ORIGINAL ARTICLE Segmentation of retinal blood vessels using a novel clustering algorithm (RACAL) with a partial supervision strategy Sameh A. Salem Nancy M. Salem Asoke K. Nandi Received: 12 May 2006 / Accepted: 5 December 2006 / Published online: 15 February 2007 Ó 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, UK e-mail: [email protected]S. A. Salem e-mail: [email protected]N. M. Salem e-mail: [email protected]123 Med Bio Eng Comput (2007) 45:261–273 DOI 10.1007/s11517-006-0141-2
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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
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]
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)
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175(b)
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6(c)
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1
1.5
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2.5
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3.5(d)
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1
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4(e)
(f)
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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
264 Med Bio Eng Comput (2007) 45:261–273
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
Med Bio Eng Comput (2007) 45:261–273 265
123
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-
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
achieved at average specificity of 98.48% from our
RACAL compared with average sensitivity of 85.47%
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
270 Med Bio Eng Comput (2007) 45:261–273
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at average specificity of 92.74% from the KNN classi-
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)]
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
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