Differential Entropy in Wavelet Sub-Band for Assessmentof Glaucoma

Malaya Kumar Nath, Samarendra Dandapat

Department of Electronics and Electrical Engineering, IIT Guwahati, Guwahati, Assam, India

Received 23 April 2012; revised 18 May 2012; accepted 24 May 2012

ABSTRACT: Glaucoma is an eye disease that causes progressive

optic neuropathy and vision loss due to degeneration of the opticnerves. Cup to disc ratio (CDR) is the standard measure for evaluation

of glaucoma. It is difficult to estimate the value of CDR if the bounda-

ries of cup and disc are not well defined. In this work, we propose anovel method based on differential entropy (DE) for evaluation of

glaucoma. DE can be used as a measure of glaucoma as it is propor-

tional to the probability of number of glaucoma pixels in wavelet sub-

bands. It has been shown that DE or negentropy value of 0.25 as anoptimum threshold for glaucoma detection. This method is evaluated

and its performance is compared with three existing methods using

54 retinal images. The proposed method shows the best result with

an accuracy value of 92.59%. VVC 2012 Wiley Periodicals, Inc. Int J Imag-

ing Syst Technol, 22, 161–165, 2012; Published online in Wiley Online Library

(wileyonlinelibrary.com). DOI 10.1002/ima.22017

Key words: glaucoma; differential entropy; cup to disc ratio; wavelet

sub-band

I. INTRODUCTION

Glaucoma (Leite et al., 2011) is the leading cause of blindness after

diabetic retinopathy (Niemeijer et al., 2010) worldwide. It occurs

due to the elevated intraocular pressure (IOP) exerted by aqueous

humor of the eye (Schacknow and Samples, 2010). IOP can be

measured by Tonometry, Goldman Applanation Tonometry, and

Tonopen. These methods of defining glaucoma do not provide accu-

rate measurement always, as tissue damage does not have a direct

relation with IOP. So, IOP cannot be used as a standard measure for

glaucoma. It is a critical job for the doctors to detect the vision loss

or glaucoma by measuring IOP (Jonas et al., 1999). Visual field is

more specific indicator than IOP. Visual field test is done by perim-

etry, which document the level of peripheral vision. In this case, the

patient responds to a perceived flash of light by looking at it every

time. The accuracy of the testing depends on patient’s patience,

attention, and retinal sensitivity. Limitations in IOP measurement

and visual field test are reduced by looking at the appearance of

optic disc (OD). Glaucoma affects the structure of optic nerve head

by reducing the neuroretinal rim. Glaucoma minimally affects the

other regions except the OD. Figures 1a and 1b show the cup and

disc regions in fundus images. Figures 1c and 1d show the OD with

glaucoma. Cup to disc ratio (CDR) increases with the progression

of the disease. CDR is used as a measure for progression of glau-

coma (Mishra et al., 2011). Bock et al. (2010) used the concept of

principal component analysis (PCA) and support vector machine

(SVM) for glaucoma prediction. Mishra et al. (2011) used active

contour-based method for finding CDR value for evaluation of glau-

coma (Mishra et al., 2011). In some glaucoma cases, the cup and

disc are not distinguished clearly as shown in Figures 1c and 1d. In

such cases, CDR cannot be used as a measure for glaucoma. The in-

formation regarding the changes in cup size is most vital for assess-

ment of glaucoma. In this article, we propose a novel method which

is based on evaluation of differential entropy (DE) in wavelet sub-

band-5 for prediction of glaucoma. Wavelet sub-band-5 highlights

the OD region by suppressing the blood vessels. Blood vessels are

minimally affected by glaucoma. The rest of the article is organized

as follows. Methodology is explained in Section II. Results are pre-

sented in Section III, and conclusions are discussed in Section IV.

II. METHODOLOGY

The proposed method for glaucoma prediction is shown in Figure 2.

It consists of preprocessing, wavelet decomposition, segmentation-

of-cup, and measurement of information by DE.

A. Preprocessing. OD appearance changes during glaucoma.

Gradually, the cup size increases with the progression of glaucoma.

Preprocessing is applied to the green channel of the color fundus

image as green channel provides higher contrast between the

features and the background. Preprocessing consists of cropping,

illumination correction, and histogram equalization to provide the

details of OD. Cropping provides the details about the OD. Illumi-

nation correction is performed to have homogeneous background,

which is obtained by subtracting the mean value of the image from

the original image. Histogram equalization is applied to all the

images in order to spread energy of all the pixels inside the image

and then normalize them to equalize the amount of energy related

to each image.

Figure 3 shows the different preprocessing stages for glaucoma

detection. Figure 3a is the cropped color fundus image with 128 3

128 pixels in bit-map format taken from OD organization (MishraCorrespondence to: Malaya Kumar Nath; e-mail: malaya@iitg.ernet.in

' 2012 Wiley Periodicals, Inc.

et al., 2011). Figures 3b, 3c, 3d show the red, green, and blue chan-

nel of the cropped color fundus image, respectively. Red channel is

highly saturated whereas blue channel is under saturated and noisy.

Green channel image, shown in Figure 3c is minimally saturated.

So, green channel image is used for glaucoma detection. Figure 3e

is the illuminated corrected image. It has homogeneous background.

Figure 3f shows the histogram-equalized image. Histogram equal-

ization provides uniform distribution of energy. Wavelet decompo-

sition is applied to histogram equalized image.

B. Wavelet Decomposition. Spatial and frequency localization

of an image is obtained by wavelet transform (WT) (Mallat, 1999;

Gonzalez, 2006). In multiresolution analysis, dilation and transla-

tion generates a series of approximations function uj,k (x) by the

help of scaling function u (x). In the same way, dilation and transla-

tion over mother wavelet f(x) generates a family of wavelet fj,k

(x). 2D discrete WT (2-DWT) decomposes the image into approxi-

mation sub-band (A) and three detail sub-bands. The detail sub-

bands contain the horizontal detail (H), vertical detail (V), and diag-

onal detail (D) coefficients. N-Level DWT yields an approximation

band of the final decomposition level and three detail bands of each

level. The DWT of an image p(x, y) of size (P 3 Q) can be defined

as follows.

WTuðj0;m; nÞ ¼1ffiffiffiffiffiffiffiPQ

pXP�1

x¼0

XQ�1

y¼0

pðx; yÞuj0;m;nðx; yÞ ð1Þ

WTb/ðj;m; nÞ ¼

1ffiffiffiffiffiffiffiPQ

pXP�1

x¼0

XQ�1

y¼0

pðx; yÞ/bj;m;nðx; yÞ ð2Þ

Here (m, n) determines the position of wavelet function and j0 is thestarting level. WTu (j0,m,n) and WTf

b (j,m,n) coefficients representthe approximation and detail coefficients of p(x, y), respectively.

Wavelet sub-bands highlight different information of features in

a fundus image (Quellec et al., 2008; Nirmala et al., 2010). In this

work, five-level wavelet decomposition with Daubechies-4 (D4)

mother wavelet is implemented. Five-level decomposition gener-

ates one approximation band and 15 detail bands. Five-level decom-

position is sufficient to highlight the OD region by suppressing the

blood vessels. Blood vessels present in OD are minimally affected

by glaucoma. Figure 4a shows a fundus image, and two wavelet

sub-band images are shown in Figures 4b and 4c. It can be observed

that blood vessels appear with the cup in the sub-band-3 image

shown in Figure 4b. In sub-band-5 image shown in Figure 4c, the

blood vessels are suppressed. This image contains only the cup in-

formation. This is due to the low frequency characteristics of cup

information. Different wavelet sub-bands for a number of fundus

images are evaluated. It is observed that sub-band-5 contains domi-

nantly the cup information. Watershed segmentation (Petrou and

Petrou, 2010) is used in wavelet sub-band-5 for detection of cup.

C. Differential Entropy as a Measure for Glaucoma. CDR

is the ratio of cup area (Ac) to disc area (Ad). The cup area and disc

area are proportional to the number of cup pixels (Nc) and the num-

ber of disc pixels (Nd), respectively. If the cup probability (pc(u)) isdefined as the ratio of number of cup pixels to the total number of

pixels in the image, then the cup area is proportional to the cup

probability. Similarly, the disc area is proportional to the disc prob-

ability (pd(u)) So, CDR can be written as

CDR ¼ Ac

Ad

¼ k:pcðuÞpdðuÞ

ð3Þ

where k is a constant. The cup size increases with the progression

of glaucoma. Normally, the disc size does not change. So the

change in CDR value will be proportional to the probability of cup.

The relative change in the cup probability can be used as a measure

of glaucoma in place of CDR. The change of cup probability can be

estimated by the differential entropy (DEc) (Hyvarinen et al., 2001)

of the cup

DEc ¼ZpcðuÞ log2

pcðuÞp/ðuÞ

du ð4Þ

where pf(u) is the probability of the Gaussian random variable

with same mean and variance as that of pc(u). This measure does

not require the evaluation of disc size, which is difficult to estimate

Figure 1. Different types of disc: (a) normal disc; (b) glaucoma disc with increase in cup size; (c) glaucoma with inflamed disc; (d) glaucoma

with disc anomalies. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Figure 2. Proposed method: Assessment of glaucoma from color fundus image.

162 Vol. 22, 161–165 (2012)

in some glaucoma cases. By choosing a suitable threshold, the nor-

mal and glaucoma images can be separated. The optimum threshold

value for DEc is calculated by the simulated cup and disc. Figure 5

shows CDR value versus DEc value for different sizes of cup. The

DEc value of cup lies below 0.26 for the CDR value ranges from

0.3 to 0.5. DEc value is higher than 0.26 for glaucoma images. The

linear relationship between CDR and DEc values suggests that DEc

can be used not only for detection of glaucoma but also for evalua-

tion and progression of glaucoma.

III. RESULTS AND DISCUSSIONS

The proposed method is applied on the data obtained from the

optic-disc organization (Mishra et al., 2011). It consists of eight

normal images and 37 glaucoma images of dimension of 144 3 144

pixels in bit-map format. From DRIVE database (Niemeijer and

Ginneken, 2002), nine color images of the retina are considered for

the testing purpose. Five-level wavelet decomposition is performed

on the preprocessed images using D4 mother wavelet. Watershed

segmentation is performed in wavelet sub-band-5, and DEc values

for the segmented cup are calculated. Table I shows the results for

54 images. Out of 37 glaucoma images, 35 glaucoma images are

classified correctly. Out of 17 normal images, 14 normal images are

classified correctly. For normal images, the DEc value is found to

be less than 0.25. For glaucoma images, the value is found to be

greater than 0.25. Im-7 and Im-49 are normal images, but they are

classified as glaucoma images. Im-14 and Im-15 are glaucoma

images, but they are classified as normal images. In this case, all

types of glaucoma having different disc appearance are classified.

The performance of the method is evaluated by true positive (TP),

true negative (TN), false positive (FP), and false negative (FN) val-

ues (Walter et al., 2002; Chang et al., 2009). TP, TN, FP, and FN

for the proposed method are found to be 0.9459, 0.8823, 0.1176,

Figure 4. Appearance of different features of color fundus image indifferent wavelet sub-bands: (a) preprocessed green channel image;

(b) sub-band-3 image; (c) sub-band-5 image. Figure 5. CDR value versus DE value of different size of cup.

Figure 3. Preprocessing: (a) cropped color image; (b) red channel image; (c) green channel image; (d) blue channel image; (e) illumination cor-

rected image; (f) histogram-equalized image. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Vol. 22, 161–165 (2012) 163

and 0.0540, respectively. Sensitivity (Sn) and specificity (Sp) are

defined as

Sn ¼TP

TPþ FNð5Þ

Sp ¼TN

TNþ FPð6Þ

For this method, Sn and Sp are found to be 94.59% and 88.23%,

respectively. Sn and Sp should be high value for better performance.

Figure 6 shows the receiver operating characteristic (ROC) for the

proposed method. It is the plot between the specificity versus the

sensitivity (Zou et al., 2012). The accuracy becomes maximum if

the ROC curve runs from (0, 0) coordinate to (1, 1) coordinate

through the (0, 1) coordinate. Accuracy becomes 50%, when the

ROC curve passes through the diagonal. In the proposed method,

the ROC curve lies toward the higher accuracy side. Figure 6

explains the better separation of the cup as it is more inclined to the

sensitivity. So, the method can perform better classification.

The proposed method is compared with three existing methods

(Fink et al., 2009; Bock et al., 2010; Hatanaka et al., 2011) in the

literature. Bock et al. (2010) have used PCA and SVM for glau-

coma classification. In their paper, they have reported an accuracy

value of 80%. Fink et al. (2009) have used ICA and K-nearest

neighbor (KNN) classifier for glaucoma classification. In their pa-

per, they have reported an accuracy value of 85%. Hatanaka et al.

(2011) finds the CDR which is based on line profile analysis in reti-

nal images. In this method, they have found the ratio of vertical cup

diameter (Cv) to the vertical disc diameter (Dv) as a measure of

glaucoma. For glaucoma images, the CDR value is higher than the

CDR value of normal images. They have reported an accuracy of

94.7%. The works in these papers are carried out with different

databases. In this work, the proposed method and the above three

methods are evaluated with the same dataset for comparison of their

performances. Fifty four images (37 images are glaucoma and 17

images are normal) are used for evaluation. Bock et al. (2010)

method shows different accuracy values for different kernel func-

tions. The mean accuracy value for Bock et al. (2010) with five ker-

nel functions is found to be 80%. The accuracy value for Fink et al.

(2009) is 85%. The accuracy of the Hatanaka et al. (2011) method

is found to be 79.62%. This method fails in case of disc dursen and

disc anomalies. In the proposed method, out of 54 images, a total of

50 images are correctly detected. The proposed method shows the

best result with an accuracy value of 92.59%. This shows that the

proposed method performs better compared to the existing

methods.

IV. CONCLUSIONS

In this article, normal and glaucoma images are classified by meas-

uring the DEc value of the segmented cup in wavelet sub-band. It is

not possible to evaluate the CDR if the disc is not segmented from

the image. The proposed method is effective in evaluation of glau-

coma images in different disc conditions. Accuracy of 92.59% is

obtained in the proposed method.

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