Retinal Blood Vessel Segmentation Using Gabor Wavelet and Line Operator

Transcription

1 Internatinal Jurnal f Machine Learning and Cmputing, Vl., N. 5, Octber 01 Retinal Bld Vessel Segmentatin Using Gabr Wavelet and Line Operatr Reza Kharghanian and Alireza Ahmadyfard classificatin: the grey level f the inverted green channel image and respnse f tw line detectrs t the neighbrhd f the pixel, ne perpendicular t anther. The basic line detectr has length 15 pixels which rtate at 1 different rientatins between 0 t 360 degrees. The respnse f line peratr at each pixel alng a specific angle is btained by averaging the grey level f pixels alng the line peratr. Then the largest respnse is ne f tw line features. The average grey level f line with length equal t three pixels rthgnal t the basic line detectr is used as anther line feature. A linear supprt vectr machine (SVM) [3] is emplyed as a classifier fr segmenting vessels in retinal image. In [4] a first-rder derivative filters, knwn as difference f ffset Gaussians filters (DOG filters) is used, with prevailing respnses t hrizntal, vertical, and diagnal directins. These filters are used fr the cmputatin f the lcal image gradient in a specific directin. Then each f the fur directinal images resulting frm the DOG filters is searched fr specific cmbinatins f signs t extract vessel centerline. Vessel recnstructin phase includes multiscale TpHat filtering and a binary recnstructin. The main prblem in the abve segmentatin methds is the failure fr detecting thin vessels as well as vessels in lw cntrast regins. In this paper we prpsed a methd fr classificatin f pixels in retinal image t extract vessels. We use a feature vectr cnsist f seven cmpnents: the grey level f green channel, respnse f Gabr filter bank [1] (fur scales) and the respnse f tw line peratrs. We use Gaussian mixture mdel t estimate class cnditinal density f vessels and nn-vessels. We use Bayesian classifier t classify pixels in retinal image. The rest f the paper rganized as fllws. In sectin, the prpsed methd is described. The experimental results are presented in Sectin 3. Abstract In this paper, we prpse a methd fr segmenting bld vessels frm retinal images. We extract tw sets f features fr image classificatin: features based n Gabr wavelet and line peratr. At each pixel f retinal image we cnstruct a feature vectr cnsisting f the pixel intensity, fur features frm Gabr wavelet transfrm in different scales and tw features frm rthgnal line peratrs. We cmpare the result f classificatin using tw classifiers: Bayesian and SVM. First we estimate class-cnditinal prbability density functins fr vessel and nn-vessel using Gaussian mixture mdel. Then using a Bayesian classifier we implement a fast classificatin. The result f experiments shw the cmbinatin f Gabr features and line features prvides a gd perfrmance fr vessel segmentatin. We tested the prpsed algrithm n DRIVE database which is publicly available. As the secnd classifier we emply Supprt Vectr Machine. The results shws SVM classifier in sme cases perfrms better than Bayesian classifier. Index Terms Retinal image, vessel segmentatin, Gabr wavelet, line detectr, supervised classificatin. I. INTRODUCTION Assessment f the characteristics f vessels plays an imprtant rle in a variety f medical diagnses. Fr these tasks measurements f vessel width, clr, reflectivity, trtusity and abnrmal branching are needed. Previus methds fr vessel segmentatin in images f the retina can be divided int tw grups. The first grup cnsists f rule-based methds. The secnd grup cnsists f supervised methds, which require manually labeled images fr training. Interesting results have been btained by pixel classificatin based n supervised learning. The gal f classificatin appraches is t assign each pixel t ne f tw classes, namely vessel and nn-vessel, based n sme features extracted frm the image in the neighbrhds f the cnsidered pixel. In [1], a methd based n multi-scale Gabr analysis f retinal image was prpsed. A feature vectr cnsist f five features was used fr vessel segmentatin. At each pixel the grey level f the inverted green channel and the respnse f Gabr transfrm fr fur different scales are used as features. At each scale the maximum respnse f Gabr wavelet ver II. THEORY A. Feature Extractin We describe each pixel using a feature vectr cnsist f seven features: the grey level f the inverted green channel image, the maximum Gabr transfrm respnse ver angels at fur different scales and the respnse f tw rthgnal line peratrs. different rientatins spanning frm 0 t 179 at step f 10 is calculated. Image pixels in this methd are classified using Bayesian classifier. In [], Ricci et al. use nly three features fr pixel 1) Inverted green channel The analysis f RGB cmpnents f retinal images shws the green channel has the best vessel/backgrund cntrast, whereas the red and blue channels tend t be very nisy. Therefre, the inverted green channel in which the vessels Manuscript received June 6, revised July 30, 01. The authrs are with the Electrical and rbtic engineering, Shahrd university f technlgy Shahrd, Iran ( r_kharghanian@yah.cm; ahmadyfard@shahrdut.ac.ir) /IJMLC.01.V

2 Internatinal Jurnal f Machine Learning and Cmputing, Vl., N. 5, Octber 01 appear brighter than the backgrund is used as input image t ur vessel detectin system. An iterative algrithm as prpsed in [1] is used t remve the strng cntrast between the retinal fundus and the regin utside the aperture. This imprves the undesired respnse f bth the wavelet transfrm and the line peratrs at brder f retinal disk. Fig. 1 shws the result f extending image at brder f retinal image. Fig. 1. (Left) inverted green channel f clred fundus image, (right) image with extended brder ) Gabr wavelet features Let f be an image defined n the real plane with finite energy and be the analyzing wavelet [5]. A family f wavelet can be defined by translatins, rtatins and dilatins f the analyzing wavelet. The cntinuus wavelet transfrm is defined in terms f the scalar prduct f f with the transfrmed wavelet [1], [6]: T (b, θ, a) = C C a 1 b, θ, a f ( a 1 r θ ( X b)) f ( X ) d Where C ϕ, ϕ,b, θ and a dente the nrmalizing cnstant, analyzing wavelet, the displacement vectr, the rtatin angle and the dilatin parameter (als knwn as scale) respectively. The dentes the cmplex cnjugate f. The wavelet transfrm can be easily implemented using the fast Furier transfrm algrithm and the equivalent Furier definitin f the wavelet transfrm [7]: T (b, θ, a) = C a exp( jkb) ˆ ( ar k) fˆ(k) d k () where j = 1, and the hat dentes a Furier transfrm. Since retinal bld vessels can appear in any directin, a directinal filter has been chsen t prminent vessel patterns. -D Gabr wavelet has directinal selectiveness capability f detecting riented features and fine tuning t specific frequencies [7],[6]. This latter prperty is especially imprtant in filtering ut the backgrund nise f the fundus images. The -D Gabr wavelet is defined as: θ X (1) 1 G ( X ) = exp( jk0x )exp( AX ) (3) 1 where A = diag[ ε 1], ε 1 is a diagnal matrix that defines the anistrpy f the filter, i.e., its elngatin in any desired directin. The Gabr wavelet is actually a cmplex expnential mdulated Gaussian, where k is a vectr that defines the frequency f the cmplex 0 expnential. At a specific scale the maximum mdulus f the wavelet transfrm ver all angles, frm 0 t 179 at step f 10 steps is selected: M ( b, a) = maxt (b, θ, a) (4) θ Using this prcess at each pixel fur Gabr features is prvided. Each feature is the respnse f Gabr filter in a specific scale. B. Line Operatrs At each pixel f image we extract tw features using rthgnal line peratrs. The basic line peratr is a line with length l [] centered at cnsidered pixel. At each pixel the average f image gray level alng line peratrs with 1 different rientatins spanning 360 degrees are evaluated. The directin fr which line peratr prvides the maximum gray level is selected and the crrespnding gray level is dented by L. This value is cmpared with average gray level f image, N, within a square windw centered at the pixel. The difference S = L N is used as a feature which measures the ptential f the pixel being n a vessel [8]. The secnd feature f line peratr is evaluated using gray level f the pixel neighbrhd alng the line perpendicular t the line peratr f the first feature. The secnd line has three pixels length centered at the midpint f the basic line peratr and rthgnal t it. Its average value is dented by L 0 and its strength is btained by S 0 = L 0 N. In fact fr a pixel n vessel this value must be relatively large. When a pixel is lcated n the backgrund r thin vessels with lw cntrast, feature L fr bth cases wuld be clse, but feature L 0 extracted using rthgnal line peratr can discriminates between the tw cases. L0 wuld be negligible fr pixels n backgrund while relatively large fr pixels n thin vessels. C. Feature Nrmalizatin Accrdingly each pixel f image is described by a feature vectr with seven cmpnents. In the next step we nrmalize feature vectr s that each feature has zer mean and unit 594

3 Internatinal Jurnal f Machine Learning and Cmputing, Vl., N. 5, Octber 01 standard deviatins [9]: ) vi μi vi = σ where v i is the ith feature assumed by each pixel, μ i is the average value f the ith feature, and σ i is the standard deviatin f assciated feature. Features extracted frm each image must be nrmalized separately in rder t cmpensate the inherent variatin amng images. D. Supervised Classificatin Several classifiers have been used fr classificatin f pixels in a retinal image. In [1] a Bayesian classifier in [10], [11] and [1] a K-Nearest Neighbr and in [] Supprt Vectr Machine have been used as classifiers fr pixel segmentatin. In classificatin prcess each pixel f retinal image takes ne f tw labels: vessel r nn-vessel. Bayesian and K-Nearest Neighbr require a large number f training pixels fr design f classifier. In cmpare, the training f a Supprt Vectr Machine requires less data. In this paper we used Bayesian and SVM classifiers separately t classify pixels in retinal images. Fr estimatin f class cnditinal densities fr Bayesian classifier we use Gaussian Mixture Mdel in Matlab. The SVM classifier has been implemented using SVMlight libraries [3], [13]. III. EXPERIMENTAL RESULTS A. Experimental Evaluatin We tested the prpsed methd n database DRIVE [11]. The DRIVE database cnsists f 40 images (seven f which present pathlgy), alng with manual segmentatins f the vessels. The images are captured in digital frm frm a Cann CR5 nnmydriatic 3CCD camera at 45 field f view (FOV). The images are f size pixels, eight bits per clr channel and have a FOV f apprximately 540 pixels in diameter. The 40 images have been divided int training and test set, each cntaining 0 images (the training set has three images with pathlgy). They have been manually segmented by three bservers trained by an phthalmlgist. The images in the training set were segmented nce, while images in the test set were segmented twice, resulting in sets A and B. The bservers f sets A and B prduced similar segmentatins. In set A, 1.7% f pixels where marked as vessel, against 1.3% vessel fr set B. In feature extractin step the inverted green channel f clred retinal image is used as the input image. Gabr wavelet transfrm applied in fur scales, 3, 4 and 5; furthermre, we set the ε parameter in the Gabr functin t 4, making the filter elngated and k 0 = [ 0 3], i.e., a lw-frequency cmplex expnential with few significant scillatins perpendicular t the large axis f the wavelet [1]. These tw characteristics are specially suited fr the detectin f directinal features and have been chsen in rder t enable the transfrm t present strnger respnses fr pixels assciated with the bld vessels. Basic line i (5) detectr has used with l = 15 pixels length []. In the first experiment 700,000 pixel samples were randmly chsen frm 0 labeled training images t estimate density functin f vessel and nn vessel using GMM. The number f Gaussians in the mixture set t 0. In cmpare we used nly 0,000 pixels frm the huge number f training samples fr finding the supprt vectrs in SVM classifier. In rder t evaluate hw discriminative are features in the feature vectr we designed the secnd experiment. In this experiment each classifier has been designed using three different feature vectrs. In the first set the feature vectr cntains three cmpnents: inverted green channel and the respnse f tw line peratrs. In the secnd set a feature vectr has 5 elements: inverted green channel, Gabr wavelet respnse fr 4 scales. Finally in the third set feature vectr augments the feature vectrs in tw previus cases including seven features. B. Results We tested the prpsed methd n the DRIVE database. The perfrmance has been measured based n the segmentatins f set A as grund truth. The segmentatins f set B are tested against thse f A, serving as a human bserver reference fr perfrmance cmparisn. We have selected accuracy criteria t facilitate the cmparisn with ther retinal vessel segmentatin algrithms. We define classificatin accuracy as the rati f the number f crrectly classified pixels by the ttal number f pixels in the image. Table I shws the accuracy fr different methds. In this table the prpsed methd has been cmpared with Sares et al. [1] and Ricci et al. [] methds. TABLE I: ACCURACY MEASUREMENT FOR DIFFERENT METHODS Methd ACC Min Max Avg. Sares et al.(drive) [1], GMM & K= Ricci et al.(drive) [], SVM & l = 15 Prpsed SVM & 7 features Prpsed GMM with K=0 & 7 features As the result shws the cmbinatin f Gabr features and line features imprves the perfrmance. We bserved the result f image classificatin using [1] and [] t find the reasn fr methd. In [], thse pixels lcated between tw thick vessels are misclassified as vessel while they belng t nn vessel class (Fig. ). Fig.. Misclassificatin fr pixels between thick vessels 595

4 Internatinal Jurnal f Machine Learning and Cmputing, Vl., N. 5, Octber 01 The prpsed methd in [1] fails in presence f the central reflex. This is bserved n wide vessels as a bright strip alng the center line. In Fig. 3 demnstrates this effect n segmentatin result using the methd in [1]. Fig. 4. Tw thick vessels have been jinted In sme cases bth methds in [1] and [] fail. Nne f these methds are capable t segment the ptic disk regin and thin vessels prperly. Cmbining the Gabr and line peratr features imprves the segmentatin result. In the secnd experiment we use different feature vectrs fr classificatin. Table II shws the result f this experiment. The result f vessel segmentatin fr tw images frm DRIVE database are shwn in Fig. 5. Fig. 3. Misclassificatin fr central reflex Als when tw thick vessels are clse, the methd [1] fails t separate them (shwn in Fig. 4). TABLE II: RESULT OF OUR EXPERIMENT Classifier Min Bayesian, GMM, k=0, 3features Bayesian, GMM, k=0, 5features Bayesian, GMM, k=0, 7features SVM, 3features SVM, 5features SVM, 7features 7 features: intensity + 4 Gabr utput + line peratr 5 features: intensity + 4 Gabr utput 3 features: intensity + line peratr ACC Max Avg Fig. 5. The result f segmentatin frm the left: first clumn is input images. The secnd, third and frth clumns are results f segmentatin using 3, 5 and 7 features respectively. The last clumn is manual segmentatin by specialist. Final vessel segmentatin results fr tw images frm DRIVE database alng with the grundtruth are shwn in Fig. 8. Frm the left, first clumn shws the clred image and secnd, third and frth clumns are shwn segmentatin results using 3, 5 and 7 features respectively and the last clumn is shwn the grundtruth f clred image. REFERENCES [1] [] [3] IV. CONCLUSION In this paper a methd fr segmenting vessels in the retinal image was prpsed. Frm each pixel a set f features using Gabr analysis and line peratr are extracted. Using the extracted feature vectr the classificatin was perfrmed using Bayesian and SVM classifier. Very prmising result fr vessel segmentatin was prvided. [4] [5] 596 J. V. B. Sares, J. J. G. Leandr, R. M. Cesar, Jr., H. F. Jelinek, and M.J. Cree, Retinal vessel segmentatin using the D Gabr wavelet and supervised classificatin, IEEE Trans. Med. Image., vl. 5, n. 9, pp.114 1, Sep E. Ricci and R. Perfetti, Retinal bld vessel segmentatin using line peratrs and supprt vectr classificatin, IEEE Trans. Med. Image., vl. 6, n. 10, Oct J.-P. Antine, R. Murenzi, P. Vandergheynst and S. Twareque Ali, Tw-Dimensinal Wavelets and their Relatives, Cambridge University Press, 004. J. P. Antine, P. Carette, R. Murenzi, and B. Piette, Image analysis with tw-dimensinal cntinuus wavelet transfrm, Signal Prcess.,vl. 31, pp. 41 7, Nancy M.Salem and Aske K. Nandi, Segmentatin f Retinal Bld Vessels Using Scale Space Features and K-Nearest Neighbr Classifier, IEEE Cnf 006.

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