The 3
rd
European Medical and Biological Engineering Conference November 20 – 25, 2005
EMBEC'05 Prague, Czech Republic
IFMBE Proc. 2005 11(1) ISSN: 1727-1983 © 2005 IFMBE
A RIBBON OF TWINS FOR EXTRACTING VESSEL BOUNDARIES
B. Al-Diri
∗
and A. Hunter
∗
∗
The University of Lincoln
baldiri@lincoln.ac.uk
Abstract: This paper presents an efficient model for
automatic detection and extraction of blood vessels in
ocular fundus images. The model is formed using a
combination of the concept of ribbon snakes and twin
snakes. On each edge, the twin concept is introduced
by using two snakes, one inside and one outside the
boundary. The ribbon concept integrates the pair of
twins on the two vessel edges into a single ribbon. The
twins maintain the consistency of the vessel width,
particularly on very blurred, thin and noisy vessels.
The model exhibits excellent performance in extract-
ing the boundaries of vessels, with improved robust-
ness compared to alternative models in the presence
of occlusion, poor contrast or noise. Results are pre-
sented which demonstrate the performance of the dis-
cussed edge extraction method, and show a signifi-
cant improvement compared to classical snake formu-
lations.
Introduction
Vessel segmentation algorithms are a critical compo-
nent of blood vessel analysis systems. The segmentation
of vascular structures plays an important role in diagno-
sis, surgery and research, in many important systematic
diseases such as diabetes and hypertension. Furthermore,
the vascular tree seems to be the most appropriate repre-
sentation for image registration applications.
A number of authors have investigated the use of
active contour models in retinal vascular segmentation.
However, none have reached the level of performance re-
quired for robust automatic detection of the entire net-
work of blood vessels, which is needed for measurement
techniques used for identifying and grading the sever-
ity of diabetic retinopathy. We have thus introduced a
new parametric active contour model called a ribbon of
twins. our model uses the Gradient Vector Flow method
– which provides good performance through concavi-
ties and noise features; the “twin” method – which uses
two contours coupled by spring models to overcome ini-
tialization and localized feature problems; and the “rib-
bon” method, which couples two snakes with a consis-
tent width parameter. Our model integrates these differ-
ent features to produce a novel hybrid model.
Parametric contours
In the parametric approach, an active contour [1] is
represented as a curve or spline, v(s)=(x(s), y(s), where
v is a “vertex” and x and y represent the coordinates of
the vertices and are functions of the normalised arc length
0 ≤ s ≥ 1. The active contour has a dynamic behaviour
that deforms from an initial position and hopefully con-
verges to the boundary of the object. The energy func-
tional E
∗
snake
composed of energy terms defines this be-
haviour:
E
∗
snake
=
1
0
E
snake
(v(s))ds (1)
=
1
0
E
int
(v(s)) + E
pho
(v(s)) + E
ext
(v(s))
ds (2)
– where E
int
is the internal energy term that is based
on the curve itself, which is designed to keep the model
smooth during deformation; E
pho
is the photometric en-
ergy term that arise from the image information, which is
defined to move the model toward an object boundary or
other desired feature within an image; E
ext
is the external
energy term that is proposed to improve the capture range
of the photometric force.
Internal energy
The internal energy consists of a first order term and
a second order term [1].
E
int
=
α (s)|v
′
(s)|
2
+ β (s)|v
′′
(s)|
2
2
(3)
where v
′
(s) and v
′′
(s) denote the first and second deriva-
tive respectively, and parameters α and β are the coeffi-
cients of the internal energy term and represent tension
and rigidity, respectively.
Photometric energy
The photometric energy is derived from the image to
attract the snake toward desired objects such as bound-
aries. Given a grey-level image I (x, y),the photometric
energy leading an active contour towards edges is defined
by [1]:
E
(1)
pho
= −|∇I (x, y)|
2
(4)
E
(2)
pho
= −|∇(G
σ
(x, y) ∗ I (x, y))|
2
(5)
where G
σ
(x, y) is a two-dimensional gaussian filter with
standard deviation σ , ∇ is the gradient operator, and ∗ is
the 2D image convolution operator. The blurred gradi-
ent based approach has a number of limitations. First,