A Novel Approach for Coin Identification using Eigenvalues of Covariance Matrix, Hough Transform and Raster Scan Algorithms

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1 Iteratioal Joural of Computer, Electrical, Automatio, Cotrol ad Iformatio Egieerig Vol:, No:8, 008 A Novel Approach for Coi Idetificatio usig Eigevalues of Covariace Matrix, Hough Trasform ad Raster Sca Algorithms J. Prakash, ad K. Rajesh Iteratioal Sciece Idex, Computer ad Iformatio Egieerig Vol:, No:8, 008 waset.org/publicatio/4579 Abstract I this paper we preset a ew method for coi idetificatio. The proposed method adopts a hybrid scheme usig Eigevalues of covariace matrix, Circular Hough Trasform (CHT) ad Breseham s circle algorithm. The statistical ad geometrical properties of the small ad large Eigevalues of the covariace matrix of a set of edge pixels over a coected regio of support are explored for the purpose of circular object detectio. Sparse matrix techique is used to perform CHT. Sice sparse matrices squeeze zero elemets ad cotai oly a small umber of o-zero elemets, they provide a advatage of matrix storage space ad computatioal time. Neighborhood suppressio scheme is used to fid the valid Hough peaks. The accurate positio of the circumferece pixels is idetified usig Raster sca algorithm which uses geometrical symmetry property. After fidig circular objects, the proposed method uses the texture o the surface of the cois called texto, which are uique properties of cois, refers to the fudametal micro structure i geeric atural images. This method has bee tested o several real world images icludig coi ad o-coi images. The performace is also evaluated based o the oise withstadig capability. Keywords Circular Hough Trasform, Coi detectio, Covariace matrix, Eigevalues, Raster sca Algorithm, Texto. I. INTRODUCTION NE of the most sigificat problems i object recogitio O is to fid the importat features of a image. Successful idetificatio of the features ca be helpful i various fields icludig scietific research, idustrial ad biomedical applicatios. The detectio of circular objects from a image is oe of the basic tasks of model based computer visio. The problem of detectig circular features arises i may areas of image processig, aalysis ad object detectio. The Hough Trasform (HT) [] ad its variats [] costitute a popular method for extractig geometrical features. Over decades may researchers modified the basic HT to detect geometrical primitives more efficietly. The typical Hough based approaches to the problem of Mauscript received Aug 5, 008. J. Prakash, Research scholar, Departmet of Computer Sciece ad Egieerig, Dr. M.G.R. Uiversity, Madhuravoyal, Cheai, , Tamiladu state, Idia (phoe: ; fax: , e- mail: jogaiah_prakash@yahoo.co.i). K. Rajesh, Techology Specialist, Philips Electroic Idia Ltd., Mayata Tech Park, Nagavara, Bagalore, , Karataka state, Idia (phoe: , rajesh.air@philips.com). circular object detectio employs a edge detector ad uses edge iformatio to deduce the cetre locatios. A variety of approaches have bee suggested for detectig the circle ad estimatig the associated parameters. I particular, the Stadard Hough Trasform (SHT) method [3] is used to characterize the aalytical curves such as lies, circles ad ellipses. It is less sesitive to oise, shape discotiuities ad partial occlusios. However, it suffers the disadvatage of a massive requiremet of computatios ad memory storage ad the complexities grow expoetially with the umber of feature poits. To solve this problem may improvemets have bee suggested. Tsuji ad Matsumoto [4] decomposed the parameter space ad used the symmetric property of circles. Based o gradiet iformatio, Ballard D.H et al. [5] [6] preseted a method which simplifies the parameterizatio by derivig the circle cetre usig the coordiates ad taget of a edge pixel. Illigworth et al. [7] fids better cetre fidig process ad used Adaptive Hough Trasform (AHT) to estimate other parameters. Davis [8] used a two pass algorithm to locate a circle cetre i two -D arrays. Based o both magitude ad directio of image gradiets Michele et al. [9] detected the circular objects usig orietatio matchig. It is capable to overcome the problems arisig due to gradiet based votig schemes. Several other methods [0] [] utilize the radomized selectio of edge poits ad geometrical properties of circles, istead of usig the iformatio of edge pixels ad evidece gatherig histograms i parameter space. O the other had, some o-ht methods for circle detectio were proposed by other researchers. I particular Chu Ta Ho et al. [] proposed a simple algorithm to detect circles usig geometric symmetry properties. Peg-Yeg Yi [3] proposed a ew method for circle detector, which adopts a hybrid scheme, cosists of a Geetic Algorithm (GA) phase ad a local search phase. This method cosiderably reduces the computatio ad storage cost. Based o the statistical parameters such as Eigevalues of covariace matrix of boudary poits over a small regio of support, Du-Mig Tsai et al. [4] idetifies the corer ad circular arcs. D.S. Guru et al. [5] proposed statistical ad geometrical properties of the small Eigevalues of the covariace matrix for the purpose of straight lie idetificatio. I this method small Eigevalue aalysis is used to decide o the promiece of a pixel as a liear pixel. The same cocept alog with HT ad Raster sca Iteratioal Scholarly ad Scietific Research & Iovatio (8) scholar.waset.org/999.4/4579

2 Iteratioal Joural of Computer, Electrical, Automatio, Cotrol ad Iformatio Egieerig Vol:, No:8, 008 Iteratioal Sciece Idex, Computer ad Iformatio Egieerig Vol:, No:8, 008 waset.org/publicatio/4579 techique is utilized to extract liear, circular ad elliptical objects i images [6] [7]. From the above discussio, it is evidet that, the parametric space aalysis of Hough Trasform, statistical aalysis of edge images ad geometrical properties of objects are the three parameters used to detect the circular primitives i images. I our proposed method, we utilized the features of all the three parameters. I this paper, our problem is to detect cois from a combied image of cois ad circular objects. To distiguish the cois from geeral circular objects, we used the texture o the surface of the cois. II. PROPOSED METHODOLOGY The proposed method for detectig cois i real world images has the followig steps. Step : For the give grayscale image, fid the edge image usig suitable edge detectio operators. Step : Fid the covariace matrix for the edge image ad obtai the small ad large Eigevalues. Step 3: Obtai the CHT for Eigevalue image usig sparse matrix techique. Step 4: Fid the meaigful set of distict Hough peaks usig eighborhood suppressio scheme [8]. Step 5: Oce the cadidate peaks ad their locatios are idetified, fid ceter of the circular objects ad obtai the circumferece pixel locatios usig Breseham s Raster sca algorithm [9]. Step 6: After extractig circular objects, idetify the cois based o the texto. III. CIRCULAR OBJECT DETECTION Extractig geometrical primitives such as circles from digital image has received more attetio for several decades. The Circular Hough Trasform (CHT) idetifies the circular shape with a give radius. For ukow radii the algorithm should be ru for all possible radii to form a 3-D parameter space. I our work we used the fact that the Eigevalues of the covariace matrix characterize the shape iformatio of the geometric objects. To Fid the Eigevalues of the covariace matrix for the set of edge pixels covered by the widow w = + ± + λ a a ( a a ) 4a () a a where is the covariace matrix ad the a a coefficiets a or a is the variace ad a or a is the covariace of w. var(x) =a = ( x i x), where x = x i i= i= var(y) =a = ( y i y),where y = i= y i i= ad cov(x, y) = a = a = ( xi x)( yi y) i= From Eq. () the small ad large Eigevalues of a covariace matrix ca be expressed as = + + λ s a a ( a a ) 4a () = λ l a a ( a a ) 4a (3) I our work, we used the fact that, the small ad large Eigevalues for the circular segmet i the cotiuous domai will be equal regardless of the size ad orietatio of the circular segmet [4]. So λs λl = t f ( x, y) is a poit of a circular segmet λ = { Noisy pixel where t is the predefied threshold value. To test the characteristics of small ad large Eigevalues for a circle, a experimet has bee coducted for differet radii circles. The small ad large Eigevalues for the covariace matrix of the circles with differet widow sizes is listed i the Table I. From this we observe that the icremet of circle radius yields the decremet of the λ s ad λl values. If the rage of the desired radius is kow priori, the cetre of the circle ca be easily foud by fidig local maxima of the Hough peaks. For ukow radii, the widow size ca be varied util the correct radius is obtaied. The correctess of the coordiate poits ad the coordiates of the discotiuity regio are calculated usig the Breseham s or midpoit raster sca circle algorithms. I Breseham s algorithm, to elimiate the uequal spacig betwee poits alog the circular boudary, parametric polar form, x = x + c r cosθ ad y = yc + rsiθ is used. I midpoit algorithm [9] the circle fuctio is defied as f ( x, y) = x + y r. For uit step i ' x ' directio use a decisio parameter to determie, which of the two possible ' y ' positios is closer to the circle path. The iitial value of the decisio parameter is p 0 = 5 4 r. At each x k positio, startig at k = 0, if p k < 0, the ext poit alog the circle is ( x k +, yk ) ad p k + = p k + x k + +. ( x +, ) Otherwise the ext poit alog the circle is k yk ad p k+ = pk + xk + + yk +, where x k+ = xk + ad y k+ = yk. I the same way symmetry poits are calculated for other octats also. Iteratioal Scholarly ad Scietific Research & Iovatio (8) scholar.waset.org/999.4/4579

3 Iteratioal Joural of Computer, Electrical, Automatio, Cotrol ad Iformatio Egieerig Vol:, No:8, 008 Iteratioal Sciece Idex, Computer ad Iformatio Egieerig Vol:, No:8, 008 waset.org/publicatio/4579 TABLE I SMALL AND LARGE EIGENVALUES OF A CIRCLE x + y = Radius r Regio of support W=5x5 Regio of support W=7x7 r Regio of support W=9x9 λ s λ L λ s λ L λ s λ L IV. EXPERIMENTAL RESULTS I this sectio, we preset the results of experimet i which the proposed method is applied to several coi ad ocoi images. I the first phase, we extract the circles from the edge data. This ivolves, locatig all edge fragmets i a image ad the small Eigevalues λ s ad large Eigevalues λ L of covariace matrix costituted by the edge image. The CHT is performed for the Eigevalue image to fid the cetre ad radius of the circles which uses highest Hough peaks i the accumulator space. A circle is draw at the idetified cetre ad radius usig Breseham s algorithm. The circles extracted from the first phase correspod to both coi ad o-coi structures. I the secod phase to distiguish cois from o-cois, we use texto [0] of the cois. Sice texto as a cetre of the cluster i filter respose space [], we used k-meas clusterig [] [3] i our experimets. To describe the first phase of the proposed work, a experimet is coducted o a real world image which has oly Idia cois. Fig. (a) shows 5 paise, 50 paise, Rupee, Rupees ad 5 Rupees cois. The correspodig edge image usig cay operators is as show i Fig. (b). The CHT for the Eigevalues of the covariace matrix of edge image is as show i Fig. (c). The circles extracted for the desired Hough peaks represetig the circumferece of the cois is as show i Fig. (d). To reveal the correctess ad accuracy, the circles idetified are overlapped with origial image is as show i Fig. (e). To test the robustess of circular object idetificatio capability i our proposed approach, a experimet is coducted o a image which has circular ad o-circular cois. Fig. (a) shows 5, 50 paise ad 0, 05 rupees circular cois alog with o-circular cois. Amog o-circular cois 05 paise has square structure, 0 paise has half sie wave edged ad 0 paise has hexago structure. The edge mapped image is as show i Fig. (b). Sice the small Eigevalues λs for lie segmets is zero [4], we ca elimiate the 5 paise ad 0 paise cois from the test set easily. The large ad small Eigevalues of 0 paise are ot equal, sice it is ot represetig the either circular feature or liear feature. So it ca also be elimiated from the test set easily. The CHT with valid Hough peaks for edge image is as show i Fig. (c). The circles extracted correspod to oly circular cois from the proposed approach are as show i Fig. (d). The idetified circular cois from o-circular cois are as show i Fig. (e). From this, it is evidet that the proposed approach is very effective i idetifyig circular features. (a) (b) (c) (d) Fig. Idetificatio of circular features (a) Origial cois image (b) Edge extracted image (c) CHT image (d) Circles idetified (e) Circles overlapped with origial image (e) Iteratioal Scholarly ad Scietific Research & Iovatio (8) scholar.waset.org/999.4/4579

4 Iteratioal Joural of Computer, Electrical, Automatio, Cotrol ad Iformatio Egieerig Vol:, No:8, 008 (a) (b) (c) Iteratioal Sciece Idex, Computer ad Iformatio Egieerig Vol:, No:8, 008 waset.org/publicatio/4579 (d) Fig. Idetificatio of circular features from circular ad o-circular cois (a) Origial Image (b) Edge image (c) CHT with valid Hough peaks (d) Circles extracted (e) Circles overlapped with origial image To describe the secod phase of the proposed method ad to idetify the valid cois from a image, we coducted a experimet based o texto structure of the cois. Sice textos represet the cluster cetre i the filter respose space, we used the classical k-meas algorithm for clusterig. For experimetatio the two faces of the cois, Kig ad Quee are cosidered. A set of 5 cois with two faces each ad 3 combiatios for each coi are take ito accout. Fig. 3 represets the clustered images with k=5 for the kig face side of 5, 50 paise ad 0, 0 ad 05 rupees images. I the modellig stage, each pixel of the give image is mapped to its earest texto. Sice each texto represets the microstructure to discrimiate or recogize the smallest elemet, each pixel is labeled exactly as oe texto. Fig. 4 shows the Probability Desity Fuctio (PDF) of ormalized histogram model of the texto images. From this figure we oticed that, all texto histogram graphs of statistical models are almost same. This fact is used i our approach to distiguish coi ad o-coi i images. The PDF of the o-coi structures is as show i Fig. 5, which represets the false positive circular feature from Hough Trasform. From this, we observed that the PDFs of circular coi ad circular o-coi images are absolutely differet from each other. We ca classify the coi ad o-cois by just comparig two PDF models. For idetificatio purpose, if the miimum distace amog the PDFs of the kow cois ad the PDF of the test image is less tha a give threshold T, the it may be cosidered as a coi or o-coi otherwise. The followig equatio ca be used for idetificatio purpose. N ( H ( i) h( i) ) C = MIN ( + ) i= H ( i) h( i) (e) where H(i) ad h(i) represets the PDFs of testig ad origial coi images respectively, N deotes the umber of test classes. If C<T, the H is cosidered as PDF of the coi image. Fig. 6(a) shows the circular features idetified from the Stadard Hough Trasform method. It extracts the all the circles, but does ot distiguish the cois ad o-cois. The circular features extracted are overlapped with origial image is as show i Fig. 6(b). The circles which represet the o-cois are marked with arrows. The result of our proposed approach is as show i Fig. 6(c). It idetifies oly the circular features correspods to cois. It discards the circles of o-coi images. To test the accuracy the circles idetified are overlapped with origial image is as show i Fig. 6(d). From this, it is evidet that, the proposed techique based o texto ca idetify the cois very accurately ad also distiguishes the cois from o-coi images. Aother evaluatio is doe to test the robustess of our method agaist oise. I this evaluatio for the origial image show i Fig. 7(a), a Gaussia white oise with variace of 0.0 ad 0 % desity of salt ad pepper oise is added as show i Fig 7(b). The edge image show i Fig. 7(c) is a very complex image, sice it has cosiderable amout of oise. The best fit circles correspod to cois extracted from the proposed approach are as show i Fig. 7(d). To test the accuracy the extracted circles are overlapped with the oisy image ad origial image are as show i Fig. 7(e), 7(f) respectively. From this evaluatio, we coclude that the proposed method gives accurate circular features for cois i oise coditios also. Iteratioal Scholarly ad Scietific Research & Iovatio (8) scholar.waset.org/999.4/4579

5 Iteratioal Joural of Computer, Electrical, Automatio, Cotrol ad Iformatio Egieerig Vol:, No:8, 008 Iteratioal Sciece Idex, Computer ad Iformatio Egieerig Vol:, No:8, 008 waset.org/publicatio/4579 Fig. 4 PDFs of Coi images Fig. 3 Circular cois clustered with k=5 iteratios Fig. 5 PDF of No-Coi image (a) (b) (c) (d) Fig. 6 Cois Idetified usig Texto structures (a) Circles extracted from HT method (b) Circles overlapped wit origial image (c) Circles correspod to Cois (d) Idetified Cois Iteratioal Scholarly ad Scietific Research & Iovatio (8) scholar.waset.org/999.4/4579

6 Iteratioal Joural of Computer, Electrical, Automatio, Cotrol ad Iformatio Egieerig Vol:, No:8, 008 (a) (b) (c) Iteratioal Sciece Idex, Computer ad Iformatio Egieerig Vol:, No:8, 008 waset.org/publicatio/4579 (d) (e) (f) Fig. 7 Cois detected i oisy image (a) Origial image (b) Noisy image (c) Edge image (d) Circles detected for cois (e) Circles overlapped with oisy image (f) Circles overlapped with origial image To test the oise withstadig capability of our method, a additioal experimet is coducted usig salt ad pepper oise with differet desities. I this evaluatio the desity of salt ad pepper oise was icreased from 0 to 80 percet ad the idetificatio rate was evaluated. Results of this experimet show that the oise with less tha 34% desity has o effect o the accuracy of the coi idetificatio. Further icreasig the oise desity icreases the complexity i CHT causig the cetre ad Eigevalues of the circle chages. Hece the idetificatio rate reduces. Fig. 8 draws the idetificatio rate versus oise desity. From this it is evidet that our proposed method ca withstad oise ad is efficiet to idetify the cois up to 56 percet of oise desity. Fig. 8 Noise resistace curve V. CONCLUDING REMARKS I this paper we discussed a efficiet ad accurate method for coi detectio. The distict features of our proposed method from HT based methods are that, it is a hybrid scheme cosistig of Eigevalues approach, CHT ad Raster sca algorithms. As compared to covetioal HT methods, the mai stregths of our method are its low computatioal time, less memory requiremet ad accuracy of detectio. Sice sparse matrix techique is used for CHT, the amout of data required for circle detectio ad coi idetificatio is reduced. The proposed method also uses the texture o the surface of the cois for its idetificatio. The PDFs of cois are compared with PDFs of o-coi images to distiguish the cois from o-cois. Performace evaluatio is doe by coductig the experimets o o-coi images ad oisy images. The limitatios of our approach icludes, scalig of texto classifier ad idetificatio of spatial texture property of coi ad o-coi images. REFERENCES [] P.V.C Hough, Methods ad meas for recogizig complex patter, U.S. Patet No [] J. Illigworth ad J. Kittler, A survey of the Hough trasforms, Computer visio, Graphics ad Image processig 44, pp. 87-6, 988. [3] R.O. Duda ad P.E. Hart, Use of the Hough trasform to detect lies ad curves i pictures, CACM 5, No., pp. -5, 97. [4] S. Tsuji, F. Matsumoto, Detectio of circles/ellipses by a modified Hough trasforms, IEEE Tras. Computers., 7(8), pp , 978. [5] D. H. Ballard, Geeralizig the Hough trasforms to detect arbitrary shapes, Patter Recog., 3(), pp., 98. Iteratioal Scholarly ad Scietific Research & Iovatio (8) scholar.waset.org/999.4/4579

7 Iteratioal Joural of Computer, Electrical, Automatio, Cotrol ad Iformatio Egieerig Vol:, No:8, 008 Iteratioal Sciece Idex, Computer ad Iformatio Egieerig Vol:, No:8, 008 waset.org/publicatio/4579 [6] D.H Ballard, C. Kimme ad J. Sklasky, Fidig circles by a array of accumulators, Commu, ACM, 8(), pp. 0-, 975. [7] J. Illigworth ad J. Kittler, The adaptive Hough Trasform, IEEE Tras, PAMI-9(5), pp , 987. [8] E. R. Davis, A modified Hough scheme for geeral circle locatio,, Patter Recog,7(), pp , 988. [9] Michele Ceccarelli, Alfredo Petrosio ad Giuliao, Circle detectio based o orietatio matchig, IEEE tras. PAMI Vol 0, pp. 9-4, 00. [0] J. Illigworth, J. Kittler ad H.K Yue, Comparative study of Hough Trasform methods for circle detectio, Image visio, Comput. 8(), pp 7-77, 990. [] G. Gerig ad F. Klei, Fast cotour idetificatio through efficiet Hough Trasform ad simplest iterpretatio strategy, Proceedigs of 8 th iteratioal coferece o patter recogitio, 986, pp [] Chu-Ta Ho ad Lig-Hwei Che, A fast ellipse/circle detector usig geometric symmetry, Patter Recogitio Vol. 8, No., 995, 7-4 [3] Peg-Yeg Yi, A ew circle/ellipse detector usig geetic algorithms, Patter Recogitio Letters 0, pp , 999. [4] Du-Mig Tsai, H. T. Hou, H.J. Su, Boudary based corer detectio usig Eige values of covariace matrices, Patter. Recog. 0, pp. 3-40, 998. [5] D. S. Guru B, H. Shekar, P. Nagabhusha, A simple ad robust lie detectio algorithm based o small Eige value aalysis, Patter Recog. 5, pp. -3, 003. [6] J. Prakash ad K. Rajesh, A Novel ad Accurate method for Circular object idetificatio - combied approach of Hough trasform, Eigevalues ad Raster sca algorithms, IEEE Iteratioal coferece o Sigal ad Image processig,vol., 006, pp [7] J. Prakash, K. Rajesh, Extractig geometric primitives: Combied approach of Hough trasform, Eigevalues ad Raster sca algorithms, Iteratioal Joural of systemics, Cyberetics ad Iformatics (IJSCI), pp , 007. [8] Rafael C. Gozalez, Richard E. Woods, Digital Image processig (5 th editio), Addiso Wesley, 000 [9] Doald Hear, M. Paulie Baker, Computer graphics ( d editio), Pearso Educatio,003 [0] S.C. Zhu, C. Guo, Y. Wu ad Y.Wag, What are Textos?, ECCV, pp , Spriger Verlag, 00 [] T. Leug ad J.Malik, Represetig ad recogizig the visual appearace of materials usig three dimesioal textos, IJCV, 999. [] R.M Haralick ad L.G. Shapiro, Survey-Image segmetatio techiques, Computer Visio Graphics ad Image processig, vol.9, pp. 00-3, 985. [3] M.K. Ng, A ote o K-meas algorithm, Patter Recogitio, vol.33, pp , 000. J. Prakash received the B.E degree i Computer Sciece ad Egieerig from Mysore Uiversity, Karataka, Idia, i 989 ad the M.S degree i IT from Uiversity of Idore, Madhya Pradesh, Idia i 995. From 989 to 996 he was worked as a lecturer i the departmet of Computer Sciece ad Egieerig at Adichuchaagiri Istitute of Techology, Chikmagalur, Karataka, Idia. Sice 997 he is workig as Assistat Professor of Iformatio Sciece ad Egieerig, at Bagalore Istitute of Techology, Bagalore, Karataka, Idia. Curretly he is a PhD cadidate i the departmet of Computer Sciece ad Egieerig at Dr. MGR Educatioal ad Research Istitute, Deemed Uiversity, Cheai, Idia. His research area of iterest is Digital Sigal Processig ad Digital Image Processig with applicatios. Prof. J. Prakash is a life member of ISTE (Idia Society for Techical Educatio). K. Rajesh received the Ph.D. degree from the Departmet of Geology ad Geophysics, Idia Istitute of Techology, Kharagpur, West Begal, Idia, i 003. He is presetly with Philips Electroics Idia Ltd., Bagalore, Idia. His research iterests iclude image filter desigs, image segmetatio ad texture studies. Iteratioal Scholarly ad Scietific Research & Iovatio (8) scholar.waset.org/999.4/4579