Biomedical Signal Processing and Control 10 (2014) 174–183
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Biomedical Signal Processing and Control journal homepage: www.elsevier.com/locate/bspc
Automated classification of glaucoma stages using higher order cumulant features Kevin P. Noronha a,∗ , U. Rajendra Acharya b,c , K. Prabhakar Nayak a , Roshan Joy Martis b , Sulatha V. Bhandary d a
Department of E&C, MIT Manipal, India Department of Electronics and Computer Engineering, Ngee Ann Polytechnic, Singapore c Department of Biomedical Engineering, Faculty of Engineering, University of Malaya, Malaysia d Department of Ophthalmology, Kasturba Medical College, Manipal, India b
a r t i c l e
i n f o
Article history: Received 15 August 2013 Received in revised form 4 November 2013 Accepted 20 November 2013 Available online 13 December 2013 Keywords: Fundus image Glaucoma Radon transform Higher order cumulant Naïve Bayesian
a b s t r a c t Glaucoma is a group of disease often causing visual impairment without any prior symptoms. It is usually caused due to high intra ocular pressure (IOP) which can result in blindness by damaging the optic nerve. Hence, diagnosing the glaucoma in the early stage can prevent the vision loss. This paper proposes a novel automated glaucoma diagnosis system using higher order spectra (HOS) cumulants extracted from Radon transform (RT) applied on digital fundus images. In this work, the images are classified into three classes: normal, mild glaucoma and moderate/severe glaucoma. The 3rd order HOS cumulant features are subjected to linear discriminant analysis (LDA) to reduce the number of features and then these clinically significant linear discriminant (LD) features are fed to the support vector machine (SVM) and Naïve Bayesian (NB) classifiers for automated diagnosis. This work is validated using 272 fundus images with 100 normal, 72 mild glaucoma and 100 moderate/severe glaucoma images using ten-fold cross validation method. The proposed system can detect the early glaucoma stage with an average accuracy of 84.72%, and the three classes with an average accuracy of 92.65%, sensitivity of 100% and specificity of 92% using NB classifier. This automated system can be used during the mass screening of glaucoma. © 2013 Elsevier Ltd. All rights reserved.
1. Introduction Glaucoma is a group of eye disorder that produce increased intraocular pressure (IOP) within the eye [1]. The higher IOP in the eye is usually caused by an imbalance in the production and drainage of the fluid in the eye which over a period of time damage the optic nerve causing vision loss [2]. The progress of glaucoma usually goes undetected until the optic nerve gets irreversibly damaged resulting in varying degrees of permanent vision loss [3]. It has been reported that almost 14 million people worldwide and 3 million people in the United States have glaucoma [4]. By 2020, it is estimated that approximately 79.6 million people worldwide will be diagnosed with glaucoma [5]. Also it has been reported that there is an elevated IOP of about 2% in the population between 40 and 50 years old and 8% over 70 years old making them vulnerable to loss of vision [6] and even blindness. Diagnosing the symptoms of glaucoma in an early stage helps to save the vision loss [7]. The American Academy of Ophthalmology
∗ Corresponding author. Tel.: +91 9845538161. E-mail address:
[email protected] (K.P. Noronha). 1746-8094/$ – see front matter © 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.bspc.2013.11.006
recommends a routine screening once in every 2–4 years, for people between the age group of 40–64 years and in every 1–2 years, after 65 years of age which might help in detecting the disease in its early stage [8]. Geometric parameters of the optic nerve head (ONH) are used to diagnose and to measure the progression of the glaucoma. The geometric parameters measure the changing structures of the ONH such as the diameter of the Optic disk (OD), area of the OD, cup diameter, area of the rim, and mean cup depth [9]. The treatment for the glaucoma involves medical management, trabeculectomy, laser surgery and drainage implants [10]. Mass screening of the patients helps to diagnose the glaucoma in the early stage and can help to save from the surgery [11]. The main characteristics of glaucoma are the deterioration of optic nerve fibers and astrocytes followed by a high IOP. The deterioration of optic nerve fibers decreases the thickness of retinal nerve fiber layer (RNFL). The degeneration of astrocytes and axons leads to the changes in the ONH configuration and thereby decreasing the functional capability of retina. The loss of astrocytes and axons expands the cup and makes the neoretinal rim thinner [12]. Opthalmoscopy or stereo fundus photography of ONH can easily detect these changes and are widely used by ophthalmologists to document the disk, rim, cup areas and disk diameter [13].
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Digital fundus image analysis is valuable in understanding the natural development of the disease which relies on computational techniques to make qualitative assessments of the eye [14]. These methods can reduce inter-observer and intra-observer variability errors arising during the screening of the disease by clinicians. Various morphological features like disk, cup and rim areas, disk diameter and cup to disk (C/D) ratio extracted from the digital fundus image can help to diagnose the glaucoma [15]. C/D ratio is one of the key parameter used by the ophthalmologists while screening the glaucoma [16]. A healthy OD contains more than 1.2 million fibers passing through it which makes the size of the cup very small. Glaucoma causes ONH to loose the optic nerve fibers resulting in increase in the size of the cup. The progress of glaucoma leaves optic nerve with very less optic nerve fibers causing the cup to enlarge [17]. An increased C/D ratio indicates the decrease in the quantity of healthy neuro-retinal tissue and hence, glaucomatous change [16]. The normal C/D ratio typically equals to 0.3 [18]. Glaucoma can be broadly classified into the following stages, depending on the C/D ratio and presence of focal notches (inferior or superior) on the fundus image [19]. • Mild glaucoma: The progress of glaucoma starts with the loss of nerve fibers causing the damage to the optic nerve with a normal visual field or very less vision loss (side or peripheral) [20]. As a result the size of the cup enlarges and the C/D ratio at this stage is usually between 0.4 and 0.7. • Moderate/severe glaucoma: This is an advanced stage of glaucoma where the presence of a small number of optic nerve fibers causes severe damage to optic nerve [21]. The C/D ratio at this stage is usually more than 0.7. This stage also shows the presence of focal notches (inferior or superior) [22] and optic nerve hemorrhages. In moderate cases the central vision may not be affected. But if not controlled, the severe stage of glaucoma can cause the central vision loss [18]. Typical normal, mild, moderate and severe glaucomatous fundus images are shown in Fig. 1. While evaluating the patients for glaucoma the ophthalmologist monitors three things. First the intra-ocular pressure which is measured using a Goldmann applanation tonometer [23]. Second the visual field analysis which is carried out using the Humphrey field analyzer [24] that generates a computerized print out marking areas within the central 30◦ of patient’s visual field. The final parameter is the optic nerve head (ONH) appearance [25]. In the screening programs these parameters play a significant role in identifying the patients with glaucoma. Since the measurement of IOP and visual fields are not suitable for mass screening, detection of OD plays a major role in diagnosing glaucoma suspects [26] by measuring cup to disk ratio. Hough transform [27], geometric parametric model [28], fuzzy convergence [29], contour model based approaches [30]
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and template matching [31] are the few techniques used to detect the ONH automatically. Manual and semi-automated diagnosis of glaucoma is tedious, time consuming and may cause observer variability errors (intra/inter) while assessing the structural abnormalities of the eye by different clinicians. The diagnostic outcome might get affected even if there is a small error in the segmentation. Hence, a computer aided diagnosis (CAD) can help the clinicians to overcome these problems and can be used as adjunct tools by the clinicians to cross check their diagnosis [32,33]. These CAD tools analyze the entire input image and extract the salient features. CAD techniques do not depend on the individual segmentation and measurement of the various geometric parameters because even a small error in the segmentation may lead to wrong diagnosis [34]. The CAD methods are fast, inexpensive and can be executed even without an expert’s assistance. Fig. 2 shows the block diagram of the proposed system which is divided into offline and real time system. Image pre-processing is the first step in the offline mode where the entire set of fundus images (normal, mild and moderate/severe) is pre-processed. The 3rd order HOS cumulants features are then extracted after applying the Radon transform on the pre-processed fundus images. Analysis of variance (ANOVA) test is conducted for the evaluation of clinical significance of the extracted features. The ground truth (given by the ophthalmologist) about the different classes to which the fundus image belongs as well as the extracted significant feature set are then fed into the classifier. The classifier performance is measured using a ten-fold cross validation strategy. In the real time mode, the fundus images are pre-processed first and the significant features are extracted from them and fed to the trained classifier for classification. It then performs the classification into normal, mild glaucoma and moderate/severe glaucoma classes based on the extracted significant features. The present paper is organized as follows: The images used for this study, pre-processing, feature extraction by HOS cumulants and LDA is explained in Section 2. Classifiers used for automated diagnosis namely, SVM and NB are discussed in Section 3. The result obtained is presented in Section 4. Result is discussed in Section 5 and the paper concludes in Section 6. 2. Methods 2.1. Data acquisition This study uses the fundus images acquired from a TOPCON non-mydriatic fundus camera TRCNW200 which provides 3.1 megapixels fundus images. The fundus images were collected from the Ophthalmology department of KMC, Manipal, India. The ophthalmologists of the department have certified these photographs
Fig. 1. Typical fundus images: (a) normal, (b) mild glaucoma, (c) moderate glaucoma, and (d) severe glaucoma.
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Fig. 2. The proposed system.
and this research have been approved by the research ethics committee of the institute. In this study 272 fundus images (100 normal, 72 mild glaucoma and 100 moderate/severe glaucoma) were collected in JPEG format within the age group of 24–57 year olds with a resolution of 2588 × 1958 (rows × columns). 2.2. Pre-processing The acquired fundus images were of a very high resolution of 2588 × 1958. To process these images directly takes a lot of processing time. Hence to reduce the computation time we resize the fundus images into 740 × 576. The fundus images were resized using the interpolation method [35]. The fundus images are normally photographed in non-uniform lighting environments. These images need to be pre-processed before we apply any image processing techniques for feature analysis. To remove the nonuniform background which may be due to the non-uniform illumination or variation in the pigment color of eye, we use adaptive histogram equalization technique [36]. This technique computes several histograms, each corresponding to a distinct section of the image and uses them to redistribute the lightness values of the image. It increases the dynamic range of the histogram of an image and assigns the intensity values of pixels in the input image such that the output image contains uniform distribution of intensities. 2.3. Radon transform Radon transform is a special case of image projection operations [37]. The 2D Radon transformation is the projection of the image
intensity along a radial line oriented at a specific angle. This property of the transformation helps in applications where detection of features along line integrals plays an important role. Applying the Radon transform on an image g(x, y) for a given set of angles is similar to computing the projection of the image along the given angles [38]. The resulting projection is the sum of the intensities of the pixels in each direction, i.e. a line integral. The Radon transform of a function g(x, y) is given by
∞
R(, ) =
g(x, y)ı( − x cos − y sin )dxdy
(1)
−∞
where is the angles at which the line integrals are calculated and = x cos + y sin with ı being the Kronecker delta function. The Kronecker delta is a function of two variables, usually integers. The function is 1 if the variables are equal and 0 otherwise:
ıij =
0
if i = / j
1
if i = j
(2)
where Kronecker delta ıij is a piecewise function of variables i and j. In this study, we have computed RT for every 10◦ angle. Third order HOS cumulants are computed from these one-dimensional signals. 2.4. Higher order cumulant features The first two order statistics have been used extensively in biosignal processing. The first two order statistics are the first two order moments and their derived statistics such as power spectral density (PSD). However, most of the bio-signals are nonlinear,
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Fig. 3. Typical 3rd order HOS cumulant of normal images at 60◦ (a) magnitude and (b) contour plot of (a).
non-stationary and non-Gaussian in nature, and thus need to model the higher order statistics of the signal such as third and fourth order statistics. The higher order spectra cumulants are the higher order correlations of the given signal [39]. They are derived from the higher order moments. HOS finds its application in the analysis of epileptic EEG signals [40], cardiac health diagnosis [41], automated analysis of sleep stages [42], etc. Let X(k), k = 0, ± 1, ± 2, ± 3, . . . be a sampled digital signal. The first four moments [43] m1X , m2X , m3X and m4X are defined as
⎧ m1X ⎪ ⎪ ⎪ ⎪ ⎨ m2X (1 )
⎪ m3X (1 , 2 ) ⎪ ⎪ ⎪ ⎩
= E[X(k)] = E[X(k)X(k + 1 )] = E[X(k)X(k + 1 )X(k + 2 )]
(3)
m4X (1 , 2 , 3 ) = E[X(k)X(k + 1 )X(k + 2 )X(k + 3 )] The nth order moment function is given by
mnX (1 , 2 , 3 . . .n−1 ) = E[X(k)X(k + 1 )X(k + 2 )X(k + 3 ) . . .X(k + n−1 )]
(4)
The first four cumulants C1X , C2X , C3X and C4X of a zero mean process are defined as
⎧ C1X ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ C2X (1 ) ⎨
C3X (1 , 2 )
= m1X
features, principal component analysis (PCA), linear discriminant analysis (LDA) and independent component analysis (ICA) techniques were used. However, LDA yielded the highest classification accuracy. Figs. 3–6 shows the typical 3rd order HOS cumulants and its corresponding contour plots of normal, mild, moderate and severe glaucoma images respectively. 2.5. Linear discriminant analysis (LDA) LDA helps to classify the data by providing the highest possible discrimination between different classes of data. PCA modifies the shape and location of the original data sets when projected to a different space while LDA preserves the location with maximum class separability [44]. For any dataset, LDA can guarantee maximal class separability by maximizing the ratio of between-class variance to the within-class variance. In LDA, apart from the dimensionality reduction, a maximum discriminations of classes can be obtained by using the within class scatter matrices and between class scatter matrices [45,46]. Let S˜ W be the within the class scatter matrix, S˜ B be the between class scatter matrix and S˜ T be the mixture scatter matrix which is the covariance of all samples regardless of class assignment. The matrices can be mathematically given as S˜ W =
⎪ ⎪ ⎪ C4X (1 , 2 , 3 ) = m4X (1 , 2 , 3 ) − m2X (1 )m2X (2 − 3 ) ⎪ ⎪ ⎪ − m2X (2 )m2X (3 − 1 ) ⎪ ⎩
(5)
(7)
S˜ B =
c
Ni ( ˜ i − )( ˜ ˜ i − ) ˜ T
(8)
i=1
S˜ T = S˜ W + S˜ B
− m2X (3 )m2X (1 − 2 )
The nth order cumulant can be derived using the nth order moment and is as follows. CnX (1 , 2 , 3 , . . .n−1 ) = mnX (1 , 2 , 3 , . . .n−1 ) − mnG (1 , 2 , 3 , . . .n−1 )
(y − ˜ i )(y − ˜ i )T
i=1 y∈wi
= m2X (1 ) = m3X (1 , 2 )
c
(6)
where mnX ( 1 , 2 , 3 , . . . n−1 ) is the nth order moment function and mnG ( 1 , 2 , 3 , . . . n−1 ) is the nth order moment of an equivalent Gaussian process. 3rd order HOS cumulant coefficients are extracted for every 10◦ (10◦ , 20◦ , 30◦ ,. . ., 180◦ ). In order to reduce the dimensionality of
(9)
where ˜ i = ith class mean, ˜ = global mean, Ni = number of samples in theith class. The LDA space is spanned by the set of vectors W satisfying the following equation. W = arg W max
|W T S˜ B W | |W T S˜ W W |
(10)
The projection matrix W consists of Eigen vectors corresponding −1 to k largest Eigen values of the matrix, S˜ w SB .) Suppose there are C classes, LDA reduces the dimensionality into C − 1 classes. Since we have 3 classes (normal, mild and moderate/severe) of glaucoma we get two sets of LDA features
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Fig. 4. Typical 3rd order HOS cumulant of mild images at 60◦ (a) magnitude and (b) contour plot of (b).
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Fig. 5. Typical 3rd order HOS cumulant of moderate images at 60◦ (a) magnitude and (b) contour plot of (c).
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Fig. 6. Typical 3rd order HOS cumulant of severe images at 60◦ (a) magnitude and (b) contour plot of (d).
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i.e. LDA1 and LDA2 for different angles. ANOVA test is performed on the linear discriminant values. It is a statistical hypothesis test which uses the variances to check if the means are different. The null hypothesis is rejected when p < 0.05. 2.6. Feature ranking using Fisher’s discrimination index (F) When building a robust learning model, feature selection plays an important role because it describes a range of statistical methods used to select a subset of significant features. The importance of a particular feature can be valued if we know the rank of the feature among other features based of some metric. The feature with the top rank is more valued for the classification than a feature with a lower rank. Also ignoring the features with the lower rank can increase the classification speed. In this work, the significant features are ranked based on Fisher’s discrimination index (F) [47]. The feature which has the higher F-value is ranked first and vice versa. The Fisher’s discrimination index (F) gives us the rank of a particular feature among the entire features. This is useful as we can input the highest ranked features first and lower ranked features next. To evaluate the performance, these ranked features are added one by one to a particular classifier until the highest classification accuracy is reached.
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Using Bayes theorem, we can write P(Cj |X) =
P(X|Cj )P(Cj )
(12)
P(X)
Here only P(X|Cj )P(Cj ) needs to be maximized as P(X) is same for all classes. It becomes computationally very expensive to calculate P(X|Cj ) if the given set has many attributes. In order to reduce the computational cost, the Naïve Bayesian makes an assumption which states that the attributes are conditionally independent [52]. Mathematically it can be expressed as P(X|Cj ) =
n
P(xk |Cj )
(13)
k=1
3.3. Performance measures A ten-fold cross validation strategy is employed to test the classifiers using the extracted features. Here the entire datasets is divided into ten equal parts (almost). The process begins with the training of first nine parts of the data and testing using remaining one part. The procedure is repeated nine more times for different sets of training and testing data. The accuracy, PPV (positive predictive value), sensitivity and specificity are computed for each iteration. The average of all the ten folds gives the actual accuracy, PPV, sensitivity and specificity.
3. Classifiers 4. Results Support vector machine (SVM) and Naïve Bayesian (NB) classifiers are used for the automated diagnosis of glaucoma. They are briefly explained below: 3.1. Support vector machine
4.1. Classification results
SVM is a nonlinear classifier based on the statistical learning theory which can classify the unknown data correctly because of its higher generalization ability [48]. The aim is to find a maximum margin hyperplane in the feature space that can separate positive and negative examples from each other. SVM uses a linear hyperplane to separate the dataset optimally in a higher dimensional plane when the data is non-linearly related to the input plane. When the data is linearly inseparable, the data is first projected into a new space using a kernel transformation and then the optimization is carried in the kernel space. Kernel transformation gives the inner product between two points in a suitable high dimensional space with a small computational cost [49]. In this work, we have used quadratic kernel, polynomial kernel of orders 2 and 3 and the radial basis function (RBF) kernel for the classification. 3.2. Naïve Bayesian classifier
1 ≤ j ≤ m,
Table 1 shows the classification results of SVM and NB classifier using features presented in Table A1. The performance of both classifiers increased continuously by adding the features up to thirty-five features (NB) and started to decrease after this. Hence, we have chosen 35 features for this work. We have evaluated the accuracy, positive predictive value (PPV), sensitivity and specificity for all the classifiers using these sets of features. Table 1 shows that for the given dataset the NB classifier show the best classification accuracy of 92.65%, sensitivity of 100% and specificity of 92% using first 35 ranked features. The confusion matrix of the proposed system is shown in Table 2. It can be seen from this table that, the proposed method is able to diagnose the early stage of glaucoma with an accuracy of 84.72% and all three stages with an average accuracy of 92.65%. Over all accuracy =
The NB classifier is a simple but effective classifier based on Bayes’ theorem. The main task of this classifier is to classify the unclassified objects into one of the m classes [50]. It is based on the class conditional independence [51]. The classification is based on the knowledge of the similar objects already classified known as training sets. Let D be a training set of data with the associated labels. Let C1 , C2 , C3 ,. . ., Cm be the m classes. Let X = (x1 , x2 ,. . ., xn ) be the n-dimensional vector representation for each sample illustrating n computed values of the n attributes, A1 , A2 ,. . ., An . When a data X with unknown class was given as input to the classifier, the classifier predicts that X ∈ Ci if and only if it has the maximum posteriori probability conditioned on X. P(Ci |X) > P(Cj |X) for all
Table A1 presents thirty-five clinically significant LDs computed from the third order HOS cumulant features evaluated for every 10◦ . The features are ranked according to their F-value.
j= / i
(11)
=
Correctly classified ((normal+(mild)+(moderate/severe))) Total number of images used for classification 92 + 61 + 99 = 92.65% 272
Table 1 Sensitivity, specificity, accuracy and PPV values presented by the classifiers using all features (Table A1) for training and testing (mean ± standard deviation). Classifiers
No of features
Acc (%)
PPV (%)
Sn (%)
Sp (%)
SVM, RBF (Sigma = 3) SVM, Linear SVM, Quadratic SVM, Poly3 NB
35 36 35 26 35
90.07 86.03 84.58 84.55 92.65
95.27 95.81 93.64 93.72 95.70
100.00 100.00 97.74 100.00 100.00
91.00 92.00 88.00 88.00 92.00
Notations used: Sn: sensitivity, Sp: specificity, Acc: accuracy, PPV: positive predictive value.
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Table 2 Confusion matrix of NB classifier after ten-fold cross validation. Classes
Normal
Mild
Normal Mild Moderate/severe
92 0 0
2 61 1
Moderate/severe 6 11 99
Total 100 72 100
Total
92
64
116
272
5. Discussion Many results have been reported on the classification of normal and glaucoma classes. Classification of normal, mild glaucoma and moderate/severe glaucoma fundus images using higher order cumulant features with a sensitivity of 100% is the novelty of this paper. Using artificial neural network (ANN) model glaucoma was detected with 95% sensitivity and 94% specificity using M-VEP (multifocal-visual evoked potential) data [53]. A Taiwan Chinese population database was classified into normal and glaucomatous using the RNFL thickness measurement data obtained from the scanning laser polarimetry variable corneal compensation using LDA and ANN [54]. They demonstrated that the nerve fiber indicator is the best parameter for differentiating normal eye from the glaucomatous eye with an area under receiver operating curve (AROC) of 0.932. The other methods such as ANN and LDA showed an AROC of 0.950 and 0.970.Hence all three methods demonstrated their usefulness in diagnosing the glaucoma with almost similar AROC. A comparative study of diagnostic accuracy of various algorithms based on the visual field loss was presented [55]. ANN was able to find the defects in the visual fields of the glaucomatous images with a sensitivity of 93%, specificity of 94% and an AROC curve of 0.984. Authors have concluded that the diagnostic performance of ANN based method was comparatively higher than the Hemifield test (sensitivity of 92% and specificity of 91%), pattern standard deviation (sensitivity of 89% and specificity of 93%), cluster algorithm (sensitivity of 95% and specificity of 82%). Various morphological features of ONH such as C/D ratio, the ratio of the distance between the cup portion of the ONH to the diameter of the OD and the ratio of blood vessels area in
inferior–superior side to area of blood vessel in the nasal–temporal side (ISNT ratio) of fundus image were used to design the ANN [3]. The classifier was able to classify the normal and glaucomatous subjects with a sensitivity 100% and specificity 80%. An orthogonal decomposition method was used to diagnose the glaucoma depending on the variations in the ONH. Image correspondence measures-L1-norm and L2-norm, correlation, and image Euclidean distance (IMED) were used to compute the changes in the ONH [56]. They obtained an AROC of 0.94 at 10◦ field of imaging, and 0.91 of AROC at 15◦ field of imaging using the L2-norm and IMED. Bock et al. have proposed a glaucoma risk index (GRI) for the automated detection of glaucoma using digital fundus images [17]. The normal images were differentiated from glaucoma images using a data driven approach by statistically analyzing the ONH. The fundus images were pre-processed first and then the extracted features were applied to principle component analysis. Using a SVM classifier they reported an accuracy of 80%. The gradual deterioration of retinal nerve fibers (RNF) is an important characteristic of glaucoma. The texture analysis of color or gray scale images was able to detect these changes and indicate RNF atrophy [57]. Fractal and power spectral features were used to differentiate the glaucoma images using SVM classifier and reported an accuracy of 74%. A random forest classifier was used to diagnose the glaucoma images using texture and HOS features and reported an accuracy of 91%[58]. The wavelet features extracted from different families of wavelet filters were subjected to various feature ranking and feature selection techniques. Various classifers were used to determine the efficiency of the selected features [59].They reported an accuracy of 93.33% using LibSVM and sequential minimal optimization (SMO) classifier in classifying normal and glaucoma images. HOS and wavelet energy features were used for the classification of normal and glaucomatous images using different kernels of the SVM classifier. An average accuracy of 95% was reported for the SVM with polynomial kernel of order 2 [60]. They have also proposed a glaucoma risk index (GRI) to identify the glaucoma and normal class using just one number. The summary of the studies by different authors is given in Table 3.
Table 3 Summary of studies that present various approaches to glaucoma detection using features extracted from fundus images used in this study. Authors
No. of classes
Features
No of images
Classifier used
Sn (%)
Sp (%)
Acc (%)
Nagarajan et al. [53]
Two (normal/glaucoma) Two (normal/glaucoma)
MVEP
399
ANN
95
94
94
PCA on pixel intensities, FFT and spline Cup to disk ratio, distance between OD center and ONH, and ISNT ratio RNF layer thickness measurement L1-norm and L2-norm, correlation, IMED Fractal and power spectral features HOS and texture
200
SVM
NA
NA
80
61
ANN
100%
80
NA
165
LDA, ANN
NA
NA
AROC= 0.932
12 Primates (24 eyes) from LEG study 30
Orthogonal decomposition
NA
NA
AROC= 0.94
SVM
NA
NA
74
60
Random-forest
NA
NA
91
Wavelet energy
60
SMO
NA
NA
93
HOS and wavelet
60
SVM
93.33
96.67
95
272
NB
100
92
92.65 84.72 for mild stage
Bock et al. [17]
Nayak et al. [3]
Two (normal/glaucoma)
Huang et al. [54]
Two (normal/glaucoma) Two (normal/glaucoma)
Balasubramanian et al. [56] Kolar et al. [57] Acharya et al. [58] Dua et al. [59] Mookiah et al. [60] Our method
Two (normal/glaucoma) Two (normal/glaucoma) Two (normal/glaucoma) Two (normal/glaucoma)
HOS cumulants Three (normal/mild/moderatesevere)
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Most of the work carried out in the literature classifies the fundus images into normal and glaucomatous classes. In the present work the fundus images were classified into three classes (normal, mild glaucoma and moderate/severe glaucoma) for the first time. In this work, a classification average accuracy of 92.65%, sensitivity of 100% and specificity of 92% for three classes and an average accuracy of 84.72% for the detection of early stage is reported using NB classifier. The proposed algorithm has the following salient features:
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accuracy of 92.65%, sensitivity of 100% and specificity of 92% and early stage of glaucoma with an average accuracy of 84.72% is the novelty of this paper.
6. Conclusion Prolonged glaucoma may cause irreparable damage to the retina resulting in permanent blindness. The early identification of glaucoma may prevent the vision loss. Regular screening of eye will help to diagnose and treat glaucoma. This work proposes a novel nonlinear method based on 3rd order HOS cumulants to detect the early stage of glaucoma. LDA is applied on the HOS cumulant features for the dimensionality reduction and clinically significant LDs are fed to the SVM and NB classifiers to select the best classifier for the automated diagnosis. The proposed technique can detect the mild glaucoma stage with an average accuracy of 84.72%, normal, mild and moderate/severe stages of glaucoma with an average accuracy of 92.65%, sensitivity of 100% and specificity of 92% using NB classifier with ten-fold cross validation. The presented automated detection of glaucoma is based on the features extracted from the entire fundus image. As a future work the features extracted from cup to disk ratio and RFNL can be used for classification and can be used to develop a glaucoma risk index (GRI) which can classify the different stages of glaucoma with just a single number.
(a) 3rd order HOS cumulant features are derived from radon transformed fundus images. The system does not rely on any complex lesion detection techniques. (b) It can be concluded from the confusion matrix shown in Table 2 that, average classification accuracy of mild glaucoma class is 84.72% and the false positive is zero. (c) The proposed system automatically extracts features and uses them with the NB classifier to predict the class (normal, mild and moderate/severe) of the subject. Since no user-interaction is necessary, the end results are more objective and reproducible compared to manual interpretations, which may lead to inter-observer variations. (d) The system is developed using ten-fold cross validation data resampling, hence it can predict the unknown class more accurately. So, the proposed method is more robust. (e) The system is able to automatically identify all the abnormal subjects as abnormal (no false positive cases), as the sensitivity of the system is 100%. This will reduce the workload of clinicians a lot, as they need to focus only on the normal classes. (f) The accuracy of this system can be increased further using huge database with diverse images, other nonlinear features and better classifiers. (g) HOS features can capture the subtle variations in the pixels easily and are more robust to noise.
Conflict of interest No conflict of interest is involved in this paper.
Acknowledgement The authors would like to express their gratitude to Dr. Lavanya G. Rao Head, Department of Ophthalmology, Kasturba Medical College, Manipal, India for providing the necessary images and clinical details needed for this research work.
The limitation of the system is that, it uses 35 features to achieve 92.65% accuracy using 272 digital fundus images. This accuracy may fall with increase in the number of images. In order to obtain high performance, clinically significant features need to be extracted from diverse huge database. This will necessitate a huge storage space for the CAD system. The classification of normal, mild and moderate/severe glaucoma classes (three classes) with an average
Appendix A. See Table A1
Table A1 Range of LDs (mean ± standard deviation) extracted using higher order cumulants (p < 0.005). Feature
Normal
◦
3.688 3.445 −3.052 −3.033 2.879 2.793 2.777 2.753 2.745 −2.732 −2.696 −2.680 −2.642 2.639 2.626 2.619 −2.567 −2.467 −0.052 0.036 −0.016
110 LDA1 100◦ LDA1 120◦ LDA1 80◦ LDA1 160◦ LDA1 170◦ LDA1 90◦ LDA1 30◦ LDA1 10◦ LDA1 180◦ LDA1 150◦ LDA1 130◦ LDA1 20◦ LDA1 70◦ LDA1 50◦ LDA1 60◦ LDA1 140◦ LDA1 40◦ LDA1 10◦ LDA2 100◦ LDA2 30◦ LDA2
Mild ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
1.149 1.107 1.198 1.157 1.148 1.024 1.168 1.043 1.035 1.060 1.103 1.170 1.145 1.147 1.131 1.131 1.185 1.178 0.879 0.765 0.701
−2.508 −1.909 1.863 1.747 −1.582 −1.795 −1.831 −1.636 −1.492 1.863 1.683 1.711 1.278 −1.531 −1.771 −1.780 1.339 1.596 1.804 −1.721 −1.627
± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
0.875 0.911 0.925 0.898 0.922 1.041 0.988 0.950 0.977 1.059 0.904 0.841 0.980 0.924 1.007 0.987 1.026 0.925 1.099 1.350 1.382
Moderate/severe
F-Value
−1.882 −2.071 1.710 1.774 −1.740 −1.500 −1.458 −1.575 −1.671 1.390 1.484 1.449 1.721 −1.537 −1.350 −1.336 1.602 1.318 −1.247 1.202 1.187
1088.577 942.761 739.730 730.327 658.560 621.342 615.299 601.332 598.097 594.423 577.780 570.997 557.552 551.709 550.672 548.342 524.208 484.611 195.996 179.853 166.713
± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
0.913 0.941 0.811 0.887 0.882 0.936 0.800 0.985 0.976 0.889 0.950 0.912 0.841 0.886 0.836 0.853 0.740 0.840 1.032 0.900 0.916
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Table A1 (Continued) Feature ◦
20 LDA2 170◦ LDA2 180◦ LDA2 90◦ LDA2 70◦ LDA2 40◦ LDA2 140◦ LDA2 50◦ LDA2 110◦ LDA2 150◦ LDA2 120◦ LDA2 130◦ LDA2 160◦ LDA2 80◦ LDA2 60◦ LDA2
Normal −0.121 −0.075 0.115 −0.091 −0.001 0.071 −0.062 0.097 −0.101 0.043 0.029 0.057 0.032 −0.005 0.091
Mild ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
0.831 0.728 0.719 0.707 0.756 0.752 0.788 0.885 0.807 0.733 0.668 0.719 0.907 0.805 0.765
1.658 −1.511 1.424 −1.430 1.427 1.362 1.390 1.282 −1.249 1.278 1.283 1.255 −1.307 1.280 1.130
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F-Value 158.515 150.846 139.420 137.585 126.447 123.043 114.248 112.043 107.304 105.897 105.254 103.556 103.183 101.555 87.849
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