Rotation-invariant pattern matching using color ring projection

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1 otaton-nvaant atten mathng usng olo ng oeton D. M. Tsa and Y. H. Tsa Mahne Vson Lab. Deatment of Industal Engneeng and Management Yuan-Ze Unvesty Chung-L Tawan.O.C. E-mal: INTODUCTION Temlate mathng has been a oula and easly-mlemented method fo obet deteton [] OC [] and PCB nseton [3]. It fnds a atten n the sene mage by sldng the wndow of a efeene temlate n a xel-by-xel bass and omutng the degee of smlaty between them n whh the measue of smlaty s ommonly gven by oelaton o nomalzed oelaton [4]. Pxel-by-xel temlate mathng s vey tme-onsumng. Fo an nut mage of wdth N and the temlate of wdth the omutatonal omlexty s n the ode of N gven that the obet oentatons n both mages to be mathed ae ondent. hen we seah an obet wth unknown oentaton the staghtfowad way to do temlate mathng s to otate the efeene temlate n evey ossble oentaton. The exhaustve temlate mathng s extemely omutaton-ntensve and beomes matal when abtay otaton s esent. In the ast few yeas new temlate mathng algothms fo multle otated temlates have been oosed usng the Kahune-Loeve K-L tansfom [56] and Foue and K-L deomoston [7]. In the methods the K-L tansfom s fst aled to a set of otated temlates and egenvetos ae extated fom them. Eah temlate n the tanng set s aoxmated by a lnea ombnaton of salent egenvetos. Nomalzed oelaton

2 between otated temlates and the nut mage s then omuted by substtutng the aoxmatons fo the temlates. Mathed flteng aoahes usng abo fltes and wavelets [890] ae oula altenatves n eent yeas fo detetng obets n omlated mages. Howeve they geneally eque sgnfant amount of omutaton and ae of lmted use beause eah vew of the obet may eque a unque flte. Exstng temlate mathng algothms geneally fous on detetng obets n gay-level mages. Chomat nfomaton of obet attens s not fully utlzed to enhane the dsmnaton. Sne olo mages ontan moe nfomaton e xel than gay-level ones olo mahne vson has been an atve feld dung the last few yeas n atten eognton alatons. A smle and effetve eognton sheme s to eesent and math mages on the bass of olo hstogams. Swan and Ballad [] have oosed a olo ndexng method based on mathng of olo hstogams fo mage eteval. eves and Smeuldes [] analyze and evaluate vaous olo models fo the uose of eognton of multoloed obets n the hanges of llumnaton. In the exement efeene obets ae eoded n solaton one e mage aganst a smle whte adboad bakgound. The olo ndexng method s used to measue the smlaty. Mehte et al. [3] oose the efeene olo table method fo mage eteval. The method defnes a table of efeene olos whh ontans a set of e-seleted olo lasses. In the mathng oess eah xel n the olo mage s assgned to ts neaest olo lass n the table and the dstane measue s used to omute the smlaty based on the hstogam of the newly assgned olo lasses. Kankanhall et al. [45] use unsuevsed lusteng algothms to detemne the olo lasses so

3 that a o knowledge s not neessay to set u the efeene olo table. Exstng olo-mage mathng algothms basally use only olo nfomaton fom the olo hstogam of an mage wthout utlzng satal nfomaton of the obet atten. Those aoahes may be sutable fo mage eteval alatons o detetng oloed obets n a smle bakgound. They ossbly geneate false math fo oloed obets n omlex mages. Ou wok has been motvated by a need to develo an effent olo mathng tehnque so that the deteton of oloed obets n a omlex bakgound an be effetve and fast. Fo solvng the oblem of abtay oentaton we oose a otaton-nvaant eesentaton of oloed attens based on the olo ng-oeton tansfomaton. Colo ng-oeton tansfoms the -D olo mage ontaned n a ula wndow nto -D olo sgnals as a funton of adus. The olo featues of eah ng wth a sef adus ae eesented by the mean B tstmulus values of all xels fallng on the ng. The oosed mathng oess nvolves two hases. Phase I adly selets the most lkely egons of a efeene temlate n the sene mage by omutng the nomalzed oelaton of olo ng-oeton attens between them. Sne the olo ng-oeton eesentaton eseves only atal satal nfomaton of the ognal -D mage atten hase II then vefes the anddate loatons seleted n hase I by measung the nomalzed oelaton between the efeene temlate and the anddate egons usng the xel-to-xel temlate mathng. In ode to make the xel-to-xel mathng otaton-nvaant we oose a new estmaton sheme to detemne the oentaton of a oloed atten. e an smly otate the efeene temlate so that t algns tself wth the degee of otaton n the sene mage. Theefoe the xel-to-xel mathng n hase II s only omuted fo a few anddate loatons eah n a sef oentaton. Ths esults n sgnfant savng of omutatonal tme. 3

4 Ths ae s oganzed as follows: Seton fst desbes the oosed olo ng-oeton eesentaton of oloed obets and the smlaty measue of nomalzed oelaton. Then the estmaton of oloed-obet oentaton s esented and the nomalzed oelaton of xel-to-xel temlate mathng n olo mages s defned. The estmaton auay of otatonal angles s evaluated based on the exemental esults of fve oloed test samles. Seton 3 esents the exemental esults fo evaluatng the effay of the oosed atten mathng algothm. The ae s onluded n Seton 4.. COLO PATTEN MATCHIN. Colo ng-poeton Patten mathng basally nvolves two tasks: atten eesentaton followed by a mathng oess based on some smlaty measues. In ode to edue the omutatonal buden n the mathng oess a new olo ng-oeton s oosed. It tansfoms a -D olo mage nto a otaton-nvaant eesentaton n the -D ng oeton sae. The oosed tansfomaton sheme fo oloed attens s nsed by the ng oeton algothm [67] whh s ognally develoed fo haate eognton n bnay mages. Colo ovdes oweful nfomaton fo atten mathng. The olo of a xel s tyally eesented wth the B tstmulus values eah oesondng to the ed geen and blue B fequeny bands of the vsble lght setum. Images n the B olo model onsst of thee ndeendent olo lanes. The olo 4

5 ng-oeton tansfomaton s aed out seaately n eah of the thee may-olo lanes. Let xy xy and Bxy denote the and B stmulus values at xel oodnates xy esetvely. The atten of nteest s ontaned n a ula wndow of adus. The adus hosen fo the wndow deends on the sze of the efeene temlate. The olo ng-oeton of mage lane xy s gven as follows. Fst xy n the Catesan oodnates s tansfomed nto the ola oodnates : Hene xy osθ sn θ x osθ y snθ. The olo ng-oeton of mage xy at adus denoted by s defned as the mean value of os θ sn θ sef adus. That s π osθ snθ dθ π 0 at the Takng the mean of stmulus values fo eah sef ng edues the effet of nose. The dsete eesentaton of n a seah wndow of adus s gven by osθ k snθ k n k whee n s the total numbe of xels fallng on the le of adus 0. The olo ng-oetons and B of mage lanes xy and Bxy ae defned n a smla way as.e. osθ k snθ k n k B B osθ k snθ k 3 n k fo 0. Theefoe a -D mage wth two ndeendent vaables x and y n 5

6 eah olo lane s now eesented by the -D ng-oeton atten wth one sngle vaable. Sne the oeton s onstuted along ula ngs of neasng ad the deved -D olo ng-oeton atten s nvaant to the otaton of ts ognal -D mage atten. Fgues a and b show the olo mages of a snal n two dstnt oentatons. Fgues - h esent the lots of ng oetons of thee olo lanes as a funton of adus. It an be seen fom the fgues that the lots of ng oetons ae aoxmately dental egadless of oentaton hanges. An ognal -D B mage an now be eesented by a sequene of B ng-oeton vetos P fo 0. B In the mathng hase the measue of smlaty s gven by the nomalzed oelaton. Let P M B P M and P S P S B denote the B ng-oeton vetos of the efeene temlate and a sene submage esetvely at the ng of adus 0 whee s the adus of the seah wndow. The elements of both P M and ae alulated fom eqs. -3. The nomalzed oelaton between two olo ng-oeton sequenes { P M 0... } and { P S 0... } s defned by P S 6

7 7 [ ] [ ] [ ] [ ] [ ] S M B B B P P σ σ µ µ µ µ µ µ δ 4 whee [ ] B 0 3 µ [ ] B 0 3 µ [ ] 0 3 µ σ [ ] 3 µ σ P P S M s the nne odut of P M and P S. Hee µ and µ ae the aveage values of the efeene temlate and the sene submage esetvely. σ and σ ae assoated wth the vaanes of the temlate and the sene submage. Nomalzed oelaton between the efeene temlate and a otated sene submage s effently omuted by substtutng the -D ng-oeton atten fo the ognal -D xel-mage. The omutatonal omlexty s sgnfantly edued fom O n -D mages to O n the -D ng-oeton sae. The nomalzed oelaton s between - and and a efet math of two dental attens wll have the maxmum value of unty.

8 8. Pxel-to-Pxel Mathng wth the Estmated Oentaton The nomalzed oelaton defned n eq. 4 s ntally used n the mathng oess to selet the best-mathed anddates. Sne the -D olo ng-oeton eesentaton does not suffently eseve the satal nfomaton of the ognal -D olo mage the loatons of the seleted anddates n the mathng hase ae vefed usng the xel-to-xel temlate mathng. Let B C M y x B y x y x y x C S C M and y x C S eesent esetvely the ognal B mages of the efeene temlate and a sene submage ontaned n a ula wndow of adus whee the elements of C M and y x C S ae the and B tstmulus values of a xel. The nomalzed oelaton between two B mages } { C M and } { y x C S s gven by [ ] 3 v v w w S M N y x C C σ σ µ µ δ 5 whee [ ] v v w w B N 3 µ [ ] v v w w y x B y x y x N 3 µ [ ] [ ] [ ] { } v v w w N B 3 µ σ

9 σ v w v w {[ x y ] [ x y ] [ B x y ] } 3N µ v N the total numbe of xels n the ula wndow. The value of xel-based oelaton s also between - and and the efet math wll have a maxmum value of unty. Sne the oelaton omutes the olo nfomaton based on the -D satal loaton of eah xel n the mage the esultng oelaton oeffent s senstve to oentaton hanges. If a lue egadng otaton an be extated fom the nut submage { x y } C S then smly otate the temlate { } C M so that t algns tself wth the degee of otaton n { x y } C S. Ths nomalzaton fo otaton avods exhaustve otatons of the temlate to look fo the best math. In bnay mages the oentaton of an obet an be easly detemned fom the nal axes egenvetos of the ovaane matx of the xel oodnates [4]. In olo mages the oentaton of a oloed atten s dffult to defne. Pxels wth dffeent olo values n olo mages an be onsdeed as atles wth dffeent denstes n hysal obets. Then the usual ate n hyss s to hoose the axs of least seond moment [8] as the obet deton. e fnd the lne fo whh the ntegal of the squae of the dstane to onts n the obet s a mnmum E d ρ x y dxdy whee d s the eendula dstane fom the ont xy to the lne sough afte and ρ x y s the densty at xy. By mnmzng E we an obtan the oentaton of 9

10 the lne [8]: b θ tan 6 a whee a x' ρ x' y' y' x' x' b y' ρ x' y' y' x' y ρ y' x' ' x' y' x ' y' ae the shfted oodnates wth the ogn 00 at the ente of the seah wndow. Fo an obet n the bnay mage the densty ρ x' y' s unfom and s smly gven by the bnay gay-value of xels. In olo mages the value of a olo featue an be used to eesent the densty ρ x' y' of eah xel n the seah wndow. In ths study we smly selet one salent olo featue deved fom vaous olo models and then nomalze the value of the olo featue that sums to unty fo all xels n the seah wndow to eesent the densty of a oloed xel. e onsde two oula olo models HSI and CIELAB [49] to obtan vaous olo featues. The onveson fom the B sae to the HSI sae s gven by I B 3 3 S B B [ mn ] H os [ B ] [ B B ] If B / I > / I then H 360 H. Hee olo featues I S and H eesent ntensty satuaton and hue of a olo esetvely. 0

11 The CIELAB olo sae s an ntenatonal standad whh oesonds to human olo eeton and vey losely esembles unfom olo sae. The CIELAB sae eques an ntemedate tansfom to the XYZ sae fom the system deendent B sae. The tansfom fo NTSC olo vson senso s X Y 0.99 Z B The CIELAB equaton s then aled fo tstmulus values X Y and Z: L 6 Y Y n a 500 b 00 X X Y Y Y n Y n 3 n Z n Z whee X n Y n and Z n ae the tstmulus values of the efeene whte. L* s a oelate 3 3 to eeved lghtness. The a and b dmensons oelate aoxmately wth ed-geen and yellow-blue homa eetons. The CIELAB olo sae an also be eesented n tems of ylndal oodnates whh ovde edtos of homa C ab and hue h ab as exessed below : C ab h ab tan a b b a ven a olo featue x y whee f f x y the densty ρ x y at xel xy s defned by { H S I L a b h C } ab ab

12 ρ x y f x y f fo all xy ontaned wthn the seah wndow. The gay value of a xel n ts oesondng gay-level mage s also onsdeed as one of the olo featues so that the efomane of the densty eesentaton n both olo mages and gay-sale mages an be evaluated n the exement. Fgues a - e show fve test samles used n ths study fo evaluatng the angula auay of the oosed oentaton estmato. Eah test samle s ontaned n a ula wndow of adus 5 xels wth eght-bt ntensty e olo band. Also eah test samle s synthetally otated fom 0 to 360 n nement so that the estmated oentatons an be omaed wth the atual ones. A total of 360 otated mages s eated fo eah of the fve test samles. Table summazes means standad devatons and maxmum values of the angula eos of the estmated oentatons. It an be seen fom Table that olo featue a deved fom the CIELAB sae gves the best oveall efomane. The mean angula eo of oentaton s less than 5 and the standad devaton s smalle than.7. The maxmum angula eo n oentatons 5 test samles mages s only 8. The gay values n gay-level mages efom unstably fo the fve test samles. Colo featue S deved fom the HSI sae woks ooly fo the test samles shown n Fgues b and e and the esultant statsts ae not nluded n Table. Colo featue H fom the HSI sae gves the mean angula eo less than 7. Howeve t yelds the maxmum angula eo of 8 and the standad devaton as lage as 5.3. It s unstable fo angula estmaton. Comaed wth the exhaustve mathng of the efeene temlate n all ossble oentatons the oosed

13 xel-to-xel temlate mathng n the vefaton hase an be alulated effently by seahng only the neghbohood of the estmated oentaton. Based on ou emal study seah angles between -5 and 5 n the vnty of the estmated oentaton s geneally suffent to eah the best math wth the use of olo featue a. 3. EXPEIMENTAL ESULTS In ths seton we esent the exemental esults fo evaluatng the effay of the oosed olo atten mathng method. In ou mlementatons all algothms ae ogammed n the C language and exeuted on a esonal omute wth a Pentum 300 MHz oesso. The effetve mage sze s 5656 xels wth eght bts of ntensty e olo band. In ode to evaluate the effet of otaton hanges two test samles shown n Fgues 3a and 4a ae otated n two dstnt oentatons as shown n Fgues 3b - 3 and 4b - 4. The attens maked by yellow les n Fgues 3a and 4a ae used as efeene temlates. The fve lagest oelaton oeffents deved fom the olo ng-oeton mathng ae maked by les of olos ed geen blue yellow and ndgo n the desendng ode. Fgue 3a shows an mage that ontans many small obets smla n shaes and olos. Fgues 3b and 3 esent the anddate loatons of the efeene temlates deteted by the olo ng-oeton mathng. Fgues 3b and 3 dslay the vefaton esults fom the xel-to-xel temlate mathng. Fgue 4a shows the mage ontanng many smla essto omonents of dffeent esstanes oded by dffeent olo stes n a omlex bakgound. The taget essto of 39laed n abtay loatons and oentatons s elably deteted n both sene mages as shown n Fgues 4b 3

14 and 4. Note that the loaton wth the lagest oelaton oeffent maked by a ed le n Fgues 3b3 4b and 4 obtaned fom the olo ng-oeton mathng s ondent wth the best math found n the xel-to-xel temlate mathng fo eah of the two test samles. All nstanes of efeene temlates ae oetly loated egadless of otaton hanges. Fgues 5 and 6 show addtonal exemental esults of detetng small ats on nted ut boads PCBs. Fgue 5a esents the ognal mage wth the taget omonent maked by a yellow le. Fgues 5b and 5 show that the taget omonent s well loated n olo ng-oeton and xel-to-xel mathng hases esetvely. Note that the sene mage s otated by 90 wth eset to the ognal one and the estmated oentaton s 89. In Fgue 6a the taget obet s the solde ad labeled 07 on the PCB and s maked by a yellow le n the mage. Fgue 6b shows the loatons of the fve lagest oelaton oeffents n the ng-oeton mathng hase. Fgue 6 esents the best math vefed by the xel-to-xel temlate mathng. The sene mage s a shfted veson of the ognal one and the estmated oentaton s. It an be seen fom Fgues 6b and 6 that the taget obet s well loated as ndated by the ed les n the mages. Fgues 7 and 8 show the exements that detet obets n moe hostle envonments. Fgue 7 llustates the deteton esult fo obets n seveely oveexosed and undeexosed mages. Fgue 8 esents the deteton esult fo obets n dffeent olo bakgounds. It an be seen fom both Fgues 7 and 8 that the oosed method also woks well fo detetng obets n vayng envonment. 4. CONCLUSION 4

15 Temlate mathng has been a fundamental tehnque n mahne vson fo detetng obets n omlex mages. One of the mao lmtatons of tadtonal xel-by-xel temlate mathng s that an enomous numbe of temlates must be mathed aganst an mage feld to aount fo hanges n otaton of efeene temlates. Many exstng temlate mathng methods ae manly aled to gay-level mages. They gnoe the oweful olo nfomaton and make the obet deteton task unelable. In ths study we have oosed a otaton-nvaant temlate mathng method fo detetng obets n olo mages. The omlexty and omutaton load of the oelaton funton method fo detetng obets n abtay oentatons ae edued sgnfantly by the -D olo ng-oeton eesentaton. It an adly selet the ossble loatons of a efeene temlate n the nut sene by omutng the nomalzed oelaton of -D olo ng-oeton attens. The anddate loatons wth hgh oelaton oeffents obtaned n the olo ng-oeton mathng hase ae then vefed by the xel-to-xel temlate mathng. To make the xel-based mathng nvaant to otaton the olo featue a deved fom the CIELAB sae s used as xel densty and the axs of least seond moment s emloyed to estmate the otatonal angle of the efeene temlate. Ths allevates the exhaustve seah of unknown oentaton n tadtonal temlate mathng methods. Fo an mage of sze NN and a ula wndow of adus the omutatonal omlexty of the oosed olo ng-oeton mathng s gven by O N fo obets n abtay oentatons omaed wth O N of the tadtonal xel-by-xel temlate mathng fo obets n eah ossble oentaton. The oosed xel-to-xel mathng n the vefaton hase s only omuted fo a few 5

16 anddate loatons n a sef oentaton. Theefoe the oosed atten mathng sheme s effent n omutaton usng the otaton-nvaant eesentaton and s obust n mathng usng the olo nfomaton. Comutatonal tme of the oosed olo ng-oeton mathng s 6 seonds on the Pentum 300 MHz esonal omute fo an abtaly-otated mage of sze 5656 xels and a ula wndow of adus 5 xels. Fo tadtonal temlate mathng methods omutatonal tme s 0 seonds fo mages n a fxed oentaton. If the obet oentaton an be abtay and the seah angle anges fom 0 to 360 wth esoluton omutatonal tme of tadtonal methods wll damatally nease to 700 seonds. 6

17 EFEENCES.. K. Patt Dgtal Image Poessng ley-intesene New Yok N.Y S. Mo C. Y. Suen and K. Yamamoto Hstoal evews of OC eseah and develoment Poeedngs of the IEEE M. Mogant and F. Eal Automat PCB nseton algothms: a suvey Comute Vson and Image Undestandng C. onzalez and. E. oods Dgtal Image Poessng Addson-esley eadng Mass S. Yoshmua and T. Kanade Fast temlate mathng based on the nomalzed oelaton by usng multesoluton egen-mages Po. IOS 94 Munh emany O. Amd Y. Mesak T. Kanada and M. Uenohaa eseah on an autonomous vson-guded helote Po. Ffth I/SME old Conf. obots eseah Cambdge Mass M. Uenohaa and T. Kanada Use of Foue and Kahunen-Loeve deomoston fo fast atten mathng wth a lage set of temlates IEEE Tans. Patten Anal. Mah. Intell A. K. Jan N. K. atha and S. Lakshmanan Obet deteton usng abo fltes Patten eognton D. P. Casasent J. -S. Smokeln and A. Ye avelet and abo tansfoms fo deteton Otal Engneeng N. Stkland and H. I. Hahn avelet tansfom methods fo obet deteton and eovey IEEE Tans. Image Poessng M. J. Swan and D. H. Ballad Colo ndexng Intl. J. Comute Vson T. eves and A.. M. Smeuldes Colo-based obet eognton Patten eognton B. M. Mehte M. S. Kankanhall A. D. Naasmhalu and. C. Man Colo mathng fo mage eteval Patten eognton Lettes M. S. Kankanhall B. M. Mehte and J. K. u Cluste-based olo mathng fo 7

18 mage eteval Patten eognton M. S. Kankanhall B. M. Mehte and H. Y. Huang Colo and satal featue fo ontent-based mage eteval Patten eognton Lettes Y. Y. Tang H. D. Cheng and C. Y. Suen Tansfomaton-ng-oeton TP algothm and ts VLSI mlementaton Int. J. Patten eogn. Atf. Intell P. C. Yuen. C. Feng and Y. Y. Tang Pnted Chnese haate smlaty measuement usng ng oeton and dstane tansfom Int. J. Patten eogn. Atf. Intell B. K. P. Hon obot Vson The MIT Pess Cambdge Mass M. D. Fahld Colo Aeaane Models Addson-esley eadng Mass

19 a Ognal mage b otated mage of x y n a d of x y n b e of x y n a f of x y n b g B of B x y n h B of B x y n b Fgue. Colo ng-oeton eesentaton of a snal mage n two dstnt oentatons. 9

20 a b d e Fgue. Fve test samles used fo oentaton estmaton. Table. Estmated otatonal eos fom vaous olo featues. ay-level Colo mage Test Statsts mage HSI CIELAB Samle degee ay level H S I L a* b* h * C ab ab Mean eo Fg. a Std. dev Max. eo Mean eo Fg. b Std. dev Max. eo Mean eo Fg. Std. dev Max. eo Mean eo Fg. d Std. dev Max. eo Mean eo Fg. e Std. dev Max. eo

hase olo ng-oeton mathng and the vefaton hase xel-to-xel

21 a b b Fgue 3. An magewhh ontans many smla obets used to evaluate the effet of oentaton hanges: a the ognal olo mage the efeene temlate s maked by a yellow le; bb the deteton esults fom the mathng hase olo ng-oeton mathng and the vefaton hase xel-to-xel mathng esetvely fo one otated mage; the deteton esults fom the mathng hase and the vefaton hase fo anothe otated mage.

ng-oeton mathng and the vefaton hase xel-to-xel mathng

22 a b b Fgue 4. A essto mage used to evaluate the effet of oentaton hanges: a the ognal olo mage the efeene temlate s maked by a yellow le; bb the deteton esults fom the mathng hase olo ng-oeton mathng and the vefaton hase xel-to-xel mathng esetvely fo one otated mage; the deteton esults fom the mathng hase and the vefaton hase fo anothe otated mage.

23 a a b b Fgue 5. Deteton of a essto omonent on the PCB: a the ognal mage; b the anddates wth fve lagest oelaton values obtaned fom the mathng hase; the best math vefed. Fgue 6. Deteton of a solde ad labeled 07 : a the ognal mage; b the anddates wth fve lagest oelaton values obtaned fom the mathng hase; the best math vefed.

24 a a b b Fgue 7. Deteton of an obet n vayng llumnaton : a the temlate mage; b the oveexosed mage; the undeexosed mage. Fgue 8. Deteton of an obet n vayng bakgound: a the temlate mage; b the mage wth a yellow bakgound; the mage wth a blue bakgound.

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