1

A Hierarchical Image Matting Model for Blood
Vessel Segmentation in Fundus images

arXiv:1701.00892v3 [] 9 Oct 2017

Zhun Fan, Senior Member, IEEE, Jiewei Lu, Wenji Li,
Caimin Wei, Han Huang, Xinye Cai, Xinjian Chen∗ , Senior Member, IEEE,

Abstract—In this paper, a hierarchical image matting model
is proposed to extract blood vessels from fundus images. More
specifically, a hierarchical strategy utilizing the continuity and
extendibility of retinal blood vessels is integrated into the
image matting model for blood vessel segmentation. Normally
the matting models require the user specified trimap, which
separates the input image into three regions manually: the
foreground, background and unknown regions. However, since
creating a user specified trimap is a tedious and time-consuming
task, region features of blood vessels are used to generate the
trimap automatically in this paper. The proposed model has low
computational complexity and outperforms many other state-ofart supervised and unsupervised methods in terms of accuracy,
which achieves a vessel segmentation accuracy of 96.0%, 95.7%
and 95.1% in an average time of 10.72s, 15.74s and 50.71s
on images from three publicly available fundus image datasets
DRIVE, STARE, and CHASE DB1, respectively.
Index Terms—Image matting, hierarchical strategy, fundus,
trimap, region features, segmentation, vessel.

I. I NTRODUCTION

R

ETINAL blood vessels generally show a coarse to fine
centrifugal distribution and appear as a wire mesh-like
structure or tree-like structure. Their morphological features,
such as length, width and branching, play an important role in
diagnosis, screening, early detection and treatment of various
cardiovascular and ophthalmologic diseases such as stroke,
vein occlusions, diabetes and arteriosclerosis [1]. The analysis
of morphological features of retinal blood vessels can facilitate
a timely detection and treatment of a disease when it is still
in its early stage. Moreover, the analysis of retinal blood
vessels can assist in evaluation of retinal image registration
[2], the relationship between vessel tortuosity and hypertensive
This work was supported by the National Natural Foundation of Guangdong
Province, Integrated Platform of Evolutionary Intelligence and Robot, support
no.(2015KGJHZ015).
Zhun Fan, Jiewei Lu and Wenji Li are with the Guangdong Provincial
Key Laboratory of Digital Signal and Image Processing, College of Engineering, Shantou University, Shan’tou 515063, China (email: zfan, 12jwlu1,
liwj@stu.edu.cn).
Caimin Wei is with the Department of Mathematics, Shantou University,
Shan’tou 515063, China (email: cmwei@stu.edu.cn).
Han Huang is with the School of Software Engineering, South China University of Technology, Guang’zhou 510006, China (email: hhan@scut.edu.cn).
Xinye Cai is with the College of Computer Science and Technology,
Nanjing University of Aeronautics and Astronautics, Jiang’su 210016, China
(email:xinye@nuaa.edu.cn).
Xinjian Chen is with the Medical Image Processing and Analysis Lab,
School of Electronics and Information Engineering, Soochow University,
Su’zhou 215006, China (email: xjchen@suda.edu.cn).

retinopathy [3], retinopathy of prematurity [4], arteriolar narrowing [5], mosaic synthesis [6], biometric identification [7],
foveal avascular region detection [8] and computer-assisted
laser surgery [1]. Since cardiovascular and ophthalmologic
diseases have a serious impact on human’s life, the analysis
of retinal blood vessels becomes more and more important.
It is of great significance in many clinical applications to
reveal important information of systemic diseases and support
diagnosis and treatment. As a result, the requirement of vessel
analysis system grows rapidly in which the segmentation of
retinal blood vessels is the first and one of the most crucial
steps.
The segmentation of retinal blood vessels has been a heavily
researched area in recent years [9]. Broadly speaking, existing
algorithms can be divided into supervised and unsupervised
methods. In supervised methods, a number of different features
are extracted from fundus images, and applied to train the
effective classifiers with the purpose of extracting retinal blood
vessels. In [10], Staal et al. extracts 27 features for each image
pixel with ridge profiles, and performs feature selection by
using sequential forward selection method to pick those pixels
that result in better segmentation performance by a K-Nearest
Neighbor (KNN) classifier. Soares et al. [11] introduces a
feature-based Bayesian classifier with Gaussian mixtures for
vessel segmentation, which uses the intensity information and
Gabor wavelet transform responses to build a 7-D feature
vector for each pixel. In [12], Lupascu et al. utilizes an
AdaBoost classifier and a 41-D feature vector which includes
information on the local intensity structure, spatial properties,
and geometry at multiple scales. Marin et al. [13] constructs a
7-D vector composed of gray-level and moment invariantsbased features, and then trains a neural network (NN) for
pixel classification. Roychowdhury et al. [14] extracts the
major vessel from the fundus images and uses a Gaussian
Mixture Model classifier for vessel segmentation with a set of
8 features, which are extracted based on pixel neighborhood
and first and second-order gradient images. In [15], Liskowski
et al. employs a deep neural network to extract vessel pixels
from fundus images. In unsupervised methods, the researchers
try to find inherent properties of retinal blood vessels that can
be applied to extract vessel pixels from fundus images. The
unsupervised methods can be further divided into multiscale
approaches, matched filtering, vessel tracking, mathematical
morphology and model based methods [9]. The multiscale approach introduced by [16] develops a vessel enhancement filter
with the analysis of multiscale second order local structure
of an image (Hessian), and obtains a vesselness measure by

2

(a)

(b)

(c)

Fig. 1. The process of image matting. (a) An input image. (b) A trimap
generated by the user. The white, black and gray regions belong to the
foreground, background and unknown regions, respectively. (c) A result
achieved by [24].

using the eigenvalues of the Hessian. The matched filtering
method described by [17] employs different threshold probes
to extract blood vessels from matched filter response images.
In [18], the methodology based on vessel tracking applies a
wave propagation and traceback mechanism to label each pixel
the likelihood of belonging to vessels in angiography images.
The mathematical morphology with the extraction of vessel
centerlines [19] is also developed to find the morphological
characteristics of retinal blood vessels. Model based methods
generally use geometric deformable models [20], parametric
deformable models [21], vessel profile models [22] and active
contour models [23] for blood vessel segmentation.
Image matting refers to the problem of accurately extracting
a foreground object from an input image. Generally image
matting includes two main steps. The first step is generating a
user specified trimap. An example of a user specified trimap
is shown in Fig.1(b). The trimap is a hand-drawn segmented
image, which separates the input image into three regions:
foreground (shown in white), background (shown in black)
and unknown (shown in gray). The second step is applying
the image matting model to extract the pixels belonging to
the foreground object from the unknown regions, based on
the samples of foreground and background pixels marked by
the user. An exemplary result achieved by [24] is shown in
Fig.1(c). Image matting is very useful in many important applications, such as image (or video) segmentation, image editing,
video production, new view synthesis, and film making. To
the best of our knowledge, image matting has never been
employed before to extract blood vessels from fundus images.
The major reason is that for retinal blood vessel segmentation,
generating a user specified trimap is a tedious and timeconsuming task. In other words, it is not appropriate to create
a trimap manually for retinal blood vessel segmentation. In
addition, a normal image matting model needs to be designed
carefully to improve the performance of blood vessel segmentation. In order to overcome these problems, region features of
blood vessels are applied to generate the trimap automatically.
Then a hierarchical image matting model is proposed to extract
the pixels of blood vessel from the unknown regions. More
specifically, a hierarchical strategy utilizing the continuity
and extendibility of retinal blood vessels is integrated into
the image matting model for blood vessel segmentation. The
proposed model is evaluated on three public available datasets
DRIVE, STARE, and CHASE DB1, which have been widely
used by other researchers to develop their own methods. The
vessel segmentation performance demonstrates the efficiency

and effectiveness of the proposed hierarchical image matting
model.
The rest of this paper is structured as follows: Section II
provides some background knowledge of image matting, and
a brief introduction of vessel enhancement filters applied in
our work. Section III details the process of generating the
trimap of a fundus image automatically, and the proposed
hierarchical image matting model. Section IV introduces the
public available datasets and the commonly used evaluation
metrics. Section V presents the experimental results. In Section
VI, the discussion and conclusion are given.
II. R ELATED W ORK
In this section, we will first review some background
knowledge of image matting, and then briefly introduce vessel
enhancement filters used in our work.
A. Image Matting
As aforementioned, image matting aims to accurately extract the foreground given a trimap of an image. Specifically,
the input image I(z)(z = (x, y)) is modeled as a linear
combination of a foreground image F (z) and a background
image B(z):
I(z) = αz F (z) + (1 − αz )B(z)

(1)

where αz , called alpha matte, is the opacity of the foreground.
αz ranges from 0 to 1. If αz is constrained to be either 0 or 1,
then the matting problem becomes the segmentation problem,
where each pixel belongs to either foreground or background.
After obtaining the user specified trimap, to infer the alpha
matte in the unknown regions, Chuang et al. [25] uses sets
of Gaussian distribution to model the color distributions of
the foreground and background images, and estimates the
optimal alpha value with a maximum-likelihood criterion. In
[26], Levin et al. derives an effective cost function from the
assumption that the foreground and background colors are
locally smooth, and employs this function to find the optimal
alpha matte. Zheng et al. [24] proposes a local learning based
approach and a global learning based approach to perform
image matting. In [27], Kaiming et al. solves a large kernel
matting Laplacian, and achieves a fast matting algorithm. In
[28], Shahrian and Rajan analyze the texture and color features
of the image, and optimize an objective function containing the
color and texture components to choose the best foreground
and background pair for image matting. Shahrian et al. [29]
expands the sampling range of foreground and background
regions, and collects a representative set of samples to estimate
the alpha matte. In [30], Cho et al. presents an image matting
method to extract alpha mattes across sub-images of a light
field image.
B. Vessel Enhancement filters
Vessel enhancement filters plays an important role in retinal
blood vessel segmentation [9]. Here two effective filters [31],
[32] used in our work are introduced.

3

1) Morphologically Reconstructed Filter: Morphologically
reconstructed filter is an effective tool for blood vessel enhancement [31]. For each input fundus image I, the green
channel image Ig is extracted firstly since Ig has the best
vessel-background contrast [13]. Then the morphological tophat transformation is performed:
θ
Ith
= Igc − (Igc ◦ Seθ )

(2)

θ
where Igc is the complement image of Ig , Ith
represents the
top-hat transformed image, Se is a structuring element for
morphological opening ◦, and θ specifies the angle (in degrees)
of the structuring element. The structuring element is of 1pixel width and 21-pixels length, which approximately fits the
diameter of the biggest vessels in the fundus images [31].
Since the morphological top-hat transformation transformation
given in Equation (2) can only brighten blood vessels in one
θ
direction, the sum of top-hat transformation Ith
along each
direction is performed in order to enhance the whole vessel
image:
X
θ
Imr =
Ith
(3)
θ∈A

where Imr represents the enhanced vessel image using morphologically reconstructed filter, ”A” is the set of angles
of the structuring element and defined as {x|0 < x <
π & x mod (π/12) = 0}.
2) Isotropic Undecimated Wavelet Filter: The isotropic
undecimated wavelet filter has been used for blood vessel segmentation, and has a good performance on vessel enhancement
[32]. Applied to a signal c0 = Ig (Ig is the input green channel
image), scaling coefficients are computed by convolution with
a filter h↑j firstly:
cj+1 = cj ∗ h↑j

Reconstruction of the original signal from all wavelet coefficients and the final set of scaling coefficients is straightforward, and requires only addition. The final enhanced vessel
image is depicted as follows:
Iiuw = cn +

n
X

wj

(6)

j=1

where Iiuw represents the enhanced vessel image using
isotropic undecimated wavelet filter. In blood vessel segmentation, wavelet scales: 2 − 3 are selected according to [32].
III. M ETHODOLOGY
In this section, the process of generating the trimap of an
input fundus image automatically is introduced, followed by
detailing the proposed hierarchical image matting model.

(c)

TABLE I
T HE DEFAULT THRESHOLD VALUES OF REGION FEATURES :Extent, VRatio,
Solidity AND THEIR RECOMMENDED RANGES USED IN THIS WORK
Threshold values
Default values
Recommended Ranges

e1
0.35
[0.2, 0.4]

e2
0.25
[0.15, 0.3]

r
2.2
[2, 6]

s
0.53
[0.4, 0.6]

A. Trimap Generation
Region features of blood vessels have been used for blood
vessel segmentation and performed well on segmentation accuracy and computational efficiency [33]. In this paper, region
features of blood vessels are applied to generate the trimap
of the input fundus image automatically. The definitions of
regions features are given as follows:
•
•

•

(5)

(b)

Fig. 2. An example to illustrate the bounding box and convex hull. (a) The
exemplary image. (b) The image for the illustration of bounding box. The red
boxes are the bounding boxes. (c) The image for the illustration of convex
hull. The red polygons are the convex hulls.

(4)

where h0 = [1, 4, 6, 4, 1]/16 is derived form the cubic Bspline, h↑j is the upsampled filter obtained by inserting 2j − 1
zeros between each pair of adjacent coefficients of h0 . Wavelet
coefficients are the difference between two adjacent sets of
scaling coefficients, i.e.,
wj+1 = cj − cj+1

(a)

•
•

•

Area indicates the actual number of pixels in the region.
Bounding Box specifies the smallest rectangle containing
the region. An example for the illustration of bounding
box is shown in Fig.2(b).
Extent is the ratio of pixels in the region to pixels in the
total bounding box.
VRatio is the ratio of the length to the width of the
bounding box.
Convex Hull specifies the smallest convex polygon that
can contain the region. An example for the illustration of
convex hull is shown in Fig.2(c).
Solidity is the ratio of pixels in the region to pixels in
the total convex hull.

The default threshold values of region features:Extent, VRatio,
Solidity and their recommended ranges used in this work are
reported in Table I. e1 and e2 are two threshold values of
Extent features used in this work; r is the threshold value of
V Ratio feature; s is the threshold value of Solidity feature.
For Area feature, two threshold values: a1 = fi × 2 and
a2 = fi ×35 are used in this work. fi , called the internal factor,
is calculated as d × max(h,w)
min(h,w) , where d = 21 is approximately
the diameter of the biggest vessels in fundus images [31], h
and w are the height and width of the fundus image.
The proposed model is not sensitive to above mentioned
region features. In other words, these region features can be
selected in a relatively large range without sacrificing the performance. In Section V(D)-”Sensitivity analysis of threshold
values of region features”, empirical study is conducted to
verify the insensitivity of the proposed model to the threshold
values of region features.

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Fig. 3. The process of trimap generation. B represents the background regions;
U represents the unknown regions; V2 represents the denoised preliminary
vessel regions; S represents the skeleton of blood vessels; V represents the
vessel regions.

Fig. 5. Vessel skeleton extraction. (a) The green channel of the fundus image
Ig . (b) The vessel enhanced image Iiuw . (c) The binary image T . (d) The
background regions T1 . (e) The candidate regions T2 . (f) The vessel regions
T3 . (g) T4 : The preserved regions in T2 . (h) The combined regions of T3
and T4 . (i) The vessel skeletons S.

(a)

(b)

(c)

(d)

(e)

(f)

Fig. 4. Image segmentation. (a) The fundus image I. (b) The green channel of
the fundus image Ig . (c) The enhanced vessel image Imr . (d) The background
regions B. (e) The unknown regions U . (f) The denoised preliminary vessel
regions V2

Creating the trimap of the input fundus image includes two
main steps: 1) Image Segmentation and 2) Vessel Skeleton
Extraction. The process of trimap generation is given in Fig.3.
1) Image Segmentation: The goal of image segmentation
is to divide the input image into three regions: the vessel
(foreground), background and unknown regions. Firstly the
enhanced vessel image Imr is segmented into three regions:
the background regions (B), unknown regions (U ) and preliminary vessel regions (V1 )

Imr


 B
U
=

V1

if 0 < Imr < p1
if p1 6 Imr < p2
if p2 6 Imr

(7)

where p1 = 0.2 and p2 = 0.35 restrict the unknown region as
thin as possible in order to achieve the better matting result
[28], [34]. In order to remove the noise regions in V1 , the
regions with Area > a1 in V1 are extracted firstly (V1∗ ). Then
regions in V1∗ whose Extent ≤ e1 && V Ratio ≤ r &&
Solidity ≥ s are abandoned, resulting in the denoised preliminary vessel regions V2 . An example of image segmentation
is shown in Fig.4.
2) Vessel Skeleton Extraction: Vessel Skeleton Extraction
aims to further distinguish the unknown regions and provide
more information on blood vessels. In Section V(B)-”Vessel
Segmentation Performance”, the effectiveness of vessel skeleton extraction will be presented. Firstly, a binary image T is
obtained by global thresholding the enhanced vessel image
Iiuw .

1 Iiuw > t
T =
(8)
0 Iiuw 6 t
where t = Otsu(Iiuw ) − ε, ε is set as 0.03. Then T is
divided into three regions according to the Area feature:

 T1 if 0 < Area < a1
T2 if a1 ≤ Area ≤ a2
T =
(9)

T3 if a2 < Area
In vessel skeleton extraction, the regions in T3 are preserved
while the regions in T1 are abandoned. Then the regions in
T2 with Extent > e2 && V Ratio ≤ r are preserved as T4 .
Finally skeleton extraction [35] is performed on the combined
regions of T3 and T4 in order to obtain the skeleton of blood

5

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ࢊ૟ ൌ ૚૙

(a)

(b)

(c)

Fig. 6. An example to illustrate the process of initialization. (a) An exemplary image (green pixels represent vessel pixels, red pixels represent unknown
pixels). (b) Calculating the closest distance for each unknown pixel (di means the closest distance for the ith unknown pixel). (c) Stratifying unknown pixels
into different hierarchies.

(a)

(b)

(c)

Fig. 7. (a) An input image. (b) A trimap generated by the proposed method.
The white, black and red regions belong to the foreground, background
and unknown regions, respectively. (c) The result achieved by the proposed
hierarchical image matting model.

vessels S. An example of vessel skeleton extraction is shown
in Fig.5.
After performing image segmentation and vessel skeleton
extraction, the trimap of the input fundus image is generated
(as shown in Fig.7(b)), which is composed of the background
regions (B), unknown regions (U ) and vessel (or foreground)
regions (V = V2 ∪ S).
B. Hierarchical Image Matting Model
Hierarchical image matting model is proposed to label the
pixels in the unknown regions as vessels or background in
an incremental way. Specifically, after stratifying the pixels in
unknown regions (called unknown pixels) into m hierarchies
by a hierarchical strategy, let uji indicates the ith unknown
pixel in the jth hierarchy, the segmented vessel image Iv (uji )
is modeled as follows:

1 if corre(uji , V ) > corre(uji , B)
Iv (z) =
(10)
0 else
where corre indicates the correlation function (depicted in
Equation (13)). The implementation of the hierarchical image
matting model consists of two main steps:
Step 1 Stratifying the unknown pixels: Stratify pixels in the
unknown regions into different hierarchies.
Step 2 Hierarchical update: Assign new labels (V or B) to
pixels in each hierarchy.
The pseudocode of implementing this model is given in
Algorithm 1.

Algorithm 1: Implementing the hierarchical image matting
model
Input: Trimap composed of B, U , V
Output: The segmented vessel image Iv
Step 1: Stratifying the unknown pixels:
a) For i = 1, . . . , nU , set D(i) = di , where nU is the
number of unknown pixels in U , di is the distance
between the ith unknown pixel and the closest vessel
pixel in V , D is the set of di .
b) Sort the unknown pixels in U in an ascending order
according to the distances D , cluster the pixels
with the same distance into one hierarchy, stratify
the pixels into m hierarchies and denote them as
an hierarchical order set: H = {H1 , H2 , . . . , Hm },
Hj = {uji |i ∈ 1, 2, . . . , ni }, where ni is the number
of unknown pixels in the jth hierarchy Hj .
Step 2: Hierarchical Update
For j = 1, . . . , m, do
For i = 1, . . . , ni , do
a) Compute the correlations (Defined in Equation (13))
between uji and its neighboring labelled pixels(vessel
pixels and background pixels) included in a 9×9 grid.
b) Choose the labelled pixel with the closest correlation,
and assign its label (V or B) to uji .
end for
end for

Stratifying the unknown pixels: In this stage, the unknown
pixels are stratified into different hierarchies. For the ith
unknown pixel in U , its distances with all vessel pixels in
V are calculated first. Then the closest distance di is chosen
and assigned to the ith unknown pixel. After that, the unknown
pixels are stratified into different hierarchies according to the
closest distances. The first hierarchy has the lowest value of
the closet distance while the last hierarchy has the highest
value of the closet distance. The unknown pixels reside in
low hierarchy suggests that they are close to blood vessels;
The unknown pixels stay in high hierarchy indicates that they
are far away from blood vessels. An example to illustrate the
process of stratifying the unknown pixels is shown in Fig.6.
Correlation Function: In step 2 of Algorithm 1, given an
unknown pixel uji and its neighboring labelled pixel klj , a color
cost function βc is defined to describe the fitness of uji and

6

濪澥

updated, they are used for the update of the next hierarchy.
The unknown pixels are updated from the first hierarchy to the
last hierarchy. An example to illustrate the process of updating
unknown pixels in one hierarchy is shown in Fig.8.

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C. Postprocessing
濪澧

Since some non-vessel regions may still exist in the final
segmented vessel image Iv , the regions whose Area < a2 &&
Extensibility > e2 && V Ratio < r in Iv are abandoned to
remove these non-vessel regions.

(b)
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IV. DATASETS AND E VALUATION M ETRICS

濖澨

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In this section, three publicly available datasets are introduced. These datasets have been widely used by researchers
to test their own vessel segmentation algorithms. Then some
commonly used evaluation metrics are presented, which are
also utilized in our experiment and to compare the proposed
method with other state-of-art methods.

濖澧
濖澦

濖澦

濪澧

(c)

濪澧

(d)

Fig. 8. An example for the illustration of assigning a label (V or B) to
an unknown pixel. (a) An exemplary image (green triangles represent vessel
pixels, blue pluses represent background pixels, red points represent unknown
pixels). vi indicates the ith vessel pixel, bi indicates the ith background pixel.
(b) Calculating the correlation functions between a unknown pixel and its
neighboring labelled pixels (vessel pixels and background pixels) (βi means
the correlation between the unknown pixel and the ith labelled pixel). (c)
Assigning a label (V or B) to the unknown pixel. (d) The resultant image.

klj first:

βc (uji , klj ) = ||cuj − ckj ||
i

(11)

l

where cuj and ckj are intensity level of uji and klj in Imr . A
i
l
spatial cost function βs is further defined:
βs (uji , klj ) =

||xuj − xkj || − xmin
i

l

xmax − xmin

(12)

where xuj and xkj are the spatial coordinates of uji and
i

l

klj . The terms xmax = maxj ||xuj − xkj || and xmin =
i
l
minj ||xuj − xkj || are the maximum and minimum distance
i

l

of the unknown pixel uji to the labelled pixel klj . The normalization factors xmin and xmax ensure that βs is independent
from the absolute distance.
Our final correlation function β is a combination of the
color fitness and the spatial distance:
β(uji , klj ) = βc (uji , klj ) + ωβs (uji , klj )

(13)

where ω is a weight to trade off the color fitness and spatial
distance. ω is set as 0.5 in our experiment. Intuitively, a small
β indicates that the labelled pixel has a close correlation with
the unknown pixel.
Hierarchical Update: After performing initialization with
the hierarchical strategy, in each hierarchy, the correlations
between each unknown pixel and its neighboring labelled
pixels (vessel pixels and background pixels) included in a
9 × 9 grid are computed. Then the labelled pixel with the
closest correlation is chosen, and its label is assigned to the
unknown pixel. After all unknown pixels in one hierarchy are

A. Datasets
The proposed model is evaluated on three standard datasets:
DRIVE [10], STARE [17] and CHASE DB1 [31].
DRIVE1 consists of 40 fundus images obtained from a
screening program in the Netherlands. These images are
captured by a Canon CR5 non-mydriatic 3-CCD camera at
45◦ field of view (FOV), and the size of each image is of
584 × 565 pixels. The DRIVE dataset is divided into two
sets: a training set (DRIVE Training) and a test set (DRIVE
Test) each containing 20 fundus images. The training set is
annotated by two observers; The test set is annotated by two
independent human observers.
STARE2 consists of 20 fundus images. These images are
captured by a TopCon TRV-50 fundus camera at 35◦ FOV,
and the size of each image is of 605 × 700 pixels. Ten images
contain pathology while the other ten images are normal. The
STARE dataset is annotated by two independent observers.
CHASE DB13 consists of 28 fundus images acquired from
multiethnic school children. These images are captured by
a hand-held Nidek NM-200-D fundus camera at 30◦ FOV,
and the size of each image is of 960 × 999 pixels. The
CHASE DB1 is annotated by two independent observers.
For the DRIVE, STARE and CHASE DB1 datasets, the
manual segmentations of the first observer are used in this
work, which is a common choice for these datasets [9], [15],
[23], [36].
B. Evaluation Metrics
In the process of retinal vessel segmentation, each pixel
is classified as vessels or background, thereby resulting in
four events: two correct (true) classifications and two incorrect
(false) classifications, which are defined in Table III.
1 http://www.isi.uu.nl/Research/Databases/DRIVE/
2 http://www.ces.clemson.edu/

ahoover/stare/

3 https://blogs.kingston.ac.uk/retinal/chasedb1/

7

TABLE II
PERFORMANCE OF DIFFERENT SEGMENTATION MODELS ON THE DRIVE AND STARE DATASETS
Test Datasets

DRIVE

Methods

STARE

Acc

AUC

Se

Sp

Time

Acc

AUC

Se

Sp

Time

System

Supervised Methods
Staal et.al [10]
Soares et.al [11]
Lupascu et.al [12]
Marin et.al [13]
Roychowdhury et.al [14]
Liskowski et.al [15]

0.944
0.946
0.959
0.945
0.952
0.954

0.843
0.844
0.881

0.720
0.706
0.725
0.781

0.980
0.962
0.981

15min
∼3min
∼90s
3.11s
-

0.952
0.948
0.952
0.951
0.973

0.838
0.873
0.921

0.694
0.772
0.855

0.982
0.973
0.986

15min
∼3min
∼90s
6.7s
-

1.0 GHz, 1-GB RAM
2.17 GHz, 1-GB RAM
2.13 GHz, 2-GB RAM
2.6 GHz, 2-GB RAM
NVIDIA GTX Tian GPU

Unsupervised Methods
Hoover et.al [17]
Mendonca et.al [19]
Lam et.al [37]
Al-Diri et.al [21]
Lam and Yan et.al [22]
Perez et.al [38]
Miri et.al [39]
Budai et.al [40]
Nguyen et.al [41]
Yitian et.al [23]
Annunziata et.al [36]
Orlando et.al [42]
Proposed

0.945
0.947
0.925
0.943
0.957
0.941
0.954
0.960

0.855
0.806
0.846
0.816
0.862
0.879
0.858

0.734
0.728
0.644
0.715
0.644
0.742
0.790
0.736

0.976
0.955
0.967
0.976
0.987
0.982
0.968
0.981

2.5min
11min
13min
∼2min
∼50s
2.5s
10.72s

0.928
0.944
0.947
0.957
0.926
0.938
0.932
0.956
0.956
0.957

0.730
0.836
0.857
0.781
0.874
0.849
0.871
0.880

0.650
0.699
0.752
0.769
0.580
0.780
0.713
0.768
0.791

0.810
0.973
0.968
0.944
0.982
0.978
0.984
0.974
0.970

5min
3min
8min
13min
∼2min
2.5s
<25s
15.74s

Sun SPARCstation 20
3.2 GHz, 980-MB RAM
1.83 GHz, 2-GB RAM
1.2 GHz
1.83 GHz, 2-GB RAM
Parallel Cluster
3 GHz, 1-GB RAM
2.3 GHz, 4-GB RAM
2.4 GHz, 2-GB RAM
3.1 GHz, 8-GB RAM
1.9 GHz, 6-GB RAM
2.9 GHz, 64-GB RAM
2.5 GHz, 4-GB RAM

TABLE III
FOUR EVENTS OF VESSEL CLASSIFICATION
vessel detected
vessel not detected

Vessel present
True Positive (TP)
False Negative (FN)

vessel absent
False Positive (FP)
True Negative(TN)

only one operating point is used. The segmentation time
required per image in seconds for implementing the proposed
segmentation algorithm in MATLAB on a Laptop with Intel
Core i7 processor, 2.5GHz and 8GB RAM is also recorded.
V. E XPERIMENTS AND R ESULTS

In order to evaluate the performance of the vessel segmentation algorithms, three commonly used metrics are applied.
TP
TP + FN
TN
Specif icity =
TN + FP
TP + TN
Accuracy =
TP + TN + FP + FN
Sensitivity (Se) reflects the algorithm’s ability of detecting
vessel pixels while Specificity (Sp) is a measure of the
algorithm’s effectiveness in identifying background pixels. Accuracy (Acc) is a global measure of classification performance
combing both Se and Sp. The performance of the vessel
segmentation method is also measured by the area under a
receiver operating characteristic (ROC) curve (AU C). The
conventional AU C is calculated from a number of operating
points, and normally used to evaluate the balanced data
classification problem. However, in practice the researchers
need to select an operating point to compare their method
with other methods. Also blood vessel segmentation is an
unbalanced data classification problem, in which there are
much fewer vessel pixels than the background pixels. In order
to evaluate the performance of blood vessel segmentation
properly, AU C = (Se+Sp)/2 [23], [43] is applied to indicate
the overall performance of blood vessel segmentation, which
is suitable to describe the overall performance of imbalanced
data classification problem and specifically for the case when
Sensitivity =

In this section, four sets of experiments are performed with
the purpose of evaluating the proposed hierarchical image
matting model. In the first experiment, the segmentation performance of the proposed model was compared with other
state-of-art methods. In the second experiment, the vessel
segmentation performance of the proposed model was analyzed. In the third experiment, the proposed hierarchical image
matting model was compared with image matting models. In
the last experiment, the sensitivity analysis of threshold values
of region features used in the work was given.
A. Comparison with other methods
In this section, the proposed model is compared with other
state-of-art methods on two most popular public datasets:
DRIVE and STARE. The CHASE DB1 dataset is not used
here since it is relatively new and has relatively few results
in the literature. The segmentation performance and computational complexity of the proposed model in comparison with
other state-of-art methods on the DRIVE and STARE datasets
are given in Table II. It can be observed that for the DRIVE
dataset, the accuracy of the proposed model is the highest
among all existing methods with Acc = 0.960, Se = 0.736
and Sp = 0.981. On the STARE dataset, the accuracy and
AU C of the proposed model are the highest among unsupervised methods with Acc = 0.957, AU C = 0.880. Although
one supervised method [15] has the best performance on
STARE dataset, the method is computationally more complex

8

TABLE IV
THE SEGMENTATION PERFORMANCE OF THE PROPOSED MODEL ON THREE TEST DATASETS
Dataset

Method

Acc

AUC

Se

Sp

Time(s)

DRIVE

Trimap (Treating the unknown regions as background regions)
Model without vessel skeleton extraction
Proposed

0.959
0.960
0.960

0.833
0.837
0.859

0.679
0.688
0.736

0.986
0.986
0.981

5.841
11.959
10.720

STARE

Trimap (Treating the unknown regions as background regions)
Model without vessel skeleton extraction
Proposed

0.958
0.959
0.957

0.853
0.862
0.881

0.728
0.748
0.791

0.977
0.976
0.970

7.741
16.563
15.740

CHASE DB1

Trimap (Treating the unknown regions as background regions)
Model without vessel skeleton extraction
Proposed

0.948
0.954
0.951

0.771
0.789
0.815

0.565
0.597
0.657

0.977
0.981
0.973

21.088
60.847
50.710

(a)

(b)

(c)

(d)

Fig. 9. Ground truth (left) and segmentation result (right): (a) and (b) are the images from DRIVE dataset, (c) and (d) are the images from the STARE dataset

due to the use of deep neural networks, which may need
retraining for new datasets. In addition, the proposed model
has a low computational complexity compared with other
segmentation methods.

Sensitivity and 2% increase of AU C compared with the
model without vessel skeleton extraction while Acc of the
model with vessel skeleton extraction is similar to the model
without vessel skeleton extraction, which demonstrates the
effectiveness of vessel skeleton extraction.

B. Vessel Segmentation Performance
The segmentation performance of the proposed model on
three public available datasets is given in Table IV. It can
be observed that the proposed model can achieve more
than 95% segmentation accuracy on the DRIVE, STARE
and CHASE DB1 datasets, with the highest accuracy score
Acc = 96.0% achieved in the DRIVE dataset. Some exemplary segmentation results are shown in Fig.9. When treating
the unknown regions as background regions, AUC=0.833 of
trimap is 2.6% lower than the proposed model while Acc
of trimap is similar to the proposed model. In addition,
Se = 0.679 of trimap is 5.7% lower than the proposed model.
These observations show that trimap can already have good
segmentation performance, which indicates that the selection
of region features is very effective in segmenting blood vessels.
From Table IV, it can be observed that the model with vessel
skeleton extraction can achieve more than 5% increase of

C. Comparison with image matting models
The effectiveness of the proposed model in blood vessel segmentation has been validated through previous experiments.
In order to further verify the effectiveness of our model, the
proposed model is compared with four other image matting
models: Anat Model [26], Zheng Model [24], Shahrian Model
[28] and Improving Model [29]. The segmemtation results
of these models on the DRIVE, STARE, and CHASE DB1
datasets are given in Table V. It can be observed that the
proposed model outperforms other image matting models
in terms of Acc in the DRIVE, STARE and CHASE DB1
datasets. Also the proposed model achieves the highest scores
of Sp in three datasets.

9

TABLE V
SEGMENTATION PERFORMANCE OF FOUR DIFFERENT IMAGE
MATTING MODELS AND THE PROPOSED MODEL
Dataset

Model

Acc

AUC

Se

Sp

Time(s)

DRIVE

Anat Model
Zheng Model
Shahrian Model
Improving Model
Proposed

0.958
0.958
0.921
0.958
0.960

0.862
0.862
0.903
0.862
0.859

0.746
0.746
0.881
0.746
0.736

0.978
0.978
0.925
0.978
0.981

10.036
11.837
120.552
360.000
10.720

STARE

Anat Model
Zheng Model
Shahrian Model
Improving Model
Proposed

0.944
0.954
0.912
0.954
0.957

0.839
0.883
0.906
0.883
0.881

0.714
0.799
0.899
0.799
0.791

0.964
0.966
0.913
0.966
0.970

11.376
14.185
145.860
381.923
15.740

CHASE DB1

Anat Model
Zheng Model
Shahrian Model
Improving Model
Proposed

0.944
0.944
0.918
0.944
0.951

0.820
0.820
0.858
0.820
0.815

0.675
0.675
0.790
0.675
0.657

0.964
0.964
0.927
0.965
0.973

29.047
40.587
340.899
797.960
50.710

0.96

Acc

Acc

0.96
DRIVE
STARE
CHASE_DB1

0.955

0.95
0.1 0.2 0.3 0.4 0.5 0.6

0.94
0.92
0.9
0

0.4

0.6

0.8

1

R EFERENCES

(b)

0.962

0.94

Acc

0.96

Acc

0.2

e2

e1
(a)

0.92
0

DRIVE
STARE
CHASE_DB1

DRIVE
STARE
CHASE_DB1

2

4

6

8

10

0.956

DRIVE
STARE
CHASE_DB1

0.95
0.4

0.6

r
(c)

VI. C ONCLUSION
Image matting refers to the problem of accurately extracting
a foreground object from an input image, which is very useful
in many important applications. However, to the best of our
knowledge, image matting has never been employed before to
extract blood vessels from fundus image. The major reason
is that for retinal blood vessel segmentation, generating a
user specified trimap is a tedious and time-consuming task. In
addition, a normal image matting model needs to be designed
carefully to improve the performance of blood vessel segmentation. In order to overcome these problems, region features of
blood vessels are applied to generate the trimap automatically.
Then a hierarchical image matting model is proposed to extract
the pixels of blood vessel from the unknown regions. More
specifically, a hierarchical strategy utilizing the continuity and
extendibility of retinal blood vessels is integrated into the
image matting model for blood vessel segmentation.
The proposed model is very efficient and effective in
blood vessel segmentation, which achieves a segmentation
accuracy of 96.0%, 95.7% and 95.1% on three public available
datasets with an average time of 10.72s, 15.74s and 50.71s,
respectively. The experimental results show that it is a very
competitive model compared with many other segmentation
approaches, and has a low computational time.

0.8

s
(d)

Fig. 10. Sensitivity analysis of threshold values of region features used in
the work. (a) Variations in mean segmentation accuracy by varying e1 when
r = 2.2, s = 0.53, e2 = 0.25. (b) Variations in mean segmentation accuracy
by varying e2 when r = 2.2, e1 = 0.35, s = 0.53. (c) Variations in mean
segmentation accuracy by varying r when e1 = 0.35, s = 0.53, e2 = 0.25.
(d) Variations in mean segmentation accuracy by varying s when r = 2.2,
e1 = 0.35, e2 = 0.25.

D. Sensitivity analysis of threshold values of region features
The default threshold values of region features: e1 = 0.35,
r = 2.2, s = 0.53, e2 = 0.25 are used in our work. In
order to demonstrate the insensitivity of the proposed model
to these threshold values, the variations in Acc by varying
e1 , e2 , r and s are given in Fig.10.(a), (b), (c) and (d).
From Fig.10, it can be observed that the proposed model can
maintain high segmentation accuracy on the DRIVE, STARE
and CHASE DB1 datasets as e1 varies in [0.2, 0.4] or e2 varies
in [0.15, 0.3]; For r and s, the proposed model can maintain
high segmentation accuracy as r varies in [2, 6] or s varies in
[0.4, 0.6]. From the above observation, it can be seen that the
proposed model is not sensitive to these threshold values of
region features when they change in a relatively large range.

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