SEGMENTATION OF RETINAL BLOOD VESSELS BASED ON ANALYSIS OF THE HESSIAN MATRIX AND CLUSTERING ALGORITHM

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1 15th European Signal Proceing Conference (EUSIPCO 7), Poznan, Poland, September 3-7, 7, copyright by EURASIP SEGMENTATION OF RETINAL BLOOD VESSELS BASED ON ANALYSIS OF THE HESSIAN MATRIX AND CLUSTERING ALGORITHM Nancy M. Salem, Sameh A. Salem, and Aoke K. Nandi Signal Proceing and Communication Group, Department of Electrical Engineering and Electronic, The Univerity of Liverpool, Brownlow Hill, L69 3GJ, Liverpool, U.K. phone: , fax: , {nancy.alem, ameh.alem, ABSTRACT In thi paper, a novel unupervied method to egment retinal blood veel from colour fundu image i propoed. A new veelne meaure i introduced which i baed on detecting veel centerline and orientation in cale pace. Baed on thi veelne meaure a generated ground truth (GGT) image i obtained by threholding and removing egment of mall ize. The egmentation i obtained by uing thi GGT image in conjunction with a RAdiu-baed Clutering Algorithm (RACAL). A dataet of image publicly available i ued to evaluate the performance of our propoed method. Experimental reult how that a true poitive rate (TPR) of 81% at fale poitive rate (FPR) of 4.5% i achieved compared with TPR of 76% at the ame FPR from the piecewie threhold probing method [1]. 1. INTRODUCTION Automated analyi of retinal image i a challenging reearch area that aim to provide automated method to help in the early detection and diagnoi of many eye dieae uch a diabetic retinopathy and age-related macular degeneration (AMD). Automated egmentation of retinal blood veel i an important tep in creening program for diabetic retinopathy [], evaluation of the retinopathy of prematurity [3], regitration of retinal image for treatment evaluation [4], generating retinal map for the diagnoi and treatment of AMD [5], or locating the optic dic [6] and the fovea. Retinal blood veel egmentation method, according to the claification method, can be divided into two group - upervied and unupervied method [7]. Unupervied method in the literature comprie the matched filter repone [1], grouping of edge pixel [5], adaptive threholding [8, 9], veel tracking [9, 1], topology adaptive nake [11], and morphology-baed technique [1]. Supervied method are the mot recent approache in veel egmentation and ue the neural network [], the K-nearet neighbour claifier [7], or the Bayeian claifier [13] for claifying image pixel a blood veel or non-blood veel pixel. Thee method depend on generating a feature vector for every pixel in the image and then uing training ample (with known clae) to deign a claifier to claify thee training ample into their correponding clae. In thi paper, we introduce an unupervied method for egmentation of retinal blood veel from colour fundu image. Blood veel centerline and orientation are ued to meaure the veelne, then by removing egment of mall ize an image that repreent blood veel i obtained, which we call generated ground truth (GGT) image. Next, a feature vector of three feature i ued in conjunction with RACAL algorithm [14] to cluter image pixel into cluter. Finally, thee cluter are claified a veel or non-veel uing the GGT image. The main advantage of our propoed method i that it i completely unupervied, o there i no need for manually labeled image which i time conuming and require an expert.. PROPOSED SEGMENTATION METHOD.1 Preproceing of Retinal Image Unupervied method for egmenting blood veel in colour fundu image ue the green channel [1, 7, 8, 15] becaue generally it ha the highet contrat between blood veel and the retinal background while the red channel i rather aturated and the blue channel i rather dark. For efficient egmentation of retinal blood veel, it i deirable to have high contrat between the retinal blood veel and retinal background whilt there hould be low contrat between retinal background and retinal abnormalitie. Combining the advantage of both channel, brightne in red channel and high contrat in green channel, reult in decreaing the contrat between the abnormalitie and the retinal background. Thi help to reduce ome repone, which do not reemble to any blood veel and that would otherwie decreae the performance of blood veel egmentation method. Hitogram matching i an approach that i ued to generate a proceed image that ha a pecified hitogram, it ha the advantage of producing more realitic looking image than thoe generating by equaliation. We ue the concept of hitogram matching to modify the hitogram of the green channel image uing that of the red channel image in order to combine the ditribution of gray-level of both image [16]. Figure 1 how the effect of thi preproceing tep uing two tet image.. Veelne Meaure Blood veel can be conidered a dark elongated or line tructure - of different diameter and orientation - on a brighter background. Our propoed veelne meaure i baed on detecting veel centerline and orientation over cale. The large eigenvalue of the Heian matrix i ued a an indicator of the veel centerline. A veel are of different diameter, then different cale are ued to calculate the eigenvalue and then keeping the maximum repone at each image pixel over cale. 7 EURASIP 48

2 15th European Signal Proceing Conference (EUSIPCO 7), Poznan, Poland, September 3-7, 7, copyright by EURASIP (a) (b) (c) (d) Figure 1: Preproceing tep for normal (top) and abnormal (bottom) image. (a) colour image, (b) red channel, (c) green channel, and (d) hitogram matched image. The appropriate local coordinate ytem in cae of line tructure i defined by the eigenvector of the Heian matrix, matrix of the econd order derivative of the intenity image L(x, y). Image derivative can be taken by convolving the image with derivative of Gauian uing the Gauian cale-pace technique [17] =1 = =3 =4 = =1 = =3 =4 =5 L x j = L(x,σ) = 1 x R e x x /σ x j πσ L(x )dx x j (1) where x j i the image coordinate with repect to which the derivative i taken. Mixed and higher order derivative are computed by taking mixed and higher order derivative of the Gauian kernel. Eigenvalue (the large eigenvalue, λ +, and the mall eigenvalue, λ, where λ + > λ ) of the Heian matrix of the intenity image L(x,y) are calculated a [18]: λ + = L xx + L yy + α λ = L xx + L yy α where L xx, L yy are the econd derivative of the intenity image in x and y direction, and α = (L xx L yy ) + 4L xy. Then, the local maximum of the large eigenvalue λ max i calculated a : λ max = max () (3) [λ + ()] (4) Figure how eigenvector correponding to large and mall eigenvalue at different cale. Orientation from the eigenvector that correpond to the mall eigenvalue how the direction of the veel, while the orientation from the eigenvector that correpond to the large eigenvalue how the direction of the large change in the intenity value (a) Figure : Eigenvector (blood veel orientation) correponding to (a) large eigenvalue, and (b) mall eigenvalue at different cale. which repreent the perpendicular direction to the veel. Veel orientation in angle, θ, are calculated from the eigenvector of the Heian matrix a: ê + = 1 L xy N L yy L xx + α (5) ê = 1 N L yy L xx + α L xy (6) θ + = tan 1 Lyy L xx + α L xy (7) θ = tan 1 L xy L yy L xx + α (8) where ê +,θ +,ê and θ are the eigenvector and θ correponding to λ +, λ and N = (L yy L xx + α) + 4L xy. What ha been oberved from our experiment i that a the cale parameter value increae o doe the apparent diameter of the detected blood veel. Thi can be clearly appreciated from Fig. 3 which diplay a ub-image and the (b) 7 EURASIP 49

3 15th European Signal Proceing Conference (EUSIPCO 7), Poznan, Poland, September 3-7, 7, copyright by EURASIP correponding ub-image containing the large eigenvalue at every pixel at ix different cale..5 blood veel non blood veel..15 ub image = 1 = = = 4 = 5 = 6 maximum over cale Figure 5: Probability denity function of the tandard deviation value of θ over cale for veel and non-veel pixel. Figure 3: The large eigenvalue for a retinal blood veel at different cale. = 1 = = 3 (a) (b) (c) Figure 6: (a) Veelne meaure, (b) GGT image, and (c) ground truth (manually labeled) for a normal(top) and abnormal (bottom) image. = 4 = 5 = 6 Figure 4: Eigenvector at different cale Direction of eigenvector correponding to the mall eigenvalue at each pixel are depicted in the ub-image for ix different cale in Fig. 4. It ha alo been oberved that the variation of the direction of the eigenvector in a pixel over ix different cale i maller for blood veel pixel compared with non-blood veel pixel. We ue the tandard deviation of orientation value over cale a a meaure of veel orientation variation over cale. At veel center, the tandard deviation of θ, angle with repect to x axi calculated from the eigenvector that correpond to mall eigenvalue λ, over cale tend toward zero, or a very mall value, compared with higher value outide blood veel. Figure 5 how the probability denity function of the tandard deviation value of θ over cale calculated for veel and non-veel pixel in a ub image. The tandard deviation of θ over cale i calculated a: θ td = td [θ ()] (9) The propoed veelne meaure V i calculated a : V = λ max θ td + ε (1) where λ max i the local maximum of the large eigenvalue over cale, θ td i the tandard deviation of the θ over cale, and ε i a mall value to avoid ingularitie. The GGT image i obtained from the veelne meaure after threholding and removing egment of ize maller than 3 pixel, thee image are hown in Fig. 6 with the manually labeled image (ground truth) by the human oberver..3 Clutering Procedure A feature vector for each image pixel i generated, then thee feature are ued to cluter image pixel to a number of nonoverlapped cluter. GGT image i ued a known label for clutered pixel in order to claify each cluter to it correponding cla (veel or non-veel). 7 EURASIP 43

4 15th European Signal Proceing Conference (EUSIPCO 7), Poznan, Poland, September 3-7, 7, copyright by EURASIP In the clutering tep we ue the RACAL algorithm [14], which i a RAdiu-baed Clutering ALgorithm (RACAL), that ue a ditance baed principle to map the ditribution of the pixel in feature pace by utiliing the premie that cluter are determined by a ditance parameter (without having to pecify the number of cluter). Simply expreed, RACAL define a normalied ditance parameter, δ o ( δ o 1), which act a the determinant of the cluter. From a given object (pixel) which i characteried by p feature, any other object that fall within δ o are regarded a belonging to the ame cluter. The control of the cluter ize i achieved through the manipulation of δ o parameter. Small value will lead to a high number of mall, tight cluter, and large value of δ o will create a maller number of larger cluter, while extremely large value will caue only one cluter to be formed. The feature vector ued with RACAL conit of colour and cale-pace feature. Baed on the property that a blood veel can be een in the colour retinal image a a dark object on a brighter background, from the three colour channel (red, green and blue) the green channel i choen to repreent thi characteritic a it ha the highet contrat between blood veel and the retinal background. The two characteriing attribute of any veel, i.e. piecewie linearity and parallel edge [19], are conidered when chooing the et of feature for every pixel in retinal image. The piecewie linear property of a blood veel can be recognied by extracting centerline of blood veel, imply by extracting the image ridge. The parallel edge property i well recognied by calculating the gradient magnitude of the image intenity. Becaue the veel are of different diameter, o thee feature are extracted at different cale and then the local maximum over cale i calculated for both feature a in Eq. 1 and 13. Feat1 = Green channel image (11) Feat = max where L = L x + L y Feat3 = max L() λ+ () (1) (13) Thee three feature were normalied to zero mean and unit tandard deviation. 3. DATASET For performance evaluation, a publicly available dataet [] conit of image which are digitized lide captured by a TopCon TRV-5 fundu camera at 35 FOV. Each lide wa digitized to produce a 65 7 pixel image, tandard RGB, 8 bit per colour channel. Every image ha been manually egmented by two oberver to produce ground truth veel egmentation. Ten of thee image contain pathology and the other ten are normal, giving a good opportunity to tet the propoed method in both normal and abnormal retina. Figure 7: Segmentation reult uing RACAL algorithm. Table 1: Clutering reult (average for image) Image FPR TPR Type % % Normal Abnormal All image RESULTS AND DISCUSSION In our experiment, each image i preproceed uing the hitogram matching to reduce the contrat between abnormalitie and the retinal background. Then the veelne meaure i ued for veel egmentation by finding the local maximum of the large eigenvalue and the tandard deviation of veel orientation at different cale value, a in Eq.1. The GGT image i obtained by threholding and removing egment of ize le than 3 pixel. In the clutering tep; the RACAL i ued with a feature vector, of three feature, to cluter image pixel to a number of non-overlapped cluter. The final egmentation i achieved by finding the correponding cla of each of the obtained cluter baed on labeled pixel from the GGT image, a hown in Fig. 7. The performance i meaured with Receiver Operating Characteritic (ROC) curve. An ROC curve plot the fale poitive rate againt the true poitive rate, and thee rate are defined in the ame way a in [1]. Reult after the clutering tep are ummaried in Table 1, while Table how egmentation reult for other method [1, 8, 9]. On average, for the image in the dataet, a TPR of 81% i achieved at FPR of 4.5% by our propoed method compared with TPR of 76% by the piecewie threhold probing method [1] at the ame FPR. It i important to note that in [1, 8], there are five parameter required for thee two algorithm, and the reported reult are for proceing all the image in the STARE dataet uing ten and eight et of value for thee parameter repectively. While in [9], a it ue a veel tracing technique o it i affected by incorrectly identified initial tracing point alo it require manually labeled image 7 EURASIP 431

5 15th European Signal Proceing Conference (EUSIPCO 7), Poznan, Poland, September 3-7, 7, copyright by EURASIP Table : Performance of veel egmentation method uing STARE image Method FPR TPR nd Human oberver Wu [9] Jiang [8] Hoover [1] propoed method for training the parameter, (one for normal and one for abnormal image). Significantly, for our propoed algorithm, we need to et one parameter only, which i the δ for the RACAL, δ =.4 i choen after ome exploratory experiment. To generate the GGT image we threhold the image reult from the propoed veelne meaure at threhold =.5. One of the main advantage of the propoed method, it i completely unupervied, o there i no need for manually labeled image, egmented by a human oberver, which i time conuming and ubject to the oberver. Reult can be enhanced by introducing a pot proceing tep to reduce number of fale poitive depending on a et of feature uch a: pixel intenity information, egment (region) ize, probability of belonging to a blood veel, and egment mean intenity. Further invetigation are under way in the potproceing tep. 5. CONCLUSIONS A novel unupervied method for retinal blood veel egmentation i propoed. Thi method i baed on a veelne meaure, which depend on veel centerline and orientation, in conjunction with RACAL algorithm. A demontrated, at 4.5% FPR, retinal blood veel have been egmented uing the propoed unupervied method with TPR of 81%, our reult can be improved when introducing a pot proceing tep to reduce fale poitive. 6. ACKNOWLEDGMENT The author would like to thank A. Hoover for making the retinal image publicly available. N.M. Salem and S.A. Salem would like to acknowledge the financial upport of the Minitry of Higher Education, Egypt, for thi reearch. REFERENCES [1] A. Hoover, V. 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