Automatic Diagnosis of Glaucoma Using Digital Fundus Images

Fig. 6.6. Block diagram to evaluate the area of blood vessels (reprinted from Ref. [14], with kind permission from Journal of Medical Systems).

was estimated by summing up the number of white pixels in a specified region, as illustrated in Fig. 6.7.

6.2.3. Measuring the ISNT Ratio

Both superior and inferior regions of the optic disc host most of the blood vessels. It has been estimated that about 27% of the optic disc area is covered with blood vessels.16 A shift in the optic nerve head is likely to cause a small increase in the blood vessel area in both nasal and temporal regions of the optic disc. This shift is likely to cause a decrease in both inferior and superior regions. The ratio between the blood vessel area in both inferior and superior regions and the blood vessel area in

215

Rajendra Acharya U. et al.

Fig. 6.7. (a) Green component, (b) complemented image, (c) subtracted image, and (d) detected blood vessels for normal fundus image.

both nasal and temporal regions can be taken as another feature. A larger ISNT ratio is a significant feature indicating the presence of glaucoma. Figure 6.8 shows a fundus image where the four quadrants are labeled. The mapping is as follows: upper quadrant maps to superior (S) region, lower quadrant maps to inferior (I) region, the quadrant nearest to the nose maps to nasal (N), and the opposite quadrant maps to the temporal (T) region. The flowchart of the computation of ISNT ratio is illustrated in Fig. 6.9.

For this experiment, blood vessels were extracted, as discussed in Sec. 6.2.2. Then, a mask of size 720 × 560 was created to identify the inferior, superior, nasal, and temporal regions. Figure 6.10 shows the masks used to identify blood vessels in each of the regions in the optic disc. Next, the mask was overlapped onto the segmented image consisting only of blood

216

Automatic Diagnosis of Glaucoma Using Digital Fundus Images

Fig. 6.8. The four quadrants of a fundus image. Clockwise: S denotes the superior quadrant, N denotes the nasal quadrant, I denotes the inferior quadrant, and T denotes the temporal quadrant (reprinted from Ref. [14], with kind permission from Journal of Medical Systems).

vessels in order to display the blood vessels. Figure 6.11 illustrates the blood vessels near ISNT.

6.2.4. Classifier

The previous section described the feature extractions step of the proposed method. Now, we discuss the classifier GMM, which was used for classification. This classification method can be categorized into one of two types: parametric and nonparametric classifiers. Parametric classifiers use data statistics to implement a so-called best discriminated function. In general, the classification error in both supervised and unsupervised learning methods can be minimized with the parametric approach. GMM uses a set of multidimensional features to estimate a continuous probability density function. A GMM probability density is composed from the sum of N multidimensional Gaussian components. GMM is described by mixture

component weights wi, means µi, and covariances i. For a single observation, x, the probability density of a GMM is described by λ:

N

217

Rajendra Acharya U. et al.

Fig. 6.9. Block diagram of ISNT ratio.

The probability density of a single Gaussian component of D dimensions is given as:

The symbol ( ) represents either vector or matrix transpose. To determine the GMM parameters requires a solution of the maximum likelihood (ML) parameter estimation criterion. The joint likelihood of T independent and identically distributed feature vector observations,

218

Automatic Diagnosis of Glaucoma Using Digital Fundus Images

Fig. 6.10. (a) Inferior mask, (b) superior mask, (c) nasal mask, and (d) temporal mask (reprinted from Ref. [14], with kind permission from Springer Science + Business Medical).

X = {x1, x2, x3, . . . , xT }, may be specified according to Eq. (6.5).

In terms of the mixture component densities, the log-likelihood function to be maximized is defined as:

219

Rajendra Acharya U. et al.

Fig. 6.11. (a) Inferior region, (b) superior region, (c) nasal region, and (d) temporal region.

In this case, ML means that the selected model parameter maximizes the likelihood of the observations. The expectation-maximization (E-M) algorithm is a general method for maximizing the log-likelihood from given observations.17 The E-M algorithm requires input parameters in the following form:

Based on these parameters, the algorithm will determine new estimates:

such that the following holds | ≥ | ˆ . p(X λ) p(X λ)

220