daubechies, Ten Lectures on Wavelets. Philadelphia, PA: Society forIndustrial and Applied Mathematics, 1992.

[16] R. C. Gonzalez and R. E. Woods, Digital Image Processing. NJ: PrenticeHall, 2001.

[17] M. H. Dunham, Data Mining Introductory and Advance Topics. NJ: Pren-tice Hall, 2002.

[18] H. Liu and R. Setiono, “Chi2: Feature selection and discretization ofnumeric attributes,” in Proc. IEEE 7th Int. Conf. Tools With Artif. Intell.,1995, pp. 338–391.

[19] J. R. Quinlan, “Induction of desion trees,” Mach. Learning, vol. 1, pp. 81–106, 1986.

[20] J. R. Quinlan, C4.5 Programs for Machine Learning. San Mateo:Morgan Kaufmann, 1993.


[21] K. Kira and L. A. Rendell, “A practical approach to feature selection,”in Proc. 9th Int. Workshop Mach. Learning, San Francisco, CA, 1992,pp. 249–256.

[22] H. Liu and R. Setinono, “A probabilistic approach to feature selection—Afilter solution,” in Proc. 13th Int. Conf. Mach. Learning, Bari, Italy, 1996,pp. 319–327.

[23] M. Hall et al., “The WEKA data mining software: An update,” SIGKDDExplorations, vol. 11, pp. 10–18, 2009.

[24] D. Furcy and S. Koenig, “Limited discrepancy beam search,” in Proc. Int.Joint Conf. Artif. Intell., 2005, pp. 125–131.

[25] D. E. Goldberg, Genetic Algorithms in Search, Optimization and MachineLearning. Boston, MA: Addison-Wesley, 1989.

[26] C.-C. Chang and C.-J. Lin. (2001). LIBSVM: A library for supportvector machines. [Online]. Available: [Accessed: March 10, 2011.]http://www.csie.ntu.edu.tw/∼cjlin/libsvm

[27] S. S. Keerthi et al., “Improvements to Platt’s SMO algorithm for SVMclassifier design,” Neural Comput., vol. 13, pp. 637–649, 2001.

[28] L. Breiman, “Random forests,” Mach. Learning, vol. 45, pp. 5–32, 2001.[29] G. H. John and P. Langley, “Estimating continuous distributions in

Bayesian classifiers,” in Proc. 11th Conf. Uncertainty Artif. Intell., SanMateo, 1995, pp. 338–345.

[30] J. Nayak, U. R. Acharya, P. S. Bhat, A. Shetty, and T. C. Lim, “Automateddiagnosis of glaucoma using digital fundus images,” J. Med. Syst., vol. 33,no. 5, pp. 337–346, Aug. 2009.

[31] Glaucoma guide. (2010). [Online]. Available: http://www.medrounds.org/glaucoma-guide/2006/02/section-1-b-meaning-of-cupping.html

Sumeet Dua (SM’08) received the M.S. and Ph.D.degrees in computer science from Louisiana StateUniversity, Baton Rouge.

He is currently the Upchurch endowed AssociateProfessor of computer science and the coordinatorof IT research for the Computer Science Programat Louisiana Tech University, Ruston. He is also anadjunct faculty member at the School of Medicine,Louisiana State University Health Sciences Center atNew Orleans. The U.S. National Institutes of HealthNIH), the U.S. National Science Foundation (NSF),

the Air Force Research Laboratory, and the Louisiana Board of Regents havefunded his research in the past five years. He has authored more than 50 researchpapers and is a co-author/editor of 3 books. He is a regular reviewer of morethan 20 international journals, has served on more than 17 NIH study sectionand NSF/CISE review panels. His research interests include database miningand indexing, pattern recognition, dimensionality reduction, bioinformatics, andheterogeneous distributed data integration.

Dr. Dua is a senior member of the ACM and the American Association forthe Advancement of Science.

U. Rajendra Acharya received the Ph.D. degreefrom the National Institute of Technology Karnataka,Surathkal, India, and the D.Engg. degree from ChibaUniversity, Japan.

He serves as visiting faculty at the Ngee Ann Poly-technic, Singapore, adjunct faculty at the SingaporeInstitute of Technology- University of Glasgow, Sin-gapore and at the Manipal Institute of Technology,Manipal, India, and associate faculty at SIM Univer-sity, Singapore. He has published more than 240 pa-pers, in refereed international SCI-IF journals (140),

international conference proceedings (41), textbook chapters (62), books (11including in those in press) with h-index of 14 (Scopus). He has received fund-ing of more than 1.5 million SGD, is on the editorial board of many journals,and has served as a guest editor for several journals. His major interests includebiomedical signal processing, bioimaging, data mining, visualization, and bio-physics for better healthcare design, delivery, and therapy.

Pradeep Chowriappa (M’09) received the B.Sc. de-gree in engineering from Osmania University, India,in 2000, the master’s degree in computer applicationsfrom the University of Madras, India, in 2003, andthe Ph.D. degree in computational analysis and mod-eling from Louisiana Tech University, in 2008.

He is currently a Postdoctoral Research Associatein the Data Mining Research Laboratory at LouisianaTech University, Ruston. His research interests in-clude bioinformatics, data mining, feature discovery,and machine learning in high-dimensional domains.

S. Vinitha Sree received the M.S. degree in biomed-ical engineering and the Ph.D. degree from NanyangTechnological University, Singapore.

She is a visiting scientist at Global BiomedicalTechnologies, Inc., CA. Her areas of interest includemedical data mining, breast imaging systems, andhealthcare systems and management. She has pub-lished over 30 peer-reviewed publications and is anassociate editor for Journal of Medical Imaging andHealth Informatics and a reviewer for the Journal ofMechanics in medicine and biology.

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