Segmentation of retinal blood vessels using normalized ...

12 Research Article – SACJ No. 55, December 2014

Segmentation of retinal blood vessels using normalized Gabor

filters and automatic thresholding

Mandlenkosi Victor Gwetu, Jules Raymond Tapamo, Serestina Viriri

University of KwaZulu-Natal, South Africa

ABSTRACT

Although computerized retinal image blood vessel segmentation has been extensively researched, there is still room for

improvement in the quality of the segmented images. Since retinal image analysis is still widely used in the diagnosis of

diabetic retinopathy, efficient and accurate image characterization techniques are required. Previous work has mainly

focused on improving segmentation accuracy rates with little regard to the false positives that are produced by illumination

variation. This research work presents a hybrid approach towards the segmentation of retinal blood vessels. New approaches

towards the reduction of background illumination variation are proposed using normalized Gabor filtering. These are the

base-offset encoding and a modified version of an existing zero-integral kernel technique. The valley emphasis automatic

thresholding scheme is used to segment the Gabor response images. Experiments are conducted on the DRIVE and STARE

retinal image data sets. Accuracy rates of up to 94% are achieved through the zero-integral and base offset methods. This

is comparable with results from literature, where the same data sets are segmented using other classification techniques.

The median-offset method is found to most effectively reduce background illumination variation.

KEYWORDS: retinal blood vessel, normalized Gabor filter, illumination variation, thresholding, segmentation

CATEGORIES: I.2.10, I.4.6

1 INTRODUCTION

Humans inherently possess image processing abilitiesthrough their complex visual system. The role thatthe retina plays in this process is substantial as it is es-timated that 80% of all sensory information in humansoriginates from the retina [1]. This indicates its impor-tance in our interaction with the physical world andexplains why it remains one of the most scientificallyexplored components of the human body. The retina islocated on the posterior hemisphere of the eye and canbe clinically examined using an ophthalmoscope [2].This instrument projects a light beam through the irisand then magnifies the corresponding reflection fromthe retina [3]. The reflected image which is known asthe fundus image, reveals a few prominent tissues suchas the optic disk and blood vessels [4].

The diagnosis of disorders such as diabetic retinopa-thy relies on the analysis of retinal vasculature [2]. Thisanalysis has traditionally been done with the aid ofa process known as fluorescence angiography whichrequires a patient to be injected with a dye called fluo-rescein [5]. This dye travels through the blood streamand eventually causes the blood vessels in the retinato have high contrast for easier visual analysis. Alter-native and less invasive automated digital techniques

Email: Mandlenkosi Victor Gwetu [email protected],Jules Raymond Tapamo [email protected], Serestina [email protected]

are now being sought after in order to expedite retinalvisual analysis [6]. These techniques typically rely on alaser digital ophthalmoscope to produce digital fundusimages which are then electronically registered andanalyzed [7].

To analyze blood vessels in electronic images, it isimportant to first detect them accurately. Althoughfeatures such as branching angle, shape and thicknessof vessels are essential for diagnosis, their effectivenesscan be compromised by inaccurate segmentation. [8].Two approaches commonly used for vascular segmen-tation are supervised and unsupervised segmentation.Supervised segmentation is dependent on a trainingset and comprises methods such as Support VectorMachines (SVM) [8] and neural networks [9], [10]. Un-supervised segmentation is independent of a trainingset and is exemplified by rule-based methods suchas vessel tracking [11], [12] and thresholding [6], [13].The focus of thresholding schemes is the selection ofa gray level that optimally segments an object fromits background. This optimization problem remains achallenge due to the smooth distribution of gray levelfrequencies in retinal image histograms.

Some of the previous work on retinal blood vesselsegmentation has used features based on the intensityprofile of vessel cross-sections. Examples include thematched filter [14], [15], [16] and Gabor filter [6], [17],[18]. Although Gabor filters are an effective line detec-tion tool, they are dependent on response normaliza-tion and parameter tuning. Sub-optimal normalization

Research Article – SACJ No. 55, December 2014 13

can lead to image blurring, poor contrast and false linedetection. Poor parameter selection can lead to thesuppression of lines that should otherwise be enhanced.Previous studies have not focused on the effect of nor-malization on Gabor filter effectiveness and only a fewnormalization techniques have been proposed [19], [20],[21].

This work investigates the performance of new andexisting Gabor filter normalization methods. Differentvariants of Gabor filter normalization are investigatedin the context of Valley Emphasis Thresholding (VET)[22]. This technique was originally designed for defectdetection in industrial artifacts and is, to the best of ourknowledge, being applied to blood vessel segmentationfor the first time.

The remainder of this paper is structured as follows:Section 1.1 gives a review of related previous work whileSection 2 outlines the techniques and methodology usedin this study. This is followed by a presentation anddiscussion of the results obtained. Finally a comparisonwith previous literature is drawn and possible areas ofextension are highlighted.

1.1 Literature Survey

Many techniques exist for the segmentation of retinalimage blood vessels. They can be broadly categorizedas supervised and unsupervised segmentation tech-niques. Both are dependent on an effective feature set.Previous studies document a detailed review of the var-ious features that have been applied to retinal bloodvessel segmentation [5], [9], [23]. These studies showthat line detection features such as matched filters[24] and Gabor filters [25] are favored for the enhance-ment of vasculature because vessels are generally linear.They also highlight the DRIVE [23] and STARE [26]data sets as the most commonly used image collectionsfor bench-marking retinal segmentation results. Someof the recent works that utilize line detection filters forvascular segmentation on these data sets are discussedbelow.

Chaudhuri et al. [24] document the first use ofmatched filters for blood vessel segmentation. TheOtsu method [27] is used for automatic thresholdingand a segmentation accuracy of 87.73% is achieved onthe DRIVE data set [9]. Hoover et al. [26] improvethe work of Chaudhuri et al. by using a rule-basedclassification method in addition to local thresholding.A segmentation accuracy of 92.67% is reported forexperiments on the STARE data set. HongQing et al.[13] apply Gray Level Gradient Co-occurrence Matrix(GLGCM) entropy thresholding to the Matched FilterResponse (MFR) image. The results are evaluated byvisually inspecting the output based on 3 specimenfundus images1.

Sofka et al. [28] improve the detection of low-contrast and narrow vessels through multiscalematched filters in conjuction with confidence and edgemeasures. The vessel confidence measure calculates thesimilarity of a MFR to an ideal vessel profile. Receiver

1The source of these images is not specified in [13].

Operating Characteristic (ROC) curves based on boththe DRIVE and STARE data sets show that the hybridmethod is superior to multiscale MFR alone. Al-Rawiet al. [29] improve the MFR by using optimal filterparameters obtained through an exhaustive search onthe DRIVE training image set. A segmentation accu-racy of 95.35% is reported. Zhang et al. [14] generatea Matched Filter Response (MFR) image using fixedparameters and a thresholding scheme that is enhancedby a first order derivative of Gaussian response. Ac-curacy rates of 93.82% and 94.84% are reported forexperiments on the DRIVE test set and STARE dataset respectively.

Gabor filters use kernels that are Gaussian modu-lated sinusoidal waves [25], [30] while matched filtersare based primarily on the Gaussian distribution [24].Gabor filters therefore have an advantage over matchedfilters in that they can be used for texture filtering inaddition to line detection. This makes them a moresuitable option for blood vessel enhancement [6]. Liet al. [18] modify Gabor filters to include a scale pa-rameter in a bid to increase the detection of vessels ofvarying width. The thresholding scheme of Hoover etal. [26] is used to binarize the output image. The re-sults are presented visually and no empirical evidenceis given to show the effectiveness of the approach.

The robustness of Gabor filters has traditionallybeen ensured through rotation and scale invariance.Kyrki et al. [19] highlight the significance of illumina-tion invariance for object recognition and recommendnormalized Gabor filters for implementing it. Nor-malization is achieved through dividing the featurematrix by the Euclidean norm of all the responses ata given pixel. Effectively, this is the normalization bydivision approach that is discussed in Section 2.4.1.Other normalization approaches are not explored inthe study.

Azzopardi et al. [20] propose a trainable filter calledCombination Of Shifted FIlter REsponses (COSFIRE)for keypoint detection and pattern recognition. Inthese filters, normalization is important for suppress-ing constant intensities and ensuring that lines of aspecific width have a maximum filter response. TheCOSFIRE filters are demonstrated on retinal imagesthat are already manually segmented. They are shownto detect vessel of specified widths, bifurcations andcrossings. The effectiveness of the filters is however nottested on normal unsegmented retinal images whichare more complex. Wu et al. [21] use adaptive contrastenhancement that is based on the standard deviationof a Gabor Filter Response (GFR) image window tohighlight vessels. Two randomly selected images fromthe STARE data set are used for parameter training.A tracking segmentation method is tested on the re-maining 18 images. An accuracy of 75% is reportedon the small vessels which consistute 42% of the totalvessel pixel count.

Rangayyan et al. [31] improve the orientation sen-sitivity of Gabor filters by introducing a coherencescore to measure the dominant direction of flow in awindow. Predetermined wavelengths and a threshold


are used to achieve an Area Under the Curve2 (AUC)of 95% for the DRIVE test set. Osareh et al. [32]rotate Gabor filters through several orientations andwavelengths in search of an optimal response. Classifi-cation is done through principal component analysis,Gaussian Mixture Models (GMMs) and SVMs. AnAUC of 96.5% is achieved on the DRIVE test set.Siddalingaswamy et al. [33] modify the approach ofHongQing et al. [13] by using Gray level co-occurrencematrix (GLCM) entropy instead of GLGCM entropyand replacing MFR with GFR. Although Gabor filternormalization is not documented in the study, averagesensitivity rates of 86.47% and 85% are reported forthe DRIVE and STARE data sets respectively.

The surveyed literature reveals that not much at-tention has been given to the development of moreeffective Gabor filter normalization techniques for ves-sel segmentation. In most cases, this aspect of the filterdesign is not mentioned. Image processing literaturedocuments two options for Gabor filter normalization,namely the normalization by division [34], [35], [36]and zero integral methods [20], [37]. This study seeksto demonstrate that Gabor filter normalization is es-sential to robust vessel enhancement and that it affectsthe effectiveness of automatic thresholding. Only afew automatic thresholding schemes such as the Otsumethod [27], [26] and GLGCM entropy [13] have beenexplored. The VET method [22] has previously beensuccessfully applied to automatic defect detection. Inthis study, it is applied to vessel segmentation.

2 TECHNIQUES AND METHODOLOGY

2.1 Segmentation System Overview

Figure 1: Overview of the design of a retinal imagesegmentation system

Figure 1 shows an overview of the segmentationsystem. The main steps are preprocessing, Gaborfiltering and thresholding. Preprocessing prepares theretinal image for filtering by converting its intensitiesto an inverted gray scale. The intensities are taken

2An ROC curve.

from the green channel of the color image as it is knownto contain the most contrast [8]. The inversion is toensure that the blood vessels are brighter than thebackground in preparation for further enhancement bythe Gabor filter. Different normalization techniquessuch as zero integral [20] and base-offset normalizationare tested in the Gabor filter.

A bank of Gabor filters with varying orientationand wavelength is used. The maximum response fromthe bank is chosen for each pixel [32], [38]. In thethresholding phase, the normalized Gabor responseimage is segmented using the VET method [22].

2.2 Gabor Filter Vessel Enhancement

Gabor filters convolve images with a sinusoidal Gaus-sian modulated function that is sensitive to orientation,frequency and bandwidth [30]. The filter response is acomplex number with real and imaginary componentsthat are orthogonal [11]. This results in four optionsfor representing the filter response, namely the real,imaginary, phase and magnitude components. Thereal component can be represented as follows:

g(x′, y′, λ, θ, ψ, σ, γ) = G(x′, y′, σ, γ)W (x′, λ, ψ), (1)

where G, W , x′ and y′ are defined by the respectiveequations (2-5) below.

G(x′, y′, σ, γ) = exp

[−π

(x′

2

σ+γy′

2

σ

)]. (2)

W (x′, λ, ψ) = cos

(2πx′

λ+ ψ

). (3)

x′ = x cos θ + y sin θ. (4)

y′ = −x sin θ + y cos θ. (5)

The Gaussian envelope is represented by G while thesinusoidal wave is represented by W . The wavelengthand phase-offset of the sinusoidal wave are symbolizedby λ and ψ respectively. The angle of orientationis represented by θ while the sigma and aspect ratioof the Gaussian envelope are represented by σ andγ respectively. The co-ordinates of the point to befiltered are represented by x and y. The half responsebandwidth, b of the Gabor filter is measured in octavesand is used to regulate the spread and shape of thefilter. It is related to σ and λ according to equation (6)[36]. Given λ and b, it is therefore possible to calculateσ.

σ

λ=

1

π

√ln 2

2

[2b + 1

2b − 1

]. (6)

Gabor filters are suited for texture segmentationand are known to be a good model of how the humanvisual system processes light signals [39]. Their effec-tiveness is however hindered by the tedious task ofparameter selection. Research that implements Ga-bor filters therefore usually either uses predeterminedparameters or has an elaborate optimal parameter se-lection process. Cross sections of blood vessels whichare perpendicular to the direction of blood flow usu-ally have a Gaussian gray level distribution. As such,


Gabor filters are seen as effective features for vesseldetection.

2.3 Gabor Filter Parameters

The Gabor filter requires several parameters to betuned based on the context of application. In thisstudy, the real component of the Gabor filter is useddue to its observed superior vessel enhancement incomparison with the imaginary, magnitude and phaseresponses. A phase offset of 0 is used due to the factthat every retinal pixel is overlapped by the centerof a kernel window when it is convolved. This meansthat the peak of the Gabor wave will correspond tothe pixel being convolved.

In standard data sets such as the DRIVE andSTARE collections, the width of a retina vessel maylie within the range of [2,10] pixels [29]. In order todetect a complete vessel profile at a given pixel, a waveneeds to be centered on the vessel’s cross section andbe oriented in the direction of the vessel. Additionally,the kernel window needs to be large enough to capturethe vessel’s neighborhood so that the Gabor filter re-sponse is effectively contextualized. A kernel size of21x21 pixels was used in this study. Kernel sizes largerthan this were explored but they did not lead to anyimprovement in results. The spread of the Gaussianfunction in the kernel is ensured by using a bandwidthof 0.25 octaves in all experiments. The ellipticity ofthe Gabor filter is implemented using an aspect ratioof 0.75. The wavelengths that are used in this studyare 4, 8 and 12. They are considered individually aswell as collectively. Wavelengths of less than 4 pixelswere found to be susceptible to noise interference.

The orientations are rotated by 15 degrees in therange [0, 180) degrees as is the case in previous litera-ture [9]. In the case of all 3 wavelengths being used,each combination of wavelength and orientation is con-sidered, resulting in 36 combinations. Each of thesewavelength-orientation combinations is used to createa Gabor kernel of size: 21x21 pixels. Every retinalpixel is convolved with each of these kernels, resultingin 36 Gabor filter responses. Non-retinal pixels withinthe kernel’s corresponding image window are not con-volved. The response image comprises of the highestGabor filter response for each pixel. This image issubsequently thresholded in order to yield a binaryimage.

2.4 Gabor Filter Normalization

The GFR may be affected by the general illuminationof a pixel’s neighborhood. Hence, normalization isessential to ensure invariant responses [19]. In general,normalization has the effect of scaling responses downto a specific range whilst attempting to either preservedesired characteristics of an image or suppress noise.

2.4.1 Gabor Filter Normalization by Division

One of the oldest methods for Gabor filter normaliza-tion uses division to scale intensities down. It divides

a pixel’s GFR by a factor that is derived from itsneighborhood [36]. In [35], this factor is the averagegray level in a pixel window. The weakness of thisapproach is that it does not adequately suppress theillumination in the optic disc and the resulting contrastis very low. Figure 2 shows a typical histogram derivedfrom a normalization by division GFR image. The leftskewed histogram distribution shows the low contrastin the response image. The multiple discontinuities ofthis histogram make it cumbersome to automaticallydetect the threshold that optimally separates vesselsfrom the background.

Figure 2: Histogram of a normalization by divisionGabor Filter Normalization response image.

2.4.2 Zero-Integral Gabor Filter Normalization

Figure 3: Gabor kernel superimposed on 2 surfaces ofconstant intensity.

Illumination variation is suppressed when regionsof constant illumination generate a zero response. Inthis case, non-zero responses are strictly a result of linedetection as opposed to high pixel intensities. Figure3 shows a surface plot of a Gabor filter kernel witha size of 21x21 pixels. This filter has been generatedusing equation (1) with a bandwidth of 0.25 Octaves,a wavelength of 8 pixels, an aspect ratio of 0.75 and


an orientation of 45 degrees. The filter is superim-posed on two surfaces of constant intensity. SurfaceA represents an image of size 21x21 pixels, each ofwhich has an intensity of 0.5. Surface B represents aslightly darker image of the same size with an intensityof 0.2. If this Gabor filter were illumination invariantit would produce the same response when filtering eachsurface. It however produces a response of 1.0173 and0.4069 for surface A and B respectively. An effectivenormalization method is needed to complement thisfilter such that it is illumination invariant.

Algorithm 1 Method 1 for calculating Zero-Integral Normalized Gabor Kernel, K ′w×w

Require: Kw×w: Un-normalized Gabor kernel ofsize w × w

Ensure: K ′w×w: Zero-Integral normalized Gaborkernel of size w × w

1: sum+ve := 02: sum−ve := 03: for all pixel(x, y) in Kw×w do4: if pixel(x, y) ≥ 0 then5: sum+ve = sum+ve + pixel(x, y)6: else7: sum−ve = sum−ve + pixel(x, y)8: end if9: end for

10: for all pixel(x, y) in Kw×w do11: if pixel(x, y) ≥ 0 then12: K ′w×w(x, y) :=pixel(x, y)× sum−ve

sum+ve+sum−ve

13: else14: K ′w×w(x, y) :=pixel(x, y)× sum+ve

sum+ve+sum−ve

15: end if16: end for

The sinusoidal component of the Gabor filter thatis represented in equation (3) creates both positive andnegative responses within a filter window. An effectiveway of implementing illumination invariance is ensuringthat both the positive and negative responses sum upto zero [37]. This is tantamount to ensuring that theintegral of a Gabor filter is zero.

This study uses two algorithms for implementingzero-integral normalization. Their details are shownin Algorithms 1 and 2. The algorithms are inspired bythe implementation in [20], which is designed to workwith images that are already segmented. Algorithm 2is same as that specified in [20] while algorithm 1 is amodification thereof. The objective of both algorithmsis to ensure that a Gabor filter yields the same responsefor image windows of constant intensity.

In Algorithm 1, the proportion of positive re-sponses is used as a weight for each negative responsewhile the proportion of negative responses is used asa weight for each positive response. This ultimatelybalances the effect of positive and negative responseswhen computing the response of a pixel based on itsneighborhood. In Algorithm 2, the positive and nega-tive responses are normalized so that they both havean absolute total value of 1, resulting in a zero integral.Effectively these algorithms both work by scaling the

positive and negative responses of the Gabor kernelseparately such that the sum of all intensities in thekernel is zero. Because algorithm 2 scales the positiveand negative responses separately, it resembles theoriginal kernel more than the former. It is therefore ex-pected to yield a smoother response image. Algorithm1 on the other hand, swaps the proportions of positiveand negative intensities in the kernel. The gradient ofthe resulting kernel surface is expected to change whenit intersects with the plane of zero intensity. Althoughthis will effectively result in the loss of some visualinformation, it is likely to increase the contrast of theresponse image.

Algorithm 2 Method 2 for calculating Zero-Integral Normalized Gabor Kernel, K ′w×w

Require: Kw×w: Un-normalized Gabor kernel ofsize w × w

Ensure: K ′w×w: Zero-Integral normalized Gaborkernel of size w × w

1: sum+ve := 02: sum−ve := 03: for all pixel(x, y) in Kw×w do4: if pixel(x, y) ≥ 0 then5: sum+ve = sum+ve + pixel(x, y)6: else7: sum−ve = sum−ve + pixel(x, y)8: end if9: end for

10: for all pixel(x, y) in Kw×w do11: if pixel(x, y) ≥ 0 then

12: K ′w×w(x, y) := pixel(x,y)sum+ve

13: else14: K ′w×w(x, y) := pixel(x,y)

sum−ve

15: end if16: end for

2.4.3 Base-offset Gabor Filter Normalization

This study proposes the incorporation of base-offsetencoding to Gabor filter normalization in a bid toavert illumination inconsistency and improve vessel en-hancement in retinal images. The base-offset encodingscheme is a common loss-less compression method thatis adequate for medical images [40].

A given neighborhood in an image exhibits smooth-ness when its pixels have a high similarity with eachother. In such a case, the difference between the maxi-mum and minimum intensity in the neighborhood issmall. This property may be used to efficiently encodethe intensities by representing them based on theirrelative distance from a chosen base intensity. In thisstudy, either the median or mean of an image windowis used as the base. Effectively, this technique reducesthe importance of the actual intensity whilst empha-sizing on its relative intensity within a neighborhood.Algorithm 3 describes the proposed new method inthe case of a median offset. The algorithm accepts aninput image that has been convolved with the scaled


Gabor equation in equation (7).

g′(x, y, λ, θ, ψ, σ, γ) =√

γ2πσ2 g(x, y, λ, θ, ψ, σ, γ). (7)

The scale factor represents the inverse of the volumeunder the Gaussian surface [41] and this volume isequivalent to the sum of intensities on the surface.The scale factor therefore ensures that the integralof the Gaussian surface in the Gabor kernel windowsums up to one. The median is calculated from awindow that is cropped around a center pixel andhas the same size as the Gabor kernel. This medianis used as the base for calculating offsets within thecropped sub-image due to its low rate of informationloss during filtering. When it is computed, its valueis one of the actual intensities in an image window.The resulting filtered image is therefore likely to havea high resemblance of the original image. This is notthe case with bases such as the mean as they do notnecessarily correspond to an existing intensity in animage window. The mean yields both negative andpositive values like the median when used as a base.This is desirable due to the preservation of relativeintensity information within an image window.

Algorithm 3 Calculation of Median-offset nor-malized GFR, IMGR, of an image, Isrc

Require: Isrc: Source ImageRequire: Kw×w: Normalized Gabor kernel of

size w × wEnsure: IMGR: Median-offset normalized Gabor

filter Response image1: for all pixel(x, y) in Isrc do2: rxy := 03: Cw×w = Square sub-image of Isrc centered at

(x, y) and of width w4: mxy := Cw×w.median()5: for i := −w2 to w

2 do6: for j := −w2 to w

2 do7: offset := Isrc(x+ i, y + j)−mxy

8: rxy := rxy + (offset× Cw×w(i, j))9: end for

10: end for11: IMGR(x, y) := rxy12: end for

2.5 Vessel Segmentation

2.5.1 Valley Emphasis Thresholding (VET)

The VET method [22] is a revised version of the Otsu[27] method and is recommended for detecting defects.The VET method seeks to identify all the local mini-mum points in a histogram and determine which onemaximizes the variance between an object and its back-ground. It can be formulated as follows [22]:

t∗ = arg max0≤t<L

{(1− pt)(ω1(t)µ2

1(t) + ω2(t)µ22(t)

)}, (8)

where the probability of occurrence of a gray level isdefined as:

pt =nin

. (9)

Given an image of n pixels and L distinct gray levels,ni represents the number of pixels with the ith graylevel, where 0 ≤ i < L. A threshold t divides the graylevels of an image into two clusters C1 = {0, 1, ..., t}and C2 = {t+ 1, t+ 2, ..., L− 1}. C1 and C2 generallysymbolize the object of interest and the backgroundrespectively. The probabilities of clusters C1 and C2

are represented by ω1 and ω2 respectively in equation(10). These probabilities are calculated by summingthe probabilities of all the gray levels in a cluster.

ω1(t) =

t∑i=0

pi and ω2(t) =

L−1∑i=t+1

pi. (10)

The average gray level index3 of the clusters C1 and C2

are represented by µ1 and µ2 in equation (11). Eachgray level index, i is weighted by its probability, pi.The sum of the weighted indicies is normalized by thecorresponding cluster probability, ω1 or ω2.

µ1(t) =

t∑i=0

ipiω1(t)

and µ2(t) =

L−1∑i=t+1

ipiω2(t)

. (11)

When retinal images are effectively normalized, theresulting histograms are usually either unimodal orbimodal. In a unimodal histogram, the background istypically represented by tail while the foreground isdepicted by a prominent spike. In a bimodal histogram,the background and foreground are both representedby spikes, the latter being more prominent than thelatter. In both unimodal and bimodal histograms,the VET views the foreground and background asseparate clusters in the histogram and attempts tofind a threshold that optimally delineates them. Thisthreshold is a local minimum that lies between thedistributions of the two clusters. The most optimallocal minimum has the highest inter-cluster variance.The advantage of VET over the Otsu method is that itis capable of effectively segmenting the foreground andbackground of images with either unimodal or bimodalhistograms. Since background pixels are generally ofhigher frequency, a bimodal histogram implies a highvessel pixel count while a unimodal one correspondsto an image whose vessels are less prominent. TheVET method is therefore a viable option for automaticsegmentation. In the context of retinal image segmen-tation, the foreground is the vessel network while thebackground is the non-vascular tissue.

2.6 Segmentation Evaluation

Automated segmentation is a classification problemand hence its different possible outcomes can be illus-trated using a contingency table as shown in Table1. The ultimate goal of retinal image segmentation isto accurately partition all the pixels as either vesselor non vessel members. If a ground truth standard ismade available, it can be used to evaluate a segmenta-tion system’s accuracy. In the contingency table, the

3Gray levels are numbered from 0 to L− 1, therefore i repre-sents the gray level’s index as opposed to its value.


system’s decisions are judged against the ground truthas being either true or false. The desirable systemdecisions are true positives and true negatives as theyoccur when the system segments pixels accurately.

Ground TruthVessel↓ Non-Vessel↓

System

Verdict

Vessel→ True +ve False +veNon-Vessel→ False -ve True -ve

Table 1: Pixel classification contingency table

Let GV and GN represent the ground truth setsof all the vessel and non-vessel pixels respectively. LetSV and SN represent the sets of all pixels classified bythe system as pixels and non-pixels respectively. Thesesets are used to define sensitivity, specificity, accuracyand False Positive Rate (FPR) as shown in equations(12-15) below.

Sensitivity =|GV ∩ SV ||GV |

. (12)

Specificity =|GN ∩ SN ||GN |

. (13)

Accuracy =|GV ∩ SV |+ |GN ∩ SN |

|GV ∪GN |. (14)

FPR = 1− Specificity. (15)

These criteria are used to establish the effectivenessof the different thresholding approaches in this study.They represent the trade-off between true positive andtrue negative optimization. An effective classifier willhave both values close to one. ROC curves can alsobe used to evaluate segmentation effectiveness. Theyare a graph plot of sensitivity against the FPR in thecontext of a regulated parameter. For each value of theregulated parameter within a given range, sensitivityand the FPR are measured and plotted. An effectiveclassifier has an AUC close to one.

2.7 Data Sets

The implementation of this study is based on the pub-licly available DRIVE [23] and STARE [26] data sets.The DRIVE data set consists of 40 color retinal imagesfrom different individuals. The images are dividedequally into training and testing samples for conve-nient supervised classification experimentation. Theexperiments in this study have been performed on thetest set to enable comparison with both supervisedand unsupervised approaches as is the case in [14]. Toassist with finding the retinal Field Of View (FOV), amask which identifies the retinal area and circumfer-ence is also provided. All the images in the trainingand testing sets come with a binary classified (goldstandard) retinal image prepared by ophthalmologyexperts. This is useful for comparing computed resultsagainst those of human experts. This data set has beenused in several previous studies such as [8, 42]. It there-fore lends itself well as a benchmark for comparativeresearch.

Other studies such as [17], [18] used the STAREdata set which is older than the DRIVE data set.Additional experiments are carried out on this set tovalidate the performance of our methods on a differentcollection of images. Of the 20 images in the STAREdata set, 10 contain pathology. It is of interest toassess the effectiveness of our methods in this context.

Unlike the DRIVE data set, the STARE data setdoes not come with a mask to enable convenient isola-tion of the FOV. The interpretation of true negativeclassifications is dependent on whether all the pixelsin the entire fundus image are considered or just thosein the FOV. If the evaluation is limited to pixels in theFOV, it is expected that the true positive rate is lowerthan when evaluation is open to all pixels in entireimage. To provide consistency with our experimentson the DRIVE data set, only pixels in the FOV are con-sidered for classification evaluation in this study. Tothis end, a mask is created manually for all images inthe data set as is consistent with other studies on thiscollection such as [8]. This is achieved using the GIMPimage editor which allows images to be converted tograyscale and manually thresholded with the aid of anintensity histogram. This process was straightforwardfor all the images.

All images in the data sets are manually segmentedby 2 observers resulting in the first and second observersegmentation gold standards. The second observersegments more thinner vessels that the first. Sincethe general practice in previous studies is to use thefirst observer’s standard as the ground truth [9], thisapproach is followed in this study.

3 RESULTS AND DISCUSSION

3.1 Response Image Comparison

Figure 4(a) and 5(a) show an inverted gray scale retinalimage that exhibits several enhancement challenges.The optic disk region is visibly the darkest area in theimage. Its boundary is likely to be detected as an edgeand could eventually be segmented as a vessel. Thefovea appears as a high intensity blob in the middle ofthe image. Effective normalization should not detectthis region as a vessel as it is biologically known tohave limited vasculature [1]. Segmenting the invertedimage based on gray level thresholding is not viableas the blood vessels and the fundus background areboth of visibly varying intensity. Adaptive Gaborfiltering is therefore required to enhance vessels basedon their relative local intensity profile as opposed totheir actual gray level. In addition to the challengesstated above, the image in 5(a) contains pathology. Arobust segmentation method should not falsely detectthis pathology as vessels.

Blood vessels have stabler inter-pixel gradients dueto their consistent pigmentation. The background hasmore pronounced local intensity variation due to illumi-nation and textural inconsistency. Failure to suppressbackground inconsistency leads to increased false pos-itive segmentation. Effective comparison of retinal


image segmentation methods should therefore considerbackground suppression, illumination invariance as wellas vessel contrast enhancement.

The median-offset response image in Figure 4(e)appears to be the best at suppressing the optic diskboundary. All the approaches effectively filter the fovearegion. The normalization by division response imagein Figure 4(b) is seen to be the most affected by theoptic disk illumination. Its low contrast ensures thatit suppresses background noise effectively, albeit at theexpense of vessel enhancement. Although the zero-integral response images in Figures 4(c) and 4(d) showthe least background noise suppression, their vesselcontrast enhancement is of higher quality than that ofthe normalization by division response image. Zero-integral2 normalization shows more pronounced vesselsthan zero-integral1 normalization. This demonstratesthe effectiveness of the independent normalization ofpositive and negative kernel weights in zero-integral2normalization. Both zero-integral response imagesshow erroneous enhancement of the optic disk border.

(a) Inverted Gray Scale (b) Division

(c) Zero-Integral1 (d) Zero-Integral2

(e) Median-offset (f) Mean-offset

Figure 4: Gabor Filter Normalization on DRIVE Im-age.

The mean-offset response image in Figure 4(f) has

smoother vessel enhancement than the median-offsetresponse image. The vessels of the former are howeverthinner than those of the latter. The smoothness of themean-offset response image is as a result of the blurringeffect that results from averaging intensities. Median-offset normalization does not perform averaging but itinstead, uses actual intensities for its base. This resultsin increased vessel enhancement and optic disk bordersuppression. Figure 5 shows normalization by divisionand median offset as the most effective at suppressingpathology. The former however has poor contrast. Thechoice of wavelength or combinations thereof to usein the Gabor filter is likely to have a bearing on theeffectiveness of these normalization methods. Section3.2 investigates this issue further.

(a) Inverted Gray Scale (b) Division



Figure 5: Gabor Filter Normalization on STARE Im-age.

3.2 Automatic Thresholding

Table 2 shows the segmentation effectiveness of thefive Gabor filter normalization methods in conjunctionwith VET for specific wavelengths. Siddalingaswamyet al. [33] recommend a wavelength of 4 pixels as idealfor detecting most vessels within fundus images. Inthis study, wavelengths of 4, 8 and 12 pixels are pre-sented as wavelengths within the range [4,12] showedthe highest effectiveness in our experiments for boththick and thin vessel detection. Sensitivity reflects therate of accurate vessel detection and the median-offset


method shows the highest sensitivity in the context ofa high specificity. This is 67.81% with a correspondingspecificity of 97.9% when a wavelength of 8 pixels isused for median offset normalization.

sen

siti

vit

y

spec

ifici

ty

accu

racy

Wav

elen

gth

:4 Division 1 0 0.1332

ZeroIntegral1 0.4872 0.9801 0.9172

ZeroIntegral2 0.4982 0.9747 0.914

MedianOffset 0.5109 0.9953 0.9335

MeanOffset 0.465 0.9965 0.9275

Wav

elen

gth

:8 Division 0.9699 0.0716 0.1912

ZeroIntegral1 0.4901 0.9929 0.9286

ZeroIntegral2 0.5106 0.9916 0.93

MedianOffset 0.6781 0.979 0.9404

MeanOffset 0.612 0.9845 0.937

Wav

elen

gth

:12 Division 0.9699 0.0717 0.1913

ZeroIntegral1 0.4943 0.9916 0.928

ZeroIntegral2 0.511 0.9906 0.9293

MedianOffset 0.676 0.9714 0.9338

MeanOffset 0.627 0.979 0.935

Table 2: Segmentation effectiveness of normalizationmethods on DRIVE test data set at wavelengths of 4,8 and 12 pixels.

sen

siti

vit

y

spec

ifici

ty

accu

racy

DR

IVE

Division 0.9698 0.0712 0.1856

ZeroIntegral1 0.5014 0.9924 0.9296

ZeroIntegral2 0.5229 0.9908 0.931

MedianOffset 0.683 0.9722 0.9354

MeanOffset 0.652 0.9785 0.9365

ST

AR

E

Division 0.9698 0.0712 0.1856

ZeroIntegral1 0.5995 0.9795 0.94

ZeroIntegral2 0.6125 0.978 0.94

MedianOffset 0.6885 0.9615 0.932

MeanOffset 0.682 0.9655 0.9355

Table 3: Segmentation effectiveness of normalizationmethods on DRIVE and STARE test data set formaximum response over wavelengths: 4,8 and 12

The normalization by division method consistentlyshows low overall accuracy for all wavelengths con-sidered and hence it can be confirmed that the VETmethod does not effectively threshold its histogram asis alluded to in section 2.4.1. The other normalizationmethods show similar effectiveness with accuracy ratesof over 90% for each wavelength. The actual individ-ual wavelength used seems to have very little effecton the average accuracy and relative performance ofeach normalization method. It is however notable thatthe mean offset method has a higher accuracy than

the median offset method at a wavelength of 12 pixels.Since this wavelength is the highest of those used inthis study, it more effectively enhances thick vesselsthan the other wavelengths. As previously noted, themedian offset method yields thicker vessels that themean offset method when enhancing retinal images.At high wavelengths this enhancement may be overem-phasized and hence the median offset method has alower specificity than the mean offset method.

Table 3 shows segmentation effectiveness of thenormalization methods over a sequence of wavelengthsfor both the DRIVE and STARE data set. When eachpixel is filtered, all wavelengths within the sequenceare considered and the maximum response is recorded.The accuracy rates show a similar trend to that ofTable 2 and very little improvement is achieved. Themedian-offset method shows the highest vessel segmen-tation accuracy with a sensitivity and specificity of68.3% and 97.2% on the DRIVE data set. Similarresults are obtained on the STARE data set, namely asensitivity and specificity of 68.85% and 96.15% respec-tively. The average accuracy rates are 18.56%, 92.96%,93.1%, 93.54% and 92.87% for the normalization bydivision, zero-integral1, zero-integral2, median-offsetand mean-offset methods respectively on the DRIVEdata set. A similar trend is shown on the STARE dataset despite the existence of pathology in this data set.A notable improvement is shown in the sensitivity ofzero-integral methods. This may be attributed to thelower illumination variation in this data set.

0 0.5 10.5

0.525

0.55

0.575

0.6

0.625

0.65

0.675

0.7

0.725

0.75

0.775

0.8

0.825

0.85

0.875

0.9

0.925

0.95

0.975

1

divisive

median-offset

zero-Integral1

zero-Integral2

mean-offset

FPR

Sensiti

vity

Figure 6: ROC curves for segmentation based on nor-malization methods and manual thresholding

The ROC curves in Figure 6 show the trade-off be-tween sensitivity/true-positive rate and FPR for eachnormalization method when the image in Figure 4(a)is manually thresholded. The regulated parameter inthese ROC curves is the threshold intensity used tosegment the image. The GFR images from each nor-malization method are repeatedly thresholded usingeach gray level within the minimum and maximumintensity of the response image. For each threshold,corresponding sensitivity and FPR values are calcu-


lated and plotted on the ROC curve. All normalizationmethods record an area under the curve of at least75%. This shows that they are all viable for use inretinal image segmentation. The zero-integral methodsboth yield very smooth curves while the graphs of theother methods are angular. The angular graphs are asa result of multi-modal histograms and small responseranges.

Normalization Manual Auto MaximumDivision 18 8 110Zero1 10 16 101Zero2 7 9 72Median-offset 1 1 11Mean-offset 1 1 11

Table 4: Comparison of manual and automatic thresh-olding

(a) Gold standard (b) Division (manual threshold-ing)



Figure 7: DRIVE Image segmented through automaticthresholding.

Table 4 compares the optimal thresholds ob-tained manually against those obtained using the VETmethod for all the normalization methods considered

in this study. It also shows the maximum gray level in-tensity produced by each normalization method. In allcases the minimum was 0. The VET method predictedthe most optimal threshold for both the median-offsetand mean-offset methods. The normalization by divi-sion Gabor filter gave a maximum gray level responsevalue of 110. The VET predicted the intensity 8 insteadof 18 as the most optimal threshold. This is the high-est error margin between the manual and automaticthresholds from all the normalization methods.

Figure 7(a) shows an example of a segmentationperformed by an expert for comparison with the thresh-olded images from normalized response images. Fig-ures 7(c) and 7(d) show that the zero-integral methodsgenerally tend to produce thin vessels. This explainstheir low sensitivity rates of below 55% on the DRIVEdata set. The median-offset method seems to havemost effectively suppressed the optic disk illumina-tion. Generally all methods perform well with regardsto detecting thick vessels. There is room for moreimprovement with regards to thin vessel detection.

(a) Gold standard (b) Division (manual threshold-ing)



Figure 8: STARE Image segmented through automaticthresholding.

Figure 8 shows segmentation results for a STAREimage with pathology. Although the manually thresh-olded image from the normalization by division re-sponse image shows high pathology suppression, asignificant proportion of the vessel network is also sup-pressed. The zero-integral and mean offset methods


showed poor pathology suppression. Although themedian offset method yields an image showing littleevidence of pathology, there is room for improvementin this regard.

4 LITERATURE COMPARISON

Approach Sen

siti

vit

y(%

)

Sp

ecifi

cit

y(%

)

Accu

racy(%

)

DR

IVE

Siddalingaswamy et al.[6]

86.47 96 —

Human observer [9] 77.63 97.23 94.70Yin et al. [12] 62.52 97.10 92.67Zhang et al. [14] 71.20 97.24 93.82Niemeijer et al. [23] 68.98 96.96 94.17Chaudhuri et al. [24] — — 87.73Median-offset 68.3 97.22 93.54

ST

AR

E

Siddalingaswamy et al.[6]

85 96 —

Human observer [9] 89.51 93.84 93.48Hoover et al. [26], [9] 67.51 95.67 92.67Zhang et al. [14] 71.77 97.53 94.84Mendonca et al. [43] 69.96 97.3 94.4Median-offset 68.85 96.15 93.2

Table 5: Performance comparison of vessel segmenta-tion methods on DRIVE and STARE data sets

(a) Gray scale (b) Gold standard

(c) Median-offset (d) Siddalingaswamy

Figure 9: Comparison of median-offset and Siddalin-gaswamy et al. [6] segmentation of DRIVE image.

Table 5 compares the segmentation results from

previous studies that are based on the DRIVE andSTARE data sets. The performance of the thresholdedmedian-offset normalized Gabor filter is comparablewith previous methods. The sensitivity of the median-offset approach outperforms some of the recent studiessuch as that of Yin et al. [12] on the DRIVE data set.Performance on the STARE data set is not as compet-itive against recent studies. It is notable that althoughthe sensitivity and specificity reported by Zhang et al.[14] are higher than those of Niemeijer et al. [23], theaverage accuracy is lower. Siddalingaswamy et al. [6]report a sensitivity that is significantly higher thanthat of other approaches, including the performance ofa trained human observer on the DRIVE data set. Thisobserver’s segmentations are included in the DRIVEdata set for comparison with the performance of hu-man experts. Due to the number of previous studieson the segmentation of DRIVE and STARE images,compiling an exhaustive list in Table 5 is impractical.A comprehensive review of the segmentation results ofprevious studies can be found in [9].

(a) Gold standard (b) Median-offset

(c) Hoover (d) Li

Figure 10: Comparison of median-offset, Hoover et al.[26] and Li et al. [18] segmentation of STARE image.

Figure 9 visually compares an example segmentedimage obtained by Siddalingaswamy et al. against thatof the median-offset approach. There is very littledifference between the two output images. The medianapproach suppressed the fovea and optic disk moreeffectively resulting in fewer false positives in theseregions. Figure 10 compares the segmentation outputfrom the median offset with that of Hoover et al. and Liet al. on a STARE image. Although the former showsthe lowest pathology suppression, its detected vesselsare more prominent that those from other methods.In addition, it successfully detected the illuminationvariation around the optic disk as non-vascular tissueunlike the other methods.


5 CONCLUSION

To investigate the effect of Gabor filter normaliza-tion on retinal image segmentation, five normalizationtechniques were tested with application to the VETtechnique. All the investigated normalization methodsexcept normalization by division achieved an averageaccuracy of approximately 93% on both data sets. Themedian offset method managed to suppress illumina-tion variation in the fundus images from both data sets.Although the other normalization techniques in thisstudy achieved lower sensitivity rates, they effectivelyhandle the illumination variation in the fovea. Thisshows that normalization techniques have a bearingon the effectiveness of Gabor filter based retinal imagesegmentation.

Future work will focus on exploring the effect of nor-malization in the context of other automatic threshold-ing techniques, such as first and second order entropythresholding; and combining the different approachesto create an adaptive thresholding approach. Focuswill also be given to improving the performance onthe STARE data set such that pathology is suppressedduring classification. This study has investigated im-age enhancement using normalization in the spatialdomain; future work will also explore normalizationbased on the image frequency domain.

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