Automated Blood Vessel Segmentation of Fundus Images Based on Region Features and Hierarchical Growth Algorithm

3.2 MB·

by  Zhun Fan

1
Unsupervised Blood Vessel Segmentation of
Fundus Images Based on Region Features and
Hierarchical Growth Algorithm
Zhun Fan, Senior Member, IEEE, Jiewei Lu, Wenji Li
Abstract—Automated blood vessel segmentation plays an im- and is of great significance in many clinical applications to
7 portant role in the diagnosis and treatment of various cardio- reveal important information of systemic diseases and support
1 vascular and ophthalmologic diseases. In this paper, a novel
diagnosisandtreatment.Asaresult,therequirementofvessel
0 unsupervisedsegmentationalgorithmisproposedtoextractblood
2 vessels from fundus images. At first, an enhanced vessel image analysis system grows rapidly in which the segmentation of
r is generated by morphological reconstruction, and then divided retinal blood vessels is the first and one of the most crucial
a into three parts: preliminary vessel regions, background regions steps.
M and undetermined regions. Secondly, a list of region features of Thesegmentationofretinalbloodvesselshasbeenaheavily
blood vessels are defined and used to remove the noise regions
researchedareainrecentyears[9].Broadlyspeaking,existing
6 in preliminary vessel regions and extract the skeletons of blood
algorithms can be divided into supervised and unsupervised
2 vessels.Anintermediatevesselimageisobtainedbycombingthe
denoised preliminary vessel regions with vessel skeletons. After methods.Insupervisedmethods,anumberofdifferentfeatures

] that, a novel hierarchical growth algorithm, namely HGA, is are extracted from fundus images, and applied to train the
V proposed to label each pixel in undetermined regions as vessel effectiveclassifierswiththepurposeofextractingretinalblood
C ornon-vesselinanincrementalway,whichtakestheadvantageof vessels.In[10],Staaletal.extracts27featuresforeachimage
colorandspatialinformationfromtheintermediatevesselimage
. pixel with ridge profiles, and performs feature selection by
s andthebackgroundregions.Finally,postprocessingisperformed
c toremovethenon-vesselregions.Theproposedalgorithmhaslow usingsequentialforwardselectionmethodtopickthosepixels
[ computational complexity and outperforms many other state-of- that result in better segmentation performance by a K-Nearest

2 art supervised and unsupervised methods in terms of accuracy. Neighbor (KNN) classifier. Soares et al. [11] introduces a
It achieves a vessel segmentation accuracy of 96.0%, 95.7% and
v feature-based Bayesian classifier with Gaussian mixtures for
95.1%inanaveragetimeof10.72s,15.74sand50.71sonimages
2 vessel segmentation, which uses the intensity information and
from three publicly available fundus image datasets DRIVE,
9
STARE, and CHASE DB1, respectively. Gabor wavelet transform responses to build a 7-D feature
8
vector for each pixel. In [12], Lupascu et al. utilizes an
0 Index Terms—Vessel segmentation, fundus images, region fea-
0 tures, vessel skeletons, hierarchical growth algorithm. AdaBoost classifier and a 41-D feature vector which includes
. information on the local intensity structure, spatial properties,
1
andgeometryatmultiplescales.Marinetal.[13]constructsa
0
7 I. INTRODUCTION 7-D vector composed of gray-level and moment invariants-
1 RETINAL blood vessels generally show a coarse to fine based features, and then trains a neural network (NN) for
: centrifugal distribution and appear as a wire mesh-like pixel classification. Roychowdhury et al. [14] extracts the
v
i structure or tree-like structure. Their morphological features, major vessel from the fundus images and uses a Gaussian
X
suchaslength,widthandbranching,playanimportantrolein Mixture Model classifier for vessel segmentation with a set of
r diagnosis, screening, early detection and treatment of various 8 features, which are extracted based on pixel neighborhood
a
cardiovascular and ophthalmologic diseases such as stroke, andfirstandsecond-ordergradientimages.In[15],Liskowski
veinocclusions,diabetesandarteriosclerosis[1].Theanalysis employs a deep neural network to extract vessel pixels from
ofmorphologicalfeaturesofretinalbloodvesselscanfacilitate fundus images. In unsupervised methods, the researchers try
a timely detection and treatment of a disease when it is still to find inherent properties of retinal blood vessels that can
in its early stage. Moreover, the analysis of retinal blood be applied to extract vessel pixels from fundus images. The
vessels can assist in evaluation of retinal image registration unsupervised methods can be further divided into multiscale
[2],therelationshipbetweenvesseltortuosityandhypertensive approaches, matched filtering, vessel tracking, mathematical
retinopathy [3], retinopathy of prematurity [4], arteriolar nar- morphologyandmodelbasedmethods[9].Themultiscaleap-
rowing [5], mosaic synthesis [6], biometric identification [7], proachintroducedby[16]developsavesselenhancementfilter
foveal avascular region detection [8] and computer-assisted with the analysis of multiscale second order local structure
laser surgery [1]. Since cardiovascular and ophthalmologic of an image (Hessian), and obtains a vesselness measure by
diseases have a serious impact on human’s life, the analysis using the eigenvalues of the Hessian. The matched filtering
of retinal blood vessels becomes more and more important, method described by [17] employs different threshold probes
to extract blood vessels from matched filter response images.
Zhun Fan, Jiewei Lu and Wenji Li are with the Department of Electrical
In [18], the methodology based on vessel tracking applies a
Information Engineering, Shantou University, Shantou, GuangDong (email:
fzfan,12jwlu1,[email protected]) wavepropagationandtracebackmechanismtolabeleachpixel
2
(cid:57)(cid:90)(cid:71)(cid:77)(cid:75)(cid:3)(cid:23)(cid:32)(cid:3)(cid:58)(cid:78)(cid:75)(cid:3) (cid:57)(cid:90)(cid:71)(cid:77)(cid:75)(cid:3)(cid:24)(cid:32)(cid:3)
(cid:47)(cid:84)(cid:86)(cid:91)(cid:90)(cid:32) (cid:53)(cid:91)(cid:90)(cid:86)(cid:91)(cid:90)(cid:32)
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(cid:39)(cid:44)(cid:91)(cid:84)(cid:74)(cid:91)(cid:89)(cid:3) (cid:58)(cid:78)(cid:75)(cid:3)(cid:57)(cid:75)(cid:77)(cid:83)(cid:75)(cid:84)(cid:90)(cid:75)(cid:74)(cid:3)
(cid:47)(cid:84)(cid:90)(cid:75)(cid:88)(cid:83)(cid:75)(cid:74)(cid:79)(cid:71)(cid:90)(cid:75)(cid:3)(cid:3)(cid:56)(cid:75)(cid:77)(cid:79)(cid:85)(cid:84)(cid:3) (cid:45)(cid:88)(cid:85)(cid:93)(cid:90)(cid:78)(cid:3) (cid:54)(cid:85)(cid:89)(cid:90)(cid:86)(cid:88)(cid:85)(cid:73)(cid:75)(cid:89)(cid:89)(cid:79)(cid:84)(cid:77)
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(cid:57)(cid:75)(cid:77)(cid:83)(cid:75)(cid:84)(cid:90)(cid:71)(cid:90)(cid:79)(cid:85)(cid:84) (cid:39)(cid:82)(cid:77)(cid:85)(cid:88)(cid:79)(cid:90)(cid:78)(cid:83)
Fig. 1: The process of the proposed algorithm
TABLE I: DEFINITIONS OF IMAGE NOTATIONS
the likelihood of belonging to vessels in angiography images.
The mathematical morphology with the extraction of vessel
Notations Meanings
centerlines [19] is also developed to find the morphological
characteristics of retinal blood vessels. Model based methods Ie1 Thefirstenhancedvesselimage
B Backgroundregions
generally use geometric deformable models [20], parametric U Undeterminedregion
deformable models [21], vessel profile models [22] and active V1 Preliminaryvesselregions
contour models [23] for blood vessel segmentation. V2 Denoisedpreliminaryvesselregions
Ie2 Thesecondenhancedvesselimage
Most unsupervised methods do not make full use of the S Vesselskeletons
determined information (determined vessel information and V3 Anintermediatevesselimage
V Theestimatedvesselimage
backgroundinformation)toestimatetheundeterminedregions.
In order to take full advantage of the determined information,
a novel unsupervised algorithm is proposed for blood vessel
segmentation. The proposed algorithm divides the image into (cid:47)(cid:84)(cid:86)(cid:91)(cid:90)(cid:32)(cid:3)(cid:39)(cid:3)(cid:44)(cid:91)(cid:84)(cid:74)(cid:91)(cid:89)(cid:3)
(cid:47)(cid:83)(cid:71)(cid:77)(cid:75)(cid:89)
determined regions (vessel regions and background regions)
and undetermined regions, and extracts vessel pixels in the
undetermined regions by using HGA. Moreover, the proposed (cid:57)(cid:90)(cid:75)(cid:86)(cid:3)(cid:23) (cid:57)(cid:90)(cid:75)(cid:86)(cid:3)(cid:25) (cid:58)(cid:78)(cid:75)(cid:3)(cid:47)(cid:89)(cid:85)(cid:90)(cid:88)(cid:85)(cid:86)(cid:79)(cid:73)(cid:3)(cid:59)(cid:84)(cid:74)(cid:75)(cid:73)(cid:79)(cid:83)(cid:71)(cid:90)(cid:75)(cid:74)
algorithm extracts the vessel regions and background regions (cid:61)(cid:71)(cid:92)(cid:75)(cid:82)(cid:75)(cid:90)(cid:3)(cid:58)(cid:88)(cid:71)(cid:84)(cid:89)(cid:76)(cid:85)(cid:88)(cid:83)
(cid:51)(cid:85)(cid:88)(cid:86)(cid:78)(cid:85)(cid:82)(cid:85)(cid:77)(cid:79)(cid:73)(cid:71)(cid:82)(cid:3)
first,whichleadstoasignificantreductionontheloadofpixel (cid:56)(cid:75)(cid:73)(cid:85)(cid:84)(cid:89)(cid:90)(cid:88)(cid:91)(cid:73)(cid:90)(cid:79)(cid:85)(cid:84)
classification of the fundus image. The proposed method is
evaluated on three public available datasets DRIVE, STARE, (cid:60)(cid:75)(cid:89)(cid:89)(cid:75)(cid:82)(cid:3)(cid:57)(cid:81)(cid:75)(cid:82)(cid:75)(cid:90)(cid:85)(cid:84)(cid:3)(cid:43)(cid:1835)(cid:94)(cid:3032)(cid:90)(cid:2870)(cid:88)(cid:71)(cid:73)(cid:90)(cid:79)(cid:85)(cid:84)
and CHASE DB1, which have been widely used by other
(cid:57)(cid:90)(cid:75)(cid:86)(cid:3)(cid:24)
researchers to develop their own algorithms. The vessel seg-
(cid:1835)(cid:3032)(cid:2869)
mentation performance demonstrates the effectiveness of the
(cid:47)(cid:83)(cid:71)(cid:77)(cid:75)(cid:3)(cid:42)(cid:79)(cid:92)(cid:79)(cid:89)(cid:79)(cid:85)(cid:84) (cid:52)(cid:85)(cid:79)(cid:89)(cid:75)(cid:3)(cid:56)(cid:75)(cid:77)(cid:79)(cid:85)(cid:84)(cid:3) (cid:41)(cid:85)(cid:83)(cid:72)(cid:79)(cid:84)(cid:71)(cid:1845)(cid:90)(cid:79)(cid:85)(cid:84) (cid:57)(cid:90)(cid:75)(cid:86)(cid:3)(cid:26)
proposed vessel segmentation algorithm. (cid:56)(cid:75)(cid:83)(cid:85)(cid:92)(cid:71)(cid:82)
(cid:1848)(cid:2869) (cid:1848)(cid:2870)
The rest of this paper is structured as follows: Section II
details the proposed methodology. Section III introduces the
public available datasets and the commonly used evaluation
metrics. Section IV presents the experimental results. In Sec- (cid:53)(cid:91)(cid:90)(cid:86)(cid:91)(cid:90)(cid:32)(cid:3) (cid:53)(cid:91)(cid:90)(cid:86)(cid:91)(cid:90)(cid:32)(cid:3) (cid:53)(cid:91)(cid:90)(cid:86)(cid:91)(cid:90)(cid:32)(cid:3)(cid:39)(cid:84)(cid:3)(cid:47)(cid:84)(cid:90)(cid:75)(cid:88)(cid:83)(cid:75)(cid:74)(cid:79)(cid:71)(cid:90)(cid:75)(cid:3)
(cid:40)(cid:71)(cid:73)(cid:81)(cid:77)(cid:88)(cid:85)(cid:91)(cid:84)(cid:74)(cid:3) (cid:59)(cid:84)(cid:74)(cid:75)(cid:90)(cid:75)(cid:88)(cid:83)(cid:79)(cid:84)(cid:75)(cid:74)(cid:3)
tion V, the discussion and conclusion are given. (cid:60)(cid:75)(cid:89)(cid:89)(cid:75)(cid:82)(cid:3)(cid:47)(cid:83)(cid:71)(cid:77)(cid:75)(cid:3)
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(cid:1848)(cid:2871)
(cid:1828) Fig. 2: (cid:1847)The framework of stage 1
II. METHODOLOGY
The proposed algorithm is inspired by image matting [24]–
[26], which refers to the problem of accurately extracting In the second stage, a novel hierarchical growth algorithm
the foreground from an image. Image matting is often im- (HGA) is proposed to classify all undetermined pixels in the
plemented with a user-specified trimap [24], which separates undetermined image. HGA labels each pixel in the undeter-
the image into three parts: a foreground image, a background mined regions as vessel or non-vessel in an incremental way
image and an undetermined image. The matting methods try by using color and spatial information from the intermediate
toestimatetheundeterminedimagewiththeforegroundimage vessel image and the background regions. In the last stage,
and the background image. postprocessing is applied to remove the non-vessel regions.
Inspired by the basic idea of image matting, the proposed The process of the proposed algorithm is shown in Fig.1.
vessel segmentation algorithm is performed in three stages. Theimagenotationsandtheirdefinitionsusedintheproposed
In the first stage, an enhanced vessel image is generated algorithm are shown in Table I.
by morphological reconstruction, and then divided into three
parts: preliminary vessel regions, background regions and
A. Stage 1: The Preliminary and Intermediate Region Seg-
undetermined regions. Then a list of region features of blood
mentation
vesselsaredefinedandusedtoremovethenoiseregionsinthe
preliminaryvesselregions.Theregionfeaturesarealsoapplied Instage1,themaingoalistoobtainundeterminedregions,
toextractvesselskeletonsfromanotherenhancedvesselimage determined vessel regions and background regions. This stage
generatedbytheisotropicundecimatedwavelettransform[27]. consists of the following four steps: 1) image division, 2)
An intermediate vessel image is obtained by combing the noise region removal, 3) vessel skeleton extraction and 4)
denoised preliminary vessel regions with the vessel skeletons. combination.Theframeworkofstage1isshowninFig.2.The
3
TABLE II: DEFINITIONS OF MASTER PARAMETERS
MasterParameters Meaning
th1 Theupperthresholdusedtosegmenttheimage
e1 TheuppervalueofExtensibility
e2 ThelowervalueofExtensibility
r ThethresholdofVRatio
s ThethresholdofSolidity
fi Theinternalfactor. (a) (b) (c)
fi iscalculatedasd× mmainx((hh,,ww)),
d=21isapproximatelythediameterofthe
biggestvesselsinfundusimages[28],hand
w aretheheightandwidthofthefundusimage.
TABLE III: DEFINITIONS OF DERIVATIVE PARAMETERS
DerivativeParameters Meaning
th2 Thelowerthreshodusedtosegmenttheimage. (d) (e) (f)
th2iscalculatedasth1−0.15.
a1 ThefirstthresholdofArea Fig. 3: Image division of an image from DRIVE dataset. (a) The
a1 iscalculatedasfi×2. fundusimage(b)Thegreenchannelofthefundusimagefg.(c)The
a2 ThesecondthresholdofArea enhanced vessel image Ie1. (d) Preliminary vessel regions V1. (e)
a2 iscalculatedasfi×8. Background regions B. (f) Undetermined regions U.
a3 ThethirdthresholdofArea
a3 iscalculatedasfi×2.5.
a4 ThefourththresholdofArea the set of angles of the structuring element and defined as
a4 iscalculatedasfi×35.
{x|0<x<π &xmod(π/12)=0}.
For each enhanced vessel image I , in order to make full
e1
definitions of master parameters used in stage 1 are shown in useofthevesselinformationandbackgroundinformation,Ie1
Table II, and the definitions of derivative parameters used in is divided into three parts: preliminary vessel regions (V1),
stage 1 are shown in Table III. The experimental setting and backgroundregions(B)andundeterminedregions(U)bytwo
analysis of master parameters will be presented in Section III. fixed thresholds th1 and th2.

1) Image Division: Before performing image division, B if 0<I <th2
 e1
since color fundus images often show poor contrast between I = U if th2(cid:54)I <th1 (3)
e1 e1
vessels and background [13], morphological reconstruction is  V if th1(cid:54)I
1 e1
applied to enhance the contrast and generate images more
AnexampleofimagedivisionusinganimagefromDRIVE
suitable for image division.
dataset [10] is shown in Fig.3.
Foreachfundusimage,thegreenchannelfg isextractedat
2) NoiseRegionRemoval: Alistofregionfeaturesofblood
first [29]. Then fg scaled in [0,1] is processed by an adaptive
vessels are defined and used to remove the noise regions in
medianfilterwiththepurposeofremovingthesalt-and-pepper
preliminary vessel regions. These region features characterize
noise.Themedianfilterstartsatsize3-by-3anditeratesupto
the morphological properties of blood vessels [9] and are
size7-by-7.Next,thecomplementimagefg oftheprocessed
c suitable to be applied for blood vessel segmentation. The
green channel image is subjected to contrast enhancement by
definition of region features are given as follows [30], [31].
morphological reconstruction [28]:
• Area is the actual number of pixels in each connected
Iθ =fg −(fg ◦Sθ) (1) region.
th c c e
• Bounding Box (Fig.4) specifies the smallest rectangle
Themorphologicaltop-hattransformationisgiveninEqua-
containing the region.
tion (1), where Itθh represents the top-hat transformed image, • Extensibilityistheratioofpixelsintheconnectedregion
Se isastructuringelementformorphologicalopening◦,andθ to pixels in the total bounding box.
specifiestheangle(indegrees)ofthestructuringelement.The • VRatio is the ratio of width and length of the bounding
structuring element is of 1-pixel width and 21-pixels length, box.
which approximately fits the diameter of the biggest vessels • Convex Hull (Fig.4) specifies the smallest convex poly-
in the fundus images [28]. Since the morphological top-hat gon that can contain the connected region.
transformation transformation given in Equation (1) can only • ConvexArea specifies the number of pixels in convex
hull.
brighten blood vessels in one direction, the sum of top-hat
transformation Iθ along each direction is performed in order • Solidity is the ratio of pixels in the connected region to
th pixels in the total convex hull.
to enhance the whole vessel image.
For preliminary vessel regions, the regions with a ≤
(cid:88) 1
Ie1 = Itθh (2) AreaVI ≤ a2 are extracted first (V1∗). Then connected
θ∈A regions in V∗ with Extensibility ≤ e1 && VRatio ≤ r
1
The sum of top-hat transformation is depicted in Equation && Solidity ≥ s are abandoned, resulting in the denoised
(2), where I represents the enhanced vessel image, ”A” is preliminary vessel regions V .
e1 2
4
(a) (b) (c) (a) (b) (c)
Fig. 4: 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.
3) Vessel Skeleton Extraction: The basic idea of the pro-
(d) (e) (f)
posed algorithm is making use of the determined information
(determined vessel information and background information)
to estimate the undetermined regions. After applying image
division and noise region removal, the determined vessel
informationandbackgroundinformationcanbeobtainedfrom
V and B. In order to provide enough vessel information,
2
vesselskeletonextractionisperformed.Theanalysisofvessel
skeleton extraction will be given in Section IV. (g) (h) (i)
Since the enhanced vessel image I could not reflect the
e1
Fig. 5: Vessel skeleton extraction of an image from DRIVE
connected properties of blood vessels completely [32], it is
dataset.(a)Thegreenchannelofthefundusimagefg.(b)Thevessel
difficult to extract sufficient available vessel skeletons from
enhancedimageI .(c)ThebinaryimageT.(d)Backgroundregions
e2
Ie1 alone.Hence,theisotropicundecimatedwavelettransform T1. (e) Candidate regions T2. (f) Vessel regions T3. (g) T4: The
[27] is employed to generate another vessel enhanced image, preservedregionsinT2.(h)ThecombinedregionsofT andT (h)
3 4
which is more suitable for vessel skeleton extraction. The vessel skeletons S.
The isotropic undecimated wavelet transform (IUWT) is
a powerful wavelet transform, which has been applied for
vessel segmentation and shows good performance. Applied For image T, the connected regions are divided into three
to a signal c0 = fg, scaling coefficients are computed by parts: background regions(T1), candidate regions(T2) and ves-
convolution with a filter h↑j sel regions(T3) according to the Area feature of each con-
nected region:
c =c ∗h↑j (4)
j+1 j

T1 if 0<Area <a
where h = [1,4,6,4,1]/16 is derived form the cubic B-  T 3
0 T = T2 if a ≤Area ≤a (8)
spline,h↑j istheupsampledfilterobtainedbyinserting2j−1 3 T 4
 T3 if a <Area
zerosbetweeneachpairofadjacentcoefficientsofh .Wavelet 4 T
0
coefficients are the difference between two adjacent sets of The regions in T3 are preserved while the regions in T1 are
scaling coefficients, i.e., abandoned. Then the regions in T with Extensibility > e
2 2
&& VRatio ≤ r are preserved as T . Finally skeleton
w =c −c (5) 4
j+1 j j+1
extraction [33] is performed on the combined regions of T
3
Reconstruction of the original signal from all wavelet coeffi- andT inordertoobtaintheskeletonofbloodvesselsS.Fig.5
4
cients and the final set of scaling coefficients is straightfor- gives an example of vessel skeleton extraction using the same
ward, and requires only addition. The enhanced vessel image image from DRIVE dataset.
after IUWT is depicted as follows:
4) Combination: After performing noise region removal
3 and vessel skeleton extraction, an intermediate vessel image
(cid:88)
Ie2 =cn+ wj (6) V3 is obtained by combing the denoised preliminary vessel
j=2 regions V2 with vessel skeletons S.
The wavelet scales:2-3 in Equation (6) are selected according
to [27].
B. Stage 2: Hierarchical Growth Algorithm (HGA)
After performing the isotropic undecimated wavelet trans-
form,abinaryimageT isobtainedbyglobalthresholdingthe In order to classify the pixels in U, HGA is proposed to
enhanced vessel image Ie2 for pixels greater than 0.003. label each undetermined pixel as vessel or non-vessel in an
(cid:26) 1 I >0.003 incremental way. HGA is inspired by the non-dominated sort-
T = e2 (7)
0 I (cid:54)0.003 ing approach [34], [35]. The non-dominated sorting approach
e2
5
(a) (b) (c)
Fig.6: Asimpleexampletoillustratetheprocessofinitialization.(a)Anexemplaryimage(whitepixelsrepresentvesselpixels,redpixels
represent undetermined pixels). (b) Calculating the closest distance for each undetermined pixel (di means the closest distance for the ith
undetermined pixel). (c) Separating undetermined pixels into different hierarchies.
plays an important role in multiobjective evolutionary algo-
rithms(MOEAs),andcaneffectivelyseperatetheoverallnon-
dominated set of solutions into different ranks [36] (Fig.7). (cid:1858)(cid:2870) (cid:1858)(cid:2870)
HGA consists of two main steps.
The 4th rank
Step 1Initialization: Separate pixels in U into different
The 3rd rank
hierarchies.
Step 2Hierarchy Update: Assign new labels(V or B) to The 2nd rank
pixels in each hierarchy.
The 1st rank
The pseudocode of HGA is given in Algorithm 1.
Algorithm 1: Hierarchical Growth Algorithm
Input: (a) (cid:1858)(cid:2869) (b) (cid:1858)(cid:2869)
1) V3: an intermediate vessel image; Fig. 7: The effect of non-dominated sorting. f1 and f2 are the
2) B: background regions; objectives. Red points represent the solution individuals.
3) U: undetermined regions;
Output: The estimated vessel image V
arecalculatedfirst.Thenthe closest distanceischosenforthe
Step 1: Initialization:
ith undetermined pixel. After that, undetermined pixels are
a) For i = 1,...,n , set D(i) = d , where n is
U i U separated into different hierarchies according to the closest
the number of undetermined pixels in U, d is the
i distances. The undetermined pixels reside in low hierarchy
distance between the ith undetermined pixel and
means that they are close to blood vessels; The undetermined
the closest vessel pixel in V, D is the set of d .
i pixelsstayinhighhierarchymeansthattheyarefarawayfrom
b) SorttheundeterminedpixelsinU inanascending
blood vessels. A simple example to illustrate the process of
order according to the distances D , cluster the
initialization is shown in Fig.6.
pixels with the same distance into one hierar-
Correlation Function: In step 2 of the algorithm, given an
chy, divide the pixels into m hierarchies and
undetermined pixel uj and its neighboring labeled pixel kj, a
denote them as an hierarchical order set: H = i l
{H1,H2,...,Hm}, Hj = {uji|i ∈ 1,2,...,ni}, caonldorkjcofisrtstf:unction ξc is defined to describe the fitness of uji
where ni is the number of undetermined pixels in l
the jth hierarchy H . ξ (uj,kj)=||c −c || (9)
j c i l uj kj
i l
Step 2: Hierarchy Update
For j =1,...,m, do where cuj and ckj are intensity level of uji and klj in Ie1. A
For i=1,...,n , do spatial coist functilon ξ is further defined:
i s
a) Compute the correlations (Defined in Equation
||x −x ||−x
(e1ls1()v)ebsseetwl peeixnelusjiaannddbiatsckngerioguhnbdorpinixgellas)beinlecdlupdiexd- ξs(uji,klj)= uxjimaxk−lj xminmin (10)
in a 9×9 grid.
where x and x are the spatial coordinates of uj and
b) Choose the labeled pixel with the closest correla- uj kj i
i l
tion, and assign its label(V or B) to uji. klj. The terms xmax = maxj||xuji − xklj|| and xmin =
end for minj||xuj−xkj||arethemaximumandminimumdistanceof
i l
end for theundeterminedpixeluj tothelabeledpixelkj.Thenormal-
i l
Initialization: In the initialization stage, for the ith unde- ization factors x and x ensure that ξ is independent
min max s
termined pixel in U, its distances with all vessel pixels in V from the absolute distance.
6
(a) j=0 (c) j=4 (g) The final estimated (h) The estimated image
vessel image after postprocessing
Fig. 8: Hierarchical growth algorithm and postprocessing. (a) Estimated vessel image in the hierarchy j = 0 (The intermediate vessel
image V ). (b) Estimated vessel image in the hierarchy j =4. (c) The final estimated vessel image V. (d) The final estimated vessel image
3
after postprocessing.
Ourfinalcorrelationfunctionξisacombinationofthecolor
fitness and the spatial distance:
ξ(uj,kj)=ξ (uj,kj)+ωξ (uj,kj) (11)
i l c i l s i l
where ω is a weight to trade off the color fitness and spatial
distance.ωissetas0.5inourexperiment.Intuitively,asmallξ
indicatesthatthelabeledpixelhaveaclosecorrelationwiththe
undetermined pixel and can well represent the undetermined (a) (b)
pixel.
Hierarchy Update: After defining the correlation function,
ineachhierarchy,thecorrelationsbetweeneachundetermined
pixel and its neighboring labeled pixels (vessel pixels and
background pixels) included in a 9 × 9 grid are computed.
Then the label pixel with the closest correlation is chosen,
and its label is assigned to the undetermined pixel (Fig.9).
After all undetermined pixels in one hierarchy are updated,
theyareusedfortheupdateofthenexthierarchy.HGAiterates (c) (d)
from the first hierarchy to the last one, which emulates a
Fig. 9: An example for the illustration of assigning a label(V or
process that blood vessels grow from the intermediate vessel
B) to an undetermined pixel. (a) An exemplary image (white pixels
regions to the whole vessel regions.
representvesselpixels,yellowpixelsrepresentbackgroundpixels,red
An example of HGA is shown in Fig.8. pixelsrepresentundeterminedpixels).(2)Calculatingthecorrelation
functions between a undetermined pixel and its neighboring labeled
pixels(vesselpixelsandbackgroundpixels)(cimeansthecorrelation
between the undetermined pixel and the ith labeled pixel). (3)
C. Stage 3: Postprocessing Assigning a label(V or B) to the undetermined pixel. (4) The
resultant image.
Some non-vessel regions may still exist in the estimated
vessel image V. To remove these non-vessel regions, the
connected regions with Area < a && Extensibility > e
4 2 A. Datasets
&& VRatio<r in V are abandoned.
DRIVE1 [10] consists of 40 fundus images obtained from
a screening program in the Netherlands. These images are
III. DATASETSANDEVALUATIONMETRICS captured by a Canon CR5 non-mydriatic 3-CCD camera at
45◦ field of view (FOV), and the size of each image is of
In this section, three publicly available datasets are intro- 584×565pixels.TheDRIVEdatasetisdividedintotwosets:
duced at first. These datasets have been widely used by a lot a training set (DRIVE Training) and a test set (DRIVE Test)
of researchers to develop their own vessel segmentation algo- each containing 20 fundus images. The test set is annotated
rithms.Thenthewidelyusedevaluationmetricsarepresented, by two independent human observers, resulting in a set X and
which are utilized in our experiment and for comparison with
other state-of-art methods. 1http://www.isi.uu.nl/Research/Databases/DRIVE/
7
0.97 0.96 0.96
0.96 0.959 0.955
0.958
0.95 0.95
0.957
0.94 0.956 0.945
Acc0.93 Acc0.955 Acc 0.94
0.92 0.954 DRIVE 0.935
0.953 STARE
0.91 DSTRAIVREE 0.952 CHASE_DB1 0.93 DSTRAIVREE
0.9 CHASE_DB1 0.951 0.925 CHASE_DB1
0.89 0.95 0.92
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0 1 2 3 4 5 6 7 8 9 10
th1 e1 r
(a) (b) (c)
0.96 0.96
0.959 0.955
0.958 0.95
0.957 0.945
0.956 0.94
Acc0.955 Acc0.935
0.954 0.93
0.953 DRIVE 0.925
STARE
0.952 CHASE_DB1 0.92 DRIVE
STARE
0.951 0.915 CHASE_DB1
0.95 0.91
0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
s e2
(d) (e)
Fig. 10: The influence of different parameters. (a) Variations in mean segmentation accuracy by varying th1. (b) Variations in mean
segmentation accuracy by varying e1. (c) Variations in mean segmentation accuracy by varying r. (d) Variations in mean segmentation
accuracy by varying s. (e) Variations in mean segmentation accuracy by varying e2.
Y. In set X 12.7% pixels are marked as vessels while in set In order to evaluate the performance of the vessel segmen-
Y 12.3% are annotated as vessels. tation algorithms, three commonly used metrics are applied.
STARE2 [17] consists of 20 fundus images. These images
TP
arecapturedbyaTopConTRV-50funduscameraat35◦ FOV, Sensitivity =
TP +FN
and the size of each image is of 605×700 pixels. Ten images
TN
contain pathology while the other ten images are normal. The Specificity =
TN +FP
STARE dataset is annotated by two independent observers.
TP +TN
Thefirstobserver(O1)annotates10.4%pixelsasvesselswhile Accuracy =
TP +TN +FP +FN
the second observer (O ) segments 14.9% vessel pixels.
2
CHASE DB13 [28] consists of 28 fundus images acquired Sensitivity (Se) reflects the algorithm’s ability of detecting
from multiethnic school children. These images are captured vessel pixels while Specificity (Sp) is a measure of the
by a hand-held Nidek NM-200-D fundus camera at 30◦ algorithm’seffectivenessinidentifyingbackgroundpixels.Ac-
FOV, and the size of each image is of 960 × 999 pixels. curacy(Acc)isaglobalmeasureofclassificationperformance
The CHASE DB1 is annotated by two independent human combing both Se and Sp. The performance of the vessel
observers, resulting in set gt1 and gt2. segmentation method is also measured by the area under a
receiver operating characteristic (ROC) curve (AUC). The
conventional AUC is calculated from a number of operating
B. Evaluation Metrics points, and normally used to evaluate the balanced data
classification problem. However, in practice the researchers
In the process of retinal vessel segmentation, each pixel
need to select an operating point to compare their method
is classified as vessels or background, thereby resulting in
with other methods. Also blood vessel segmentation is an
four events: two correct classifications and two incorrect
unbalanced data classification problem, in which there are
classifications, which are defined in Table IV.
muchfewervesselpixelsthanthebackgroundpixels.Inorder
TABLE IV: FOUR EVENTS OF VESSEL CLASSIFICATION to evaluate the performance of blood vessel segmentation
properly,AUC =(Se+Sp)/2[23],[37]isappliedtoindicate
Vesselpresent vesselabsent
the overall performance of blood vessel segmentation, which
vesseldetected TruePositive(TP) FalsePositive(FP)
vesselnotdetected FalseNegative(FN) TrueNegative(TN) is suitable to describe the overall performance of imbalanced
data classification problem and specifically for the case when
2http://www.ces.clemson.edu/ahoover/stare/ only one operating point is used. The segmentation time
3https://blogs.kingston.ac.uk/retinal/chasedb1/ required per image in seconds for implementing the proposed
8
segmentation algorithm in MATLAB on a Laptop with Intel Thesegmentationperformanceandcomputationalcomplex-
Core i7 processor, 2.5GHz and 8GB RAM is recorded. ity of the proposed algorithm in comparison with other state-
of-art methods on the DRIVE and STARE datasets are given
in Table VI. From Table VI, it can be observed that for
IV. EXPERIMENTSANDRESULTS
the DRIVE dataset, the accuracy of the proposed model are
Inthissection,threesetsofexperimentsareperformedwith
the highest among all existing methods with Acc = 0.960,
the purpose of evaluating the proposed vessel segmentation
Se = 0.736 and Sp = 0.981. On the STARE dataset, the
algorithm. In the first experiment, parameters setting was
accuracy and AUC of the proposed model are the highest
provided.Inthesecond experiment,vesselskeletonextraction
among unsupervised methods with Acc = 0.957, AUC =
was analyzed for segmentation performance. In the third
0.880. Although the supervised method [15] has the best
experiment, the proposed method was compared with other
performanceonSTAREdataset,themethodiscomputationally
supervised and unsupervised methods.
morecomplexduetotheuseofdeepneuralnetworks,andthe
deep neural network may need retraining for new datasets. In
A. Parameters Setting addition, the proposed algorithm has a lower computational
complexity than many other segmentation methods.
Allparametersoftheproposedalgorithmaresetasfollows:
th1 = 0.35, e = 0.35, r = 2.2, s = 0.53, e = 0.25. In
1 2
order to demonstrate the sensitivity of the algorithm to these V. CONCLUSIONANDDISCUSSION
parameters, the variations in Acc by varying th1, e1, r, s and
In this paper, a novel unsupervised segmentation algorithm
e are given in Fig.10.(a), (b), (c), (d) and (e).
2 is proposed to extract blood vessels from the fundus images.
From Fig.10, it can observed that the proposed algorithm
The proposed method is inspired by image matting [24]–
can maintain high segmentation accuracy on the DRIVE,
[26].Imagemattingisacomplicatedandchallengingproblem,
STARE and CHASE DB1 datasets as th1 varies in [0.3,0.5]
which aims to accurately extract a foreground from an image.
or e varies in [0.15,0.3]; For the parameters e and s, the
2 1 Most image matting models are based on a user-specified
imagesfromthreedatasetscanmaintainhighsegmentationac-
trimap, which consists of foreground regions, background
curacywhene belongsto[0.2,0.4]orsbelongsto[0.4,0.6];
1 regionsandundeterminedregions.Inessence,mattingmodels
For the parameter r, the proposed method can achieve a high
make use of the priori knowledge (foreground knowledge and
segmentation accuracy as s varies in [2,6]. From the above
backgroundknowledge)toestimatetheundeterminedregions,
observation, it can be seen that the algorithm is not sensitive
whichcannotbeclassifiedeasily.Similarly,inafundusimage,
toparameterswhentheparameterschangeinarelativelylarge
a few vessel regions and background regions can be extracted
range.
easily without complicated extraction methods. Thus, the
usefulinformationfromvesselregionsandbackgroundregions
B. The Segmentation Performance and Analysis of Vessel can be applied to classify the pixels in the undetermined
Skeleton Extraction regions, which are difficult to be classified correctly. This
is the basic idea of the proposed method. It is worthwhile
Thesegmentationperformanceoftheproposedalgorithmon
to point out that by dividing the fundus image into vessel
threepublicavailabledatasetsisgiveninTableV.FromTable
regions, background regions and undetermined regions, the
V, it can be observed that the proposed algorithm can achieve
computational complexity is decreased since the number of
morethan95%segmentationaccuracyontheDRIVE,STARE
pixelswhichneedtobefurtherdividedbyclassifierisreduced.
and CHASE DB1 datasets, with the highest accuracy score is
achieved in the DRIVE dataset. The exemplary segmentation The proposed algorithm divides the enhanced vessel image
results are shown in Fig.11. into preliminary vessel regions, background regions and un-
determined regions. Then a list of region features are defined
Moreover,fromTableV,itcanobservedthatvesselskeleton
and used to perform noise region removal. Also these region
extraction can improve the performance of the proposed algo-
featuresareappliedtoextracttheskeletonsofbloodvesselsin
rithm, especially the ability of detecting vessel pixels. With
fundus images. The region features characterize the morpho-
vessel skeleton extraction, the proposed method can achieve
more than 5% increase of Sensitivity and 2% increase logical properties of blood vessels and are suitable for vessel
of AUC. Also the processing time is reduced when vessel segmentation. In order to classify the pixels in undetermined
regions, HGA is proposed to label the undetermined pixels
skeleton extraction is applied.
as vessel or non-vessel. HGA is inspired by by the non-
dominated sorting method, which is first by proposed by
C. Comparison With the Other Methods
Deb et.al [34] and can effectively seperate the overall non-
Since most of researchers compare their algorithm with dominatedsetofsolutionsintodifferentranks.HGAseparates
other methods by using manual segmentations form set X in theundeterminedpixelsintodifferenthierarchiesaccordingto
theDRIVEdatasetandthemanualsegmentationsfromthefirst the distance between the undetermined pixel and the closest
observerintheSTAREdataset,inourworkthesegmentations vessel pixel, and then updates the undetermined pixels in an
of set X are used as the ground truth for the DRIVE dataset, incremental way according to correlation functions.
and for the STARE dataset, the segmentations of the first The proposed algorithm is very efficient and effective in
observer are used as the ground truth. blood vessel segmentation, which achieves a segmentation
9
TABLE V: THE SEGMENTATION PERFORMANCE OF THE PROPOSED ALGORITHM ON THREE TEST DATASETS
TheAlgorithmwithVesselSkeletonExtraction TheAlgorithmwithoutVesselSkeletonExtraction
Dataset Ground-Truth Acc AUC Se Sp Time(s) Acc AUC Se Sp Time(s)
SetX 0.960 0.859 0.736 0.981 0.960 0.837 0.688 0.986
DRIVETest SetY 0.964 0.877 0.772 0.982 10.720 0.964 0.853 0.720 0.987 11.959
O1 0.957 0.881 0.791 0.970 0.959 0.862 0.748 0.976
STARE O2 0.946 0.815 0.648 0.981 15.740 0.945 0.795 0.604 0.986 16.563
gt1 0.951 0.815 0.657 0.973 0.954 0.789 0.597 0.981
CHASE DB1 gt2 0.950 0.812 0.652 0.971 50.710 0.952 0.783 0.588 0.978 60.847
(a) (b)
(c) (d)
Fig. 11: 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
TABLE VI: PERFORMANCE OF DIFFERENT SEGMENTATION MODELS ON THE DRIVE TEST AND STARE DATASETS
TestDatasets DRIVETest STARE
Methods Acc AUC Se Sp Time Acc AUC Se Sp Time System
SupervisedMethods
Staalet.al[10] 0.944 - - - 15min 0.952 - - - 15min 1.0GHz,1-GBRAM
Soareset.al[11] 0.946 - - - ∼3min 0.948 - - - ∼3min 2.17GHz,1-GBRAM
Lupascuet.al[12] 0.959 - 0.720 - - - - - - - -
Marinet.al[13] 0.945 0.843 0.706 0.980 ∼90s 0.952 0.838 0.694 0.982 ∼90s 2.13GHz,2-GBRAM
Roychowdhuryet.al[14] 0.952 0.844 0.725 0.962 3.11s 0.951 0.873 0.772 0.973 6.7s 2.6GHz,2-GBRAM
Liskowskiet.al[15] 0.954 0.881 0.781 0.981 - 0.973 0.921 0.855 0.986 - NVIDIAGTXTianGPU
UnsupervisedMethods
Hooveret.al[17] - - - - - 0.928 0.730 0.650 0.810 5min SunSPARCstation20
Mendoncaet.al[19] 0.945 0.855 0.734 0.976 2.5min 0.944 0.836 0.699 0.973 3min 3.2GHz,980-MBRAM
Lamet.al[38] - - - - - 0.947 - - - 8min 1.83GHz,2-GBRAM
Al-Diriet.al[21] - - 0.728 0.955 11min - - 0.752 0.968 - 1.2GHz
LamandYanet.al[22] 0.947 - - - 13min 0.957 - - - 13min 1.83GHz,2-GBRAM
Perezet.al[39] 0.925 0.806 0.644 0.967 ∼2min 0.926 0.857 0.769 0.944 ∼2min ParallelCluster
Miriet.al[40] 0.943 0.846 0.715 0.976 ∼50s - - - - - 3GHz,1-GBRAM
Budaiet.al[41] 0.957 0.816 0.644 0.987 - 0.938 0.781 0.580 0.982 - 2.3GHz,4-GBRAM
Nguyenet.al[42] 0.941 - - - 2.5s 0.932 - - - 2.5s 2.4GHz,2-GBRAM
Yitianet.al[23] 0.954 0.862 0.742 0.982 - 0.956 0.874 0.780 0.978 - 3.1GHz,8-GBRAM
Proposed 0.960 0.858 0.736 0.981 10.72s 0.957 0.880 0.791 0.970 15.74s 2.5GHz,4-GBRAM
10
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