RETINAL VASCULAR NETWORK MODEL

An Automatic Approach

Alauddin Bhuiyan, Baikunth Nath and Kotagiri Ramamohanarao

Computer Science and Software Engineering, The University of Melbourne, Melbourne 3010, Australia

Keywords:

Vascular bifurcation/branching and crossover point, Binary tree, Invariant features, Tree traversal algorithm,

Disease prediction.

Abstract:

In this paper, we propose a retinal vascular network model, which is an automatic process of generating a

graph representation (i.e., a tree) of the retinal blood vessels and includes vessel geometrical features. It maps

the retinal blood vessels and can facilitate vascular features such as the vessel width, bifurcation angle, among

others to predict or earlier diagnose cardiovascular and related diseases. The proposed tree-model is based

on vessel’s centerline, cross-sectional width, and bifurcation, branching and crossover points. The optic disc

center is computed using the Hough transformation and vessel centerlines are tracked from out side its radius.

Blood vessels are fragmented as vessel-segments based on the bifurcation, branching and crossover points.

For each blood vessel we construct a binary tree which is linked in the root of the tree-model. Our automated

method achieves an accuracy of 91.23% in extracting the vessel-segments.

1 INTRODUCTION

Recent research suggests that retinal imaging can play

an important role in prediction or earlier diagnosis

of diseases. For example, research shows that reti-

nal vessel caliber changes are associated with hyper-

tension, diabetes and cardiovasculardiseases (CVDs).

Usually, the retina is analyzed by direct viewing or

a semi-automatic method. However, direct viewing

of the eye or the manual analysis of the retinal pho-

tographs is time-consuming and expensive as it re-

quires human effort. Semi-automatic method also re-

quires an expert intervention and signiﬁcant amount

of time. Thus an automated image analysis should

play a central role in analyzing large volume of im-

ages.

An automatic method of mapping the retinal vas-

culature and corresponding features, with high accu-

racy, will greatly enhance the speed and signiﬁcantly

reduce the costs involved in diagnosing diseases.

This paper presents a retinal vascular network model

(i.e., tree-model) to achieve these goals. Although a

number of schemes (Pinz et al., 1998),(Chow et al.,

2006),(Li and Qu, 1998),(Mattes et al., 1999) has

been proposed to represent image features in a tree

structure, none of these methods is concerned with

retinal vascular imaging. The tree-model is an auto-

mated method for mapping the blood vessels and cor-

responding features in a color retinal image. It repre-

sents the vascular features in a graph form shown in

Figure 1b. The features are incorporated in consider-

ation of their importance in the diagnosis of diabetes,

hypertension or cardiovascular diseases.

Several research articles (Lin et al., 2009), (Zhou

et al., 2005), (Martinez-Perez et al., 2002), (Taarn-

hoj et al., 2008), (Stanton et al., 1995), (Hart et al.,

1999) have appeared on retinal vascular feature anal-

ysis for disease diagnosis. Most of these techniques

are manual or semi-automatic, require expert inter-

vention and none of these techniques is based on a

graphical representation of the vascular features. In

(Martinez-Perez et al., 2002), the authors have pre-

sented a method which can trace an individual vessel

and summarize its features. Another method for ves-

sel tracing is presented in (Lin et al., 2009). None of

the methods obtain vascular features with maintain-

ing actual vessel-segments’ hierarchy. None of these

techniques is able to match the vascular features from

two images based on vessel-segments’ hierarchical

position, which is important for patient’s longitudinal

studies.

Previous methods of tree representations (Mat-

tes et al., 1999),(Li and Qu, 1998),(Mosorov,

2005),(Chow et al., 2006) mainly consider the global

higher level features (i.e., histogram) and segmented

regions as corresponding features of the images. For

233

Bhuiyan A., Nath B. and Kotagiri R..

RETINAL VASCULAR NETWORK MODEL - An Automatic Approach.

DOI: 10.5220/0003161602330238

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing (BIOSIGNALS-2011), pages 233-238

ISBN: 978-989-8425-35-5

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

(a) (b)

Figure 1: A retinal image showing the blood vessels (a) and proposed graph model of the retinal vascular network (b).

instance, an image is represented with its histogram

on the root and the local region based features on

the children nodes of a tree, which is used for image

classiﬁcation. None of these schemes consider a reti-

nal vascular network and its feature(s) representation

which is the main focus in our work.

The rest of the paper is organized as follows. Sec-

tion 2 provides the method of tree-model construc-

tion, and section 3 provides evaluation of the tree-

model. Conclusions are drawn in section 4.

2 TREE-MODEL

CONSTRUCTION

The tree-model is constructed by traversing through

the vessel centerline image. The details of the tree-

model construction procedureare described in the fol-

lowing subsections.

2.1 Vessel Centerline Detection

In (Bhuiyan et al., 2007a) a method is presented for

blood vessel segmentation based on the texture prop-

erty analysis of vessel and non vessel parts in the color

retinal image. Following this a morphological skele-

tonisation operation is applied on the segmented im-

age to extract the vessel centerlines.

2.2 Vessel Landmarks Classiﬁcation

A method for blood vessel bifurcation, branching and

crossover point (landmark points) detection using the

vessel geometrical features is proposed in (Bhuiyan

et al., 2007b). Vessel centerline image and a width

measurement method (Bhuiyan et al., 2008) are used

for landmark points classiﬁcation process.

2.3 Fragmenting Vessel Centerlines

We fragment the vessel centerlines into different

vessel-segments based on the landmark points and

use this fragmented centerline image to construct the

tree-model. This is for searching and traversing the

vessel centerlines as well as constructing the tree-

model conveniently. For fragmenting the vessel cen-

terlines, we use the landmark points along with the

corresponding vessel-segments’ start or end points.

The landmark points and their corresponding vessel-

segments’ start or end points are obtained from land-

mark points classiﬁcation method (Bhuiyan et al.,

2007b). We compute the connectivity (i.e., the path)

between each landmark point and its corresponding

vessel-segment’s start or end points, and delete the

connectivity for fragmenting the centerlines. Figure

2 shows a cropped vessel centerline image (left) and

its fragmented output image (right).

Figure 2: A cropped vessel centerline image (left) and its

fragmented output image (right).

2.4 Optic Disc Center Computation

Optic disc center is computed by applying Hough

transformation on the optic disc region in the image.

To detect the optical disc, we ﬁnd a rough estimation

of pixel positions by thresholding the retinal image on

intensity value. Then we determine a square region on

which we search for a circular object. Hence, we can

apply Hough transformation in a smaller region which

provides more efﬁciency in optic disc center compu-

tation. We apply Hough transformation in the edge

image which we obtained earlier.

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234

2.5 Binary Tree Construction

After computing the optic disc center and radius, we

ﬁnd the vessel centerline pixels by searching in a cir-

cular region outside this radius. Once a vessel center-

line pixel is found, it is inserted into the root of the

tree-model and a binary tree construction starts for

this vessel. This starting pixel is considered for ini-

tiating the traversal process in the fragmented vessel

centerline image.

The traversal process uses the 3 × 3 connectiv-

ity mask to ﬁnd the neighboring pixels in the vessel-

segment. The mask is applied by considering the

starting pixel of any vessel-segment as its center.

Once a neighboring pixel is found it replaces the pre-

vious one. Each time a pixel position is considered

a ﬂag value is assigned so that this pixel is not con-

sidered for the next time. Once the traversal process

reaches the vessel-segment’s end point, it stops if it

belongs to a bifurcation or a branch. The features

of this vessel-segment are computed and inserted into

the corresponding node in the tree-model. Using this

vessel-segment’s end point we determine the starting

point of the daughter vessels and the landmark point.

After receiving the starting points, we classify their

corresponding vessel-segments as the left and right

children in the tree-model for the current parent. We

discuss this in the next section. The vessel-segment,

which is classiﬁed as a left child, is considered for

continuing the process. The right vessel-segment’sin-

formation is inserted into a stack and considered latter

for constructing the tree-model.

For crossover points we use ﬂag values for the

end points. We determine the landmark point for

the current vessel-segment’s end point and ﬁnd the

other vessel-segments’ start or end points. Then we

measure the slopes considering the line segments be-

tween the landmark and vessel segments’ start or

end points. The traversal process selects the vessel-

segment, which has the closest slope value to the cur-

rent vessel-segment.

Determination of Left Child and Right Child in

the Tree-model

A vessel-segment is classiﬁed as the left or right child

in the tree-model, based on its starting point location

around the parent vessel. Let us consider Figure 3.

Assume that the end point returned by the traversal

process is (x

). Using this end point, we determine

other two vessel-segments’ starting points (x

) and

) along with the landmark point (x

). From

these points, we can obtain the centerline equation as

follows

(x− x

)/(x

− x

) − (y− y

)/(y

− y

) = 0 (1)

We compute the slope of the line (i.e., vessel-

segment) as m = (y

− y

)/(x

− x

). We ﬁt (x

)

and (x

) to the above line equation. If the slope

m > 0 (as in Figure 3(a)) and (x

) returns a value

less than the value returned by (x

) for the left

hand side in line equation (2), we assign (x

) (i.e.,

its vessel-segment) as a left child in the tree-model,

otherwise it is a right child. If the slope m < 0 (as in

Figure 3(b)), the rules are opposite.

Figure 3: Vessel-segment appears with positive slope (a)

and negative slope (b).

If the centerline segment is parallel to x-axis or y-

axis (Figure 4) we ﬁnd the positions (as left or right)

of these points as follows. If the vessel-segment is

parallel to y-axis (i.e., x

− x

= 0), at ﬁrst we con-

sider if y

− y

> 0 (as in Figure 4(a)). In this case,

if x

> x

, (x

) is on the left side. Otherwise it

is on the right side. If we invert the vessel direction

in Figure 4(a), i.e., y

− y

< 0, the rules are oppo-

site. Similar rules are applied for the vessel-segments

which are parallel to x-axis (Figure 4(b)).

Once we classify these vessel-segments starting

points as left and right children, we consider the left

child (i.e., vessel-segment) to be inserted into the tree-

model. The right child (i.e., starting point) is inserted

into a stack along with the address of its parent node

(to be considered latter). We implement the stack us-

ing a linked list so that it can handle essentially any

number of elements dynamically.

Each time the traversal algorithm returns a vessel-

segment’s end point, using this we search for the land-

mark point and starting points of the daughter vessel-

segments. If there is no start point, the traversal pro-

Figure 4: Vessel-segment appears as parallel to y-axis (a)

and x-axis (b).

RETINAL VASCULAR NETWORK MODEL - An Automatic Approach

235

cess is terminated. Then we compute the vascular fea-

tures for the current vessel-segment and insert them

into the corresponding node in the tree-model. Fol-

lowing that we access the stack for a vessel-segment’s

start point along with its parent address in the tree-

model. Then consider this vessel-segment for insert-

ing into the tree-model. If there is a start point of a

vessel-segment, we trace this vessel-segment and in-

sert its features into the corresponding node in the

tree-model. This process continues until the end of

the entire vessel or the stack is empty. Once a ves-

sel is considered for the tree-model, the binary tree

construction is started for the next vessel and so on.

2.6 Appending Vascular Features

The vascular features are added to each node, which

represents a vessel-segment. Each time a node is in-

serted, it also includes the corresponding vascular fea-

tures. Some vascular features require daughter vessel-

segments information. These are: ratio of trunk

width and branch width, acute angle between par-

ent and smaller daughter vessel, and bifurcation an-

gle. For these we need to consider the related vascu-

lar features for parent and daughter vessel-segments.

Therefore, a node includes only the features of the

same vessel-segment if it does not have any daughter

vessel-segments.

3 EVALUATION OF THE

TREE-MODEL

CONSTRUCTION

We evaluate our technique using two publicly avail-

able data sets with images of diseased retinas; the

STARE database (Hoover et al., 2000),(STARE-

project, 2006) and the DRIVE (Staal and Abramoff,

2004). We demonstrate the feature analysis using the

STARE database which has labeled images of dia-

betic and normal retinas. It took approximately 1.69

minutes using MATLAB version 7.5 to produce each

output tree-model on a 2.66 GHz Pentium 4 Duo CPU

with 3.25 GB of RAM. For evaluating our method, we

considered the vessel-segments’ hierarchy and posi-

tional information (i.e., daughter vessel as left or right

to the parent vessel) and observe if they are repre-

sented similarly in the tree-model.

For each image, we selected the starting point co-

ordinates of a vessel, i.e., actual starting position of

a vessel-segment (Figure 5). We observed the tree-

model to see if this point was assigned in the root.

Then we tracked the end point of that vessel-segment

Figure 5: A cropped vessel-segments with marked end

points.

and checked whether it is assigned to corresponding

binary tree of the tree-model or not (Table 1). Fol-

lowing that we considered the daughter vessels on the

labeled image and then checked the tree-model if they

are correctly assigned as left and right children nodes

in the corresponding binary tree. We continued this

process until the end of each vessel and stopped after

considering all the vessels in an image.

Table 2 shows the number of calculated vessel-

segments in a manually labeled image and the number

of vessel-segments that were represented by the cor-

responding binary tree in the tree-model. When the

number of vessel-segments were correctly inserted

into the corresponding binary tree in the tree-model, it

is true positive or agreed (column 4). The number of

vessel-segments that were missed in the correspond-

ing binary tree of the tree-model, shown as missed

(column 5). When a vessel-segment was inserted in

the binary tree of the tree-model but is not a part of

the binary tree (i.e., belong to another vessel) it is spu-

rious (column 6). After ﬁnding these segments for all

vessels we used the following formula to compute er-

ror in constructing the tree-model for an image.

Error = (Segments missed + Spurious seg-

ments)/(Total number of vessel-segments).

For each vessel the accuracy (1 − error) × 100 is

obtained in percentile. Then we measure the accuracy

of constructing the tree-model for an image by aver-

aging the accuracy of all the vessels. We considered

forty images (twenty from DRIVE and twenty from

STARE database) for evaluation process and achieved

an overallaccuracy of 91.23%. Table 3 shows the pro-

cess on ﬁve different images. We note that the con-

struction accuracy of the tree-model depends on the

segmentation of the blood vessel. If the segmentation

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236

Table 1: A binary tree representation of a blood vessel with node values.

End Point Coordinate nodes Values

Index x y parent left child right child Tortuosity

Bi Angle L/W

1 38 76 0 2 3 0.112 1.223 0.893 21.25

2 45 95 1 4 5 0.112 1.032 0.793 6.12

3 13 102 1 0 0 0.08 0 0 14.12

4 34 138 2 0 0 0.15 0 0 14.89

5 33 107 2 0 0 0.112 0 0 5.23

Table 2: The evaluation of tree-model for an image.

Vessel Tree-Model Construction Post Analysis Accuracy

Number Total Vessel-Segment Number in Tree Agreed Missed Spurious (%)

1 12 10 10 2 0 83.33

2 7 7 7 0 0 100

3 14 12 10 2 2 71.43

4 9 9 8 0 1 88.89

5 11 11 11 0 0 100

6 11 11 11 0 0 100

7 6 6 6 0 0 100

8 12 12 11 1 1 83.33

9 5 5 5 0 0 100

Average Accuracy 91.89

Table 3: Overall Accuracy on Tree-Model Construction.

Image Total Accuracy Average

Number Vessel-Segment (%) Accuracy(%)

1 80 91.89

2 67 92.98

3 79 90.05 91.44

4 82 89.29

5 73 93.01

method fails to obtain a minor vessel, the next process

fails to obtain the landmark point. Consequently, we

missed a node in the tree-model.

Among the vascular features, we evaluated the

width measurement accuracy against ﬁve different

graders and the results are reported in (Bhuiyan et al.,

2008). Further, the accuracy of bifurcation and

branching angle measurement along with landmark

classiﬁcation are reported in (Bhuiyan et al., 2007b).

Blood vessel tortuosity is reported in (Bhuiyan et al.,

2010).

4 CONCLUSIONS

In this paper we proposed and evaluated a new

method for constructing a vascular network model

(the tree-model). We used the vessel centerline and

edge image and classiﬁed landmark points to con-

struct this tree-model. We computed vascular features

which are signiﬁcant for disease diagnosis and pro-

vided an example of using the tree-model in disease

diagnosis.

The primary goal of our research is to facilitate

and access the vascular features efﬁciently by repre-

senting these in a graphical form. The medical practi-

tioners can access and analyze these vascular features

according to their requirements.

Our experimental results establish that the method

can be readily used in medical applications with high

accuracy. Further, we envisage that the tree-model

will be very efﬁcient in ﬁnding the correspondingves-

sels for matching two images. In this tree structure,

each vessel segment can be searched with O(log n)

operations where n is the number of vessel-segments.

The proposed tree-model is based on the blood

vessel segmentation accuracy, and the tree-model is

achieving 91.23% construction accuracy. We are cur-

RETINAL VASCULAR NETWORK MODEL - An Automatic Approach

237

rently investigating various approaches to improve

our segmentation method based on texture, edge in-

formation and Markov random ﬁeld. This should fur-

ther enhance the accuracy of the tree-model construc-

tion.

Our contributions in this paper are summarized

below:

• We proposed a new and efﬁcient method to con-

struct a tree-model, which includes a number of

signiﬁcant vascular invariant features.

• The tree-model is an automatic process to repre-

sent the vascular features and can readily be used

in feature analysis for earlier diagnosis of differ-

ent diseases.

REFERENCES

Bhuiyan, A., , Nath, B., Chua, J., and Ramamohanarao, K.

(2008). Vessel cross-sectional diameter measurement

on color retinal image. Communications in Computer

and Information Science, 25:214–227.

Bhuiyan, A., Nath, B., Chua, J., and Kotagiri, R. (2007a).

Blood vessel segmentation from color retinal images

using unsupervised classiﬁcation. In the proceedings

of the IEEE International Conference of Image Pro-

cessing, pages 521–524.

Bhuiyan, A., Nath, B., Chua, J., and Ramamohanarao, K.

(2007b). Automatic detection of vascular bifurcations

and crossovers from color retinal fundus images. Pro-

ceedings of Third International IEEE Conference on

Signal-Image Technologies and Internet-Based Sys-

tem (SITIS), pages 711–718.

Bhuiyan, A., Nath, B., Ramamohanarao, K., Kawasaki, R.,

and Wong, T. Y. (2010). Automated analysis of retinal

vascular tortuosity on color retinal images. Journal of

Medical Systems, pages 1–15.

Chow, T. W. S., rahman, M. K. M., and Wu, S. (2006).

Content-based image retrieval by usingtree-structured

features and multi-layer self-organizing map. Pattern

Analysis and Applications, 9:1–20.

Hart, W. E., Goldbaum, M., Cote, B., paul Kube, and nel-

son, M. (1999). Measurement and classiﬁcation of

retinal vascular tortuosity. International Journal of

Medical Informatics, 53:239–252.

Hoover, A., Kouznetsova, V., and Goldbaum, M. (2000).

Locating blood vessels in retinal images by piece-wise

threshold probing of a matched ﬁlter response. IEEE

Transactions on Medical Imaging, 19(3):203–210.

Li, X. and Qu, X. (1998). Matching spatial relations

using db-tree for image retrieval. Proceedings of

the International Conference on Pattern Recognition

(ICPR’98), 2:1230–1234.

Lin, K.-S., Tsai, C.-L., and Sofka, M. (2009). Vascu-

lar tree construction with anatomical realism for reti-

nal images. In the Proceedings of Ninth IEEE Inter-

national Conference on Bioinformatics and Bioengi-

neering, pages 313–318.

Martinez-Perez, M. E., Hughes, A. D., Stanton, V., Si-

mon A Thom, N. C., Bharath, A. A., and Parker,

K. H. (2002). Retinal vascular tree morphology: A

semi-automatic quantiﬁcation. IEEE Transactions on

Biomedical Engineering, 49(8):912–917.

Mattes, J., Richard, M., and Demongeot, J. (1999). Tree

representation for image matching and object recogni-

tion. Proceedings of the 8th International Conference

on Discrete Geometry for Computer Imagery, LNCS

1568:298–309.

Mosorov, V. (2005). A main stem concept for image match-

ing. Pattern Recognition Letters, 26:1105–1117.

Pinz, A., Bernogger, S., Datlinger, P., and Kruger, A.

(1998). Mapping the human retina. IEEE Transac-

tions on Medical Imaging, 17:606–619.

Staal, J. and Abramoff, M. D. (2004). Ridge-based ves-

sel segmentation in color images of the retina. IEEE

Transactions on Medical Imaging, 23(4):501–509.

Stanton, A. V., Wasan, B., Cerutti, A., Ford, S., Marsh, R.,

Sever, P. P., Thom, S. A., and Hughes, A. D. (1995).

Vascular network changes in the retina with age and

hypertension. Journal of Hypertension, 13:1724–

1728.

STARE-project (2006). http://www.ces.clemson.edu/

∼ahoover/stare/. last accessed on 21 November.

Taarnhoj, N. C. B. B., Munch, I. C., Sander, B., Kessel, L.,

Hougaard, J. L., and Kyvik, K. (2008). Straight ver-

sus tortuous retinal arteries in relation to blood pres-

sure and genetics. British Journal of Ophthalmology,

92:1055–1060.

Zhou, P., Wang, M., and Cao, H. (2005). Research on fea-

tures of retinal images associated with hypertension

and diabetes. Proceedings of the 2005 IEEE Engineer-

ing in Medicine and Biology 27th Annual Conference,

pages 6415–6417.

BIOSIGNALS 2011 - International Conference on Bio-inspired Systems and Signal Processing

238