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ORIGINAL ARTICLE

Segmentation of retinal blood vessels using a novel clusteringalgorithm (RACAL) with a partial supervision strategy

Sameh A. Salem Æ Nancy M. Salem Æ Asoke K. Nandi

Received: 12 May 2006 / Accepted: 5 December 2006 / Published online: 15 February 2007� International Federation for Medical and Biological Engineering 2007

Abstract In this paper, segmentation of blood vessels

from colour retinal images using a novel clustering

algorithm with a partial supervision strategy is pro-

posed. The proposed clustering algorithm, which is a

RAdius based Clustering ALgorithm (RACAL), uses

a distance based principle to map the distributions of

the data by utilising the premise that clusters are

determined by a distance parameter, without having to

specify the number of clusters. Additionally, the pro-

posed clustering algorithm is enhanced with a partial

supervision strategy and it is demonstrated that it is

able to segment blood vessels of small diameters and

low contrasts. Results are compared with those from

the KNN classifier and show that the proposed RA-

CAL performs better than the KNN in case of abnor-

mal images as it succeeds in segmenting small and low

contrast blood vessels, while it achieves comparable

results for normal images. For automation process,

RACAL can be used as a classifier and results show

that it performs better than the KNN classifier in both

normal and abnormal images.

Keywords Retinal imaging � Feature extraction �Clustering � KNN classifier

1 Introduction

Automatic segmentation of blood vessels in retinal

images is very important in early detection and diag-

nosis of many eye diseases. It is an important step in

screening programs for early detection of diabetic

retinopathy [17, 19], registration of retinal images for

treatment evaluation [22] (to follow the evaluation of

some lesions over time or to compare images obtained

under different conditions), generating retinal maps for

diagnosis and treatment of age-related macular

degeneration [15], or locating the optic disc and the

fovea [5].

Methods for blood vessels segmentation of retinal

images, according to the classification method, can be

divided into two groups—supervised and unsupervised

methods. Unsupervised methods in the literature

comprise the matched filter responses, edge detectors,

grouping of edge pixels, model based locally adaptive

thresholding, vessel tracking, topology adaptive

snakes, and morphology-based techniques [18].

Supervised methods, which require a feature vector for

each pixel and manually labeled images for training the

algorithm, are the most recent approaches in vessel

segmentation and use the neural networks [17] or the

K-nearest neighbour classifier [13, 18] for classifying

image pixels as blood vessel or non-blood vessel pixels.

These methods depend on generating a feature vector

for every pixel in the image and then using training

samples (with known classes) to design a classifier to

classify these training samples into their corresponding

classes.

Scale-space features such as the gradient magnitude

of the image intensity and the ridge strength, both at

different scales, are combined with region growing to

S. A. Salem � N. M. Salem � A. K. Nandi (&)Signal Processing and Communications Group,Department of Electrical Engineering and Electronics,The University of Liverpool, Brownlow Hill,L69 3GJ Liverpool, UKe-mail: [email protected]

S. A. Saleme-mail: [email protected]

N. M. Saleme-mail: [email protected]

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Med Bio Eng Comput (2007) 45:261–273

DOI 10.1007/s11517-006-0141-2

segment the blood vessels from red-free and fluores-

cein clinical retinal images [10]. Also, the first and

second derivatives—of the green channel image, in x-

and y-directions [13], or with respect to other image

coordinates [18] at different scales—are used as fea-

tures for every pixel in the retinal image. Derivatives of

discrete images are taken at different scales, s, using

the Gaussian scale-space technique [9]. Niemeijer et al.

[13] proposed a pixel classification method where the

KNN classifier is used with 31 features to classify pixels

in retinal images to vessel and non-vessel pixels; these

features are the green channel image intensity, and the

filtered image using the Gaussian and its derivatives at

different scale values.

Clustering algorithms such as fuzzy C-means (FCM)

clustering have been proposed for vessel tracking [21]

and exudates detection [14] in retinal images. Tolias

et al. [21] proposed a FCM clustering algorithm that is

based on the intensity information to track vessels in

fundus images. This algorithm is initialised by defining

the optic nerve as a very bright region to be the starting

point to track image vessels. However, it ignores the

possibility of locating abnormalities that have the same

properties as the optic nerve. Moreover, vessels of

small diameter and low contrast are missed. In [14],

retinal exudates are detected by normalising colour

channels using local contrast enhancement. Then, a

FCM clustering algorithm is used to highlight salient

regions and extract relevant features; subsequently

these salient regions are classified using a multi-layer

perceptron neural network.

In this paper, we propose to segment retinal blood

vessels using a novel clustering algorithm (RACAL)

with partial supervision strategy. For purposes of

comparison, results obtained from our proposed RA-

CAL are compared with the KNN classifier when using

the same features and same set of test images. This

paper is organised as follows: the feature extraction

step and the RACAL are detailed in Sect. 2. Section 3

presents the dataset and Sect. 4 demonstrates the

experiments and results. Finally, the discussion is pre-

sented in Sect. 5 and the paper is summarised in

Sect. 6.

2 Method

2.1 Feature extraction

The two characterising attributes of any vessel, i.e.,

piecewise linearity and parallel edges [8], are consid-

ered when choosing the set of features for every pixel

in retinal images. The piecewise linear property of a

blood vessel can be recognised by extracting centre-

lines of blood vessels, simply by extracting the image

ridges. The parallel edges property is well recognised

by calculating the gradient magnitude of the image

intensity. As vessels are of different diameters, these

features are extracted at different scales and then the

local maxima over all scales is calculated for both

features. In addition to the property that the blood

vessel can be seen in the colour retinal image as a dark

object on a brighter background, out of the three col-

our channels (red, green and blue) the green channel is

chosen to represent this characteristic as it has the

highest contrast between the blood vessel and the

retinal background.

The features used in this paper are the green chan-

nel intensity, the local maxima of the gradient magni-

tude, and the local maxima of the large eigenvalue [16].

Figure 1 plots intensity information, gradient magni-

tude, ridge strength and large eigenvalue along the

same horizontal line in the sub-image from red and

green channel images. From these graphs, it is clear

that the green channel has a higher contrast than the

red channel image, gradient magnitude gives two peaks

at the parallel edges of the blood vessels, and finally

the large eigenvalue is better than the ridge strength in

determining centrelines of the blood vessels when

processing colour fundus images.

2.1.1 The gradient magnitude (maximum over scales)

The gradient magnitude is calculated as:

5Lj j ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

L2x þ L2

y

q

ð1Þ

Lx ¼ Iðx; yÞ � sGx ð2Þ

Ly ¼ Iðx; yÞ � sGy ð3Þ

where Lx and Ly are the first derivatives of the image

in the x and y directions, Gx and Gy are Gaussian

derivatives in the x and y directions, and s is the scale

parameter [9].

The gradient magnitude of the image intensity is

calculated at different scales [10], then the local max-

ima of the gradient magnitude c is calculated as:

c ¼ maxs

jrLðsÞjs

h i

ð4Þ

2.1.2 The large eigenvalue (maximum over scales)

The eigenvalues (the large eigenvalue, k+, and the

small eigenvalue, k–) of the Hessian, the matrix of the

262 Med Bio Eng Comput (2007) 45:261–273

123

second order derivatives, of the intensity image I(x, y)

are calculated as [10]:

kþ ¼Lxx þ Lyy þ a

2ð5Þ

k� ¼Lxx þ Lyy � a

2ð6Þ

Lxx ¼ Iðx; yÞ � s2Gxx ð7Þ

Lyy ¼ Iðx; yÞ � s2Gyy ð8Þ

where Lxx and Lyy are the second derivatives of

the image in the x and y directions, and

a ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðLxx � LyyÞ2 þ 4L2xy

q

:

Then, the local maxima of the large eigenvalue kmax

is calculated as:

kmax ¼ maxs

kþðsÞs

h i

: ð9Þ

To evaluate the performance of our proposed algo-

rithm on the segmentation of retinal blood vessels,

another set of 31 features used in the pixel classifica-

tion method [13] are used also in this paper. These 31

features are the green channel image intensity as well

as the filtered image using the Gaussian and its deriv-

atives in x- and y-directions up to order 2 at scales

s = 1, 2, 4, 8, 16.

2.2 Radius based clustering algorithm

2.2.1 Basics and definitions

– An object Oi is a set of p image features found at a

pixel’s location.

– A dataset O is a set of objects. In many cases, a

dataset is viewed as an n · p matrix (n objects each

of p features).

– Data clustering is a problem of partitioning a given

dataset into groups (clusters) such that objects in one

cluster are more similar to each other than items in

other clusters.

– Prototype is the cluster centre.

In our application (retinal images segmentation),

each object ‘‘pixel’’ is characterised by p features (ei-

ther 3 or 31 features as described in Sect. 2.1) and the

dataset corresponds to the set of all n pixels, each with

its p feature values, as shown in Fig. 2.

2.2.2 Proposed clustering algorithm (RACAL)

The proposed algorithm operates in the relevant fea-

ture space and the basic idea of RACAL is to find the

proper prototypes that can map the distributions on

datasets at a given input parameter value without

neglecting the sparsely populated areas as in density

(a)

0 20 40150

155

160

165

170

175(b)

0 20 400

1

2

3

4

5

6(c)

0 20 400.5

1

1.5

2

2.5

3

3.5(d)

0 20 400

1

2

3

4(e)

(f)

0 20 4070

80

90

100

110(g)

0 20 400

2

4

6

8

10(h)

0 20 400

1

2

3

4

5(i)

0 20 400

1

2

3

4

5(j)

Fig. 1 Sub-image with colourand scale-space features. a, b,c, d, e sub-image and itsintensity, gradient magnitude,ridge strength, and largeeigenvalue along a horizontalline crossing a blood vesselfrom the red channel image, f,g, h, i, j the same but from thegreen channel image

Med Bio Eng Comput (2007) 45:261–273 263

123

based approaches. The proposed algorithm uses a dis-

tance based principle, which fundamentally differs

from density based methods in the way that the algo-

rithm determines what constitutes a cluster. Simply

expressed, the proposed algorithm defines a norma-

lised distance parameter, do (0 £ do £ 1), which acts as

the determinant of the cluster. From a given object

which is characterised by p features, any other objects

that fall within do are regarded as belonging to the

same cluster, i.e., have similar image features. The

control of the cluster size is achieved through the value

of do parameter, as shown in Fig. 3. Small values will

lead to a high number of small and tight clusters, while

large values of do will create a smaller number of larger

clusters. Extremely large values will cause only one

cluster to be formed, as this will swallow up all smaller

clusters.

Clustering procedure Clustering is a process of

grouping objects into clusters in such a way that each

object within a cluster is close or similar to one an-

other, but dissimilar from the objects in other clusters.

In our application (retinal blood vessels segmentation),

each object ‘‘pixel’’ is characterised by p features (ei-

ther 3 or 31 features as described in Sect. 2.1) and is to

be clustered with similar objects by the proposed

RACAL algorithm. In this section, we describe the

proposed RACAL algorithm to cluster a dataset. Let

O ¼ fOiji ¼ 1; . . . ; ng be a set of n objects, where each

object, Oi 2 Rp, is characterised by p features. As a first

step, obtain the relational matrix ‘‘normalised distance

matrix’’ R = [rij], where rij indicates relative distance

between Oi and Oj, and satisfies the following condi-

tions:

rij ¼ rji; rii ¼ 0; and rij 2 ½0; 1�:

Then, search for the proper prototypes that can repre-

sent the ‘‘spatial’’ distributions in the dataset by iden-

tifying the most centralised objects—that can attract a

large number of objects—at a given input parameter

value do. A hyperspherical region of radius do is defined

as the neighbourhood, NOi, of object Oi and the total

number of neighbouring objects within this region,

W(Oi), is considered as a weight for this object.

Prototypes generation can be summerised in the

following steps:

1. Choose the object OM with maximum weight and

all objects OM1; . . . ;OMj within its neighbourhood

NOM and find their corresponding neighbourhoods

NOM1; . . . ;NOMj.

Fig. 2 Colour retinal sub-image (top) and its groundtruth (bottom) in a imagespace, and b feature space


123

2. Find the intersection between neighbourhood of

OM and neighbourhoods of its closest objects

OM1; . . . ;OMj as:

NINT ¼ NOM \NOM1 \NOM2 � � � \NOMj:

3. Define ‘‘prototype’’ Bk as the object (or mean of

objects) that results from the intersection opera-

tion.

4. Clear all weights for OM and OM1; . . . ;OMj to

avoid possibility of generating more than one

Fig. 3 RACAL stage 1:clustering results for a sub-image when using different do

values in a feature space, andb image space


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prototype within do. This allows the possibility of

generating prototypes in the sparsely populated

areas, where the objects will have lower weights.

5. The process of generating prototypes is continued

until no more weighted object is found.

After generating proper prototypes (K proto-

types), the clustering problem is reduced to assigning

the n objects to the nearest of K prototypes to create

K clusters. The prototypes (cluster centres) are sub-

sequently updated to the mean of their assigned ob-

jects. This process is repeated until no more changes

occur in the prototypes. In order to achieve more

compact clusters and yet with wider separations be-

tween clusters, i.e., better clustering quality, RACAL

is enhanced with a reliable validity index to evaluate

the clustering result at each update of the prototypes.

The best clustering result at a given do is the one that

achieves a maximum value of the validity index.

Therefore, the enhancement of the clustering function

with a reliable validation index can be used to pro-

duce the best results for a given do value. A recently

developed cluster validity index ‘‘I’’ [11] has been

selected from a number of available validity indices.

This index has been experimentally tested on artificial

and real-world datasets and attained its maximum

value when the appropriate clustering is achieved; this

index has also been compared with the Davies–

Bouldin index [2], the Dunn’s index [3] and the

Calinski–Harabasz index [1]. The ‘‘I’’ index is defined

as:

IðKÞ ¼ 1

K� E1

EK�DK

� �P

ð10Þ

where

– EK represents compactness for K clusters and is

computed as EK ¼PK

k¼1

Pnj¼1 ukj k Oj � Bk k;

where n is number of objects in the dataset, Oj an

object, Bk cluster centre ‘‘prototype’’ of the kth

cluster, and ukj = 1 if Oj is a member of the kth

cluster; otherwise ukj = 0.

– DK represents maximum separation between two

clusters over all possible pairs of clusters and is

computed as DK ¼ maxKi;j¼1 k Bi � Bj k; where Bi

and Bj are cluster centres ‘‘prototypes’’ of i and jth

clusters, respectively.

– E1 is a constant for a given dataset and is computed

as E1 ¼Pn

j¼1 k Oj � B1 k; where B1 is cluster centre

of the entire dataset.

– P is a power used to control the contrast between

different cluster configurations. In this paper, P = 2

is used.

The objective is to maximise the ‘‘I’’ index for

achieving proper clustering at a given do value. The

proposed clustering algorithm (RACAL) is detailed in

Algorithm 1.

Due to the increase of the size and dimensions of

datasets which require higher computational time and

resources, a set of objects can be used as a subset of the

data to generate the prototypes (cluster centres) that

cover the extents of data space; these objects are nor-

mally selected at random from the data. As the number

of selected objects is increased, better distributions can

be obtained. It may be necessary to take into consid-

eration the fact that the continuing advances in com-

puter networking, data storage technologies, and

parallel computation can be used to reduce the nec-

essary computational resources as well as improving

the clustering performance and accuracy.

2.2.3 RACAL with partial supervision strategy

Clustering is unsupervised classification where there

are no predefined classes (labels). Clustering provides

groups of objects (pixels) that have not yet labeled

‘‘vessel’’ or ‘‘non-vessel’’. Labeling clusters effectively

segments the pixels of the underlying retinal image.

The process of labeling cluster objects ‘‘pixels’’ is al-


123

ways an expensive and error-prone task that requires

time and human intervention. In many situations, ob-

jects are neither perfectly labeled nor completely la-

beled. Therefore, the main idea of clustering with

partial supervision strategy is to take the advantage of

the manually labeled objects to guide the clustering

process of the unlabeled objects.

To use RACAL with partial supervision, we propose

to use some labeled objects to guide the clustering

process. The proposed method is divided into two

stages. First stage is to cluster n objects (the entire

objects) into K clusters according to the input param-

eter do, as described in Sect. 2.2.2. Second stage is to

randomly select NP objects from the ground truth

(which are manually labeled objects by a human ob-

server). Then each cluster is classified according to the

label of the majority of its objects (the choice of NP

and do ensure that all clusters can be classified). For

each labeled object, if its cluster is classified to differ-

ent class (label), then this object will be assigned to the

nearest cluster that has the same label. Once the

clusters’ memberships are updated, the cluster centres

are updated, and the process continues checking the

cluster memberships of labeled objects until conver-

gence. Then, all objects that belong to different clusters

with the same class labels can be assigned to that label.

This proposed method will bias clustering towards a

better search space. The proposed supervised method

is detailed in Algorithm 2.

A soft classification, where all objects are allowed in

principle to belong to all classes with different degrees

of membership, is achieved by adding the fuzzy mem-

berships for each object with the clusters that belong to

the same class label. Equations 11 and 12 show the

fuzzy membership (mik) of object k to cluster i, and the

soft membership ðMCikÞ of object k to class Ci,

respectively.

mik ¼1

P

K

j¼1

dik

djk

� �2=ðq�1Þð11Þ

MCik ¼X

K

j

mjk if cluster j 2 class Ci ð12Þ

where q is fuzziness exponent, dik distance from object

k to the current cluster centre i, and djk distance from

object k and any of the cluster centres j (1 £ j £ K).

Figure 2 shows a colour retinal sub-image and its

ground truth, while Figs. 3 and 4 show the clustered

sub-images by RACAL algorithm at different do values

and their corresponding segmented sub-images after

applying RACAL with partial supervision strategy

using 20% of the ground truth pixels (either vessels or

non-vessels pixels). At do = 0.045, 0.100, 0.250 and

0.450, all pixels are being clustered to 245, 46, 10, and 4

clusters, respectively. As shown in Table 1, smaller

values for do offer better sensitivity as a result of pro-

ducing higher number of small and tight clusters which

help in detection of vessels of small diameter and low

contrast.

3 STARE dataset

For performance evaluation, a publicly available

dataset is used [20] and will be referred to as the

STARE dataset. The dataset consists of 20 images

which are digitized slides captured by a TopCon TRV-

50 fundus camera at 35� FOV. Each slide was digitized

to produce a 605 · 700 pixels image, standard RGB,

eight bits per colour channel. Every image has been

manually segmented by two observers to produce

ground truth vessels segmentation. Ten of these images

contain pathology and the other ten are normal, giving

a good opportunity to test the proposed method in

both normal and abnormal retinas.

4 Experiments and results

4.1 Experiments

In our experiments, retinal blood vessels are seg-

mented using the proposed clustering algorithm with

partial supervised strategy. The performance is mea-

sured with Receiver Operating Characteristic (ROC)

curves [4, 12]. An ROC curve plots the false positive

rates against the true positive rates, and these rates are

defined in the same way as in [6], where the true (false)

positive is any pixel which was hand-labeled as a vessel

(not vessel) and whose intensity after segmentation is

above a given threshold. The true (false) positive rate

is established by dividing the number of true (false)


123

positives by the total number of pixels hand-labeled as

vessels (not vessels). The larger is the area under the

ROC curve, the better is the performance of the

algorithm.

For purposes of comparison, the KNN classifier is

also used to segment retinal blood vessels. For the

KNN classifiers, two sets are required; one for training

and the other for testing, so the dataset is randomly

divided into two sets of images, each contains five

normal and five abnormal images. The training set

contains a large number of training samples

(423,500 pixels/image), which is the main problem with

Fig. 4 RACAL stage 2: afterapplying partial supervisionstrategy, results at different do

values in a feature space, andb image space


123

this type of classifiers. To overcome such a problem, a

random number of pixels is chosen from the field of

view (FOV) of each image in the training set. The

targets for these training samples are available from

the manually segmented images. The testing set con-

tains ten images to test the performance of the classi-

fier. The value of K = 60 and each feature is

normalised to zero mean and unit standard deviation.

4.2 Experimental results

4.2.1 RACAL with partial supervision strategy

Hard classification Results for retinal blood vessels

segmentation using the proposed algorithm when ap-

plied to the 20 images in the STARE dataset are pre-

sented in this section. On the whole, using 20 images,

average sensitivity of 81.34 and 82.15% are achieved at

average specificity of 96.70 and 97.50% using the 3 and

31 features, respectively, as summarised in Table 2.

These values are calculated using the retinal field of

view only.

When comparing with the KNN classifier; the same

set of images (ten images for testing), also, the hard

decision from the KNN classifier is used and results

from this comparison are summarised in Tables 3 and

4. For 3 features, average sensitivity of 83.14% is

achieved at average specificity of 97.04% from our

RACAL compared with average sensitivity of 85.47%

at average specificity of 92.74% from the KNN classi-

fier. For 31 features, average sensitivity of 83.28% is




fier. On average, the proposed RACAL algorithm

achieves better specificity than KNN classifier with

comparable sensitivity.

Figures 5 and 6 compare results from RACAL (with

partial supervision strategy) with the KNN classifier

when using 3 and 31 features.

Soft classification For soft classification, the perfor-

mance of RACAL in terms of sensitivity and specificity

along with the effect of the fuzziness exponent (q in

Eq. 11) are obtained. As shown in Fig. 7, the choice of

the fuzziness exponent value (q) affects on pixels’

membership degrees. Table 5 shows the soft decision

results of the proposed algorithm (RACAL) in con-

junction with 3 features to segment the retinal images

(normal and abnormal). As shown, the fuzziness

exponent value, q = 1.25, achieves better sensitivity

with the corresponding specificity values for normal

and abnormal images, respectively. For 31 features, the

fuzziness exponent value, q = 1.50, achieves better

sensitivity with the corresponding specificity values for

normal and abnormal images, respectively as sum-

marised in Table 6.

For purposes of comparison, soft results obtained

from our proposed algorithm (RACAL) are compared

with soft results obtained by the KNN classifier when

using same features and the same testing set of images

are summarised in Table 7. It is clear that the proposed

algorithm (RACAL) offers better results than the

KNN classifier for abnormal images, and comparable

results for normal images.

Table 1 Specificity and sensitivity of a segmented sub-imagefrom a retinal image by RACAL with partial supervision strat-egy at different do values

do Specificity (%) Sensitivity (%)

0.045 97.90 90.040.100 98.19 89.040.250 98.43 81.730.450 99.67 70.90

Table 2 RACAL hard decision results using 3 and 31 features(average from 20 images)

Imagetype

3 Features 31 Features

Specificity(%)

Sensitivity(%)

Specificity(%)

Sensitivity(%)

Normal 97.02 85.01 97.64 86.03Abnormal 96.39 77.67 97.36 78.27All 96.70 81.34 97.50 82.15

Table 3 RACAL and KNN hard decision results using 3 fea-tures [average from ten images (testing set)]

Imagetype

RACAL KNN

Specificity(%)

Sensitivity(%)

Specificity(%)

Sensitivity(%)


Table 4 RACAL and KNN hard decision results using 31 fea-tures [average from 10 images (testing set)]

Imagetype

RACAL KNN

Specificity(%)

Sensitivity(%)

Specificity(%)

Sensitivity(%)



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4.2.2 RACAL as a classifier

For automation purposes, RACAL can be used as a

classifier by learning from ten images and testing on

the other images. In the training step, each image is

clustered to K clusters as in Sect. 2.2.2, then from

ground truth images, each cluster is assigned to the

corresponding class. Afterwards, describe each cluster

statistically and geometrically by calculating mean of

features for its objects, cluster compactness, major and

minor diameters.

For testing, cluster each image as in Sect. 2.2.2, then

for each cluster; calculate the mean of features for its

objects, cluster compactness, major and minor diame-

ters. For each cluster in the testing image, find the

nearest cluster ‘‘with known class’’ from the training

set, then assign it to the same class. Results to compare

between RACAL as a classifier and the KNN classifier

are shown in Tables 8 and 9.

For 3 features, average sensitivity of 90.43% is



Fig. 5 a Colour images,output as hard decision using3 features from b RACALwith partial supervision, and cKNN classifier

Fig. 6 Output as harddecision using 31 featuresfrom a RACAL with partialsupervision, and b KNNclassifier


123


fier. For 31 features, average sensitivity of 86.79% is

achieved at average specificity of 99.14% from RA-

CAL compared with average sensitivity of 84.46% at

average specificity of 94.01% from the KNN classifier.

On average, the proposed RACAL algorithm performs

better than the KNN classifier.

5 Discussion

For the hard classification, as demonstrated in Table 2

for 20 images in the STARE dataset, the proposed

algorithm with partial supervision strategy gives prom-

ising results of 81 and 82% average sensitivity at aver-

age specificity of 97 and 98% when using a set of 3 and

31 features, respectively. Furthermore, the results from

the proposed algorithm are comparable with the KNN

classifier as demonstrated in Tables 3 and 4, where the

proposed algorithm achieves average specificity of 97

and 98% at average sensitivity of 83% compared with

average specificity of 93 and 94% at average sensitivity

of 85 and 84% when using the KNN classifier in con-

junction with 3 and 31 features, respectively.

For soft classification, RACAL gives better results

than the KNN classifier as demonstrated in Table 7. In

Fig. 7 Effect of the choice offuzziness exponent (q) on thesegmented abnormal image(top) and the normal image(bottom) at a q = 1.25, bq = 1.50, c q = 2.00, and dq = 2.50

Table 5 The effect of thefuzziness exponent q onRACAL results [average fornormal and abnormal images(testing set with 3 features)]

Imagetype

Specificity(%)

Sensitivity (%) for q values

1.25 1.50 1.75 2.00 2.50

Normal 85.31 85.52 86.19 86.23 86.11Abnormal 95 81.04 77.30 77.68 77.77 77.19Normal 92.89 91.31 91.67 91.98 92.13Abnormal 90 93.53 85.86 86.52 86.26 86.23Normal 94.08 93.58 93.78 94.00 93.93Abnormal 85 97.70 90.58 90.17 90.39 90.37Normal 98.07 95.07 94.92 95.28 95.48Abnormal 80 96.64 91.49 92.41 92.66 93.27

Table 6 The effect of thefuzziness exponent q onRACAL results [average fornormal and abnormal images(testing set with 31 features)]

Imagetype

Specificity(%)

Sensitivity (%) for q values

1.25 1.50 1.75 2.00 2.50

Normal 89.52 90.53 89.77 89.45 87.28Abnormal 95 79.77 80.35 78.47 75.74 71.05Normal 94.04 95.18 95.05 93.87 92.83Abnormal 90 86.84 88.05 87.49 84.57 82.30Normal 95.90 96.89 96.58 96.00 95.85Abnormal 85 90.22 92.25 92.00 90.01 85.58Normal 96.66 97.95 97.75 97.52 95.75Abnormal 80 92.24 94.06 93.83 92.37 88.38


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case of normal images, the proposed algorithm gives

comparable results with the KNN classifier, on the

other hand it gives better results for the abnormal

images which can be explained as follows:

– For the KNN classifier: one training set is generated

for the whole dataset and used to find the nearest k-

neighbours for each sample in the testing set.

– For the RACAL: training samples are for each

image individually which can reflect each image

characteristics (such as background colour, intensity

levels for vessel and non-vessel pixels, contrast

between vessels and background, etc.).

– The property of multiple object classes of varying

colour/reflectance [7] and—sometimes—there is a

similarity between feature vectors for vessel and

non-vessel pixels from different images. RACAL is a

radius-based algorithm which means better segmen-

tation for small and low contrast vessels.

– For normal images there is no abnormalities and the

background is uniformly illuminated, so the results

were comparable.

– For abnormal images there are signs for abnormal-

ities which classified as vessels, also small blood

vessels of low contrast, are missed in the KNN

classifier and picked by RACAL.

When using RACAL as a classifier as in Sect. 4.2.2,

the performance is better than the KNN for both nor-

mal and abnormal images with the 3 and 31 features.

6 Conclusion

In this paper, we have proposed a novel radius-based

clustering algorithm (RACAL) to be used in segmen-

tation of retinal blood vessels. This algorithm is used to

classify pixels of retinal images into vessel and non-

vessel pixels. RACAL with partial supervision strategy

is helpful in cases where ground truth images are not

completely available. Results are compared with the

KNN classifier and show that RACAL performs better

than the KNN in case of abnormal images as it suc-

ceeds in segmenting small and low contrast blood

vessels. On the other hand it gives comparable results

for normal images. When using RACAL as a classifier

the performance is better than the KNN classifier in

either normal or abnormal images.

Acknowledgments The authors would like to thank thereviewers for their comments which have helped to improve thepresentation of our results and A. Hoover for making the retinalimages publicly available. S. A. Salem and N. M. Salem wouldlike to acknowledge the financial support of the Ministry ofHigher Education, Egypt, for this research.

Table 7 Average sensitivity(%) at certain specificityvalues for 3 and 31 features

Image type Specificity (%) RACAL KNN

3 Features 31 Feature 3 Features 31 Feature

Normal 85.31 90.53 86.60 89.24Abnormal 95 81.04 80.35 76.24 77.91All images 83.18 85.44 81.42 83.58Normal 92.89 95.18 92.56 94.32Abnormal 90 93.53 88.05 86.13 86.19All images 93.21 91.62 89.35 90.26Normal 94.08 96.89 95.03 96.40Abnormal 85 97.70 92.25 90.89 90.18All images 95.89 94.57 92.96 93.29Normal 98.07 97.95 96.51 97.45Abnormal 80 96.64 94.06 93.65 92.67All images 97.36 96.00 95.08 95.06

Table 8 RACAL as a classifier and the KNN classifier harddecision results using 3 features [average from 10 images (testingset)]

Imagetype

RACAL KNN

Specificity(%)

Sensitivity(%)

Specificity(%)

Sensitivity(%)


Table 9 RACAL as a classifier and the KNN classifier harddecision results using 31 features [average from 10 images(testing set)]

Imagetype

RACAL KNN

Specificity(%)

Sensitivity(%)

Specificity(%)

Sensitivity(%)



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