A Planar Perspective Image Matching using Point Correspondences and Rectangle-to-Quadrilateral Mapping

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1 Plnr Perspective Ige tching using Point Correspondences nd Rectngle-to-Qudrilterl pping Dong-Keun Ki Deprtent of Coputer nd Infortion Science Seon Universit Jeonbuk Nwon Kore Bung-Te Jng Electronics nd Telecounictions Reserch InstituteETRI Tejeon Kore Chi-Jung Hwng Deprtent of Coputer Science Chungn Ntionl Universit Tejeon Kore BSTRCT In this pper we considered plnr perspective trnsfortion between iges with overlpping region. It is bsed on the rectngle-to-qudrilterl pping nd norlized correltions. Initill the globl trnsltion is deterined b using block tching. nd to find the correspondence points iizing correltion in overlpping region b the perspective trnsfortion we used siulted nneling S lgorith bsed on the norlized correltion. In the block tching nd S we used Gussin prid structure. We show results of ppling our proposed lgorith to osic iges.. Introduction Ige osicing cn crete lrge ige fro sequence of iges with overlpping region. It is the process of wrping sequentil iges cptured fro rel world scene nd generting single lrge ige. We cn crete the osic iges b ige lignent nd blending first is to wrp the iges b the trnsfortion between overlpping iges. Second is to blend iges wrped b the trnsfortion. There re severl trnsfortions tht we cn use to wrp iges. Tht is pure trnsltion rigid ffine nd perspective trnsfortion. To wrp iges we use the perspective trnsfortion which hs eight degrees of freedo. It cn be deterined b iniizing the su squred of the difference intensit between overlpping res using Levenberg- rqurdt lgorith [ ]. In this pper we considered finding the perspective trnsfor between the overlpping region b the norlized correltion nd rectngle-to-qudrilterl pping. The perspective trnsfortion hs eight degrees of freedo. So the eight coefficients cn be deterined b using four correspondence points between the reference nd trget iges. The eights coefficients cn deterined b using rectngle-to-qudrilterl pping. In the net section we briefl review of rectngle-toqudrilterl pping nd propose our ethods in the net section the following section shows eperientl results to erge three iges.. Plnr Perspective Trnsfortion generl plnr perspective trnsfortion cn be represented s: Fifth IEEE Southwest Sposiu on Ige nlsis nd Interprettion SSII -9--/ $. IEEE

2 For the perspective trnsfortion the forwrd trnsfortions re The perspective trnsfortion hs eight degrees of freedo. So the eight coefficients cn be deterined b using four correspondence points between the reference I nd trget iges I. The eight coefficients re deterined b solving the liner sste. It is possible to speed up in cse of rectngle-toqudrilterl pping [ ]. We briefl review of rectngle-to-qudrilterl pping. We will consider pping rectngle to n rbitrr qudrilterl like figure. The four correspondence points re on reference ige nd on trget ige. - Figure. Rectngle-to-qudrilterl pping. Unit Squre-to- Qudrilterl pping We first consider unit squre-to- qudrilterl pping [] i.e. pping between nd. The trnsfortion is s: Where. Rectngle-to-Qudrilterl pping Net we will consider rectngle-to-qudrilterl pping between on reference ige nd on trget ige. It cn be ccoplished b scle nd trnsltion of unit squre-to-qudrilterl pping s: nd lso it cn be find the inverse projective trnsfor in qudrilterl-to-rectngle pping s: [ ] [ ] S T where w v u [ ] [ ] T S where w v u Fifth IEEE Southwest Sposiu on Ige nlsis nd Interprettion SSII -9--/ $. IEEE

3 . Finding the correspondence points. Globl Trnsltions b Initil Block tching To find n initil trnsfortion we use block tching b the norlized correltion. For ech points i i of the rectngle grid e.g. in reference ige we find the point i i of iizing the norlized correltion using the restricted window e.g.. We hve tested the tching points becuse istch be found. For ech correspondence point pirs i i nd i i we cn clculte trnsltion between esure between the reference ige I nd trget I. Then we choose the trnsltion of iizing the norlized correltion eqution in the overlpping re b the trnsltion. To gurntee good initil solution it cn be used ore grid points thn four in reference ige.. Objective Function We hve considered the norlized correltion of intensit s siilrit esure in overlpping re of the reference ige I nd trget I. It is defined within the overlpping region b the perspective trnsfor of rectngle-to-qudrilterl pping. Inferring the plnner perspective trnsfor between two iges is to find the eight coefficients of iizing eqution. E[ I I ] E[ I ] E[ I ] R σ σ I I We ssue tht the right of the reference ige is overlpping in the left of the trget. nd we fied rectngle in the reference ige I.. Finding the correspondence points b S The globl trnsltion b block tching is used s n initil solution for the perspective trnsfor. To find the solution of iizing the objective function we use siulted nneling S lgorith []. correspondence pirs b equtions nd. Deterine the overlpping region between two iges b the perspective trnsfortion nd clculte the correltion oldr b eqution. Perturb the points i i i.. in sll rnge of the trget ige nd clculte the perspective trnsfortion b equtions nd deterine the overlpping region between two iges nd clculte the correltion newr b eqution. If oldr < newr then ccept the perturbed points. Otherwise ccept with probbilit pep[-oldr-newr/kt]. Iterte step nd until oldr newr < threshold. S cn converge in few itertions becuse we cn give n initil solution close to globl. To find effectivel the solution we construct Gussin prid structure of input iges with four lers. First we perfor our ethods in the corse ler. Then the previous corse solution used in the net fine ler.. Eperientl Results In our eperients we hve considered the erging of three input iges b using the proposed ethod. We considered the norlized correltion to find globl trnsltion b block tching nd to find the perspective trnsfortion in overlpping re b S. In the overlpping region we blend two iges b the liner weight function. Figure b nd c show results of finding the correspondence points fro pirs of input iges in office. Figure show results of ppling our proposed lgorith to osic iges. nd lso figure b nd c show results of finding the correspondence points fro pirs of input iges in office. Figure d nd Figure d show results of ppling our proposed lgorith to osic ige. Figure d nd Figure d re results using both the inverse pping between the left ige nd the iddle ige b b nd the forwrd pping between the iddle b b nd the right ige c c respectivel. Initilize teperture T clculte the perspective trnsfortion using Fifth IEEE Southwest Sposiu on Ige nlsis nd Interprettion SSII -9--/ $. IEEE

4 b c d Figure. osic Ige b c d Figure. osic Ige Fifth IEEE Southwest Sposiu on Ige nlsis nd Interprettion SSII -9--/ $. IEEE

5 . Conclusions We hve considered the perspective trnsfortion between two iges tht re overlpping. It is bsed on rectngle-to-qudrilterl pping of four correspondence points. The four correspondence points re deterined b iizing the norlized correltions using block tching nd S lgorith. We show soe results of ppling our proposed ethod to erge iges. REFERENCES [] Richrd Szeliski "Video osics for virtul Environents" IEEE Coputer Grphics nd ppliction 99 pp.-. [] Richrd Szeliski "Ige osicing for Tele-Relit pplictions" Cbridge Reserch Lb Technicl Report 99. [] Hrpreet S. Swhne et l l "True ulti-ige lignent nd Its ppliction to osicing nd Lens Distortion Correction" IEEE PI vol no []. Qinfen Zheng nd R Chellpp utotic Representtion of Oblique ril Iges Proc ICIP- 9vol. pp.8-pp.. []. George Wolberg Digitl ige wrping IEEE Coputer Societ Press 99. []. Rnd Crne Siplified pproch to ige processing []. W.H.Press et l Neuericl Recipes in C: The rt of Scientific Coputing nd Edition Cbridge Univ Press 99. Fifth IEEE Southwest Sposiu on Ige nlsis nd Interprettion SSII -9--/ $. IEEE