Journal of Theoretical and Applied Information Technology.

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1 JATIT. All rghts reserved. FULLY SCALE AND IN-PLANE INVARIANT SYNTHETIC DISCRIMINANT FUNCTION BANDPASS DIFFERENCE OF GAUSSIAN COMPOSITE FILTER FOR OBJECT RECOGNITION AND DETECTION IN STILL IMAGES Saad Rehman, Rpert Yong, Phl Brch, Chrs Chatwn, Ioanns Kypraos Lasers and Optcs Research Grop Unversty of Ssse Brghton,UK Emal : S.Rehman@sssex.ac.k ABSTRACT A dffclt pattern recognton problem s to recognze objects despte dstortons n poston, orentaton and scale n clttered backgronds. A system capable of detectng target objects despte any knd of geometrcal dstorton has many potental applcatons snce t wll be able to detect target objects when the orentaton and poston of the target or camera s nknown. In ths work we report the se of flly nvarant correlaton flters for object detecton n stll mages despte any knd of geometrcal dstorton of the target object. A mappng technqe s combned wth a bandpass dfference of gassan composte correlaton flter, capable of creatng nvarance to varos types of dstorton of the target object. Keywords: Object Recognton, Random geometrcal dstorton, flly nvarant correlaton flters, mappng technqe, gassan composte correlaton flter 1. INTRODUCTION Synthetc Dscrmnaton Fncton (SDF) based technqes provde a solton to the problem of nvarant correlaton flter desgn, expected dstortons beng nclded n the flter desgn. A log r-theta mappng can be appled to the npt mage to gve nvarance to n-plane rotaton and scale by transformng rotaton and scale varatons of the target object nto vertcal and horzontal shfts[7,8]. The SDF flter s then traned sng the log-mapped mage. A Dfference of Gassan band pass flter s added n the desgn of the flter to provde edge enhancement of the npt mages and so obtan sharper correlaton peaks. Areas prodcng a strong correlaton response can then sed to determne the poston, n-plane rotaton and scale of the target objects n the scene. Log-polar mappng as a pre-processng operaton for correlaton flters may offer the capablty to extend the range of dstortons over whch correlaton flters can detect and recognse a target object, possbly also contaned n a hghly clttered envronment. In ths paper we smmarse the logpolar pre-processng operaton and dscss methods of mltplexng correlaton flters to accommodate orentaton changes of the target object. We show that a log-polar pre-processed approprately desgned mltplexed correlaton flter s able to detect and recognse a target object from a hghly clttered envronment, althogh the correlaton response s not deal de to lmtatons, n the crrent mplementaton, of the cltter model employed. A set of tranng mages of a Jagar model car were constrcted, n whch each mage dffered by 5 degrees n orentaton angle. Ths a total of 7 mages were constrcted to cover the whole range to 360 degrees.. LOGMAP PRE-PROCESSING To detect and recognze[1-3] target objects n a scene despte dfferences n scale or n-plane rotaton to the target reference mages, a log r-θ mappng, or logmap, can be employed [4-9]. The strctre of the sensor s based on a Weman polar exponental grd [10-13] and conssts of concentrc crcles of pxels whch are exponentally spaced and ncrease n sze from the centre to the edge. Each sensor pxel on the crclar regon of the x-y Cartesan space s mapped nto a rectanglar regon n polar mage space r-θ. The sensor s geometry maps concentrc crcles n the Cartesan space nto vertcal lnes n the polar space and radal lnes n the Cartesan space nto horzontal lnes n the polar space. The log-polar mappng s not shft 3

2 JATIT. All rghts reserved. nvarant, so the propertes descrbed above hold only f they are wth respect to the orgn of the Cartesan mage space. The complex logarthmc mappng can be descrbed as [10]: w = log z (1) By applyng the complex form notaton: z = x + y () where r = x + y and y θ = arctan, we x have w = log r + θ = + v (3) where = log r and v = θ. Hence, an mage n the z-plane wth co-ordnates x and y s mapped to the w-plane wth co-ordnates and v. The mapped mage from the Cartesan space (z-plane) n to the Polar space (w-plane) s referred to as the log-polar mappng or the logmap. Ths process can be reversed to prodce the nverse mappng from Polar space (w-plane) to Cartesan space (z-plane). Complex log-polar mappng s shown n fgre 1..1 In-Plane Invarance If an mage s rotated by an angle φ abot the orgn, then [10]: z = r e (4) ( θ +φ ) Fgre 1 Complex log-polar mappng Ths, w = log r + θ + φ = + v + (5) φ z = r α e θ (6) Ths, In effect, rotatng the mage by the angle φ has reslted n a vertcal shft n the mapped mage by the rotaton angle.. Scale Invarance If the mage n the z-plane s scaled by a factor α, then [10]: w = log r + log α + θ = + log α + v (7) In effect, scalng the mage by the factor α has reslted n a horzontal shft n the mapped mage by the scalng factor. 33

3 JATIT. All rghts reserved. 3. INVERSE MAPPING The nverse mappng can be shown n the w followng way. Snce we know that z = e and w = + v, combnng the two eqatons we get [10-13]: z = (8) + v e Expandng the eqaton (8): z = e [cos( v) + sn( v)] (9) As we know from the Eq () that eqaton (9) ths becomes: e [cos( v) + sn( v)] = x + y (10) Eqaton (10) mples that: x = e (11) y = e (1) cos(v) sn(v) We also know that: r = + (13) [ x y z = x + y, the 4. DIFFERENCE OF GAUSSIAN BAND PASS The Dfference of Gassan (DOG) fncton s a readly compted crclar symmetrc wavelet whch approxmates the Maxcan hat wavelet. DOG bandpass flters an mage and performs the edge enhancement operaton on the objects present n the mage[19]. The DOG fncton s defned as the dfference of two dfferently scaled Gassan fnctons, g (, where = 1,. 1 g = πσ (16) x + y.exp(. π. σ ( Therefore the DOG fncton s gven by g( = g1( g ( (17) that s: 1 x + y 1 x + y g( = exp[ ] exp[ ] πσ1 πσ1 πσ1 πσ (18) where ( σ 1σ ) represents the standard devatons of the two Gassan fnctons. The freqency doman representaton of the DOG fncton s gven below as: G (, v) = exp[. π. σ1.( + v )] exp[. π. σ.( + v )] (19) ) Pttng the vales of eqaton (11) and (1) n eqaton (13) we get r = (14) [ e cos( v)] + [ e sn( v )] Eqaton (14) mples that = log r and smlarly: e θ = arctan e (15) sn( v) = v v cos( ) Fgre Fltered mage wth standard devaton of rato 1.6 and Bandpass set at 0.35 S ) ( f The scalng of the band pass s crtcal. The vale of the band pass maxmm freqency response shold be chosen to gve the best compromse between ntra-class dstorton tolerance and nterclass dscrmnaton of the resltng flter.. The low freqences mst be redced to enhance the dscrmnaton ablty of the flter. The hgher 34

4 JATIT. All rghts reserved. freqences mst be redced enogh to gve adeqate target dstorton tolerance. The precse choce for the band pass locaton, wll ths depend on the trade-off desred between these two conflctng reqrements. The best performance of the DOG flter occrs at ts closest approxmaton to the Mexcan hat wavelet when the rato of σ 1 to σ s 1.6 [19]. Fgre shows a DOG fltered jagar car mage at 1.6 rato of standard devaton vales and the bandpass set at 0.35 of the maxmm samplng freqency ( S f ). Gray backgrond n fgre s at zero ntensty n order to show the negatve vales n the mage as darker regons. 5. SYNTHETIC DISCRIMINATION FUNCTION In the SDF [14-16,18] desgn method, the expected object dstortons are nclded n the correlaton flter by mltplexng the weghted versons of the target object nto a composte mage. The resltng correlaton otpts at the orgn of these crosscorrelatons are constraned to be the same and are eqal to a pre-specfed constant. Let h( denote the composte mage and t ( denote the tranng mage set where = 1,,...,N and N s the nmber of the tranng mages sed n the synthess of the SDF. Then the vale at the orgn of the correlaton plane between the composte mage and each of the tranng mages s assmed to be eqal to a constant c. Ths: * h(. t ( = t ( h ( dxdy (0) The composte mage s assmed to be a lnear combnaton of the N tranng mages: h = a t ( + a t ( a t ( ) ( 1 1 N N y N = = (1) 1 a t ( y ) where the coeffcents a ( = 1,,..., N) are determned to satsfy the constrant c. By sbstttng eqaton (1) nto (0) we have: N = 1 () a * Where R j = c * Rj = t( t j ( dxdy (3) Fgre 3 Examples of tranng mages Fgre 3 shows some of the tranng mages sed n the developed system. The composte mage s constrcted by sng the mages of the Jagar car rotated at 0,10,15,0,5 and 30 degrees. The resltng composte mage s shown n Fgre 4. Fgre 4 (a) Composte Image (b) Logmap of Composte 6. PERFORMANCE METRICS To measre the performance of the correlaton flters some basc measres have to be calclated. The basc performance measre s correlaton otpt peak ntensty (COPI). It sgnfes the maxmm ntensty vale of the correlaton otpt plane. It s defned as [0]: COPI = max{ C( y (4) where C( s the otpt correlaton ampltde vale at (. A flter wth hgh COPI shows good performance and a hgh detecton ablty. Another mportant performance measre s Peak-tocorrelaton energy measre (PCE). The bass of the PCE s that the COPI shold be as hgh as possble whle at the same tme the over all correlaton } 35

5 plane energy shold be as low as possble. It s defned as [0]: COPI PCE = Energy c (5) Where Energyc s the total correlaton plane energy and s defned as: JATIT. All rghts reserved. Energy c (6) = C( 7. DEPENDENCE OF FREQUENCIES ON STANDARD DEVIATION The flterng operaton performed by the DOG flter can be controlled by the standard devatons. The pass band of freqences can be altered by changng the standard devaton n the DOG constrcton whlst keepng rato of 1.6. Ths n tern translates to dfferent peak wdths n the correlaton plane. In the reslts that follow, composte mage remans the same, target mage s the car mage ot-of-plane rotated at 30 degrees. Fgre 6 Correlaton plane for standard devaton rato of 1.6, bandpass set at 0.46S f and COPI = 6.5*10-6, PCE = 0.30 Fgre 5 Correlaton plane for standard devaton rato of 1.6, bandpass set at 0.35S f and COPI = 1.1*10-5, PCE = 0. Fgre 7 Correlaton plane for standard devaton rato of 1.6, bandpass set at 0.58S f and COPI = 1.64*10-6, PCE = IN-PLANE ROTATIONAL INVARIANCE OF THE BANDPASS SDF In ths secton we dscss the reslts of the n-plane rotatonal nvarance of the SDF flter. Composte mage remans the same. The n-plane rotated mages employed are shown n Fgre 8. All the smlaton reslts are obtaned sng the standard devaton rato of 1.6 wth bandpass set at 0.35S f. 36

6 JATIT. All rghts reserved. Fgre 8 (a) 10 degrees n-plane rotaton (b) 70 degrees n-plane rotaton (c) 100 degrees n-plane rotaton (d) 150 degrees n-plane rotaton (e) -70 degrees n-plane rotaton Fgre 10 Correlaton plane for 70 degrees nplane rotaton, COPI = 4.9*10-6, PCE = 0.7 The correlaton planes generated by the rotated mages are shown n fgre 9 to fgre 13. Fgre 9 Correlaton plane for 10 degrees n-plane rotaton, COPI = 1.*10-5, PCE = 0.4 Fgre 11 Correlaton plane for 100 degrees nplane rotaton, COPI = 6.48*10-6, PCE =

7 JATIT. All rghts reserved. In the reslts shown n fgres 9-13 t s apparent that the correlaton peaks move across the correlaton plane as the rotatonal angle s changed, n lnear proporton. Ths by combnng the nplane rotaton nvarance of the logmap and the dstorton nvarance of a band pass SDF flter, a rotaton and dstorton nvarant SDF flter can be realsed for object recognton. 9. OUT-OF-PLANE INVARIANCE OF THE BANDPASS SDF In ths secton the ot-of-plane nvarance of the SDF flter s tested. The composte mage remans the same. We ntrodce a nmber of test mages wthot backgrond nose whch are rotated and scaled for the detecton of the car. The test mages are shown n fgre 14. The correlaton planes for the above test mages are shown below n fgres All the smlaton reslts are obtaned sng the standard devaton rato of 1.6 and bandpass set at 0.35 S f. Fgre 1 Correlaton plane for 150 degrees nplane rotaton, COPI = 5.34*10-5, PCE =0.8 Fgre 14 (a) Test Image car rotated at 355 degrees (b) Test Image car rotated at 195 degrees (c) Test mage car rotated 30 degrees and scaled at 90% Fgre 13 Correlaton plane for -70 degrees nplane rotaton, COPI = 1.039*10-5, PCE =

8 JATIT. All rghts reserved. Fgre 15 Correlaton plane for 30 degrees ot-ofplane rotated and 90% scaled car, COPI = 1.38*10-5, PCE = 0.1 Fgre 17 Correlaton plane for 355 degrees otof-plane rotated car, COPI = 1.853*10-5, PCE = 0.6 It can be seen from fgres 15 to 17 that as the otof-plane rotatonal angle ncreases, the peak heght decreases. Snce there s no backgrond nose the correlaton otpt plane shows mnmal dsrpton. The correlaton peaks are localsed de to the nclson of the dfference of Gassan band pass n the flter desgn. The composte reference mage accomodates the ot-of-plane rotaton of the car allowng mantenance of the correlaton peak heght over the swathe of angles covered wthn the composte mage. The correlaton plane correspondng to fgre 16 s shown n fgre 17. Let s combne all the three dstortons and test the fll nvarance of the bandpass SDF flter. Sppose that the mage of a car wth an ot-of-plane rotaton of 30 degrees, reszed at 85% of the orgnal mage and fnally n-plane rotated at 30 degrees. The correlaton plane for the above smlaton s shown n fgre 18. Fgre 16 Correlaton plane for 195 degrees otof-plane rotated car, COPI = 1.19*10-5, PCE =0. 39

9 JATIT. All rghts reserved. Fgre 18 Correlaton plane for car mage wth 30 degrees ot-of-plane rotaton, 85% sezed and 30 degrees n-plane rotated, bandpass set at 0.35 Sf and COPI = 1.113*10-5, PCE = 0.5 It can be seen that the performance of the flter decreased as all the dstortons were combned. However, the bandpass SDF flter was stll able to detect the car. 10. BACKGROUND CLUTTER TOLERANCE In ths secton the backgrond cltter tolerance of the DOG-SDF flter s assessed. Fgre 19 shows a scene where a 35 degrees ot-of-plane rotated car s sper mposed. Ths car s reszed to 85% of the orgnal sze and 5 degrees n-plane rotated. Fgre 0 Correlaton plane for car mage wth 35 degrees ot-of-plane rotaton, 5degrees n-plane and 85% reszed, bandpass set at 0.35 S f and COPI =.013*10-5, PCE = 0. Althogh the car was detected n the presence of the cltter, sgnfcant degradaton of the correlaton plane backgrond s clear. 11. CONCLUSION The reslts presented ndcate that the DOG band pass SDF flter was able to detect the rotated and scaled car, when sed n conjncton wth a logmap pre-processng operaton. The dsrpton present n the log-mapped mages ncreased sgnfcantly when scalng and n-plane rotatng the reference mage de to fnte samplng. In order to redce the dsrpton, nterpolaton was adopted for smooth renderng of the mages whch redced the dsrpton bt dd not elmnate t. Methods to frther redce the effects of fnte samplng wll be nvestgated n ftre work n order to redce ts mpact. REFERENCES [1] Rchard O.Dda, Peter E. Hart, Davd G. Stork, Pattern Classfcaton, John Wley & Sons, nd Edton. Fgre 19 Target car 35 degrees ot-of-plane rotated, 5 degrees n-plane and 85% reszed spermposed on an mage scene [] D. Casasent and D. Psalts, Poston, rotaton, and scale nvarant optcal correlaton, 40

10 JATIT. All rghts reserved. Appled Optcs Vol. 15, No. 7, (1976) [3] K. Merserea and G. Morrs, Scale, rotaton, and shft nvarant mage recognton, Appled Optcs Vol. 5, No. 14, (1986) [4] Weman, C.F.R., and Chakn, G., Logarthmc spral grds for mage processng and dsplay, Compter Graphcs and Image Processng Vol. 11, (1979) [5] Sandn, G., and Daro, P., Actve vson based on space-varant sensng, n: 5th Internatonal symposm on Robotcs Research, (1989) [6] Schwartz, E.L., Greve D., and Bonmasser, G., Space-varant actve vson: defnton, overvew and examples, Neral Networks, Vol. 8, No. 7/8, (1995) [7] P.Bone, R. C. D. Yong, C. Chatwn, Poston-, rotaton-, scale- and orentatonnvarant mltple object recognton from clttered scenes, Optcal Engneerng, Vol. 45, No. 7, to 8, (Jly 006) [8] P.Bone, I.Kypraos, R.C.D.Yong. C.R. Chatwn, Flly nvarant object recognton n clttered scenes, Invted paper, Proc. SPIE, Informaton Technologes, Edtors: A. Andresh, V. Perj, Chsna, Moldova, May 004. [9] Shlp Goyal, Naveen K. Nshchal, Vnod K. Ber, and Arn K. Gpta, Waveletmodfed maxmm average correlaton heght flter for rotaton nvarance that ses chrp encodng n a hybrd dgtal optcal correlator, Appled Optcs, Vol. 45, No. 0, 10 Jly 006. [10] Weman, C.F.R., 3-D sensng wth polar exponental sensor arrays, n: Dgtal and Optcal Shape Representaton and Pattern Recognton, Proc. SPIE Conf. on Pattern Recognton and Sgnal Processng, Vol. 938, (1988) [11] Weman, C.F.R., Exponental sensor array geometry and smlaton, n: Dgtal and Optcal Shape Representaton and Pattern Recognton, Proc. SPIE Conf. on Pattern Recognton and Sgnal Processng, Vol. 938, (1988) [1] C-G. Ho, R.C.D. Yong, C.R. Chatwn, Sensor Geometry and Samplng Methods for Space-Varant Image Processng, Jornal of Pattern Analyss and Applcatons, Vol. 5, , (00) [13] Weman, C.F.R., and Chakn, G., Logarthmc spral grds for mage processng and dsplay, Compter Graphcs and Image Processng Vol. 11, (1979) [14] H. J. Calfeld and W. Maloney, Improved dscrmnaton n optcal character recognton, Appled Optcs, Vol. 8, No. 11, (1969) [15] C. F. Hester and D. Casasent, Mltvarant technqe for mltclass pattern recognton, Appled Optcs, Vol. 19, (1980) [16] Z. Bahr and B. V. K. Kmar, Generalzed synthetc dscrmnant fnctons, Jornal of Optcal Socety of Amerca, Vol. 5, No. 4, (1988) [17] I. Kypraos, R. Yong and C. R. Chatwn, "An nvestgaton of the non-lnear propertes of correlaton flter synthess and neral network desgn", Asan Jornal of Physcs, Vol. 11, No. 3, (00) [18] Saad Rehman, Peter Bone, Rpert Yong, Chrs Chatwn, Object Detecton and Recognton n Clttered Scenes Usng Flly Scale and In-Plane Invarant Synthetc Dscrmnant Fncton Flters, Jornal of Compter and Informaton Scences, Vol 1, No 1, 15-18, 007. [19] D. Marr, E. Hldreth, Theory of edge detecton, Proc. R. Soc. Lon. B 0, pp , (1980). [0] B.V.K. Kmar and L. Hassebrook, Performance measres for correlaton flters, Appled Optcs, Vol. 9, No. 0, pp , (1990). 41