A BAND SELECTION METHOD FOR HIGH PRECISION REGISTRATION OF HYPERSPECTRAL IMAGE. Han Yang 1, Xiaorun Li *1

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1 A BAND SEECION MEHOD FOR HIGH PRECISION REGISRAION OF HYPERSPECRA IMAGE Han Yang, Xarun * Cllege f Electrcal Engneerng, Zhejang Unverty, Hangzhu 3007, Chna - lxrly@zju.edu.cn KEY WORDS: Hyperpectral Image, Hgh Spatal Relutn Image, Regtratn, CRB hery, Band Selectn, Algrthm ABSRAC: Durng the regtratn f hyperpectral mage and hgh patal relutn mage, t much band n a hyperpectral mage make t dffcult t elect band wth gd regtratn perfrmance. errble band are pble t reduce matchng peed and accuracy. lve th prblem, an algrthm baed n Cram er-ra lwer bund thery prped t elect gd matchng band n th paper. he algrthm apple the Cram er-ra lwer bund thery t the tudy f regtratn accuracy, and elect gd matchng band by CRB parameter. Experment hw that the algrthm n th paper can che gd matchng band and prvde better data fr the regtratn f hyperpectral mage and hgh patal relutn mage.. INRODUCION Hyperpectral mage are wldly appled n agrculture, fretry, gecence, and atrnmy a hyperpectral mage have a wealth f pectral nfrmatn that can detect nndetectable ubtance n panchrmatc and multpectral patal relutn mage (Yuan Zhu, 07). Cmpared wth hyperpectral mage, multpectral mage have hgher patal relutn, cllabratve prceng f hyperpectral mage and hgh patal relutn mage n the ame area wll help t effectvely detect and recgnze unknwn target n hyperpectral mage. Due t dfferent enr relutn, dfferent ptcal path, r dfferent mage mechanm, the phenmena f tranlatn, rtatn and calng may ccur between mage. Prece regtratn f multurce remte enng mage the c-prceng f hyperpectral mage and hgh patal relutn. Graycale and texture dfference between dfferent band n hyperpectral mage and hgh patal relutn mage are an mprtant rean fr pr matchng accuracy. S chng apprprate band f hyperpectral mage t match the key t mprve the regtratn accuracy f hyperpectral mage and hgh patal relutn mage. he methd f PCA wa derved t reduce hyperpectral data dmenn n (YU Xan-chuan, 03), (e Wang, 007). A new band wll be generated baed n all band f hyperpectral mage thrugh the methd f PCA. Althugh the methd accunt fr mnmzng the l f mprtant nfrmatn fr the later tage f the methdlgy, th new band wll le me detal f the rgnal mage, reultng n ncreaed regtratn dffculty. In addtn, Hang Chen et al (CHEN Hang, 03) elected a band f hyperpectral mage accrdng t the harpne f the texture nfrmatn t partcpate n the regtratn. Hwever, th methd n t baed n the quanttatve evaluatn ndex f regtratn accuracy, and the elected band regtratn accuracy need t be mprved. In (Bnd, 005), CRB thery wa appled t the feld f regtratn, and the lwer lmt f ne varance f mage wa meaured by the lwer CRB t evaluate the mage regtratn perfrmance. Mre recently, (Yetk I S, 006) appled CRB thery t the evaluatn f regtratn parameter, and theretcally deduced the methd f calculatng the lwer bund f CRB fr dfferent regtratn methd. In (Xu Bahu, 0) and (I Jng, 009), the lwer lmt f CRB fr regtratn parameter wa calculated n dfferent cenar. It wa prved expermentally that the lwer lmt f CRB culd be ued a an effectve tl fr mage regtratn perfrmance evaluatn. In th paper, a hgh-precn regtratn band electn methd baed n CRB thery prped, whch nt nly reduce the cmputatnal cmplexty f the data but al elect the band wth gd matchng perfrmance n hyperpectral mage.. REAED WORK. Affne Defrmatn Mdel Affne defrmatn mdel (Gng M, 04) the mt cmmn gemetrc defrmatn mdel. when ung an affne mdel fr regtratn, the gemetrc relatnhp between the pendng map and the baelne a fllw: c, n x t a* * x x n,c t Pnt n the reference mage S,,..., l number f whch, amng them, (), the x n the ened mage O,,..., l whch, amng them, x. Pnt, the number f, a the cale factr, and θ the rtatn angle. ( t, t ) the amunt f tranlatn n the x, y drectn. It upped that D the defrmatn matrx, the tranlatn vectr, the abve equatn can be abbrevated a: x = D* + () he real ptn n the ened mage crrepnded t the pnt R r r r, amng et S f the reference mage,,..., l h cntrbutn ha been peer-revewed. Authr 08. CC BY 4.0 cene. 067

2 them, x r r r. It upped that there nly Gauan whte ne between the crrepndng pnt and real pnt, then r n, cvarance matrx dag x, y, dag x, y amng then,, n nx n, n n, n x c, n x r t n a* * x x x n,c r t n he crrepndng abbrevatn :. CRB hery, : (3) = D* r + + n = h + n (4) he lwer lmt f CRB prped fr the prblem f parameter etmatn, and the lwer bund et fr the varance f unbaed etmatr. he unbaed etmatr varance f parameter can nly apprach the lwer CRB lmt wthut reachng. (Steven M. Key, 993) emma : It aumed that the prbablty denty functn p(x ;θ) f a parameter etmate atfe the regularty cndtn ln px ( ; ) E[ ] 0 fr all θ, when the expectatn taken wth repect t p(x ;θ). hen the varance f any unbaed etmatr ln px ( [0]; ) ˆ var( ˆ ) lwer CRB fr parameter θ. mut atfy ln px ( [0]; ) (5) the mnmum varance defned a the emma : It aumed that the prbablty denty functn p(x ;θ) f everal parameter etmate atfe the regularty ln p( x; θ) cndtn E[ ] 0 fr all θ, when the expectatn taken wth repect t p(x ;θ). hen the cvarance matrx f any unbaed etmatr ˆ atfe Amng them C I θ 0 (6) ( ) ˆ ln p( ; ) [ ( )] j E[ x θ I θ ] θ θ j defned a FIM nfrmatn matrx. Cvarance lwer bund matrx ˆ var( ) [ Cˆ] [ I ( θ )] 3. MEHODOOGY 3. Calculatn Methd f CRB wer mt Snce the varance f the parameter θ can reflect the accuracy f the parameter etmatn, the maller the varance, the mre accurate the etmatn. herefre, t feable t ue the CRB lwer bund t evaluate the parameter. We can ee frm the ecnd ectn f chapter tw, the lwer CRB lved by evaluatng the lkelhd functn f the parameter etmate by the ecnd-rder dervatve. herefre, when applyng the CRB thery t the evaluatn f regtratn parameter, a lkelhd functn huld be cntructed frt, and then the lkelhd functn derved. he fllwng the dervatn prce. he regtratn mdel ue the affne defrmatn mdel, a hwn n equatn (3) and (4). he defrmatn parameter are x y, H h, h,..., h A a,, t, t, C, C dagnal matrx f. he lg lkelhd functn f tw mage defrmatn parameter : ln p (, : ) * [ C ( ) C O S A O R O R S G ( S G )] cnt are (7) herefr the varu cmpnent f the Fh nfrmatn matrx are: J J Am, An ln( p( O, S : A)) E AA m n (8) h h h h ( * ) ( * ) x x Am, A n x Am An y Am An CRB ( ) J ( ) 3. Regtratn Perfrmance Evaluatn (9) A A (0) Cmpared wth the lwer lmt f CRB f the regtratn parameter, the regtratn ptn dfference can mre ntutvely reflect the mage regtratn perfrmance. S, n the ba f the lwer lmt f the regtratn parameter, the lwer lmt f the ptn accuracy f the regtratn calculated, and the regtratn perfrmance mre ntutvely reflected. he fllwng mple dervatn f the calculatn f ptn accuracy. Ptn errr can be wrtten a: S ( Dr ) () x y Cv( ) dag([, ]) () h cntrbutn ha been peer-revewed. Authr 08. CC BY 4.0 cene. 068

3 It aumed A a,, tx, t y ga ( ), amng them, cmbne equatn [9], then we can get the fllwng equatn: g( A) g( A) Cv( ) J ( A)[ ] (3) A A Cv J A dag A A g( A) g( A) x y ( ) ( )[ ] ([, ]) (4) he dagnal element f the matrx btaned are the lwer lmt f the ptn errr n the x and y drectn. 3.3 Algrthm Flw 3.3. Prelmnary Band Selectn: he hgh data dmennalty f hyperpectral mage ncreae the burden n data cmputatn, trage, and tranmn(swe,07). A there are t many band n the hyperpectral mage, the matchng band electn algrthm frt make a prelmnary band electn f the hyperpectral mage t reduce the amunt f data n rder t reduce the ubequent calculatn. Amng lt f band electn methd, K dvergence methd take full accunt f the crrelatn between the band, and the elected band thrugh K dvergence repreentatve, we ue the methd f K dvergence t prelmnarly elect the band. he cncrete methd a fllw: frtly, the graycale dtrbutn f each band f the hyperpectral mage cunted, and then K dvergence value f each band agant t next ne-thrd band calculated. he pecfc calculatn methd ee equatn 5. D( P Q) ( P( x)lg( P( x) / Q( x))) (Q( x)lg( Q( x) / P( x))) (5) 3.3. Regtratn: In rder t pck the bet matchng band et, a prelmnary matchng prce neceary. After a prelmnary match, we can pck ut me f the better matchng band thrugh analyzng the matchng parameter. he man purpe f th prce t calculate the regtratn parameter, rather than gettng accurate regtratn reult. herefre, regtratn methd uch a regn-baed regtratn, feature-baed regtratn are t meet the requrement. Hyperpectral mage ha t many band, w che SIF, a cmmn pnt feature baed algrthm (we D G, 004), accuntng fr the algrthm peed. In th prce, feature pnt are extracted and decrbed by SIF algrthm, and then the Eucldean dtance between feature pnt f reference mage and ene mage calculated and cmpared. Affne defrmatn mdel ued t calculate the parameter f regtratn defrmatn. Fgure: hgh-precn regtratn band electn algrthm flw chart he purpe f matchng band electn algrthm t elect utable band n a large number f band f hyperpectral mage fr regtratn, a t reduce the amunt f matchng cmputatn and prvde a band et wth better matchng perfrmance fr ubequent regtratn. Algrthm flw chart hwn n Fgure ne. he prce f the algrthm dvded nt the fllwng ectn. Frtly, a prelmnary band electn made fr the hyperpectral mage t elect me band wth rch nfrmatn and lttle relevance. hen the prelmnary elected band and hgh-relutn mage are regtered, meanwhle recrd the regtratn reult. Fnally, the CRB lwer lmt f regtratn parameter f dfferent band calculated accrdng t the regtratn reult. Several band wth gd regtratn perfrmance are elected accrdng t the CRB lwer lmt hgh-precn matchng band electn: After prelmnary match, we get a ere f matchng reult. he abve decrbe hw t calculate the CRB lwer lmt thrugh the regtratn parameter. h tep apple the abve frmula t calculate the CRB lwer lmt and the lwer lmt f ptn accuracy fr each et f regtratn parameter. Accrdng t the lcatn accuracy f the lwer lmt f the data, we can che the band wth maller regtratn errr, that hgh-precn matchng band. 4. EXPRIMEN he man purpe f th ectn t prve that the band elected by the methd prped n th paper a band that matche well. herefre, the experment elected hyperpectral mage ban accrdng t the hgh-precn regtratn band electn algrthm. he elected band regtratn reult and PCA regtratn reult were cmpared t berve the elected band regtratn perfrmance. 4. Smulated Image Data Set he reference mage n a 005 aeral hyperpectral mage wth a ttal f 4 band, 0 meter relutn (ze: 35*500). he h cntrbutn ha been peer-revewed. Authr 08. CC BY 4.0 cene. 069

4 ened mage elected frm the reference mage, delarge 4 tme and rtate 0 degree. 4. Evaluatn Crtera he rt mean quare errr(rmse) ued a an ndex t evaluate the regtratn accuracy. are randmly generated, and the crrepndng pnt par are btaned by the affne tranfrmatn mdel frmed by the requred parameter, the crrepndng pnt par are btaned by the affne tranfrmatn mdel frmed by the real parameter. he frmula fr calculatng the rt mean quare errr a fllw: RMSE x x y y 4.3 Reult and Analy N '' ' '' ' (( ) ( ) ) N (6) lwer lmt calculatn. he experment hw that the band elected by the methd n th paper a band et wth better regtratn perfrmance. he methd can make mre accurate judgment f the regtratn reult wthut knwng the true defrmatn parameter between the reference mage and the ened mage, then elect utable regtered band. Baed n the wrk, mre accurate regtratn pble between hyperpectral mage and hgh-relutn mage. ACKNOWEDGEMENS (OPIONA) h wrk wa upprted by the Natnal Natural Scence. Fun datn f Chna (n ) and the Jnt Fund f the Mntry f Educatn f Chna (n.64a0034). REFERENCES Pham., Schutte K, J., 005, Perfrmance f ptmal regtratn etmatr, Prc Spe. Chen H, Du X., Xa., Cheng X., J., 03, regtratn methd fr hyperpectral mage baed n cntrl pnt, Jurnal f Equpment Inttute, 4(3):09-3. Gng M, Zha S, u J, J., 04, A Nvel Care-t-Fne Scheme fr Autmatc Image Regtratn Baed n SIF and Mutual Infrmatn, IEEE ranactn n Gecence & Remte Senng, 5(7): Fgure rend chart f RMSE and CRB_x Wang, u X., D., 007, tudy f mage regtratn technque and applcatn, x an unverty f electrnc cence and technlgy. J, Huang P., Wang X., Pan X., J., 009, regtratn precn tudy baed n crlb thery fr ptcal bae mage and ar mage. we D., J., Dtnctve Image Feature frm Scale-Invarant Key pnt, Internatnal Jurnal f Cmputer Vn, 60():9-0. Feng S., Yuk I, Mar P, Marc, J., 07, hyperpectral band electn frm tattcal wavelet mdel, IEEE tranactn n gecence & remte enng, 55(4):-3 Fgure 3 RMSE f three methd Cmparng the curve f the CRB lwer lmt and the rt mean quare n fgure.he x ax f fgure the number f hyperpectral band. It can be fund that the trend f thee tw ndexe are cntent, whch hw that n general the CRB lwer lmt can meaure regtratn accuracy ntead f the rt mean quare. Frm fgure 3, t clear that the regtratn reult f the band elected by the CRB lwer lmt mre accurate than the band generated by PCA r PCA after nrmal band electn. 5. CONCUSION In th paper, an algrthm baed n CRB thery fr electng hyperpectral hgh-precn matchng band prped. Man tep have three: prelmnary band electn, regtratn, CRB Steven M., M., 993, Fundamental f Stattcal Sgnal Prceng Etmatn hery, page7-33. Xu B., Sh Z., Chen F., J., 0, characterzatn f mage regtratn errr baed n cramer-ra lwer bund, Jurnal f ntrumentatn. Yetk I., Nehra A, J., 006, Perfrmance bund n mage regtratn, IEEE ranactn n Sgnal Prceng, 54(5): Yu X., u Z., Hu D., J., 03, revew f remte enng mage regtratn technque, Optcal precn engneerng, (): Zhu Y, Anand R, Paul D, C., 07, nnrgd regtratn f hyperpectral and clr mage wth vatly dfferent patal and pectral relutn fr pectral unmxng and panharpenng, h cntrbutn ha been peer-revewed. Authr 08. CC BY 4.0 cene. 070

5 IEEE Cnference n Cmputer Vn and Pattern Recgntn Wrkhp, h cntrbutn ha been peer-revewed. Authr 08. CC BY 4.0 cene. 07