Announcements. Texture Mapping PA4. Geometric Registration
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1 Ross Beerdge Bre Drper Annonements Tetre Mppng Letre 5 Tesd, Noemer 7 th 5 PA grdes eng djsted Penltes for flppng dmensons to e remoed PA4 hnded ot tod De Tesd, De. 8 th See net slde for detls /7/5 PA4 Ross Beerdge Bre Drper Three ddtons oer PA Spelr Inter-refleton Rerse on refleton of ewng r Mltple reslt ks, dd to refleton Bse ses: R does not strke polgon Prodt of ks terms < /5 Hrd lmt of rersons (hose of mrrors) Trnslen Mterls now he trnslen perentges Rerse on ontnton of ewng r Angle of refrton for nfntel thn plnr srfe Sme se s oe (ks kt) Ant-lsng Fe rs throgh eer pel Rndoml postoned wthn pel sqre Ross Beerdge Bre Drper Reew: Trnsformton Mtres The mtr oe s n emple projeton mtr Q: Wht etl s eng projeted/trnsformed? A: Coordntes /7/5 /7/5 4 Geometr Regstrton Regstrton s the proes of mthng lotons n one mge to lotons n nother Does ths mtter? Geometr Regstrton (II) Geometr regstrton fnds mppng tht mps one mge onto the other We wll lmt orseles to lner trnsformton Imge from ClTeh56 dt set These two mges he the sme pels (Bt the mppng from left to rght mge s rndom) We shold e le to regster these
2 Reew: Imge Trnsformtons The smplest set of trnsformtons re trnslton, rotton, nd sle Together these re lled the smlrt trnsform. Smlrt trnsforms he 4 degrees of freedom. In mtr form these re: s s os Θ ( ) sn Θ ( ) sn Θ ( ) os Θ ( ) sle rotton nd... Smlrt Affne Trnsformtons All the smlrt trnsforms n e omned nto one gener mtr: Bt Ths mtr does more. Wht? hnt: two more trnsformton tpes nlded. hnt: 6 degrees of freedom (DOF) How n o spef ths mtr? f e d Hnt: dgonl terms re not eql, nd -d. Ths s eqlent to ddng two sher prmeters (or neql slng one sher). Smlrt s Affne Mtres Smlrt : 4 DOF Affne : 6 DOF f e d d Spefng Affne Trnsformtons There re s nknowns n the mtr ( throgh f) If o spef one pont n the sore mge nd orrespondng pont n the trget mge, tht elds two eqtons: So prodng three pont-to-pont orrespondenes spefes n ffne mtr f e d Affne Spefton: Emple There s one ffne trnsformton tht wll mp the green pont on the rght to the green pont on the left, nd lgn the red nd le ponts too. Solng Affne Trnsformtons These lner eqtons n e esl soled: WLOG, ssme then nd f so: ( ) ( ) ( ) ( ) ( ) Cllton of, s ndependent of llton of e, f g.
3 Solng Affne (ont.) Ths n e ssttted n to sole for The sme proess wth s soles for d,e,f Aot the WLOG: It ws tre ese o n trnslte the orgnl oordnte sstem (-, - ) So wht do o do to ompenste? Alterntel, set p sstem of lner eqtons nd sole Solng Affne Trnsformtons (III) Bese re ndependent: Therefore Ross Beerdge Bre Drper When does ths he solton? /7/5 4 Perspete Trnsformtons We n go eond ffne trnsformtons. We n d o n p ers pet e t rn sfo rmto n o f plne to plne. Therefore, we n model n mge s plne n spe, nd projet t onto n other mge. How does ths dffer from perspete projeton? Perspete Mtr d e f w g h w, w Wh does element [,]? How mn ponts re needed to spef ths mtr? Solng for Perspete For orrespondng ponts prode eght eqtons, eght nknowns --- t we n t osere w w g h d e f w g h,, nd re no longer ndependent of d, e nd f ese the re lnked g nd h. Solng (ont.) Mltpl to get rd of the frton ( g h ) ( g h ) d e f Now, rememer tht the s, s, s s re known; grop the nknown terms g h d e f g h
4 Solng (III) Solng (IV) And epress the reslt s sstem of lner eqtons Fnll, nert the onstnt mtr nd sole d e f 4 4 g 4 4 h 4 Ross Beerdge Bre Drper, CS CSU d e f g 4 4 h Ross Beerdge Bre Drper Now to Tetre mppng Addng srfe detl Uqtos, nd sometmes oos Srfes n the world he pperne The re seldom one flt olor. The he tre tetre repetng ptterns. The he strtred mrkngs. The he tn hnges n srfe heght. Prsts ew (don t tr ths) Use eer more een smller nform trngles. Prgmtsts ew Pnt srfes wth mges tetre mppng. Imge from /7/5 /7/5 Ross Beerdge Bre Drper Ross Beerdge Bre Drper Mppng Mppng (II) The nderlng proess s regstrton Tetres re olor mges Logl tetre oords rn from (,) to (,) (,) Coordntes fed regrdless of mge sze Polgons re D srfes n D spe (,,z) (,) t,s oordntes /7/5 (,,z) The trnsformton from tetre oordntes to srfe oordntes s epressed s mtr /7/5 4
5 Ross Beerdge Bre Drper Tetre Mtres (OpenGL) Gen ertes nd the orrespondng tetre oordntes t s d e f z Wht tpe of trnsformton s ths? How mn orrespondenes re needed? Ross Beerdge Bre Drper Tetre Mppng n OpenGL The frgment proessor omptes refletne olor for eer pel When tetres re enled, The frgment proessor lso omptes tetre le for eer pel Usng the pel to do tetre mppng These les re mltpled together to prode the fnl le /7/5 5 /7/5 6 Ross Beerdge Bre Drper Isse : Smplng The mppng from srfe ponts to tetre oordntes prodes rel les X Smplng Ross Beerdge Bre Drper Nerest-neghor: pk the losest tetre pel Blner: lnerl nterpolte n oth dmensons B: ft rd order srfe to 6 srrondng ponts Not s epense s t sonds /7/5 7 /7/5 8 Smplng (III) Ross Beerdge Bre Drper A etter solton s for the tetre mp to e roghl the sme sze s the srfe projeton. A MpMp s n mge prmd lt from tetre mp Emple: f the tetre s 6464, the prmd lso nldes, 66, et. Ross Beerdge Bre Drpe Isse : Gettng Tetres WEB mllons of tetres people se them for kgronds of we pges lot Yo n downlod them n lk pkges, et.. Bld or own Mke them semless When tled, o nnot see the edges of the tles. /7/5 9 /7/5
6 Ross Beerdge Bre Drper Ross Beerdge Bre Drper Jst for emple Tetre Mkers There re tons of them.. Some emples: ftp://zdftp.zdnet.om/p/prte/swlib/grph s_mltmed_tools/grphs_tools/terlt.zp M.zp /7/5 /7/5 Ross Beerdge Bre Drper Ross Beerdge Bre Drper More Emples Tetres Srfe /7/5 /7/5 Ross Beerdge Bre Drper Tetre Mp from Imge /7/5 5 4
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