IMAGE REPRESENTATION USING EPANECHNIKOV DENSITY FEATURE POINTS ESTIMATOR

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1 Sgnal & Iage Processng : An Internatonal Journal (SIPIJ) Vol.4, No., February 03 IMAGE REPRESENTATION USING EPANECHNIKOV DENSITY FEATURE POINTS ESTIMATOR Tranos Zuva, Kenelwe Zuva 3, Sunday O. Ojo, Selean M. Ngwra Departent of Coputer Systes Engneerng, Sosanguve Sout Capus, Sout Afrca tzuva@otal.co Faculty of Inforaton and Councaton Tecnology, Sosanguve Sout Capus, Sout Afrca 3 Departent of Coputer Scence, Unversty of Botswana, Gaborone, Botswana kzuva@yaoo.ca ABSTRACT In age retreval ost of te exstng vsual content based representaton etods are usually applcaton dependent or non robust, akng te not sutable for generc applcatons. Tese representaton etods use vsual contents suc as colour, texture, sape, sze etc. Huan age recognton s largely based on sape, tus akng t very appealng for age representaton algorts n coputer vson. In ts paper we propose a generc age representaton algort usng Epanecnkov Densty Feature Ponts Estator (EDFPE). It s nvarant to rotaton, scale and translaton. Te age densty feature ponts wtn defned rectangular rngs around te gravtatonal centre of te age are obtaned n te for of a vector. Te EDFPE s appled to te vector representaton of te age. Te Cosne Angle Dstance (CAD) algort s used to easure slarty of te ages n te database. Quanttatve evaluaton of te perforance of te syste and coparson wt oter algorts was done. K EYWORDS Iage representaton, Segentaton, Vsual content, Iage retreval. INTRODUCTION Wt vast collecton of dgtal ages on personal coputers, nsttutonal coputers and te Internet, te need to fnd a partcular age or a collecton of ages of nterest as ncreased treendously. Ts as otvated te researcers to fnd effcent, effectve and accurate algorts tat are doan ndependent for representaton, descrpton and retreval of ages of nterest. Tere ave been any algorts tat ave been developed to represent, descrbe and retreve ages usng ter vsual features suc as sape, colour and texture [], [], [3], [4], [5]. Vsual feature representaton and/or descrpton play an portant role n age classfcaton, recognton and retreval. A successful age representaton and descrpton s dependent on te selecton of sutable age features to encode and quantfcaton of tese features [4]. Sape representaton and descrpton ave been donant n researc area of age processng because sape s consdered to be te bass of uan vsual recognton [4]. Te sape representaton can be classfed as Regon based or Contour based. Te contour based tecnques use te boundary of sape to descrbe an object. It s coonly beleved tat uan bengs can dfferentate objects by ter boundares or contours []. Usually DOI : 0.5/spj

2 Sgnal & Iage Processng : An Internatonal Journal (SIPIJ) Vol.4, No., February 03 ost objects for sapes wt defned contours, akng te use of tese tecnques ost appealng. Te tecnques can generally be appled to dfferent applcaton areas wt a consderable success. Te tecnques ave a low coputaton coplexty as copared to regon based tecnques and tey are senstve to nose. Soe of te tecnques n ts group are Copactness, Eccentrcty, Sape sgnature, Hausdoff Dstance, Fourer Descrptors, Wavelet Descrptor, etc [5]. Te regon based sape representaton uses te boundary pxels and te nteror pxels of te sape. Ts group of sape representaton algorts are robust to nose, sape dstorton and tey are applcable to generc sapes [6]. Soe of te tecnques n ts group are Geoetrc oents, Legendre oents, Zernke oents, Generc Fourer Descrptor, Object representaton by te Densty Hstogra of Feature Ponts, etc [5]. In ts paper we propose an Epanecnkov Densty Feature Ponts Estator (EDFPE) representaton of an age object. Ts etod tates uan vsualzaton of age object sape and atcng slar object sapes. A coparson of retreval of slar age object sapes s done between EDFPE and DHFP representaton [7] of age object sapes.. SHAPE REPRESENTATION BY EPANECHNIKOV DENSITY FEATURE POINTS ESTIMATOR (EDFPE) Ts etod descrbes te feature ponts wtn te rectangle boundary n an age grd. Assue we ave a slouette object sape segented by soe eans suc as actve contour wtout edges [8] and let te feature ponts set P ( x, y) (ntensty functon) of te object sape be defned as P( x, y) = p ( x, y ) were =,,... n, nε Ν () We fnd te centrod of te object sape. Te followng forulae wll be used to calculate te centrod [9],[0]: x n,0 = = x c n 0,0 = () y n 0, = = y c n 0,0 = (3) were x, y ) are coordnates of age sape and,0, 0,, 0, 0 are derved fro te slouette ( oents gven by = j j x y P( x, y) x y,. (4) Te teores tat guarantee te unqueness and exstence of slouette oents can be found n [9] 76

3 Sgnal & Iage Processng : An Internatonal Journal (SIPIJ) Vol.4, No., February 03 Tus for slouette age P ( x, y), 0, 0 te oent of zero order represents te geoetrcal area of te age regon and,0, 0, oent of frst order represents te ntensty oent about te y-axs and x-axs of te age respectvely. Te centrod x, y ) geoetrcal centre of te age regon. ( c c gves te Suppose te sze of te grd occuped by te object sape s N x N. Te vector denson to represent te densty of object sape wll be N-. Fro te centrod we count te nuber of age pxels n te rngs wt defned equal wdt around te centrod. Te total nuber of pxels n eac age s gven as = ( n, n,... n ) (5) were s te nuber of rngs n eac age fro te centrod. Te EDFPE s ten appled. Te Second-order Epanecnkov Kernel Densty Estator (SEKDE) s used. Te SEKDE s gven n [] as f ( x) = k (6) = were k( u) = f < oterwse (7) were u = x Te second order Epanecnkov plug-n forula for optal bandwdt wll be as gven n (8): s o =.345 (8) 5 were s te nuber of rngs fro te centrod, s s te saple standard devaton and x s te vector eleents of te age. Te vector eleents of te age are recalculated to ake f ( x ) becoes te age representaton vector. Tus, 77

4 Sgnal & Iage Processng : An Internatonal Journal (SIPIJ) Vol.4, No., February 03 3 f ( x = ) 4 o 0 f < o oterwse (9).. To ake te deas ore clearer Suppose we ave te followng object sape features on a grd gven n fg. 0,0,0,0 3,0 4,0 0,,, 3, 4, 0,,, 3, 4, 0,3,3,3 3,3 4,3 0,4,4,4 3,4 4,4 Fgure Segented object sape Te red-bold ndcate te age pxels. Te sze of te grd occuped by te object sape s 55. It eans te vector denson to represent te densty of object sape n grd wll be 4. Te centrod calculated equatons (8) and (9) s (3, ), te centrod pxel s n blue. Te frst rectangle rng n fg. s ade up of te followng pxels (,), (3,), (4,), (4,), (4,3), (3,3), (,3), (,) and tere are seven age pxels tat consttute our frst eleent of te vector. Te vector tat represents object sape n fg. s ( 7, 7,, 0, 0), usng DHFP Rectangle rng 4 and 5 are outsde te grds so tere are represented by zeros n te vector. Te second-order Epanecnkov KDE s gven as generally: 3 3 = f ( x) 3 = 4 0 f < oterwse (0) = 3 x 4 = 0 were < oterwse Te optal bandwdt o for eac age sape s calculated usng (8). Ten we recalculate te vector eleents of te age to represent te age usng te followng 78

5 Sgnal & Iage Processng : An Internatonal Journal (SIPIJ) Vol.4, No., February 03 3 f ( x = ) 4 o 0 were < o oterwse () Te vector eleents of te age n Fgure n te exaple wll be gven as: 3. SIMILARITY MEASUREMENT ( , , , 0, 0) usng EDFPE In order to easure te slarty of te ages we used te Cosne Angle Dstance (CAD) gven n [] as s Y = cos = () Y = = Te CAD, wc s angular etrc s also called cosne coeffcent, s te noralzed nner product of two vectors because t easures te angle between tose vectors. Te cosne coeffcent as lower and upper bounds of 0 and respectvely. Ts akes t ore sutable tan Eucldean etrc to establs coparson of results produced by two dfferent age retreval etods suc as DHFP and EDFPE. 4. ACCURACY MEASUREMENT Te ost frequently and portant basc easures for nforaton retreval effectveness are precson and recall [3, 4]. Precson can be defned as te fracton of retreved tes tat are relevant to all retreved tes or te probablty gven tat an te s retreved t wll be relevant and recall as te fracton of relevant tes tat are retreved to relevant tes n te database or te probablty gven tat an te s relevant t wll retreved [3]. Tese notons can be ade clear by exanng te followng set dagra (Fgure ). Fgure ndcates te ost portant coponents of tese easureents and forulas can be derved fro te dagra. Fgure : Set Dagra sowng eleents of Precson and Recall 79

6 Sgnal & Iage Processng : An Internatonal Journal (SIPIJ) Vol.4, No., February 03 Te forulas for Precson (P) and recall (R) usng set notaton are below n 3 and 4: n P = ( AI B) n( B) (3) n R = ( AI B) n( A) (4) To te user te scalar value of recall ndcates te ablty of te syste to fnd relevant tes as per query fro te collecton of dfferent tes and precson ablty to output top ranked relevant tes as per query. In general te user s nterested n te relevant retreved tes tus te easures of precson and recall concentrate te evaluaton on te relevant output of te syste. Te lower te values ndcates bad perforance of te syste and te ger te values te ore te user s encouraged to use te syste due to te antcpaton of gettng ore of te relevant searc tes. Tese evaluaton easures are nter-dependent easures n tat as te nuber of retreved tes ncreases te precson usually decreases wle recall ncreases. We also used te bull s eye score to easure te retreval rate. Te bull s eye score n percentage s easured by te nuber of correct retrevals dvded by te nuber of relevant tes n te dataset. D B = *00 P (5) were B s a Bull s eye score n percentage, D s te total su of correct retreval and P s te total possble outcoe. Tese evaluaton tecnques were used n ts paper. 5. EPERIMENTATION Our an objectve s to ake a coparson of te representaton algorts DHFP and EDHFP n representaton and retreval of age objects. We used te cosne coeffcent Slarty n retrevng slar age objects. We created age database of soppng te age sapes. Te age objects were not rotated lossless at 90, 80 and 70 degrees tat ean degradaton of te age object occurred durng rotaton. Te query ages were captured usng dfferent caera enabled devces. Te ages objects were of dfferent densons MN or NN were M and N belong to natural nubers. Te ages tat we used were only avng one age object wt a oogeneous background. We ten segented usng Can & Vese algort [8] te age object sape by a 4545 grd. All ages were converted to gray scale ages. After segentaton te output was a bnary age object (slouette). Tey were ten represented usng EDHFPE and DHFP. Eac age was used as a query and te retreval rate was easured usng te Bull s Eye Perforance (BEP), recall and precson perforance. Matlab 7.6 was used to pleent te syste. Exaple of classes of sapes experented wt are gven n Fgure 3. In eac class tere are ten eleents wt soe tes rotated and scaled. 80

7 Sgnal & Iage Processng : An Internatonal Journal (SIPIJ) Vol.4, No., February RESULTS Fgure 3: Classes of sapes experented wt nn ts paper Fgure 4: Ten retreval results of EDFPE on left and DHFP on te rgt (query at te top left of te fgure) Fgure 5: Average precson-recall cart on Iage Retreval Fgure 4 sows te noral retreval results of te retreval syste tat te users experence. It sows EDFPE and DHFP ave a precson of 70% as a wole. If we look at dfferent recall levels t can be seen tat EDFPE perfors better tan DHFP. Fgure 5 sows te perforance easure of te retreval syste usng te recall-precson grap. Te results n fgure 4 and n fgure 5 8

8 Sgnal & Iage Processng : An Internatonal Journal (SIPIJ) Vol.4, No., February 03 sow tat EDFPE perfors better as copared wt DHFP etod. Te BEP score of for EDFPE and 9.8% for DHFP confrng te superorty of EDFPE etod. 7. SUMMARY AND CONCLUSION Fro our results we can conclude tat EDFPE etod of age object representaton was able to dfferentate slar object sapes fro dsslar object sapes just as uan bengs perceve age objects sapes. Te recall-precson grap sows te perforance of te etods at dfferent recall levels. Ts enables te users to select te best etod for dfferent stuatons. Recall and precson separately does not gve te overall pcture of perforance of a etod. Te BEP score does not also gve te overall pcture of perforance but suarses te overall perforance of te etods. We can conclude tat te EDFPE perfors better at alost every recall level and as a wole wtout lookng at te ordered perforance. We assue tat tat EDFPE s better due to te fact tat t estates te feature ponts of te age nstead of takng absolute values. REFERENCES [] M.. Rbero, et al., "Statstcal Assocaton Rules and Relevance Feedback: Power Alles to Iprove te Retreval of Medcal Iages," Proceedngs of te 9t IEEE Syposu on Coputer- Based Medcal Systes, 006. [] D. Zang and G. Lu, "Revew of sape representaton and descrpton tecnques," Pattern Recognton Socety, vol. 37, pp. -9, 004. [3] Y. L and L. Guan, "An effectve sape descrptor for te retreval of natural age collectons," n. Proceedngs of te IEEE CCECE/CCGEI, Ottawa, 006, pp [4]. Zeng, et al., "Perceptual sape-based natural age representaton and retreval," n Proceedngs of te IEEE Internatonal Conference on Seantc Coputng, 007, pp [5] Y. Mngqang, et al., "A survey of sape feature extracton tecnques," n Pattern Recognton, 008, pp [6] E. M. Celeb and A. Y. Aslandogan, "A coparatve Study of Tree Moent-Based Sape Descrptors," Proceedngs of te Internatonal Conference on Inforaton Tecnology: Codng and Coputng, 005. [7] T. Zuva, et al., "Object Sape Representaton by Kernel Densty Feature Ponts Estator," n Frst Internatonal Worksop on Sgnal and Iage Processng (SIP 0), Bangalore, Inda, 0. [8] T. F. Can and L. A. Vese, "Actve Contours Wtout Edges," IEEE, vol. 0, pp , 00. [9] J. Flusser, et al., Moents and oent nvarants n pattern recognton. West Sussex: Jon Wley & Sons Ltd., 009. [0] R. Mukundan and K. R. Raakrsnan, Moent functons n age analyss: teory and applcatons. Sngapore: World Scentc Publsng Co. Pte. Ltd., 998. [] H. Sazak and S. Snooto, "Kernel bandwdt optzaton n spke rate estaton," J Coput Neurosc, vol. 9, pp. 7-8, 00. [] S.-H. Ca, "Copreensve Survey on Dstance/Slarty Measures between Probablty Densty Functons," Internatonal Journal of Mateatcal Models and Metods n Appled Scences, vol., pp , 007. [3] C. D. Mannng, et al., Introducton to Inforaton Retreval: Cabrdge Unversty Press, 008. [4] T. Mandl, "Recent Developents n te Evaluaton of Inforaton Retreval Syste: Movng Towards Dversty and Practcal Relevance," Inforatca, vol. 3, pp. 7-38,