Different methods of image mapping, its advantages and disadvantages

Transcription

1 Interntionl Acdemic Institte for Science nd Technolog Interntionl Acdemic Jornl of Science nd Engineering Vol. No. pp. -. ISSN -89 Interntionl Acdemic Jornl of Science nd Engineering Different methods of imge mpping its dntges nd disdntges Nfise Zrei Abdolrez Sepni Institte of Optic Indstries of Esfhn Irn Abstrct Imge mpping is growing brnch of imge processing science ]. Geometric trnsformtion of digitl imges is the min discssed sbject in this brnch. Geometric trnsformtion of points locted in sorce imge pss to different coordintes in destintion imge. Mpping cn be referring to simple geometric trnsformtion sch s moing or comple conersions tht een the cnnot be epressed in closed form. In this std different mpping methods their dntges nd disdntges re discssed. Kewords: imge mpping bckwrd method ffine perspectie Introdction Historicll mpping ws condcted the first time in 9 on n nloge imge b sing opticl sstems. In 98 significnt progresses were chieed in this field. The opticl sstems with this niqe dntge work with the speed of light. The limittion of these sstems is in their lower control nd fleibilit. Digitl compters do not he these limittions nd cn do the mpping with er good precision nd qlit. Geometric conersions of digitl imges were sed for first time in the field of remote Sensing. From mpping pplictions cn be noted to the pplictions of remote sensing rdiolog compter grphics morphing rendering trcking ] imge stbiliztion ] improing the imge ] nd compression the reminder of ideo imge sing the interpoltion between frmes ].. Mpping procedres

2 Interntionl Acdemic Jornl of Science nd Engineering Vol. No. pp. -. Imge mpping cn be done in two ws Forwrd nd Bckwrd tht ech hs dntges nd disdntges.. Forwrd Method In the Forwrd method trnsfer fnction mpping is pplied to the sorce imge nd ech piel of the resorce imge is mpping to the point of destintion imge. Figre. shows this method. () f() () Figre : Forwrd Mpping In Figre ( ) coordintes of piel indictes in the sorce imge. This piel b mpping fnction f ( ) to the point with coordintes ( ) is mpped in the destintion imge. Since the imge is digitl nd piel coordintes re integers often t the mpped point there is no piel.in this cse the mpped le is ttribted to one or more piels tht he closest distnce. If the mpping le is ttribted to few piels first it shold be specified their nmbers or mimm distnce from mpping site nd secondl coefficient tht is gien to ech piel shold be determined depending on the distnce In other words for ech piel of destintion imge shold be defined plce rnge or field tht if le ws mpped to point within this rnge ws. This piel will be ffected b it nd it will lso be defined on the bsis of these inflences rtes. First it m be not mpped no les in the field of effects of destintion piels which will be csed drk spots in the imge. Second the nmber of mpped points in the inflence rnge of ech piel is ncertin nd this isse cses difficlt for weightings. In fct for ech of the imge destintion piels shold be considered bffer tht re mintined ll the mpped points in the rnge of its inflence with ech interls nd finll determine the tre le of the piel or the destintion piel is red of memor nd fter modifing gin is plced into its loction. Implementing sch procedre reqires high processing costs tht cse to prolong the processing time nd lso to increse the hrdwre olme. Howeer in pplictions where high precision is not reqired this method becse of the mentioned dntges is er sitble for implementtion The dntge of this method is tht it does not need to sppl the totl inpt imge in order to strt the process bt in generl this method is not sitble for implementtion nd in ction is fcing with two flws.. Reersed method In reersed method to clclte the le of destintion imge piel reersed trnsfer fnction is mpped to the coordintes of tht piel nd the coordintes of the corresponding point in the sorce imge is clclted. Figre shows the reersed method. Piel of the destintion imge with its coordintes ( ) is mpped to the bckwrd fnction f to the point with coordintes ( ) in the sorce imge. Sch s Forwrd method there is sll no piel t this point. In this cse or the le of the nerest piel to the mpping point s the destintion imge piel le is considered or with the help of interpoltion of seerl points of its srronding the piel les re clclted.

3 Interntionl Acdemic Jornl of Science nd Engineering Vol. No. pp. -. f - () () () Figre : Bckwrd Mpping Defects listed for the Forwrd method will neer hppen here. This method is sitble for implementtion. Most reported implementtions in esss he been sed of this method 9 8 nd ].. Mpping fnction Mpping fnction is reltion tht is connected the coordinte of points locted in n imge nd mpped imge. According to the ppliction of the mpping is determined the kind of fnction. In this chpter focs is on conersions tht re the most pplicble. These conersions he sll closed mthemticl forms nd most importnt of them re the ffine trnsformtions perspectie biliner nd polnomil which their eplntions will come. Of corse there re conersions tht cnnot be considered closed form for them tht will be lso inestigted the mnner of implementing sch conersions.. Affine trnsformtions Affine pblic displ is s follows: ] ] () In other words this conersion m be showed s reltionship (). () Affine trnsformtion is eqilent to the Prllel Plne Projection of sorce imge on the destintion imge. For this reson prllel lines remin prllel fter mpping. Also the points with sme distnce re presered fter mpping (lthogh the ctl distnce between the two imges m different) As this conersion hs si prmeters re defined b three points. For this reson tringle is mpped to n rbitrr tringle bt cnnot be mpped qdrngle to n rbitrr qdrilterl. In this conersion the stright lines re presered nd sometimes re sed of this fetre in the implementtion of this trnsformtion ]. Simpler trnsformtions re deried from this conersion tht will be epressed the pblic form for ech in the following. Trnsmission is conersion tht nd with constnt les re dded nd the conersion trnsition mtri is s follows:

4 Interntionl Acdemic Jornl of Science nd Engineering Vol. No. pp. -. ] ] T T () Rottion ll points re trned rond the origin s n mont of the ngle θ cos sin sin cos ] ] (). Resize mkes the imge lrger or smller ] ] S S () When hs liner dependence to nd tkes retrn sme mont of sme or ice ers conert tht is hppen ctting nd cn be epressed in the following form. ] ] H ] ] H () nd () Three trnsformtions rottion nd resizing nd conersion cn be combined nd cn be chieed conersion tht will be inclded ll of them. As mentioned in boe to identif the ffine conersion prmeters three cler points in the sorce imge nd their loctions fter mpping re sfficient. If three points re cler ( k k ) nd ( k k ) for k = then we he: (9) This reltionship cn be epressed s X = UA. Finll few emples of ffine trnsformtions he been shown in Figre.

5 Interntionl Acdemic Jornl of Science nd Engineering Vol. No. pp. -. (A) (B) (C) (E) (D) Figre shows few emples of ffine trnsformtions: A) Originl imge B) Rottion of the - degrees nd Conerting the scle of. C) degrees horizontl ctting D) Horizontl nd erticl trnsmission E) Chnges in. scles (from ]). Conerting the perspectie Pblic displ of perspectie trnsformtion is s follows: w] w] w w () Perspectie conersion or projection mpping occrs when ] T to be not zero. In this conersion stright lines fter mpping re presered. Onl prllel lines remin tht re prllel to the rdition plte. The grop of other prllel lines conerges towrds Vnishing Point. Using Eqtion Forwrd Mpping fnction of this conersion will be s follows: w w ()

6 Interntionl Acdemic Jornl of Science nd Engineering Vol. No. pp. -. This conersion does not he the prmeter tht b normlizing the generl mtri T ccording to decreses to eight prmeters. Therefore this conersion will be determined with for-points nd is cpble to mp tetrhedron to n rbitrr qdrilterl. Figre shows two emples of perspectie conersion. Figre : emples of perspectie mpping As ffine trnsformtions for this trnsformtion lso cn be clclted bckwrd trnsform. Reerse of perspectie trnsformtion will be s follows. w] w ] () To obtin the coefficients fter normlizing the pblic mtri T in terms of Eqtion is rewritten s follows. If ( k k ) nd ( k k ) for k = re for distinct points of sorce nd destintion cn be formed the eqtion b sing the reltionship. () In this eqtion re two ectors in forms nd. A ] T nd X ] T

7 Interntionl Acdemic Jornl of Science nd Engineering Vol. No. pp. -. X A () B soling this sstem of liner eqtions cn be obtined coefficients of perspectie mpping. trnsform biliner Pblic form of biliner trnsformtion is reltionship. The trnsformtion hs the most pplictions in mpping of rectngle to n neen qdrilterl. ] ] b b b b () In remote sensing nd medicl illstrtor to clibrte the sensor is mpped cler points to loctions tht re lred specified to be compensted sensor distrbnces nd registrtion is done er good. In compter grphics for se histogrms this trnsformtion pls mjor role. This trnsformtion of stright lines erticll nd horizontll so st right fter mpping. Eqidistnt points on the stright lines erticll nd horizontll fter mpping lso remin eqidistnt. Lines tht re not in line with the erticl rrngement re trned into second-rte cres. Figre shows two emples of this trnsformtion. Figre : emples of two liner mpping To chiee the coefficients of this conersion s perspectie conersion for points in the sorce imge nd corresponding with them mst be known in the destintion imge. If ( k k ) nd ( k k ) for k =

8 Interntionl Acdemic Jornl of Science nd Engineering Vol. No. pp. -. re these for points soling liner eqtions will be led to clclte coefficients to. b to b will be clclted with the sme reltion. ().polnomil mpping Geometric correction of n imge reqires to loction conersion to reerse n Unknown distortion fnction. This is done sing polnomil trnsformtion. This fnction is epressed b the following generl reltionship. N N i ij i j N N i b ij i j i i j j () N degree is determined with regrd to the ppliction. In most pplictions degree is sfficient bt nd degrees re lso sed. degree of this conersion is eqilent to ffine conersion. Affine conersion cn be known s combintion from seerl specific geometric conersions sch s rottion nd trnsformtion prmeters cn be obtined b this w. The reson hs mn pplictions in compter grphics. Unlike compter grphics in the fields of remote sensing medicl imging nd mchine ision often things re not like this. In these fields there is no specific model to be pplied to the imge bt in the inpt nd otpt imges some corresponding points re cler tht re sid them control points or Tie points. In sch conditions conersion prmeters shold be chieed in sch w tht conersion fnction is estblished the corresponding of control points. When the model prmeters were obtined this model is pplied to the whole imge nd the otpt imge is obtined in modified form. To obtin the coefficients of this conersion coordintes of cler points re pt in reltions ntil sstem of eqtions which sll the nmber of its eqtions is greter thn the nmber of nknowns is tken shpe. In polnomil N degree of the nmber of prmeters is obtined from the 8 reltionship. K N N i ( N )( N ) (8) i j. Pblic mpping In some circmstnces it m be mpped in sch w tht the mpping fnction cnnot be epressed in closed-form. In sch circmstnces of the LUT is sed for mpping implementtion. In reersed mode for 8

9 Interntionl Acdemic Jornl of Science nd Engineering Vol. No. pp. -. ll prts of the destintion imges corresponding coordintes in the sorce imge re clclted nd re plced in memor. Memor size shold be lrger thn the totl nmber of imge piels. Now for mpping n imge insted of piels of m destintion imge the point of sorce imge tht it s coordinte is in the m ddress of memor is selected. In Forwrd mode this method does not chnge onl the loction of two imges is chnged nd mpping fnction for sorce imge is clclted. The min dntge of this method is tht it cn perform mpping fnctions with n compleit. If the mpping fnction is the sme for ll imges this method elimintes the need to the time-consming nd high-olme clcltions nd the mpping with high-speed cn be performed with this method ]. Conclsion Biliner conersion in remote sensing nd medicl illstrtor to clibrte the sensor cler points re mpped to loctions tht re lred specified to be compensted sensor distrbnces nd registrtion is done er good. In compter grphics for se histogrms this conersion pls ke role. Pblic mpping cn perform mpping fnctions of n compleit. If the mpping fnction is the sme for ll imges this method elimintes the need to the time-consming nd high-olme clcltions nd the mpping with high-speed cn be performed with this method nd in contrst to ffine conersion the perspectie conersion cn be mpped tetrhedron to n rbitrr qdrilterl. Forwrd methods hs two mjor disdntge the first is this in the sphere of inflence of some destintion piels re not mpped to n le which will be csed drk spots in the imge. Second the nmber of mpped points in the sphere of inflence of ech ncler piel nd it mkes problem for weighting. Listed disdntges for the Forwrd method will neer hppen in reerse method. And de to the redction of implementtion time is er sitble. Figre : simlted mpping fnction (perspectie polnomils) 9

10 Interntionl Acdemic Jornl of Science nd Engineering Vol. No. pp. -. Generll for conersions sch s trnsport scle chnges rottion second-degree polnomil is sfficient ]. For more locl control ffine conersion nd piece polnomil tht their prmeters re in different prts hs mn pplictions. Reference ] Wolberg G. Digitl Imge Wrping IEEE Compter Societ Press 99. ] P. Mttson D. Kim nd Y. Kim "Generlized Imge Wrping Using Enhnced Lookp Tbles " Int. J. of Imging Sstems nd Technolog ] B. Chen F. Dchille nd A. Kfmn "Forwrd Imge Mpping" IEEE ] C. Gestrin F. Cozmn nd M. G. Simoes "Indstril pplictions of Imge mosicing nd stbiliztion " Second Interntionl Conf. on Knowledge-Bsed Inteligent Electronic Sstems ] P. J. Brt nd K. J. Hnn "Sstem nd Method for Electronic Imge Stbiliztion" U. S. Ptent NO ] I. Ghosh nd B. Mjmdr "VLSI Implementtion of n Efficient ASIC Architectre for Rel- Time Rottion of Digitl Imges " Int. J. Ptern Recogn. Artif. Intell ] B.Hwkins nd L. Smith "An Enhnced Rel-Time Video Stbiliztion Algorithm Implemented Using Reconfigrble Processing Modle " ICSPAT. 8] D. Kim R. Mngli nd Y. Kim "Dt Cche nd Forwrd Memor Access in Progrming Mediprocessors " IEEE Micro. 9] O. D. Ens nd Y. Kim "Efficient Implementtion of Imge Wrping on Mltimedi Processor " Rel-Time Imging ] S. Siegel nd B. Goetz-Greenwld "VME Bords Perform High Speed Sptil Wrping" SPIE Proceedings ] K. Prtt Digitl Imge Processing John Wile nd Sons Inc..