The cup nerve head, optic cup, optic disc ratio and neural rim configuration are observed as important for detecting glaucoma at an early stage in clinical practice. The main clinical indicator of glaucoma optic cup to disc ratio is currently determined manually by limiting the mass screening was potential. This paper proposes the following methods for an automatic cup to disc ratio determination. In the first part of the work, fundus image of the optic disc region is considered. Clustering means K is used automatically to extract the optic disc whereas K-value is automatically selected by algorithm called hill climbing. The segmented contour of optic cup has been smoothened by two methods namely elliptical fitting and morphological fitting. Cup to disc ratio is calculated for 50 normal images and 50 fundus images of glaucoma patients. Throughout this paper, the same set of images has been used and for these images, the cup to disc ratio values are provided by ophthalmologist which is taken as the gold standard value. The error is calculated with reference to this gold standard value throughout the paper for cup to disc ratio comparison. The mean error of the K-means clustering method for elliptical and morphological fitting is 4.5% and 4.1%, respectively. Since the error is high, fuzzy C-mean clustering has been chosen and the mean error of the method for elliptical and morphological fitting is 3.83% and 3.52%. The error can further be minimized by considering the inter pixel relation. To achieve another algorithm is by Spatially Weighted fuzzy C-means Clustering (SWFCM) is used. The optic disc and optic cup have clustered and segmented by SWFCM Clustering. The SWFCM mean error clustering method for elliptical and morphological fitting is 3.06% and 1.67%, respectively. In this work fundus images were collected from Aravind eye Hospital, Pondicherry.

Blindness is conditioning with lack visually perfected due to the physiological or neurological factors. The major global cause of blindness due to cataract (47.8%), glaucoma (12.3%), is age related macular degeneration (8.7%) and due to corneal opacity (5.1%).

Glaucoma is a serious ocular disease and leads to blindness if it is not detected and treated in proper way. When there is an elevated intra ocular pressure from the normal condition, the subject is affected by glaucoma and in this condition the retinal nerve fiber layer and the optic disc are affected and this leads to progressive loss of vision if not diagnosed and treated. The observation of optic nerve head, optic cup to optic disc ratio and neural rim configuration are important for detecting glaucoma at an early stage in clinical practice. However, the broad range of cup to disc ratio is difficult to identify the early changes of optic nerve head, and different ethnic groups possess various features in optic nerve head structures. Hence, it is important to develop various detection techniques to assist clinicians to diagnose glaucoma at early stages. This work presents a method for glaucoma detection using digital fundus image. As said earlier, the optic cup to disc ratio (CDR) is one of the main clinical indicators of glaucoma and is currently determined manually limiting the potential in mass screening. In this work, we propose methods for an automatic CDR determination.

Blindness causes mostly due to Glaucoma [

The cup to disc ratio is one of the most important parameters to detect the glaucoma. So, First detect the optic nerve head because disc and cup area present in optic nerve head regions only. So, in this study we are concentrated in segmentation of optic nerve head.

The discussion of the glaucoma detection was in deep convolution [

There are four features such as CDR, vertical to horizontal CDR, disc area to cup ratio and rim to disc area ratio are used for glaucoma diagnosis [

In deep learning convolutional neural network, computational time was very high. First segment optic disc and cup regions from the fundus images were used to reduce the computational time. Detected regions are fed to the convolutional neural network.

From the literature survey it is inferred that:

For the segmentation of optic disc and optic cup the level set based algorithm generally needs human interaction. The detection of incorrect boundaries by the conventional level set method is avoided by continuously reinitializing the level set function throughout the evaluation processes.

Variation level set method is introduced to eliminate the re-initialization procedure.

The energy minimization-based variation level set method does not consider the edge and region-based information, and hence the segmentation of optic cup is very difficult.

Due to large intensity variations in the cup region, thresholding techniques are not adequate.

Segmentation of optic disc and optic cup using mathematic morphological techniques highly depends on the shape and size of the selected structuring elements.

Active contour model takes more convergence time and snakes capture limited range of initialization around the region of interest.

In order to get accurate detection of optic disc and cup region, clustering techniques are proposed. In this work, proposed three unsupervised learning clustering and analysis performance of clusters using regression techniques.

In the medical field, physical measurement, manual processing and classification of medical images have increased the time and stress of clinicians. Hence this research aims to develop an automatic system for the detection of glaucoma. So, the main objectives of this research are as follows:

To determine cup to disc ratio from the retinal fundus images.

To determine regression analysis of Gold standard value and developed algorithm.

To determine any abnormality, change in retina fundus images are used. Nowadays glaucoma can be performed by measuring the key characteristic feature like Cup to Disc ratio with automated detection. In this work, three methods are described to detect glaucoma automatically based on the cup to disc ratio.

The diameter of optic cup and optic disc are calculated to compute CDR. With this method of calculations, K-means clustering technique is used to extract the optic disc in an automatic manner. By Hill climbing algorithm K-value is automatically selected. The cup is also detected by K-means clustering algorithm with the K-value of 3. In Cup segmentation process, the segmented disc output is applied to k mean clustering. In segmented disc three regions are there namely optic disc, optic cup and background, so K-value used by three.

The Green plane (G) from the RGB fundus image is separated and it is considered for the analysis, because G plane provides best contrast than other two planes is referred in [

The greater challenge in extraction was compared with the optic disc, optic cup segmentation. The optic cup region is masked in many places by the blood vessels emerging through the optic disc. Hence to correctly identify the region of optic cup, the blood vessels have to be removed from this region. In order to blur the blood vessels, wavelet transform, and morphological closing operation are used. The characteristics of biorthogonal wavelet transform is similar to shape of blood vessel, so biorthogonal wavelet transform is used for blood vessel segmentation. K-means clustering [

In this method of computation 50 normal images and 50 glaucoma images are used for analysis. In regression analysis ten images are used. These ten images collected from other data set.

Parameters | Normal images | Abnormal images |
---|---|---|

Mean value of CDR using Elliptical method | 0.2698 | 0.5461 |

Mean value of CDR using Morphological technique | 0.2529 | 0.5247 |

CDR range of Elliptical |
0.13 to 0.371 | 0.403 to 0.891 |

CDR range of Morphological |
0.12 to 0.329 | 0.401 to 0.886 |

% of Mean error of Elliptical Method | 4.5% | |

% of Mean error of Morphological Method | 4.1% |

The

The concise result was achieved through the scatter plot has been used. The scatter plot was computed CDR

In this analysis, the regression output ‘error’ is calculated from the CDR values by regression equation and proposed algorithm. For this calculation, ten new fundus images from ophthalmologist which are not used in the previous analysis are utilized along with specified gold standard CDR values. The gold standard CDR value is substituted in the

Gold standard CDR | CDR calculated by equation | CDR calculated by algorithm | Absolute error |
---|---|---|---|

0.75 | 0.7496 | 0.766 | 0.0164 |

0.65 | 0.6432 | 0.670 | 0.0268 |

0.85 | 0.8560 | 0.894 | 0.0380 |

0.80 | 0.8028 | 0.854 | 0.0512 |

0.55 | 0.5368 | 0.621 | 0.0842 |

0.45 | 0.4304 | 0.474 | 0.0436 |

0.50 | 0.4836 | 0.521 | 0.0374 |

0.70 | 0.6964 | 0.733 | 0.0366 |

0.80 | 0.8028 | 0.866 | 0.0632 |

0.90 | 0.9091 | 0.932 | 0.0229 |

Gold standard CDR | CDR calculated by equation | CDR calculated by algorithm | Absolute error |
---|---|---|---|

0.75 | 0.7126 | 0.752 | 0.0394 |

0.65 | 0.6116 | 0.644 | 0.0324 |

0.85 | 0.8136 | 0.842 | 0.0284 |

0.80 | 0.7631 | 0.811 | 0.0479 |

0.55 | 0.5106 | 0.549 | 0.0384 |

0.45 | 0.4096 | 0.459 | 0.0494 |

0.50 | 0.4601 | 0.523 | 0.0629 |

0.70 | 0.6621 | 0.696 | 0.0339 |

0.80 | 0.7631 | 0.813 | 0.0499 |

0.90 | 0.8641 | 0.892 | 0.0279 |

In K-means clustering, the detected cup region from actual method gives better results than the elliptical method. The detected optic cup cluster some of them are having small extra regions found due to the overlapped intensity variations in the cup region. Hence this cup region affects the CDR determination. In order to give the best result of segmentation in spite of overlapped intensity variations, the fuzzy C-mean (FCM) method is used. Unlike K-means where data point always belongs to only one cluster, in FCM the data point may belong to more than one cluster as data point is assigned to membership functions. Therefore, to improve the segmentation results, FCM clustering was applied as an improvement over simple K-means clustering technique.

FCM is employed by [

The developed algorithm is tested on 50 normal fundus images and 50 fundus images obtained from glaucoma patients. These images can also be used for the previous K-means clustering algorithm. The CDR values for all these images have been calculated by the developed algorithm.

The mean errors for K–means clustering technique have applied for same set of 100 images that are highlighted in the

Parameters | Normal images | Abnormal images |
---|---|---|

Mean value of CDR using Elliptical Method | 0.2648 | 0.5381 |

Mean value of CDR using Morphological Method | 0.2685 | 0.5228 |

CDR range of Elliptical Method | 0.13 to 0.359 | 0.402 to 0.881 |

CDR ranges of Morphological Method | 0.122 to 0.351 | 0.403 to 0.866 |

% of Mean Error of Elliptical Method | 3.83% (4.5% for K-means) | |

% of Mean Error of Morphological Method | 3.52% (4.1% for K-means) |

To have a concise result, the scatter plot has been used. The scatter plot of computed CDR and gold standard is generated by Minitab statistical software.

The correlation coefficient for elliptical method is 0.97 and for morphological method is 0.987.

As discussed in the previous method, (3.2.3) regression analysis has been carried over. The same set of ten new images that had been used in the previous K-means clustering method are selected here also and CDR values are obtained by FCM method and are listed in ^{rd} and 4^{th} column. The mean error of this elliptical method is 2.83% and morphological method is 2.57% whereas for K-means method, the mean errors are 4.2% and 4.1%, respectively. The standard deviation for the regression equation and developed algorithm for the elliptical method are 0.156085 and 0.155146. The standard deviation for the regression equation and developed algorithm for the morphological method are 0.158176 and 0.156366.

Gold standard CDR | CDR calculated by equation | CDR calculated by algorithm | Absolute error |
---|---|---|---|

0.75 | 0.7279 | 0.6757 | 0.052 |

0.65 | 0.6260 | 0.6681 | 0.0421 |

0.85 | 0.8297 | 0.7845 | 0.0452 |

0.80 | 0.7788 | 0.8379 | 0.0591 |

0.55 | 0.5243 | 0.4922 | 0.0321 |

0.45 | 0.4240 | 0.4423 | 0.0213 |

0.50 | 0.4733 | 0.4766 | 0.0033 |

0.70 | 0.6769 | 0.6550 | 0.0219 |

0.80 | 0.7788 | 0.7753 | 0.0032 |

0.90 | 0.8806 | 0.8777 | 0.0029 |

Gold standard CDR | CDR calculated by equation | CDR calculated by algorithm | Absolute error |
---|---|---|---|

0.75 | 0.7943 | 0.7995 | 0.042 |

0.65 | 0.6913 | 0.6543 | −0.037 |

0.85 | 0.8973 | 0.9183 | 0.021 |

0.80 | 0.8458 | 0.8228 | −0.023 |

0.55 | 0.5883 | 0.6003 | 0.012 |

0.45 | 0.4853 | 0.5083 | 0.023 |

0.50 | 0.5368 | 0.5648 | 0.028 |

0.70 | 0.7428 | 0.7778 | 0.035 |

0.80 | 0.8458 | 0.8688 | 0.023 |

0.90 | 0.9488 | 0.9618 | 0.013 |

Due to more accurate segmentation of optic cup region by FCM method, the mean error of the FCM is less compared to mean error of K-means clustering method. The method for finding optic disc region and region of optic cup has been presented in the work. Result of the proposed method for normal and glaucoma fundus images has been presented and reported. Though the FCM produces less error in the CDR values, the optic cup region from FCM does not show the complete contour and hence the error was seen in CDR. To increase the accuracy, used another algorithm for segmentation of optic disc and optic cup in fundus image is developed.

The standard FCM does not consider the spatial information of pixels this will affect the segmentation result. One of the important characteristics of an image is that neighboring pixels are highly correlated with the spatially weighted fuzzy C-mean (SWFCM) method. The pixels in optic cup and optic disc regions are correlated in their respective regions of fundus image. The optic cup is the excavation of nerve fiber and the neuro retinal rim that is the area between optic cup and disc formed by nerve fiber and glial cells. The contour of the optic disc is the outer contour of neuro retinal rim. Thus, when imaged, pixels in the cup region will be highly correlated among them compared to the above said region namely the neuro retinal rim. In this research, SWFCM is used as a novel method to detect optic cup and disc. This SWFCM method is utilized by the previous researchers [

In SWFCM, to exploit the spatial information, a spatial function is defined as

U_{ik} = Spatial domain in the entire neighborhood around the pixel

where ^{th} cluster. The spatial function of pixels is large if the majority of its neighborhood belongs to the same clusters. The spatial function is incorporated into membership function as follows:

where p and q are controlling parameters of both functions. The spatial functions simply strengthen the original membership in a homogenous region, but it does not change clustering result. However, this formula reduces the weight of a noisy cluster in noisy pixels by the labels to its neighboring pixels. As a result, misclassified pixels from noisy region or spurious blobs can easily be corrected.

The clustering is a two-pass process at each iteration. The first pass is the same as that in standard FCM to calculate the membership function. In the second pass, the membership information of each pixel is mapped to the spatial domain and the spatial domain function is computed from that. The FCM iteration proceeds with the new membership that is incorporated with spatial function. The iteration is stopped when the maximum difference between two cluster centers at two successive iterations is less than 0.00001. After the convergence, defuzzification is applied to assign each pixel to a specific cluster for which the membership is maximal.

_{i} using

where,

Vi = i^{th}cluster center

m = fuzziness parameter m = 2

where

where

The proposed SWFCM method is tested on 50 normal fundus images and 50 fundus images obtained from glaucoma patients. The results of elliptical and morphological methods are used to calculate the CDR values for these images. This was shown in

Parameters | Normal images | Abnormal images |
---|---|---|

CDR mean value elliptical method | 0.3148 | 0.5871 |

CDR Mean value morphological method | 0.2907 | 0.5468 |

Ranges of CDR elliptical method | 0.192 to 0.399 | 0.409 to 0.921 |

Ranges of CDR morphological |
0.142 to 0.361 | 0.421 to 0.876 |

CDR Mean error using elliptical method | 3.06% (3.83% for FCM) | |

CDR Mean error using morphological method | 1.67% (3.52% for FCM) |

The result from

The scatter plot has been used to analysis a result

The correlation coefficient for morphological method is 0.980.

When the scatter plots of SWFCM (

It is inferred from

As discussed in FCM method, Section 3.2.6 here also the analysis has been carried over on ten new images which are the same used in FCM regression analysis and the results are shown in

Gold standard CDR | CDR calculated by equation | CDR calculated by algorithm | Absolute error |
---|---|---|---|

0.75 | 0.7279 | 0.734 | 0.0061 |

0.65 | 0.6260 | 0.630 | 0.0040 |

0.85 | 0.8297 | 0.817 | 0.0127 |

0.80 | 0.7788 | 0.769 | 0.0098 |

0.55 | 0.5242 | 0.534 | 0.00658 |

0.45 | 0.4224 | 0.472 | 0.0496 |

0.50 | 0.4224 | 0.472 | 0.06270 |

0.70 | 0.6760 | 0.688 | 0.0120 |

0.80 | 0.7788 | 0.814 | 0.0352 |

0.90 | 0.8806 | 0.916 | 0.0354 |

Gold standard CDR | CDR calculated by equation | CDR calculated by algorithm | Absolute error |
---|---|---|---|

0.75 | 0.7069 | 0.7120 | 0.00510 |

0.65 | 0.6099 | 0.6670 | 0.05710 |

0.85 | 0.8040 | 0.8440 | 0.04000 |

0.60 | 0.5613 | 0.5728 | 0.01150 |

0.55 | 0.5128 | 0.5660 | 0.05320 |

0.45 | 0.4157 | 0.4230 | 0.00730 |

0.50 | 0.4642 | 0.4980 | 0.00338 |

0.70 | 0.6584 | 0.7190 | 0.00606 |

0.80 | 0.7555 | 0.7990 | 0.04350 |

0.90 | 0.8526 | 0.8890 | 0.03640 |

Parameter | K-means | FCM | SWFCM |
---|---|---|---|

Mean error of elliptical method | 4.5% | 3.83% | 3.06% |

Mean error of morphological method | 4.1% | 3.52% | 1.67% |

Standard deviation of elliptical method | 0.16338 | 0.13064 | 0.12968 |

Due to more accurate segmentation of optic cup region by FCM method, the mean error of FCM is less compared to the mean error of K-means clustering method. A method for detecting the optic disc region and region of optic cup has been presented here. Though the FCM produces less error in the CDR values, the optic cup region does not show the complete contour in FCM clustering (

The SWFCM is applied to the images in which blood vessels are already blurred. The neighboring pixels are highly correlated in SWFCM clustering. The standard FCM spatial relationship is not utilized but it is important in clustering. The drawback of FCM, the detection of optic cup region does not show the complete contour. To overcome the drawback, SWFCM is considered. The

In this chapter, detection of optic disc, optic cup, neuro-retinal rim and blood vessels from fundus images are discussed. Two methods are used for segmentation of optic disc and cup. In the first method, K-means clustering is used for optic disc by defining value manually. Then the method is modified by computing K-value automatically by hill climbing technique and optic disc is segmented. Since the segmentation is not yielding the correct result, FCM clustering is used for optic cup. As the standard K-means and FCM does not consider the spatial information, the segmentation result is affected. In order to account the spatial information, SWFCM is used for both optic disc and optic cup segmentation. The results show that the performance of SWFCM based glaucoma detection method is better than the other two methods. In future fast detection of Glaucoma and to reduce the false rate, images of segmented optic disc and cup is applied to convolutional neural network in deep learning classifier.

The authors wish to thank Doctor Rengaraj Venkatesh, M.D., Professor of the Aravind Eye Hospital & Post Graduate Institute of Ophthalmology, Pondicherry, India for providing the expert analysis of the fundus data.