Retinal vessel enhancement based on multi-scale top-hattransformation and histogram fitting stretching

Miao Liao, Yu-qian Zhao n, Xiao-hong Wang, Pei-shan DaiSchool of Geosciences and Info-Physics, Central South University, Changsha 410083, China

a r t i c l e i n f o

Article history:Received 17 April 2013Received in revised form11 October 2013Accepted 14 October 2013Available online 18 November 2013

Keywords:Image enhancementMulti-scale top-hat transformationLinear stretching

a b s t r a c t

Retinal vessels play an important role in the diagnostic procedure of retinopathy. A new retinal vesselenhancement method is proposed in this paper. Firstly, the optimal bright and dim image features of anoriginal retinal image are extracted by a multi-scale top-hat transformation. Then, the retinal image isenhanced preliminarily by adding the optimal bright image features and removing the optimal dimimage features. Finally, the preliminarily enhanced image is further processed by linear stretching withhistogram Gaussian curve fitting. The experiments results on the DRIVE and STARE databases show thatthe proposed method improves the contrast and enhances the details of the retinal vessels effectively.

& 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Retinal images are widely used by the ophthalmologists fordisease diagnosis, and retinal blood vessels provide considerableinformation on pathological changes caused by many kinds ofpathologies such as Age-related Macular Degeneration, DiabeticRetinopathy, and Retinopathy of Prematurity. However, the qualityof retinal vessel image is usually poor due to the non-perfectimaging environment. The purpose of retinal vessel enhancementis to highlight the vessel structure [1–4]. The existing techniquesfor vessel enhancement include histogram equalization (HE) [5],contrast limited adaptive histogram equalization (CLAHE) [6], math-ematical morphology [7,8], Gabor filter [9,10], etc. The HE methodis one of the most popular methods for retinal image contrastenhancement, but some retinal vessel details are lost due to thedecreasing of gray levels in the enhanced image. To overcome suchweakness, the CLAHE technique is developed [11]. However, theCLAHE technique shows no obvious enhancement when thehistogram of the original retinal image is narrow. It is also easyto introduce artificial boundaries at the regions where there is anabrupt change in gray levels. Oh et al. [12] proposed a medicalimage enhancement method based on morphological filter anddifferential evolution algorithm. In this method, the correspondingtarget image must be input in advance, which restricts itsapplication to a large extent. Bai et al. [13] proposed an imageenhancement technique based on multi-scale top-hat transforma-tion. The method can enhance the image details better than some

other methods, but it does not perform well in improving theimage contrast. Fraz et al. [9] applied the 2D Gabor wavelettransformation for retinal vessel enhancement. This method candetect the retinal vessels in multiple scales and directions, butsome parameters used in it are sensitive, such as the parameters s,λ, ψ and γ.

The gray levels of retinal vessel image are centralized, and itshistogram is similar to a normal distribution. Based on thisobservation, a novel retinal vessel enhancement method by usingmulti-scale top-hat transformation and histogram fitting stretchingis proposed in this paper. Firstly, we extract the optimal bright anddim image features from the original retinal image using multi-scale top-hat transformation. Then, the retinal image is enhancedpreliminarily by adding the optimal bright image features andremoving the optimal dim image features. Finally, according tothe characteristics of the histogram of the retinal image, thepreliminarily enhanced image is processed by linear stretchingwith histogram Gaussian curve fitting. The experimental resultson the DRIVE and STARE databases show that the contrast of theretinal images can be well enhanced and the retinal vessels arehighlighted by using the proposed technique.

2. Algorithm description

2.1. Multi-scale top-hat transformation

Mathematical morphology is widely used for image processing.Most of the morphological operations are defined based ondilation and erosion. Let f ðx; yÞ be a grayscale image with the sizeof M�N, and bðu; vÞ be a structuring element, the dilation and

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n Corresponding author. Tel.: þ86 139 7580 4160.E-mail address: bme@csu.edu.cn (Y. Zhao).

Optics & Laser Technology 58 (2014) 56–62

erosion of f ðx; yÞ by bðu; vÞ, denoted by f � b andfΘb, respectively,are defined as

f � b¼maxu;v

ðf ðx�u; y�vÞþbðu; vÞÞ ð1Þ

fΘb¼minu;v

ðf ðxþu; yþvÞ�bðu; vÞÞ ð2Þ

On the basis of dilation and erosion, the opening and closing off ðx; yÞ by bðu; vÞ, denoted by f 3b and f �b, respectively, are defined,as

f 3b¼ ðfΘbÞ � b ð3Þ

f �b¼ ðf � bÞΘb ð4ÞApplying opening and closing operations, the top-hat transfor-

mations of f ðx; yÞ by bðu; vÞ are defined as

WTHðx; yÞ ¼ f � f 3b ð5Þ

BTHðx; yÞ ¼ f �b� f ð6Þwhere WTHðx; yÞ is called white top-hat transformation, which isused to extract the bright regions of the image, and BTHðx; yÞ iscalled black top-hat transformation, which is used to extract thedim regions of the image. The performance of top-hat transforma-tion mostly depends on the structuring element. To avoid theunsatisfactory enhanced result caused by the inappropriate struc-turing element, we utilize multi-scale top-hat transformation inthis paper to preliminarily enhance the retinal image.

Assume

B¼ fB0;⋯;Bi;⋯;Bng ð7Þis a structuring element sequence, where B0 is the initial selectedstructuring element, Bi ¼ B0 � B0⋯ � B0|fflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflffl}

i times

and 1r irn. The top-hat

transformations of the grayscale image f by structuring element Bi

can be defined as

WTHiðx; yÞ ¼ f � f 3Bi ð8Þ

BTHiðx; yÞ ¼ f �Bi� f ð9ÞThe optimal bright and dim image regions, denoted by f rw and

f rb, respectively, are defined as

f rw ¼ arg maxWTHiðx;yÞ

1M � N

∑M

x ¼ 1∑N

y ¼ 1WTHiðx; yÞ; 1r irn

( )ð10Þ

f rb ¼ arg maxBTHiðx;yÞ

1M � N

∑M

x ¼ 1∑N

y ¼ 1BTHiðx; yÞ; 1r irn

( )ð11Þ

The multi-scale image details, denoted by DWTHi and DBTHi,are defined as

DWTHi ¼WTHiþ1�WTHi ð12Þ

DBTHi ¼ BTHiþ1�BTHi ð13ÞSimilarly, we also defined the optimal bright and dim image

details, denoted by f dw and f db, respectively, as

f dw ¼ arg maxDWTHiðx;yÞ

1M � N

∑M

x ¼ 1∑N

y ¼ 1DWTHiðx; yÞ; 1r irn

( )ð14Þ

f db ¼ arg maxDBTHiðx;yÞ

1M � N

∑M

x ¼ 1∑N

y ¼ 1DBTHiðx; yÞ; 1r irn

( )ð15Þ

The optimal bright and dim image features, denoted by f w andf b, respectively, are defined as

f w ¼ f rwþ f dw ð16Þ

f b ¼ f rbþ f db ð17ÞThe preliminary retinal image enhancement can be achieved by

adding the optimal bright image features and removing theoptimal dim image features, as shown in the following equation:

f en ¼ f þ f w� f b ¼ f þðf rwþ f dwÞ�ðf rbþ f dbÞ ð18Þwhere f en is the preliminarily enhanced image

2.2. Histogram fitting stretching

Multi-scale top-hat transformations can effectively improve thecontrast of the thin vessels, but the contrast of the whole image is notwell improved. Our experiment below shows that the histogram ofthe preliminarily enhanced retinal image is basically in line withnormal distribution. Therefore, we can further enhance it by thelinear stretching based on Gaussian curve fitting [14], which caneffectively improve the contrast of the whole image by transformingthe grayscale range of the original image into a relatively larger range.

Fig. 1 shows the histogram of three preliminarily enhancedretinal images, where the corresponding original images are thegreen channels of three randomly chosen images from the DRIVEdatabase [15]. It can be seen that the histogram of the prelimina-rily enhanced retinal image is similar to normal distribution. Notethat the black background pixels of the preliminarily enhancedretinal images are not taken into account in Fig. 1.

The purpose of the image stretching is to improve the imagecontrast, which transforms the gray levels of the original imageinto a relatively larger range by a transformation function. If thetransformation function is a linear single-valued function, thismethod is called gray linear stretching, which can be performed by

I0 ¼ Imax

0 � Imin0

Imax� IminðI� IminÞþ Imin

0 ð19Þ

where I and I0are the gray levels before and after the gray linear

stretching, respectively, I0max and I

0min are the maximum and

minimum gray levels after the gray linear stretching, and Imax

and Imin denote the selected gray-scale range in the original imagebefore the gray linear stretching.

As the histogram of the preliminarily enhanced retinal imagesatisfies the normal distribution, in order to determine thestretched gray-scale range ½Imin; Imax�, and to get a betterenhancement result, we fit gray histogram of preliminarilyenhanced image by a Gaussian function

PðxÞ ¼ ce�ðx�aÞ2=b2 ð20Þwhere the parameter a represents the center of the normaldistribution, c is the peak, and b controls the width of the curve.In this paper, the Least Square Algorithm is used to fit the gray

0 50 100 150 200 2500

0.02

0.04

Pro

babi

lity

Gray levels

Fig. 1. The histogram of three preliminarily enhanced retinal images randomlychosen from the DRIVE database.

M. Liao et al. / Optics & Laser Technology 58 (2014) 56–62 57

histogram of the preliminarily enhanced image and to determinethe values of the parameters a, b and c. In Eq. (19), the gray levelsof the final enhanced image are set to 0 if those of the prelimi-narily enhanced image are less than the minimum value Imin, andare set to 255 if greater than the maximum Imax. The stretchedrange ½Imin; Imax� depends on the parameters a and b. According tothe minimum probability event of the normal distribution, thegray-scale range of [a�b, aþb] can cover 68% of the pixels inthe retinal images, and that of [a�2b, aþ2b] can cover 95% of thepixels, while that of [a�3b, aþ3b] can cover more than 99% ofthe pixels.

If we directly truncate and stretch the grayscale of the originalretinal images without the initial multi-scale top-hat transforma-tions, the image details and thin vessels can not be well enhanced.Furthermore, due to the gray value of most thin vessels are veryclose to the background in the original image, a simple truncationand stretching probably make the grayscale of those vessels thesame as that of the background, so as to lose many vessel details.

3. Experimental results and analysis

In this section, we test the proposed method on two publiclyavailable databases: the DRIVE [15] and STARE [16] databases. TheDRIVE database consists of 40 color retinal images, which aredivided into a training set and a testing set. Each retinal image iswith the size of 565�584 pixels and eight bits per color channel,which is captured by Canon CR5 nonmydriatic 3 charge-coupled-device (CCD) cameras at 451 field of view (FOV). The STAREdatabase, originally collected by Hoover et al. [16], contains 20color retinal images with the size of 700�605 pixels and eightbits per color channel, which are captured by a TopCon TRV-50fundus camera at 351 FOV.

Two measures [12] are used to quantify the quality of theenhanced retinal images. The first measure, denoted by C, repre-sents the contrast between the object (vessels, the ground truthvessels segmented by expert as the criterion) and the background(retinal regions except the vessels) of a retinal image, which isdefined as

C ¼ Y�GYþG

�������� ð21Þ

where, Y and G are the average gray values of the object and thebackground, respectively. The larger the value of C, the moreobvious the difference between the object and the background, i.e., the image has a high contrast.

The other measure, denoted by CII, is defined as

CII ¼ Cen

Cð22Þ

where Cen and C represent the contrast of the enhanced image andthe original image (which are calculated by Eq. (21)), respectively.The larger the value of CII, the better the image is enhanced. In thispaper, we do not consider those black background pixels outsidethe pupil while calculating the values of C and Cen.

The performance of multi-scale top-hat transformationsdepends on the structuring element B0 and the parameter n. Dueto the uncertain directions of retinal vessels, a symmetric structur-ing element should be a better one. So, we select a disk structuringelement B0 with the radius of 3. In order to determine theparameter n, 20 images in the testing set of DRIVE database areenhanced by multi-scale top-hat transformation with differentvalues of n (2rnr20). Fig. 2(a) and (b) shows the average valuesof C and CII, for the enhanced images with different values of n onthe DRIVE database, respectively. It can be seen from Fig. 2 that Cand CII increase significantly when the parameter n is from 2 to 13.Additionally, C and CII will reach maxima of 0.199 and 3.95, whenn¼14, respectively. With Matlab 7.11.0 on a Microsoft Windows XP

Fig. 3. The procedure of image enhancement by the proposed method. (a) Original image, (b) enhanced result of multi-scale top-hat transformation, and (c) enhanced resultof histogram fitting stretching from (b).

0 2 4 6 8 10 12 14 16 18 200.17

0.18

0.19

0.2

Val

ue o

f C

Value of n0 2 4 6 8 10 12 14 16 18 20

3.3

3.5

3.7

3.9

Val

ue o

f CII

Value of n0 2 4 6 8 10 12 14 16 18 20

0

30

60

90

120

Tim

e(s)

Value of n

Fig. 2. Average values of C (a) and CII (b), and computational time (c) on 20 test images in the DRIVE database with different values of n.

M. Liao et al. / Optics & Laser Technology 58 (2014) 56–6258

system (3.29 GHz CPU, 3.40 GB memory), the computing time withdifferent parameter n is shown in Fig. 2(c). It is obvious that thecomputational time increases with the increase of the parameter n,and that it increases remarkably when n412. As a compromise, wechoose n as 14 in this paper.

Fig. 3(a) is the green channel of an original retinal image whichis randomly chosen from the DRIVE database. Fig. 3(b) is thepreliminarily enhanced result of the multi-scale top-hat transfor-mation, and Fig. 3(c) is the enhanced result of the histogram fittingstretching from Fig. 3(b). Fig. 4 shows the histogram Gaussianfitting curve of Fig. 3 (b), where the horizontal axis represents thegray levels of the image, the vertical axis represents the prob-ability of gray levels, blue star-shaped dots show the actualhistogram of Fig. 3 (b), and the red solid curve is the Gaussianfitting curve. Note that the black background pixels of thepreliminarily enhanced retinal image, which are shown in Fig. 4with a large probability and with the gray levels close to 0, are notto be taken into account during the histogram fitting. The para-meters a and b are determined by the Gaussian fitting curve, anda¼96.51, b¼17.18. The stretched gray-scale range is [a�2b, aþ2b].The C values of Fig. 3(a), (b) and (c) are 0.0538, 0.1645 and 0.4731,respectively, and the CII values of Fig. 3(b) and (c) are 3.058 and8.7946, respectively. It's obvious that compared with the originalimage, the quality of the enhanced image obtained by theproposed method is greatly improved.

Fig. 5 shows the enhanced results of Fig. 3(a) with othermethods including the HE, the CLAHE, the methods in [9,12,13].

Table 1 shows the comparisons of C and CII for the enhanced imageswith different methods on Fig. 3(a). Obviously, the proposedmethod is able to achieve larger C and CII compared with the othermethods. Note that, before calculating the values of C and CII, weinvert the enhanced results of the method in [9] in order tocompare them with the results of the other methods at the samecondition, i.e. the vessels appear darker than the background.

Fig. 6 shows the enhanced results from different methods forthe other three randomly chosen retinal images from the DRIVEdatabase. The first column is the green channels. The subsequentmiddle five columns (b–f) are the enhanced results of the HE, theCLAHE and the methods in [9,12,13], respectively. The last columnis the enhanced results of the proposed method.

From the experimental results, it can be clearly seen that theHE slightly improves the image contrast, and it does not performwell for low-contrast image region. Consequently, the details ofthe image may disappear after using the HE method. The CLAHEand the methods in [9,12,13] can enhance the image details, butthe contrast of the whole image is not well improved. The valuesof C and CII of each image in Fig. 6 are shown in Table 2. From Fig. 6and Table 2, we can see that the proposed method improves thecontrast of the retinal images and enhances the low-contrast thinvessels better than other methods.

To further verify the effectiveness of the proposed method onthe lesion retinal images, the green channels of three pathologicalimages with the size of 605�700 pixels are tested, which arerandomly chosen from the STARE database. The experimentalresults are shown in Fig. 7. Compared with the other imageenhancement methods, it is easy to observe that the proposedmethod not only enhances the blood vessels of retinal image muchbetter, but also highlights the diseased areas and makes the lesionsmore prominent. Table 3 shows the C and CII values of the enhancedresults on Fig. 7. It can also be seen that our proposed methodperforms better than the other methods in terms of C and CII.

Fig. 8(a) and (b) shows the C and CII values, of differentmethods on 20 images in the testing set of the DRIVE database,respectively. The X-axis denotes the sequence number of theimages in the DRIVE database, while the last point on each curveis the average value of the corresponding method. By the sametoken, Fig. 9(a) and (b) shows the C and CII values, of differentmethods on the STARE database, respectively.

From Figs. 8 and 9, it can be clearly found that our proposedmethod is able to achieve the largest C and CII, which indicatesthat it has the advantage over the existing techniques mentioned

0 50 100 150 200 2500

0.01

0.02

0.03

0.04

0.05

gray level

prob

abili

ty

Actual histogram distribution Fitting Gaussian curve

Fig. 4. The histogram Gaussian fitting curve of Fig. 3(b).

Fig. 5. Enhanced results with different methods. (a) The HE, (b) the CLAHE, and (c–e) the methods in [9,12,13], respectively.

Table 1Comparisons of C and CII for the enhanced results with different methods on Fig. 3(a).

Evaluation measures Original image HE CLAHE Method in [9] Method in [12] Method in [13] The proposed method

C 0.0538 0.1546 0.1776 0.1066 0.1806 0.1645 0.4731CII – 2.8728 3.3003 1.9816 3.3564 3.058 8.7946

The bold values clearly show that the proposed method outperform the other methods.

M. Liao et al. / Optics & Laser Technology 58 (2014) 56–62 59

Table 2Comparisons of C and CII for the enhanced results with different methods on Fig. 6.

Image Evaluation measures Original image HE CLAHE Method in [9] Method in [12] Method in [13] The proposed method

1st in Column (a) C 0.0508 0.1509 0.1481 0.0660 0.2085 0.1599 0.4144CII – 2.9708 2.9169 1.2989 4.1052 3.1496 8.1599

2nd in Column (a) C 0.0509 0.1134 0.1493 0.0742 0.2236 0.1733 0.3502CII – 2.2304 2.9362 1.4588 4.3977 3.4335 6.8865

3rd in Column (a) C 0.0567 0.0796 0.2042 0.1135 0.1641 0.2826 0.3591CII – 1.4042 3.6009 2.0011 2.8929 4.9832 6.3317

The bold values clearly show that the proposed method outperform the other methods.

Fig. 7. Experimental results comparison with different methods on the STARE database. The first column is the green channels of the original retinal images. Columns (b–f)are the enhanced results of the HE, the CLAHE and the methods in [9,12,13], respectively. The last column is the enhanced results of the proposed method.

Fig. 6. Experimental results comparison with different methods on the DRIVE database. The first column is the green channel of the original retinal images. Columns (b–f)are the enhanced results of the HE, the CLAHE and the methods in [9,12,13], respectively. The last column is the enhanced results of the proposed method.

M. Liao et al. / Optics & Laser Technology 58 (2014) 56–6260

above on improving the image contrast and highlighting retinalvessel characteristics for both normal and lesion retinal images.

4. Conclusions

In this paper, a retinal vessel enhancement method based onmulti-scale top-hat transformation and the histogram fitting stretch-ing is presented. The retinal image is preliminarily enhanced by themulti-scale top-hat transformation. Then, according to the character-istics of the histogram of the retinal image, the preliminarilyenhanced image is further processed by linear stretching withhistogram Gaussian curve fitting. The proposed method is testedon the DRIVE and STARE databases, where we select 20 retinal

images from each of the database. The average values of the contrastC of the enhanced images on the DRIVE and STARE databases reach0.3887 and 0.2214 with the corresponding CII of 7.1337 and 3.8771,respectively. Both C and CII of the proposed method are significantlylarger than those of the existing techniques mentioned in this paper.The experimental results show that, compared with the othertechniques, the proposed method achieves a much better perfor-mance on improving the contrast of the retinal vessel images.

Acknowledgments

This work is supported by the National Natural Science Foundationof China (Grant nos. 61172184, 61379107 and 81171420), Hunan

Table 3Comparisons of C and CII for the enhanced results with different methods on Fig. 7.

Image Evaluation measures Original image HE CLAHE Method in [9] Method in [12] Method in [13] The proposed method

1st in Column (a) C 0.1196 0.2159 0.1844 0.095 0.2458 0.2183 0.4478CII – 1.8057 1.5421 0.7948 2.0552 1.8252 3.7451

2nd in Column (a) C 0.1222 0.2640 0.2601 0.1066 0.2762 0.2603 0.5795CII – 2.1606 2.1284 0.8726 2.2606 2.1304 4.7423

3rd in Column (a) C 0.0904 0.1704 0.2169 0.1126 0.2792 0.2264 0.3998CII – 1.8865 2.4008 1.2462 3.0898 2.5055 4.4255

The bold values clearly show that the proposed method outperform the other methods.

Fig. 8. Comparison of C and CII values among different methods on the DRIVE database: (a) C value, and (b) CII value. The last point on each curve is the average value of thecorresponding method.

Fig. 9. Comparison of C and CII values among different methods on the STARE database: (a) C value, and (b) CII value. The last point on each curve is the average value of thecorresponding method.

M. Liao et al. / Optics & Laser Technology 58 (2014) 56–62 61

Provincial Natural Science Foundation of China (Grant no. 12JJ6062),Program for New Century Excellent Talents in University of EducationMinistry in China (Grant no. NCET-13-0603), Specialized ResearchFund for the Doctoral Program of Higher Education in China (Grant no.20130162110016), and China Postdoctoral Science Foundation(2012M521554).

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