Segmentation of vessel-like patterns using mathematical morphology and curvature evaluation

Abstract

This paper presents an algorithm based on mathematical morphology
and curvature evaluation for the detection of vessel-like patterns in a
noisy environment. Such patterns are very common in medical images.
Vessel detection is interesting for the computation of parameters
related to blood flow. Its tree-like geometry makes it a usable feature
for registration between images that can be of a different nature. In
order to define vessel-like patterns, segmentation is performed with
respect to a precise model. We define a vessel as a bright pattern,
piece-wise connected, and locally linear, mathematical morphology is
very well adapted to this description, however other patterns fit such a
morphological description. In order to differentiate vessels from
analogous background patterns, a cross-curvature evaluation is
performed. They are separated out as they have a specific Gaussian-like
profile whose curvature varies smoothly along the vessel. The detection
algorithm that derives directly from this modeling is based on four
steps: (1) noise reduction; (2) linear pattern with Gaussian-like
profile improvement; (3) cross-curvature evaluation; (4) linear
filtering. We present its theoretical background and illustrate it on
real images of various natures, then evaluate its robustness and its
accuracy with respect to noise

Full text

1010 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 10, NO.7, JULY 2001
Segmentation of Vessel-Like Patterns Using
Mathematical Morphology and Curvature Evaluation
Frédéric Zana and Jean-Claude Klein
Abstract—This paper presents an algorithm based on mathe-
matical morphology and curvature evaluation for the detection of
vessel-like patterns in a noisy environment. Such patterns are very
common in medical images. Vessel detection is interesting for the
computation of parameters related to blood flow. Its tree-like ge-
ometry makes it a usable feature for registration between images
that can be of a different nature. In order to define vessel-like pat-
terns, segmentation will be performed with respect to a precise
model. We define a vessel as a bright pattern, piece-wise connected,
and locally linear. Mathematical Morphology is very well adapted
to this description, however other patterns fit such a morpholog-
ical description. In order to differentiate vessels from analogous
background patterns, a cross-curvature evaluation is performed.
They are separated out as they have a specific Gaussian-like pro-
file whose curvature varies smoothly along the vessel. The detection
algorithm that derives directly from this modeling is based on four
steps:
1) noise reduction;
2) linear pattern with Gaussian-like profile improvement;
3) cross-curvature evaluation;
4) linear filtering.
We present its theoretical background and illustrate it on real im-
ages of various natures, then evaluate its robustness and its accu-
racy with respect to noise.
Index Terms—Blood, edge detection, image analysis, mathemat-
ical morphology, ophthalmology, vessels.
I. INTRODUCTION
A. Edge Detection
EDGE detection is an essential task in computer vision. It
covers a wide range of applications, from segmentation
to pattern matching. It reduces the complexity of the image al-
lowing more costly algorithms like object recognition [1], [2],
object matching [3], object registration [4], or surface recon-
struction from stereo images [5], [6] to be used. Vessel-like pat-
terns with a Gaussian-like profile are very common, especially
in medical images. Their detection is interesting for different
goals. They can be used to measure parameters related to blood
flow or to locate some patterns in relation to the vessels in angio-
graphic images. They can also be used as a first step before reg-
istration [4], [7], [8]. A robust algorithm, suitable for different
types of images, should allow registration of retinal images of
very different nature and should permit one to combine informa-
tion from data provided by various sources. In the case of eye
Manuscript received November 12, 1998; revised January 25, 2001. The as-
sociate editor coordinating the review of this manuscript and approving it for
publication was Prof. Robert J. Schalkoff.
The authors are with the Centre de Morphologie Mathématique, Ecole des
Mines de Paris, 77305 Fontainebleau, France (e-mail: zana@cmm.ensmp.fr;
klein@cmm.ensmp.fr).
Publisher Item Identifier S 1057-7149(01)03266-3.
fundus images, the detection of the vascular tree seems a nat-
ural approach to the registration problem. Vessels are the only
features that are common to every image of the retina. This is
particularly true for angiographic images, since the signal comes
from a dye injection.
In this paper, we present an algorithm that combines Mor-
phological filters and cross-curvature evaluation to segment
vessel-like patterns. Its application to images from retinal
angiographies has been briefly presented in [9]. We study
the behavior of this algorithm on a wider set of angiographic
images and we extend its range to other images of the retina.
Vessel-like patterns are bright features defined by morpholog-
ical properties: linearity, connectivity, width and by a specific
Gaussian-like profile whose curvature varies smoothly along
the crest line. We use mathematical morphology to highlight
vessels with respect to their morphological properties. We then
evaluate the cross curvature. Vessels are detected as the only
features whose curvature is linearly coherent. This algorithm
has been tested on retinal photographs of three different types:
fluoroangiography, gray images obtained with a green filter, and
color images with no filter. Occasionally a short preprocessing
step was necessary since the algorithm only works with bright
patterns in gray level images. We then evaluate the behavior of
this algorithm with respect to different kinds of noise, in order
to measure its robustness and its accuracy. Finally, we compare
this algorithm to other methods and we present a conclusion.
B. Morphological Operators
This section is a short reminder of some basic definitions of
extensive morphological operators. More details can be found
in [10].
We define a two-dimensional (2-D) image whose range is
as a functional , and a
2-D structuring element as a functional where is
the set of the neighborhoods of the origin. In our approach we
will only consider structuring elements invariant by translation,
that are thus identified with a subset of , and we will refer to
linear structuring elements when this subset is a segment.
We then define basic operators, with respect to the structuring
element with scaling factor , image and point :
erosion: MIN ;
dilation: MAX ;
opening: ;
closing: ;
top-hat: .
We will not use superscripts for unit scaling factor. Geodesic op-
erators are defined with respect to a norm , or a connectivity
1057–7149/01$10.00 © 2001 IEEE

ZANA AND KLEIN et al. SEGMENTATION OF VESSEL-LIKE PATTERNS 1011
graph in digitized images (a neighborhood of unit radius).
They depend on a marker image and distance .
The geodesic dilation is defined by
MAX
The geodesic reconstruction (or opening) is defined by
The geodesic closing is defined by
II. VESSEL-LIKE PATTERN DESCRIPTION
A. Crest Lines and Rotating Matched Filters
Much has been written about detection of edges with a
Gaussian-like profile. At least three different methods were
applied to vessel segmentation: crest line detection [7], rotating
matched filters [11], and neural networks [12]. Both methods
[7] and [11] use linear operators and are based on differential
properties. The crest line approach is based on the detection of
the Gaussian profile by the use of up to the third derivative.
Crest lines are lines where the magnitude of the maximum
curvature is locally maximum in the corresponding principal
direction (definition of [7]). This yields edges that are not
necessarily connected. Rotating matched filters have been
applied to the green plane of color eye fundus images in order
to detect patterns with Gaussian profile across a constant line.
Those matched filters are based on results and theory described
in [8] and [2]. In this case, vessels can be very well highlighted,
however further treatments, specific to the data, are necessary
to remove other undesired linear features. We will show
that the use of some morphological filters leads to an image
simplification that eases the computation of cross-curvatures.
Based on this observation, we have developed an algorithm
based on a precise description of vessel-like patterns and
look-alike background elements that combines morphological
and differential properties.
B. Vessel-Like Pattern Modeling
We assume that the vascular tree is the only element of our
image that is locally uniform in color or gray value completely
described by the following properties (see Fig. 1):
• the shape of a cross-section looks like a Gaussian curve;
• it is connected in a tree-like way;
• vessels have a certain width and cannot be too close to-
gether.
These properties can be separated into those related to the mor-
phological description (linearity, connectivity, vessel width) and
those related to the calculation of some parameters (the curve of
the Gaussian profile, its variation along the crest lines).
Fig. 1. Model of vessel.
(a)
(b)
(c)
Fig. 2. Various background textures. (a) Image with an addition of dark regions
surrounded by a bright gray value. (b) Regular background noise, with some
capillaries. (c) Smooth texture with linear features in the background.
There are different kinds of undesirable patterns encountered
when extracting the vascular tree. We have classified them into
different cases m that we will refer to in this article.
Case 1) Noise occurring during the digitization process, or
due to undesirable elements whose texture can be
described by a low intensity white noise.
Case 2) Background linear features that can be confused
with vessels in some parts, but that do not meet all
the requirements (they can be too thin or too close).
Case 3) Other kinds of patterns that are not linear. We can
separate them into three subcases:
case a) large bright or dark areas;
case b) bright or dark thin irregular zones;
case c) small bright or dark areas.
Case 4) Low signal/noise ratio concerning the intensity of
vessels (see Figs. 2 and 9).

1012 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 10, NO.7, JULY 2001
Fig. 3. Openings using linear structuring elements.
III. TREATMENT OF RETINAL FLUORESCEIN ANGIOGRAPHIES
A. Images of Retinal Fluorescein Angiographies
Images of retinal angiographies are obtained after an injec-
tion of fluorescein into the left arm. Retinal vessels are high-
lighted using an ultraviolet light. The diffusion process lasts a
few minutes: after 5 min, the signal is very weak and noisy.
Another difficulty is due to the histology of the eye, which is
composed of several layers. The layers below the retina create
background noise whose characteristics may vary significantly
among people.
Therefore, a sequence of photographs taken during a 5-min
injection gives adequate material for vessel detection under a
noisy environment with various signal intensities. The size of
the detected vascular structure, in angiographic images, is re-
lated to the degree of diffusion of the dye into the vessels. It can
also be used as a preprocessing step of a registration algorithm
(see [13]). Later on, we will use this algorithm on other retinal
images.
B. Morphological Treatment for the Recognition of Geometric
Features
Because of the linear property of vessels, we use morpholog-
ical filters with linear structuring elements.
1) Recognition of Linear Parts: Linear bright shapes
can easily be identified using mathematical morphology. An
opening using a linear structuring element will remove a vessel
or part of it when the structuring element cannot be included
inside the vessel, as is the case when they have orthogonal
directions and the structuring element is longer than the vessel
width. Conversely, when the structuring element and the vessel
have parallel directions, the vessel will stay nearly unchanged
(see Fig. 3). If we consider the openings along a class of linear
structuring elements, a sum of top-hats along each direction
will brighten the vessels regardless of their direction. However,
this operation requires the length of the structuring elements to
be large enough to remove big vessels, hence we will recover
a lot of noise in the sum of top hats. In order to deal with
this problem, we preprocess the image using the connectivity
property (Fig. 4).
(a) (b)
(c) (d)
Fig. 4. Each step of the morphological treatment: (a) initial image, (b)
supremum of opening, (c) reconstruction, and (d) sum of top-hats.
2) Using the Connectivity Property: We remove noise while
preserving most of the capillaries using a geodesic reconstruc-
tion of the opened images into the original image :
Max
Each structuring element (every 15 ) is 15-pixels long
(1-pixel wide). Its size is approximately the range of the diam-
eter of the biggest vessels for images of retinal
angiographies, as explained in [11]. In the image , every
isolated round and bright zone whose diameter is less than 15
pixels has been removed. Being a supremum of openings by
reconstruction this operation is an opening (see [10]), called
linear opening by reconstruction of size 15. Removed elements
include white noise (case 1) and some abnormalities (case 3c).
The sum of tophats on the filtered image will enhance
all vessels whatever their direction, including small or tortuous
vessels, even in the low signal (case 4). The large homogeneous
pathological areas (case 3b) will be set to zero since they are
unchanged by , however the image contains a lot of de-
tails corresponding to case 2 and possibly case 3b that are also
enhanced by the difference.
3) Using Differential Properties as a Separating Tool: We
assume at this stage that any nonzero point in the picture has a
dominant direction, and thus can be considered as part of some
lengthened pattern (vessels, patterns 2 or 3b). We will refer to
the curvature whenever it is the curvature in the cross direction,
which is now defined for every pixel under the former assump-
tion. Its evaluation using the Laplacian will be discussed in the
following section. In case 3b [Fig. 5(b)], the signal appears as
thin and irregular bright linear elements, therefore the curvature
gets positive values on a width smaller than in the case of the
vessels (see Fig. 6), and it is not necessarily linearly correlated.

ZANA AND KLEIN et al. SEGMENTATION OF VESSEL-LIKE PATTERNS 1013
Fig. 5. (a) Vessel and (b) and (c) cases 3b and 2 from Section II-B.
U
and
V
are the principal directions.
Fig. 6. Laplacian images highlighted around zero (positive values in white and
negative values in black) before and after the alterning filter.
In case 2 [Fig. 5(c)], the signal tends to be low and disorga-
nized, and the curvature will have alternating positive and neg-
ative values in various directions: linear morphological open-
ings performed on the curvature image are very well adapted
to such treatments. However, in a few cases, this fuzzy signal
can have a curvature that looks very much like a small vessel.
Our strategy does not separate this signal from the retinal ves-
sels [Fig. 5(a)],leading to false detection that is hopefully rare
and isolated.
After computing a Laplacian, we obtain a good estimation of
the curvature (see Fig. 6). Then we perform a linear opening by
reconstruction of size 15, then a linear closing by reconstruction
of size 15, and finally a linear opening of size 29. This alter-
nating filter removes patterns corresponding to case 3b, and in
most cases patterns corresponding to case 2. These sizes were
chosen for typical images of the retina. Values
should be adjusted to the size of the vessel-like pattern. We will
discuss this matter in Section VIII. Failing to adjust those pa-
rameters can lead to the removal of some apparently interesting
features. The algorithm was designed to segment the main ves-
sels and remove all possible false detection under various kinds
of noise. Another strategy may simply require a different alter-
nating filter, thus we will not deal with the adjustment of this
last parameter in our discussion.
C. Evaluation of the Curvature using the Laplacian
Let be a regular curve contained in , passing through
(see Fig. 7). Let be the curvature of at and ,
where (resp. ) is the normal vector to (resp. )at . The
number is called the normal curvature of
at , and principal curvatures are the two extrema of when
varies. A detailed general method for curvature calculation can
be found in [14]. The top hat filter simplifies the image before
Fig. 7. Differential elements of the image.
curvature calculation in order to compute a first order estimation
that is less computationally expensive than in [7].
We assume that the first filter leads to an image that locally
looks like one of the three cases described in Fig. 5. Hence, for
any point of image ,if and are the principal
curvatures of the surface at then we either have
or . In Fig. 5, we have denoted by the principal
direction corresponding to , and the normal direction, cor-
responding to . We will always use these local coordinates in
the following.
In order to describe these simplifications with respect to the
functional , we will express the former approximation as:
, and . It simplifies the
computation of matrices called the first and second fundamental
forms that are used to compute the curvatures (see [14]).
The first fundamental form1in the basis is given by
It is thus simplified into
The normal vector at point is given by
The second fundamental form2is given by
1The natural inner product induces an inner product on the tangent plane
whose matrix is the first fundamental form.
2If
N
is the Gaussian map and
dN
its differential form defined on the tan-
gent plane, then
F
is the matrix of the inner product:
v
!0
dN
(
v
)
1
v
.

1014 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 10, NO.7, JULY 2001
which we simplify into
As proved in [14], the principal curvatures are the eigenvalues
of the Weingarten endomorphism whose matrix is
We deduce that , .
As was expected, . We notice that
has the same sign as (since ), and
is independent of the frame.
Hence, the sign of the Laplacian can be used as a good ap-
proximation of the sign of the curvature. Experiments were al-
ways found to be in accordance with this approximation (see
Fig. 6).
IV. MAIN ALGORITHM
We can summarize our algorithm as follows:
Max
This transformation (a sum of top hats) reduces small bright
noise and improves the contrast of all linear parts. Vessels could
be manually segmented with a simple threshold on .How-
ever, most images contain noisy data requiring further treatment,
hence, the computation of the curvature
Laplacian Gaussian
Then the alternating filter, leading to the final result
Max
Min
Max
A PC Pentium 133 MHz with 16 MB of memory runs this al-
gorithm on a image in less than 3 minutes. Note
that the program was written in Visual Basic under Aphelion, an
image understanding and processing software package, and that
a C program would run much faster. Algorithmic improvements
can also be considered (see [15]).
V. RESULTS ON DIGITAL RETINAL ANGIOGRAPHY
This algorithm has been tested on a database of about 200 an-
giographies, from patients with various abnormalities. The ma-
jority of the images were taken directly with a digital camera,
but the database image also contains photographs digitized with
a scanner. The typical image size was , however
the database included images as big as . Robust-
ness was evaluated at this stage on noisy images from the late
Fig. 8. Low contrast image.
Fig. 9. Late diffusion time.
Fig. 10. Image with many dark patterns.
diffusion time (Fig. 9) and low-contrast images (Fig. 8). Images
from normal eyes produce nearly perfect images (Fig. 17)
We have encountered false detection in the following cases:
• hyper-fluorescence that looks linear (Fig. 11, center
bottom blob);
• black zone next to a brighter zone (Fig. 10);
• round linear bright structures are mistaken for vessels, and
appear as white isolated circles.
Most of those problems are rare and related to some disease,
they may be problematic when they are connected to the vas-
cular tree (which occurred once but was not significant). Parts
of vessels were not detected mostly in the late diffusion phases,
and when they were hidden by some wide hyper-fluorescence
(see Fig. 12, left) and in case of very low contrast (Fig. 13). In
every case, the detection was in accordance with the description
we gave in Section III-B: some nonvascular patterns simply fit

ZANA AND KLEIN et al. SEGMENTATION OF VESSEL-LIKE PATTERNS 1015
Fig. 11. Diffusion of the dye outside the vessel.
Fig. 12. Image on a detail.
Fig. 13. Other case, with a very low contrast.
the same model. The limit of detectable contrast is visible in
Fig. 13.
Results consist of binary images superimposed upon the orig-
inal image multiplied by a factor of 0.4.
VI. GENERALIZATION TO OTHER RETINAL IMAGES
The algorithm has been adapted to other types of retinal im-
ages: green images and color images of the eye fundus.
Green images of the retina are taken by physicians with green
filters, and color images represent the natural colors of the eye
fundus. In such images, vessels are less contrasted than in angio-
graphic images in the state of complete diffusion (in mid-phase),
and they contain less information: smaller branches of the vessel
tree are simply not in the image. Each type of image is designed
Fig. 14. Green image from diabetic patient.3
to detect specific patterns. In order to bring together the informa-
tion contained in all the images of a series of tests, it may be very
useful to be able to register images of different types (see [13]).
Since images may be very different, correlation techniques or
other techniques that use the knowledge of a neighborhood may
be hazardous. It seems necessary to use an invariant feature as a
frame. Vessels are certainly the most appropriate pattern to use
as a frame, therefore their segmentation in various types of im-
ages is of the utmost interest.
A. Green Images of the Eye Fundus
In these images, the vessels appear dark, hence the prepro-
cessing step is a simple inversion of the gray values. It is fol-
lowed by the main algorithm, no other processing is necessary.
As expected, results may be less refined than with angiographic
images (fewer vessels are visible), but they are still very precise
and in accordance with the information contained in the image.
The algorithm has been applied to several images from diabetic
patients (see Fig. 14).
B. Color Images of Eye Fundus
Color images from transparent negatives developed on paper
are digitized in RGB with a scanner. The blue band appears to be
very weak and does not contain much information. The vessels
appear in red, however the red band usually contains too much
noise or is simply saturated since most of the features emit a
signal in the red band. Imitating physicians we have used the
green band. Inversion was performed before applying the main
algorithm. The image quality was poorer than for green images
of the retina, both because of a bad exposure to light and because
of the development on paper. As a consequence, results appear
to be less robust than in the former case, howeverthey seem suf-
ficient to define a frame (see Figs. 16 and 17 for a healthy eye).
This algorithm has been tried on 31 images (of poor quality)
from ill patients and two images of normal eyes. Fourteen im-
ages (including the two of the normal eyes) were correctly seg-
mented with most of the vascular tree detected (see Fig. 15), but
in the remaining 19 images too few vessels were detected. These
results can be attributed to the lack of contrast at the end of the
digitization process, which is worse in our case because of the
nature of the illness. The contrast of the retina is thus lowered
3Since the green image has dark vessels, it has been inverted before
superimposing vessels.
4Since the image has dark vessels, it has been inverted before superimposing
vessels.

1016 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 10, NO.7, JULY 2001
Fig. 15. Green component of a color image.4
Fig. 16. Different scales of an angiographic image.
by the signal coming from lower layers which are more visible.
Further preprocessing for contrast enhancement, specific to the
disease, has allowed a full recovery of the vascular tree in the
whole set of images, however we think that a better digitiza-
tion procedure should be considered in order to have a better
treatment for images with low contrast in the green plane. The
algorithm should also be tested on a wider range of illnesses.
VII. DISCUSSION ON THE ROBUSTNESS AND THE ACCURACY
OF THE ALGORITHM
We have evaluated the performance of our algorithm on an-
giographic images modified by various noise additions or geo-
metric transformations. Robustness regarding scale, noise, con-
trast, and accuracy will be discussed.
A. Robustness with Respect to Changes of Scale
Mathematical morphology transformations are known to be
sensitive to changes of scale. Since a large part of our algorithm
relies on such transformations, scale effects cannot be avoided.
However, the algorithm has proved to be efficient on a wide
scale of Gaussian profiles (from capillaries to big vessels). This
property is due to the reconstruction procedure. Apart from the
very last opening and the tophats, all openings are computed
Fig. 17. Image from an angiography of a normal eye.
Fig. 18. Image 17 with an addition of 100 in a selected box.
Fig. 19. Image 17 with a division by 2 in a selected box (ROI).
with reconstruction allowing the recovery of smaller vessels
connected to the detected area. The scale effect is encountered
in two parts of the algorithm: 1) during the sum of top hats, big
vessels are excluded when their profiles are larger than the first
structuring element and 2) during the very last opening, vessels
that are not longer than the last structuring element or that ap-
pear tortuous compared to this structuring element are removed.
Fig. 16 illustrates this behavior for vessel detection.
B. Robustness with Respect to Different Types of Noise and
Changes in Contrast
Various types of noise and transformation were applied to
an angiographic image of the retina. Results show that the al-
gorithm is not sensitive to sudden changes in the global gray
level: addition of the value 100 that corresponds to the height
of the Gaussian profile (Fig. 18), and division by a factor 2
(Fig. 19) were tested. The addition of Gaussian noise (Fig. 20)
removes some capillaries but respects the global structure. The
addition of uniform noise (Fig. 21) is much more destructive,
although parts of the big vessels still remain. Histogram equal-
ization (Fig. 22) creates extra noisy branches that are mistaken
for capillaries.
According to the various results, the algorithm is found ro-
bust with respect to contrast change except for small areas. The
addition of 100 does not change anything in the selected box,
however the division by a factor of two decreases every gray

ZANA AND KLEIN et al. SEGMENTATION OF VESSEL-LIKE PATTERNS 1017
Fig. 20. Image 19 with added Gaussian noise of mean 75 and standard
deviation 10 in the ROI. A vertical noisy line, two pixels wide, was also added.
Fig. 21. Image 19 with added uniform noise in the range (37,113) in the ROI.
Fig. 22. Histogram equalization in the selected box.
level, which affects the smaller capillaries. The tophat filter is
then less efficient on capillaries, even though some of them are
preserved by the reconstruction. Results are less affected by
Gaussian noise than by uniform noise, and histogram equaliza-
tion produces worse results because it creates false detection.
The reconstruction as well as the curvature evaluation are dis-
turbed by the noise because it modifies the connectivity of the
vascular structures.
C. Accuracy Evaluation
The algorithm has been designed to detect patterns with
Gaussian profile limited at the inflection point. As a conse-
quence, experiments show that small capillaries appear larger
than we would think. This behavior is due to the Gaussian filter
that is used before computation of the Laplacian. It was tested
by drawing a straight line—two-pixels wide—inside an image
of the retina, with gray value equal to the mean gray value of
the surrounding vessels. The result was a set of points that
contained the drawn line and included part of the line dilated
by one pixel. A few pixels of the dilated line were missing
because the surrounding texture had changed the location of
the inflection point. This effect can be seen in Fig. 20 which
contains a two pixel-wide vertical line. In proportion, small
vessels will thus appear wider than their real size.
Fig. 23. Original image.
(a) (b)
(c) (d)
Fig. 24. Several edge detection algorithms: (a) morphological gradient, (b)
Sobel edge detector, (c) matching filter, and (d) proposed algorithm.
VIII. COMPARISON WITH OTHER METHODS:DISCUSSION
An original image is given in Fig. 23, and we apply several
filters to this image, including the algorithm that we propose. We
then discuss the quality of the result with regard to the ability
to use this segmentation for registration. For this purpose, we
define four criteria:
1) good qualitative detection of the biggest vessels;
2) small proportion of false detection;
3) significant number of bifurcation points can be visually
identified in the vascular structure;
4) segmented structure is connected.
These criteria are qualitative and will thus require a short dis-
cussion.
We have applied some edge detectors (Sobel, morphological
edge detector), the matching filter [11] based on the Canny edge
detector, as well as the algorithm that we propose to the image
23. As was foreseeable, the Sobel and the morphological edge
detector [Fig. 24(a) and (b)] produce parallel edges, the biggest
vessels are easily recognizable whereas smaller vessels appear
less contrasted. They satisfy criterion 3) however, an algorithm
for the detection of parallel edges is necessary to achieve the
other criteria. The accuracy of bifurcation points will depend
on the quality of the post-treatment as well as the proportion of
5Image generously provided by Dr. C. Heipke,reproduced from [16].

1018 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 10, NO.7, JULY 2001
(a) (b)
(c) (d)
Fig. 25. : (a) sum of tophats with histogram equalization, (b) automatic
threshold from the proposed algorithm, (c) the matching filter with histogram
equalization, and (d) manual threshold on (c).
Fig. 26. Different scales of an outdoor image with a road.5
false detection, however it is likely that criterion 2) will not be
satisfied since nonvascular structures are also detected as edges.
The matching filter algorithm Fig. 24(c) produces an image of
good quality, satisfying criteria 1) and 3) for the biggest vessels,
however some smaller vessels of poor contrast are only partially
detected. The connectivity of the structure (criterion 4) is not
guaranteed along the same capillary, as can be seen when we
threshold the image [see Fig. 25(d)]. Since this algorithm also
results in some false detection (see the two arrows in Fig. 25)
and does not produce a clean binary image, it may be difficult
to separate the good structures from the false detection.
Our method produces a binary image that is more selective.
Therefore criterion 1) is not fully satisfied if we include some
small vessels. However, it is the only algorithm, compared to the
other three methods, achieving a very small proportion of false
detection [criterion 2)], even if we use a high threshold on one
of the images produced by the other three algorithms. The cri-
teria 3) and 4) are satisfied with approximately the same quality
as with the matching filter, however the algorithm that we pro-
pose will lead to less bifurcation points and less false detection.
Concerning criterion 4), the algorithm that we propose creates
connected linear structures that are clean but not always con-
nected to each other. The detection of bifurcation points is thus
easy.
In order to illustrate the difference between the matching filter
and the algorithm that we propose, we have improved the con-
trast of an intermediate image [Fig. 25(a) and (c)]. These figures
are very similar with respect to the biggest vessels, however the
real difference between those methods lies in the structure of
the background noise. With the matching filter the background
of the image is transformed, the linear structures are more con-
trasted even when they are not relevant (for example when they
are not connected to a big vessel). Whereas with our algorithm
the background structure is noisy and does not present the same
structure as the vessels. It is thus possible to eliminate the noise
completely, for example using a curvature differentiation.
IX. CONCLUSIONS
An efficient algorithm for vessel-like pattern detection has
been presented. Robustness and accuracy have been evaluated
on different images, demonstrating that it may be useful in a
wide range of retinal images. Based on a brief comparison with
some other edge detection algorithms, we can conclude that the
complementarity of mathematical morphology and linear trans-
forms allows a more complete treatment. It was possible to se-
lect vessels using shape properties, connectivity, as well as dif-
ferential properties like curvature. The robustness and weak-
nesses of the algorithm have been evaluated and explained in
order to facilitate its use for the analysis of retinal images. This
segmentation has been used for image registration of images of
the retina [13], and it is the first step toward an automatic diag-
nosis software.
Even though the scope of this article is limited to eye fundus
images, The reader should note that the proposed algorithm has
been tested successfully on other images. In Fig. 26, the road
can be described as being a tree-like edge with a Gaussian-like
profile. Since this description fits our model, it is not surprising
to see that the road is segmented with our algorithm. Some de-
velopments in other areas cannot be excluded.
ACKNOWLEDGMENT
The authors are grateful to the Eye University Hospital of
Créteil, France, to the Clinique de la Sauvegarde in Marseille,
France, and to the hopital de la Timone in Marseille, France, for
providing pictures. They would also like to thank Dr. I. Meunier,
Dr. Riss, and Dr. Grimaldi for useful medical support.

ZANA AND KLEIN et al. SEGMENTATION OF VESSEL-LIKE PATTERNS 1019
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Frédéric Zana graduated in theoretical mathematics
from the Ecole Normale Supéerieure de Paris
(ENSP), Paris, France, in 1993, received the M.S.
degree in computer science from the ENSP in
1994, and the M.S. degree in macroeconomics from
ENSP in 1996. Since 1996 he has been pursuing the
Ph.D. degree student at the Centre de Morphologie
Mathématique, Ecole des Mines de Paris.
Jean-Claude Klein received the Ph.D. degree in
electronics from the University of Nancy, France, in
1975.
Since 1969, he has been with the Centre de
Morphologie Mathématique, Ecole des Mines de
Paris, Paris, France, where he has been in charge of
the research group devoted to the design of dedicated
hardware architectures applied to real-time image
processing and the design of a continuous blood
glucose monitoring system.