Metric 3D Surface Reconstruction from Uncalibrated Image ...

8 downloads 558405 Views 792KB Size Report
Modeling of 3D objects from image sequences is one of the .... will be used for illustration.7Г ome of the images of this sequence can be seen in ..... Moons, T. A Tutorial on Multi- ╦ iew┐є elationships, In╕ЮFЯv V¡V¢I═ цч╢7шЙгъщ$ ...
     ! !" #$% &' (  )*+,.-0/ %1234.5*6  798;:= ?@A BDCEBGFIHKJMLB NAOMPQ8$:=R*S+?I
ö D?*>@?*`)[G@?*9ED



ºL·2§

/

4

*U

ÀÁ=Â ·WxWx ÉÈ Â · x Q

M

@

ÀÁ  · ù xWx ÈÉ ù x  · x x xiQ

4

À

§Å68·

Á6 ù 5 5 6 ú 6 ÿ

6

)K

ø

ù

6

6

ú

6

ÿ È É

B

687/689:68; B 6 9 6=68øA? @ 6 ; 68?/6

6 ·­

.

c

c



(C·E0 D

øøAF

§G(C·E 0 D

ùù=F

½

X

ñ jõ ñ Kõ YT=?NAT=HUP FIØ*ØB TU:=:UFöB ÜMñ:=BGjH=B õOa8$T=OMNAOMRæWñ TUPMkBõ!B :U@AB B H=Ø*XM@AB T.OaN‚TO`?NAORMB :U?$OaYTUN‚Ì š ¾ó Œ ,¼ ,Í&® ÈÈLŸ§%¥Î ³ µ š dš mõ Tô õ ]ž Ÿ 8¡¢¶=¨ ¬g¦8Ÿ%¨§L¬n®€ L¨ §· ϋ LŸvаºÎ  %¥š L¨’Í ÑCÒ]©‹§L¨ Â1ÓLÔ¶=«Å§8ÈL®a¨LÈ ó ¼ ¹ µ ¯Õ ž Ÿ 8¡¢‰£.¤MŸv %¥¦%§L¨,© L¨ª=¦8Ÿv¦8¨ ¡¦/ L¨Ä© L«)¥¤M¬g¦8ŸI­®t°=®a L¨ í³ 'í¹´ ² µ Ö jš õ gŒ wž Ÿ 8¡¢M£ ¤MŸv %¥¦§L¨I© L¨ª=¦8Ÿv¦8¨ ¡¦Y L¨©¯ L«)¥¤M¬g¦Ÿ/­®t°=®a L¨ ² ² ¯µ i× ¯ ž Ÿ ¡8¢‰£.¤PŸ %¥¦%§L¨,© L¨=ª¦Ÿ¦8¨ ¡%¦/ L¨Ä©¯ L«)¥¤M¬g¦Ÿw­®±°®a L¨ ²³ µ ´ †¼ ¼ gØ lõ ¹ í#² M² @í º² Ù0¹ ”lõ Eô » õ Ú& L¤MŸ%¬tÎÅÆ·tÛ8¦8Ü ­®±°®a L¨Ý©¯ L¨=ª=¦8Ÿv¦8¨ ¡¦ Ù¹ í ´´ ó



S sS

®a¨ Û8§LŸ%®€§L¨ ¡%¦C®a¨Ä© L« ¥¤P¬g¦8ŸI­¯®±°®a L¨ ®a¨LÈ ³´0²@“™Œ L³

í¹

ôbõ

í¹

í´¹

² Ã)¥L¥&·t®€¡%§L¬g®a ¨P°C iª ‹´²í vË q² ¹ i@² í³ © L« ¥¤M¬n¦8ŸÇ­¯®±°®a L¨]§L¨ ÂC¶=«Ç§8ÈL¦wɨ ÂL¦8Ÿi°=¬g§L¨ ÂÆ

¹ /Þ 8ß zó iõ ž Ÿ 8¡¢&¶=¨¬n¦8Ÿ¨ §L¬g®a L¨ §·© L¨=ª=¦8Ÿ¦¨¡%¦C L¨ž §L¬g¬g¦8Ÿ%¨À.¦%¡ ÈL¨ ®a¬g®a L¨ 8Ë ³ ó ÅË Þ 8ß jš ‹µ ž.Ÿv 8¡8¢P¶%£ £ £¸©¯ L¨=ª=¦8Ÿv¦8¨ ¡¦ L¨ © L«)¥¤M¬g¦8ŸI­®t°=®a L¨‹§L¨ ÂǞ.§L¬g¬n¦8Ÿ¨IÀ.¦%¡ ÈL¨ ®a¬g®a L¨ ÝÌ 2ó ¹

‰ ;cð{*cQuEx=wGl$~w ljy9oac sQfU€fDjm†o;gÀafDxxzfDºz²G€g¹~²Kl9$´»mKxz²KpŽ ¹€‚w ~Žl$¹wG~} kfºz~¹fhÁk½$m gjfDl$}DmMfD‰§ºDƒKm ƒKuˆ$l c ‰ ;cð} ovwGc ¹eQ~²kwDljiKºDf§cŒwGs]gMm¿Zc µfDcI²k¹zŽ ¿jfhfDº¹z~xºD~f+mŒn†y }Dgj² €l`f+ºzsQÁ$² ºz€¹zÁ$f ¹zfDfDŽ+}=¿jf+l$y~½$f gjæfkm } jw x=Ž wGlfD}Dx=fKw ºDmŒcQ‰ qƒkƒ ¿ ;fDc ²Kx~fKmŒfDºz¹~Žw ¹~²Kl9fD¹ðwGÀÀ;€³~ r ‰§ƒ;c ¸zðf $cð¹zb!f,²$wG}=g¿Zº]mºz¹zp^fDxzgjfD¹z²K²kº Žk²KwGÀ$¹~~ºzºz}=}U¿j¿fÈfDl Æ!"·agjfhlx Mygjw }UŽ.¿rEfDp^lŽ+ljº²$~}=yj¿$f=¹z€³fDî~lMfDcxzgIljÚºz¹=w xzxzfD=x|mhd‹yl$xz~fUiK~y$fD~xzŽ+º~¹EfDÁ.lº² ~A´M²klaŠ^wDwG€Alfhx9lj² Æ!iKfh·;xDr m kˆ;c u!ðl fDcIxzb!Ž²$wG}=l$¿ZÁkm;m]o;‰ gƒKxƒ´EwG;}hc fo;fDkŽ+fDl$¹=w ¹~²Klw ljyè{|²$yjf=€³~lj+´»xz²kŽ¼o$¹zfDxzfD²K$ºzm }h²K~À$fD~lj}lIuw;Žm]w ‰§KƒKfƒ ;o$cfD½$gfDl}DfDºDm $‰Kc ‹ð~c;yb!fD²9²$}Uo$¿MfDm$½${*gjfhc¥ljsQ}D²Gfh€³ºDf=m´»fDulÁ$ºw ljy3e†c ,wGl !²$²G€»m{|g$€¹~ ‹~fDÂÀa² ~l$¹o;¹zfhxzfD²!´»xz²KŽ d‹jlm } jw§€³xz~fU·~x=·wGg¹zxzfDjy m ;c }D!.²KfDc xzrExzxzqŽfDºzcIwGÀIeZl$²KgÁkl²Km]yjl‰ fD|ƒKlƒ }Dw ;fDljºèc yèwGÆ.ly*c a´»wGggljKyIfDwGx=Ž¾w ºDfDmŒl$Æ.¹=w§cI€^o;ŽfU€³w ´ ¹zx~w§}D€³fD~ºD·cx=wGu¹l ~²kl*² ´,w.Ž+² iK~lj} w Ž+fDx=w´óxz²KŽ¼Àa² ~l$¹ k‡;cð{|jxz²$fU~²K·lgjjºDxzm"m$ikqm]²G‰ c€»cƒKpŃ D;rzq]c‡$mQg¹z‰§²KƒKxƒ ~‚$wD€c ²KlÈ{|g$€¹~³r ‹~fD "fU€‚wG¹~²kljºz¿$~ÀºDm!uEl Mm

„jcðÀanøfDclƋyj´ófDf l$a¹ðm${|n"c¥g;o;€¹¿$~~³xz€‚fhwGºz¹D²Gm€gp.¹c~A²kl`wGÀq]ÀafD²KÄ$À¹zÀagxz²kfDxzº"¹!´»w xzlj²Ky3ŽÃ{*uŽc *w KfhfxzŽo$fDwG½$lMgjmfhŠølj}D~kfh¿;ºDc€³~k¿$¹^wGly "f IfD}D¹~²klulyjfUr ;cð{*c]sQ² €³fU´»fDÁ$ºw ljy e†cUm "ikw ²Gl €»c‰ !²$² €»Um]mIp {ºzw ¹zxzx=}UwG¿$¹rE~ p!IfDÀyÈx~³€wGÀ‰ ƒKÀjƒxz²¥;wGc }=¿ ¹z²3ºzfU€³´ArE} wD€³~·jx=w ¹~²K$lMm oc"wGull gIwGlMm ;cðs†{*wG¹]gc$~fDlsQxzI¹z² ²l;€³~fU¹E´»ÁKfD~ma}DÁ$²juEº^l mIwGÀjlÀMyc „¥e]ˆ c D,r„wG‰ l $m]!‰ ²$ƒK²Gƒ €»;mco$fU€³´ArE} wD€³~·jx=w ¹~²$l´»xz²kŽÚ¹z¿f!w ·jºz² €gj¹zf^}D²Kl$~}!²kl.¹z¿fÀ;€‚w ljf ;cð~{*l*ckºzsQÀ$²G~¹z€³f+fU=´»²Gmfh´ Á$b‹,ºD~m fUwG€»!xzm ÁKck!~b!lfh²$xzŽ}UwG¿lwGw y\l$ljÁKd‹y¾mIÀjl e†ÀM$c ljcQ,² ‰ wGÂl Dl*rU!‰ uE²$l$² $¹z€»m]fDm$xz‰ o$lIƒKfUw§ƒ €³€ ´A;r cwGw§Ž+€³~·fhx=x=wGw¹~s]²$w l3x=wGwGŽ+ly¾fh¹z{|fDxzfDºD¹zmQx~uE} l "fD}D²kljºz¹zxzg}D¹~²Kl ;cð~{*lckºzsQÀ$~²G¹z€³f!fU² ´»fh´ Á$,ºDwGm xz!ÁKck~lb!+²$w }Ulj¿yw ljdy¾l e†$lc ² ,ÂwGll !uEl$²$¹z² x~€»ljjm$ºm$o$~ÀfU} €³ÀZ´Arc ƒKwGˆDŽ+w§rz€³ƒ ~fD·;x=x=mvwwG… s]¹~²Kw ²$Žx=l3wG·aŽ+wGwDlÁKfhy¾¹zmŒfD‰ {|xzƒkºDfDƒm$¹z;¹zx²c ~} w "ÀjÀIfD}Df ²kwGljx ºz~¹zlxzgu }D¹~²Kl c k‡kƒ;ˆ;cðcðs ovcc ""² ²KÁKgm ºzºz$fDcfD{|g$ÂfDgm l$~fDx^wGlyu=c "² Äam "ÁK€³~ljyx~} w§€ "fD}h¹~ a} w ¹~²Klj¹zm ²¾{~³€fD~l;ÁK~m Ž~ DfDf+ n]À$²k~xÀaa²GmZ€‚w ‰§xƒ µø;~cºr ¹zÀj²KÀMxzc³¹‡k~ƒK²K‡DlMrzmŒ‡kuƒKl ƒ$m]‰ ƒKƒ ;c jm ‡$‰Kcð·js x=c w o$¹z¹zfDgjyxzŽ|n]gjm }=ø€³~yjx~f ¹w ~}§l w§€^"{|fD}h²k²K¹l~²Kºz¹zlÈxzgjo;}Dfh¹½$~²kgjlZfDcŒl}DulfDº´»²kx+{|²klj²$}Dg$€‚wGx6o;fU€³´‚r wD€³~·jx=w ¹~²KlåwGly9dlj} wD€³~ r ‡ ;c Àjð¿$c¥Á q]k²Kp*Ž´Ew w º}D~Œ¹z²KwGlx~ y w q¹~c;²KblwGw lIÀjwGÀyxz²$fKmIw }Uo;¿M¿Im wG$Àam$fow wGljl y Ž+gaw ²klZ¹~mv²Ks†lg´»fDxzxz²K¹zŽÚ² ~Ž~}Dw ²jKmMf!ÀºzÀM¹zxzcîf§‰kwG‰ Ž+ˆKˆDº"r=‰Kg‰ lˆ yj;fDm]x‰§m=²kƒKƒ xzƒ ¹z$¿jc ²kK‡x=w§§rr ‡k‡;cðljs ‰ GfDcIfh„q]xmQ~²Klj‰§xzƒKèxDƒmIo;${|}Uc ~²Kfh¹lj~}D²kfkl`mŒo$d‹fDl$k~Ž+iKfDfDxzl$º¹=~¹EwGÁ¹~²k²Gl`´Æ!w ljÄK´óy²KxzÆ!yMgmQ¹‰ €³~ƒkfDƒ xð$µ‹c fD¹zfD}h¹~²KlMm]s]¿aµåq‹¿fDº~ºDmŒµfDÀj¹DcI²G´,n]lj ~³r ‡ „jcð…‹cq]x~KKºDmIq¿jfp^·jºz² €gj¹zf !gIwGyx$~}Km$mMouwGl l gaw lZmvs†gfDxz¹z² ~}D²jmMÀÀMc kˆKƒ§r $‰D„jmŒ‰ ƒkƒ ;c ‡ ;c ðb!xzc gjvÀf=Àa€³w9fDx9fD½$wGgIlwGyù~²KÆ.lºc axzfDw iKgj~kºfD~¹zx=fDwGyMºDc!m uw "Ž+ufDpx=wÛmo$ºz²KfUÀ€³´A¿;rE} ~‚wDwDr€³~p^·jl$x=w ¹~¹Àa~²$²Gl €³~‚ºDm´»xz²KjŽx=w ljiK}h~fKym fD²å"fDºzºzfDf ½$wGgjxz}=fh¿lj}Dfhøº fh.Àa¹z²K¿xzf¹ ‡ ;c ~ ljKc ƒka‡;¹¿am]Â,w ‰§²+ljƒKgjƒ m l$ðc} wDc¥€³µ‹~·jfhx=xw ~}U¹zfD¿y*fKm~Æ.Žc w aKw fDº^gjk¹zfD¿jx=xzwG²kº,gjwGkl¿y ¹z¿j.fc rExzqfD}Dck² eMiKgjfh²kxzljÁ² m$´p9¹z¿jxz²Kf·ggjl ºz$¹lj¹z² fDÂ}=¿jl*l$~fh½$À;g~f‹Àa² ´»€‚²kwGx]xŽkwGfD¹z²K}=Ž.¿;rr fD¹zxzÁKm ³m ² €»c ;maÀÀMc §r=‰K‰§ƒ;mŒÆ!}D¹z²k·afDx‰ ƒkƒ ;c "¹

¬n®€ L¨ §·© L¨=ª¦Ÿ¦8¨ ¡%¦/ L¨wž §L¬g¬g¦8Ÿ%¨À.¦¡% ÈL¨ ®a¬g®a L¨ ¼,à :à &Ø á Ñ



ó

¼



²



ó

²



ó

µ







>ž.Ÿv 8¡8¢¶=¨ ¬g¦8Ÿ%¨§Æ

)ô’Ì

à ³

žÎPÔã¬tÎ ¦"°®±°

ݞ.Ÿv 8¡8¢&¶=¨ ¬g¦8Ÿ%¨§L¬n®€ L¨ §·&© L¨=ª=¦8Ÿ¦¨¡%¦/ L¨ž.§L¬g¬n¦8Ÿ¨IÀ.¦%¡ ÈL¨ ®a¬g®a L¨ Ë ³ Ë š¼ Ë Ë Nž Ÿ 8¡¢£ ¤MŸv %¥¦§L¨>© L¨=ª¦Ÿ¦8¨ ¡%¦w L¨Q© L«)¥¤M¬g¦8Ÿä­¯®±°®a L¨ µ ¼ ´ †Ö µ ÷õ Z¶=¨¬n¦8Ÿ¨ §L¬g®a L¨,åL L¤MŸ%¨ §·  iª,© L« ¥¤M¬n¦8Ÿ ­®±°®a L¨ ²² ¹ Ë ¿ó ¸ž.Ÿv 8¡8¢1Í æç¶%艣êé LŸvаºÎ  %¥ µ ´ š

ó Õ 2ó %â ¶%£Y£ £½© L« ¥¤M¬n¦8ŸÅëŸv§%¥ÎPÆ ®a¡=°/§L¨ ÂÅÃ)¥L¥&·t®€¡%§L¬g®a ¨P° 82 ¹ ² “ ¹ Ë Ä¼ qp Zž.Ÿv 8¡8¢ ¶=¨ ¬g¦Ÿ¨ §L¬g®a L¨ §·© L¨=ª=¦8Ÿ¦¨¡%¦ L¨,© L« ¥¤P¬g¦8Ÿ]­®±°®a L¨]§L¨ Â/ž.§L¬n¬g¦8Ÿ¨çÀ.¦¡% ÈL¨ ®a¬g®a L¨ ,Ì ó ¹ 8² ¹ Ë š¼ ìp ž.Ÿv 8¡8¢P¶=¨¬n¦8Ÿ¨ §L¬g®a L¨ §·© L¨=ª=¦8Ÿv¦8¨ ¡¦  L¨,© L« ¥¤P¬g¦8Ÿ Ã/¨ §·tÜ°®±°  iª ¶=«Ç§8ÈL¦=°§L¨  ž §L¬g¬g¦8Ÿ%¨P° ¼ "¹ í "´² ¹ ó 8Ë Å¼ 'õ Gó .Ë š ‡õ Ğ Ÿ 8¡¢¶=¨ ¬g¦8Ÿ%¨§Æ ¬n®€ L¨ §·© L¨=ª¦Ÿ¦8¨ ¡%¦/ L¨ © L« ¥¤P¬g¦8ŸI­¯®±°=®€ L¨ @í ´ ó 8Ë Å¼ 'õ Gó &Ë jš õ @Ì õ)Ë =ó ‰À. LÁ8¤ì°¬‰À ¦ÈLŸv¦=°°=®a L¨‹§L¨ Âí.¤P¬a·t®a¦8Ÿ1Ԇ¦8¬n¦¡8¬g®a L¨ Õ Eô Q» š ´¹ ló Ì õ õ ‡ó qp t× Ýž.Ÿv 8¡8¢¶%£Y£ £© L¨=ª=¦8Ÿ¦¨¡%¦/ L¨Ä© L« ¥¤M¬n¦8Ÿw­®±°®a L¨§L¨Âçž.§L¬g¬g¦Ÿ¨À.¦%¡ È쨮a¬g®a L¨ ¹ ó

²² ² ²

²@í ²³ ²¹ ²´ ²

õ







­®±°®a L¨§L¨ÂǞ §L¬g¬g¦8Ÿ%¨À.¦¡% ÈL¨ ®a¬g®a L¨

õ











Ù¶=¨ ¬g¦Ÿ¨ §L¬g®a L¨ §·"åL L¤PŸ¨ §· iª¾© L« ¥¤P¬g¦8Ÿ¾­®t°=®a L¨

ÅÖ ­®±°®a L¨§L¨ÂǞ §L¬g¬g¦8Ÿ%¨À.¦¡% ÈL¨ ®a¬g®a L¨ õ ’ ŵ sõ

²¹ ³ † ٝ





,ž.Ÿv 8¡8¢&¶=¨ ¬g¦8Ÿ%¨ §L¬g®a L¨M§·&© L¨=ª¦Ÿ¦8¨ ¡%¦C L¨Ý© L« ¥¤M¬n¦8Ÿ Ì ó @í ¹ 0²@“™Œ





,ž.Ÿv 8¡8¢&¶=¨ ¬g¦8Ÿ%¨ §L¬g®a L¨M§·&© L¨=ª¦Ÿ¦8¨ ¡%¦C L¨Ý© L« ¥¤M¬n¦8Ÿ Ì ó q³ º³ ¹



&Ã/Ÿ¬g® î ¡8®a§·Ù¶=¨ ¬g¦"·€·t®qÈL¦¨¡%¦åL L¤MŸ%¨ §· ÙË



ŵ

'ôbó



q¹´

q´¹



ýó

š



Suggest Documents