Hough-Domain Image Registration By Metaheuristics

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1 Hugh-Dman mage Regstratn By etaheurstcs Shubn Zha Jangsu Autmatn Research nsttute Lanyungang, Jangsu, P. R. Chna 6 Emal: zha_shubn@63.cm Abstract mage regstratn s the prcess f regsterng tw r mre mages, whch may be acqured under dfferent magng cndtns. The crtcal ssues n mage regstratn are rbustness and speed f the algrthm, whch mst current algrthms are devted t. n ths paper, a rbust and effcent algrthm s presented fr regsterng mages n Hugh space usng heurstc appraches. By Hugh transfrm, the man structure f an mage can be represented n the pstnrentatn space. Ths representatn has almst all structural nfrmatn f the rgnal mages, especally fr mages rch wth lne segments. Ths representatn allws us t regster mages effcently n Hugh space rather than n the rgnal mage space. T accunt fr dfferences between the mages t be regstered, the generalzed partal Hausdrff dstance s prpsed and used t measure the mage smlarty. n the presented algrthm, the rtatn parameter s cmputed smply by -D crrelatn, and ther transfrmatn parameters are determned by a new hypthess-test methd, where each hypthess s generated by a heurstc apprach,.e. randm lcal search. The prpsed algrthm has very lw cmputatnal cmplexty, and wrks well fr mst natural mages rch wth lne segments resultng frm man-made structures. Keywrds mage regstratn, Hugh transfrm, randm lcal search, metaheurstc. lne ntersectns[7] and edge pnts[8], and hw t select depends n the gven task. Apart frm feature selectn, smlarty measure plays an mprtant rle n mage regstratn. Huttenlcher et al. [8] cmpare mages transfrmed by translatn r translatn plus rtatn, where edge pnts (resultng frm edge detectn are used as matchng features and the Hausdrff dstance (HD s adpted t measure the smlarty f the mages. The HDbased algrthms utperfrm the crss-crrelatn based methds, especally n mages wth perturbed pxel lcatns. rever, the algrthms are desred t cmpare partal mages when changes have taken place n the scene. That s, dfferences f sme extent wll nt lead t severe errrs n mage regstratn. n mst practcal applcatns, cmputatnal cst must be cnsdered, especally when the real-tme prcessng s needed. The cmputatnal cmplexty manly cmes frm tw aspects: the large sze f mage data and the hgh dmensnalty f transfrmatn space. ult-reslutn methds[9-], mre cmpact representatns f mage and decmpstn f transfrmatn space can be used t reduce cmputatns.. NTRODUCTON mage regstratn s the prcess f spatally regsterng tw r mre mages f the same scene taken at dfferent tmes, frm dfferent vewpnts, and/r by dfferent sensrs. t s an mprtant ssue n many applcatns f mage analyss and cmputer vsn, such as mage fusn, change detectn, vde ge-regstratn, pattern and target lcalzatn, and s n. Because f ts mprtance n varus applcatn areas and ts cmplcated nature, mage regstratn has been the tpc f much recent research. Durng the last decades, many knds f appraches have been prpsed t address mage regstratn, and the cmprehensve surveys are gven n [-]. Accrdng t what bjects are used t algn mages, the appraches can be categrzed nt tw classes: ntenstybased methds and feature-based nes. Because the magng cndtns may be qute dfferent and sme changes may take place n the scene durng the tme nterval when the mages were taken, there are almst nevtably many dfferences between the mages. Cnsequently, fr mage regstratn t be rbust, feature-based nes are preferred, whle ntenstybased methds are usually nfeasble. st cmmnly used features can be sgnfcant regns[3-4], lne segments[5-6], Fgure. Fgure. mages wth man-made structures n ths paper, we prpse an effcent mage regstratn algrthm, whch smulates behavrs f human vsn n mage regstratn. The algrthm s based n the fllwng bservatns. n many applcatns, mages are rch wth lne segments resultng frm man-made structures, as shwn n Fg.. n ths case, we ntutvely regster these mages by algnng a few pars f sgnfcant lnes, and pay n attentn t ther features. Ths s what human vsn des n regsterng mages. Based n ths dea, the crrespndences between lne segments n tw mages must be establshed t determne the transfrmatn parameters. Ths s a cmbnatral ptmzatn prblem, and fr mage regstratn t be feasble, effcent appraches are desred t establsh the crrespndences f lne segments and then cmpute the transfrmatn parameters. n recent years, a new famly f search and ptmzatn algrthms has arsen based n /6/$. 6 EEE CARCV 6

2 extendng basc heurstc methds by ncludng them nt an teratve framewrk, whch augments ther explratn capabltes[-3]. Ths grup f advanced apprxmate algrthms s called metaheurstcs and an vervew n the mst prmnent nes can be fund n[]. n ths wrk, terated lcal search s used t search the pars f lne features that match best. n ths paper, nly smlarty transfrmatn s cnsdered. Frst, pstn-rentatn ( representatns are btaned by the straght lne Hugh transfrm, and then n rder t reduce cmputatns, rtatn angle s cmputed smply by -D crrelatn. The transfrmatn parameters fr translatn and scalng are determned by a new hypthesstest methd, where the Hausdrff dstance s used as smlarty measure and each hypthess s generated by randm lcal search. The rest f ths paper s rganzed as fllws. Defntn f mage regstratn and sme general deas are gven n sectn. Hugh transfrm, ts prpertes, and smlarty measure f mages n Hugh space are gven n sectn 3. Sectn 4 descrbes the algrthm n detal. Fnally, sme expermental results and cncludng remarks are gven.. AGE REGSTRATON Gven tw mages t be regstered, ne f whch s called the reference mage and the ther s called the sensed mage, the tw mages are dented by and, respectvely. athematcally, mage regstratn prblem can be frmulated as: search a gemetrc transfrmatn g and an ntensty transfrmatn functn f, s that ( y = f ( ( g( y ( n sme cases, the gal f mage regstratn s algnng tw mages gemetrcally, hence the ntensty transfrmatn s nt necessary. Especally fr mult-sensr mages, searchng such ntensty transfrmatn s mpssble. S, all wrk fr mage regstratn amunts t determnng the gemetrc transfrmatn functn g. That s, cmpute the functn g s that the sensed mage can be perfectly regstered wth the reference mage. The transfrmatn can be translatn, rtatn, scalng, smlarty transfrmatn, r mre cmplex transfrmatns such as affne and perspectve transfrmatns. n ths paper, nly smlarty transfrmatn s cnsdered, whch s defned as fllws. ' x tx cs sn x = + s ( ' y t y sn cs y n ths case, the prblem equals t cmputng the fur parameters, whch s dented by T = ( t t y, s, n the fllwng sectns. As mentned earler, t s the structure features, nt the ntensty values f the rgnal mages that rbust mage regstratn reles n. n rder t extract the structure features f mages, perfrm edge detectn n the sensed mage and the reference mage, and the resultng edge mages are stll dented by and, whch are tw sets f edge pnts and represent the edge structures f crrespndng mages. Nw, regstratn f tw mages equals t cmparng tw sets f pnts, and the prblem can be refrmulated as: Search a gemetrc transfrmatn functn g, s that dst ( ( y, ( g( y (3 s mnmzed. Here, dst( a, b s sme knd f dstance between a andb, whch measures the dssmlarty between tw sets. T accunt fr the dfferences that may be present between the tw mages, the Hausdrff dstance s cmmnly used t measure the dssmlarty f the tw edge mages. But these knds f methds are cmputatnally demandng, especally fr hgh-dmensnal search spaces such as smlarty, affne and perspectve transfrmatns. T reduce cmputatnal csts, dstance transfrm and ther technques are used. Hwever, the cmputatnal csts are stll hgh. n many applcatns, mages are rch wth lne segments whch are resultng frm man-made structures. Nw, t further mprve the effcency fr regsterng ths knd f mages, let us bserve the behavrs f human vsn n dng ths wrk. Fr the tw mages shwn n Fg., we can determne the rtatn angle by usng nly the nfrmatn abut the dstrbutns f lne rentatns n the mages, and the prcess s smple -D crrelatn. After remvng the rtatn dfference between the mages, the ther three transfrmatn parameters,.e. translatn and scalng parameters, can be cmputed by establshng the crrespndences between three pars f lnes n mages. Ths prcess s mplemented by a hypthess-and-test methd. There are a large number f pssble crrespndences between lne segments, s evaluatng all pssble nes and then btanng the ptmal parameters s cmputatnally prhbtve. n ths paper, terated lcal search, ne f the advanced apprxmate appraches, s used t generate each hypthess. Fr rbustness, the generalzed partal Hausdrff dstance n Hugh space s used as the smlarty measure n the prpsed algrthm. These are the man deas f the algrthm.. EASURNG SLARTY N HOUGH SPACE A..Hugh Transfrm and ts Prpertes The Straght lne Hugh transfrm (SLHT s a wellknwn methd fr the detectn f lnes n bnary mages, and t s als used t lcate, recgnze sme specal shapes and regster mages[4-7]. Let a lne L be represented by = x cs + ysn (4 Then ths lne crrespnds t pnt (, n the Hugh space. S t s a mre cmpact representatn f lnes. Nw cnsder the effects f rtatn, translatn and scalng n parameters f a straght lne. As shwn n Fg., f the mage s rtated by an angle α < 8 n the

3 cunterclckwse drectn, then (, wll be mapped t, such that ( + = ( α md8 and f + α < 8 = (5 f + α 8 f the mage s translated by t, t (refer t Fg., then ( x y = and = t cs( φ + (6 where t = t x + t y, and φ = tan ( t y tx. f the mage s scaled by a factr s, then = and = s (7 Fgure. Fgure. Effects f rtatn(left and translatn(rght n the parameters f a straght lne. n the dscrete dman, the SLHT transfrm f an mage s a -D array, n whch each rw crrespnds t ne value f, and each clumn t ne value f. t s bvus that ths array has the fllwng three prpertes: Rtatn n the mage plane crrespnds t crcular shftng f the array; f the mage s translated by ( t t y, then the same ffset value t cs( φ s added t all pnts n the clumn wth value ; 3 Scalng the mage equals t nly scalng every n the array, whle the rentatn remans unchanged. B. easurng Smlarty n Hugh Space The SLHT transfrm cntans rentatn and pstn nfrmatn f all lne segments n mages. Therefre, we can reasnably suppse that f a set f parameters algn the SLHT f an mage wth that f anther ne, then the crrespndng transfrmatn wll regster these tw mages n mst cases. T accunt fr pssble errrs resultng frm lne detectn r cclusn, we use the partal drected Hausdrff dstance (PDHD t measure the dssmlarty f tw SLHT transfrms. Perfrm edge detectn n and, and the resultng edge mages are stll dented by and. Let H and H be the SLHT transfrms f and, respectvely. By peak detectn n H and H, we btan tw bnary mages and, n whch each feature pnt (ts value s represents a lne segment. The PDHD s defned as fllws. f th HD (, = f mn m (8 m where f th th x X g(x dentes the f quantle value f g (x ver the set X fr sme value f f between zer and ne, m and are feature pnts. Fr example, the th quantle value s the maxmum. Nw, the mage regstratn prblem can be refrmulated as fllws: f arg mn HD ( T (, (9 T where T ( dentes the sensed mage transfrmed by the transfrmatn functn T. V. DESCRPTONS OF THE ALGORTH A. mage Regstratn n Hugh Space Tw pars f crrespndng pnts between tw mages can unquely determne a smlarty transfrmatn. S we need three pars f pnts n the Hugh space t cmpute the fur parameters nvlved. T slve (9, all pssble cmbnatns are evaluated and then the ptmal transfrmatn parameters can be btaned. T reduce the nvlved cmputatnal cst, we utlze the frst prperty f Hugh transfrm. That s, rtatn n the mage plane crrespnds t crcular shftng f the Hugh transfrm. S by -D crrelatn, the rtatn angle can be cmputed effcently. T d ths, we cmpute tw vectrs whch shw the dstrbutns f lne segments alng the crdnate. They are defned by O = (, j ( O = (, j ( Then cmpute a -D crrelatn f O and O, and the pstn f peak ndcates the amunt f rtatn α (r α +8 snce the dstrbutn vectrs O and O are perdc n 8 f the sensed mage. Once the rtatn angle s btaned, we can rearrange by crcular shftng s that the rentatn dfference between tw mages s remved. Nw, tw bservatns can be used t further reduce cmputatnal cst. Frst, tw lne segments can match each ther nly when they are parallel. Secnd, the crrespndence between lnger lne segments s

4 mre rbust fr regsterng mages. Based n these bservatns, we can sequentally select feature pnts n by ther vtng values n H (nes wth larger values are always preferred and the crrespndng nes n, evaluate the crrespndence by cmputng the PDHD dstance, untl the dstance s acceptable r all pssble crrespndences are evaluated. Ths s a hypthess-and-test prcess, and n mst cases, we can btan the transfrmatn parameters n a lttle number f tmes. Frm all the dscussns gven abve, we can descrbe the prcedure f mage regstratn as fllws: Step : Perfrm edge detectn n the rgnal mages and, and cmpute the SLHT transfrms f the resultng edge mages, whch are dented by H and H. Then, btan tw bnary mages and by peak detectn. Step : Determne the rtatn angle f the sensed mage by cmputng a -D crrelatn f the dstrbutns f lne segments alng the crdnate. Step 3: Accrdng t the rtatn angle btaned, rearrange the bnary mage wth by crcular shftng. Step 4: Select feature pnts n and the crrespndng nes n, evaluate the crrespndence by cmputng The PDHD dstance. Step 5: Step 4 s repeated untl The PDHD dstance s acceptable r all pssble crrespndences are evaluated. f the number f lne segments n each mage s small, the pssble cmbnatns are f cnsderable sze. n ths case, the apprach descrbed abve can slve the mage regstratn prblem n acceptable tme. Otherwse, the algrthm wll cst t much tme and we must slve the prblem usng ther technques. n the fllwng subsectns, we wll descrbe an apprxmate methd called the randm lcal search apprach. B. Randm Lcal Search Randm lcal search (RLS s ne f the heurstc methds fr slvng the cmbnatral ptmzatn prblems, whch extends classcal lcal search methds by randmly generatng ntal slutns. RLS wrks as fllws: Randm Lcal Search Randmly generate ntal slutn; Perfrm lcal search and btan the lcal ptmal slutn; Repeat Randmly generate ntal slutn; Perfrm lcal search and btan the lcal ptmal slutn; Cmpare ths slutn wth the last lcal ptmal slutn and btan the current ptmal slutn; Untl termnatn cndtns met. Hence, the algrthm starts by randmly generatng ntal slutn, and then by lcal search, a lcal ptmal slutn s btaned; then generate anther randm ntal slutn and btan the crrespndng lcal ptmal slutn by lcal search; cmpare the tw lcal ptmal slutns and get the current ptmal slutn. terate ths prcedure untl the teratn number r ther termnatn cndtns are met. C. mage Regstratn Usng Randm Lcal Search mage regstratn usng RLS s lke that descrbed n subsectn V-A, and the man dfference s n step 4, where randm lcal search s used t select feature pnts n and the crrespndng nes n. Accrdng t the prcedure f RLS, three feature pnts n s randmly selected wth the prbabltes prprtnal t ther vtng values, and the crrespndng features n s selected wth the prbabltes prprtnal t ther vtng values when they are smaller than the vtng values f ther crrespndng features n, and wth prbabltes equal t sme cnstant when they are larger. The randm lcal search apprach mprves the explratn capablty. Ths helps t fnd the glbal ptmal slutn wth mderate cmputatnal csts. V. EXPERENTAL RESULTS any experments are cnducted t demnstrate the effcency f the prpsed algrthm bth fr synthetc and real-wrld mages. n experments, we take sme mages fr the references, and small mages are cut frm these mages. The small mages are rtated, scaled, and the resultng mages are used as the sensed mages. The expermental results are shwn n Fg. 3 fr synthetc mages and n Fg. 4 fr realwrld mages. n experments, the rtatn angle can be cmputed usng the dstrbutns f lne segments alng the crdnate, and ther parameters are btaned thrugh a few hypthess-and-test prcesses. n practce, lne segments can be detected usng methds ther than Hugh transfrm t reduce cmputatnal cmplexty. V. CONCLUSONS An effcent Hugh-dman mage regstratn algrthm s presented n ths paper. Theretcal analyses and expermental results shw that t s bth rbust and effcent fr mst mages rch wth lne features. n ths paper, nly smlarty transfrm s cnsdered, and mre cmplex gemetrc transfrm wll be addressed n the future. REFERENCES [] L. G. Brwn, A Survey f mage Regstratn Technques, AC Cmputng Surveys, Vl. 4, pp , 99. [] Barbara Ztva and Jan Flusser, mage Regstratn ethds: A Survey, mage and Vsn Cmputng, Vl., pp. 977-, 3. [3] A. Gshtasby, G. C. Stckman and C. V. Page, A Regn-Based Apprach t Dgtal mage Regstratn wth Subpxel Accuracy, EEE Transactns n Gescence and Remte Sensng, Vl. 4, pp , 986.

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