Fast and reliable object pose estimation from line correspondences
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(28) *. ä B 9 <? FÔHHG=Ê 9 F¡S:B Ö Õ = >@EGS¬Ò:FÔL<=AÙ×+=kB<=EAyÅIFIÜA 9 F¡S:BS+È 9 ?<= A+ÄÐS¬Ò+=A+Å¡×CSCEGF 9 ?@Æ 9 SØL<=A+ÅhÕ5F 9 ? 9 ?<= >@ACEGAC>M=kEGH>Ð=Ê 9 F¡ÒC='ÊA+HG=+Ó $ =RÊSCBMHFÔL<=E Ay×CA+FIB 9 ?<=Ø>Ð=EH>M=kÊ 9 FIÒ+=O=ÚP@A 9 F¡S:B@H Ë A+B@LçÕ =ØÆÙA+ê+==ë@><ÅIFÔÊF 9 9 ?@= >@A+EA+>Ð=EHG>Ð=Ê 9 FIÒ+=uA+>@>MES¨ë<FÔÆA 9 FISCBOSyÈ 9 ?<= Ê&ACÆ=EA(ÆS<L<=&ÅÓ $ =SCÄ 9 AyFÔB ß ø Ö ñ Ö >¬ã 2 ?>
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(32) A F FÔBØ=kÚP@A 9 F¡S:B Ï A+BMLRÄ J ×:ES:P@><FÔB<× 9 =EÆÙH 2 J ? > 5 K ? > 5 ; 5 < 5 ø 5 5 7 ß J ? > 5 K ? > 5 ; 5 < 5 ^ã 3 Õ?<FIÊq? J FI=&ÅÔL@H Ö ACH5A+ÄÐS¬Ò+= 2 > J@?> 95 K ? > 95 ; 5 < 5 ø 5 3 â J ? > 5 K ? > 5 ; 5 < 5 3. .
(33) ä 9 FÔH$Õ SCE 9 ?:Õ?<FIÅ¡= 9 SB<S 9 FÔÊ= 9 ?MA 9 Õ?<=BÙA+Å¡Å 9 ?<= A+BML ACE={BP<Å¡Å Öy9 ?<=5>M=kEGH>M=kÊ 9 F¡ÒC= =ÚP@A 9 F¡S:B@HACÄMS¬ÒC=©ÄM=kÊS:Æ(=WFIL@=B 9 FÔÊ&A+Å 9 S 9 ?<= >@A+EA+>Ð=EHG>Ð=Ê 9 FIÒ+=1=kÚ:PMA 9 FISCBMHÑSCÄ 9 AyFÔB<=kLuÕ5F 9 ? A>MA+EA+>Ð=EHG>Ð=Ê 9 FIÒ+=uÊ&A+Æ=kEGAÆSL@=&ÅÓ Ã ?<=]F 9 =kEGA 9 FIÒ+=WA+Å¡×CSCEGF 9 ?@Æ FIH!HGFIÆFIÅIACE 9 S 9 ?<=WS:B<=WL@=HÊ&EGFIÄÐ=L FIB 9 ?<={>@EG=&ÒF¡S:P@HHG=Ê 9 FISCBhÓ Ã ?<=S:B<Å J L<F =EG=B@Ê&=FÔHWH 9 =k>ØË 2:Õ =B<S¬ÕcÊS:ÆÙ>@P 9 = J ? A+B@L K ? FIB@H 9 =kA+LOSyÈ J ACB@L K Ä J HSCÅ¡ÒFÔB<×A+BS¬Ò+=kEGÊ&SCB@H 9 EAyFÔB<=L Å¡FÔB<=ACE©H J H 9 =kÆ S+ÈY=kÚ:PMA 9 FISCBMH > A+B@L â Ó Ã ?@=B H 9 =k>aÏ wÖ Ö G ACB@L D ACE=uL<=kL@P@Ê=kLØÈ^ES:Æ J ? ACB@L K ? ß ø Ö ñ Ö >yã Ó {¹ ,
(34) ½¶Âð· * ,G½4 ¶ *¾!¸ *{»¾!·@½ ¹]¶ S 9 ? 9 ?<=]Õ =ACê4>Ð=EH>M=kÊ 9 FIÒ+= A+B@L>MA+EA+>Ð=EHG>Ð=Ê 9 FIÒ+=©F 9 =kEGA 9 FIÒ+=]A+Å¡×CSCEG F 9 ?@ÆÙ`HÑñ B<=& =kL 9 S'HSCÅ¡ÒC= A+B²S¬Ò+=EÊS:B@H 9 EAyFÔB<=L ÅIFIB@= A+Eu H J H 9 =ÆS+ÈW=ÚP@A 9 FISCB@H Ö B@A+Æ=Å J =kÚH&Ó wÖ Õ =ACê>M=kE Í HG>Ð=Ê 9 FIÒ+= A+B@L=ÚHÓ > wÖ â >@A+EA+>Ð=EH>M=kÊ 9 FIÒ+= Óyä BÙÆÙA 9 EF¡ë È}S:EGÆ 9 ?<=kH==ÚP@A 9 F¡S:B@H1Ê&ACB ÄM=ÕEGF 9G9 =kBRACH 2 ø 3
(35) 9
(36) 9
(37) 9 é SCEG=u=ë@><ÅIFIÊ&F 9 Å JCÖ Õ =u?MA¨Ò+='FIBRÕ =A+êO>M=kEGH>M=kÊ 9 F¡ÒC=uÊA+HG=2 . 02 "!$# &% "!$# % 02 "'(# )% *'(# 5,7 + 1/ 0 5,7 + 3 20 . . ä B>@A+EA+>Ð=EHG>Ð=Ê 9 FIÒ+=uÊ&ACH= Ö 02 > ! # % >! # @ ' # )% ' # . ®87:9A ; ± % 8® 7B9C ; ± D =? . % D =? . 57. 02. ®. 465 87:9<; 465 >=? ,5 + 7 . -FE . 02 E 3 + / 0 5 + 20 7. 02. ±. ®. 465 87B9C; 465 = . ± 57. +. ®t ± ® ± G6HJI LKM ij@M¥x: t ijpi 4o t ¥kl m j:lwp( f f z+l l t Ù f l t m ¥ ik f ikj:ikj-i nCm t j t iC[lqG ® t ± t jzÙi nCm t j t ©ik+lwG ® ± ¦ N. . OCPRQTS P B UWV Q VX P G Y S[Z U WQ Y1\. à ?<=ÙÅ¡FÔB<=ACE4H J H 9 =Æ ?MA+H > PMB@êB<S¬ÕB@HuA+B@L 9 ?P@HÆ(P@H 9 ?@A¨ÒC=A 9 ÅI=ACH 9 > FÔB@L<=k>M=kB@L<=kB 9 =ÚP@A 9 F¡S:B@HÓ % A+Êq?ÅIFÔB<=(×CF¡ÒC=H'P@HË=kÚP@A 9 F¡S:B@H Ö S:B<=L@=>Ð=B@L<FÔB<×RSyÈ 9 ?<= 9 EA+B@HGÅÔA 9 FISCB A+B@L-SCB<=RL<=>Ð=B@L@FIB<×3SyÈ 9 ?<=L<FÔE=kÊ 9 FISCB Ó $ =Æ P@H 9 ?@A¨Ò+=RA 9 ÅI=ACH 9 FÔB@L<=k>M=kB@L<=kB 9 FIB 9 =kEG>ME= 9 A 9 F¡S:BO><ÅÔA+B@=H Ö FÓ =+Ó<Õ =uÆ(P@H 9 ?MA¨Ò+=uA(HP@Ä@HG= 9 SyÈ ÅIFÔB<=H{FÔB 9 ?<=FÔÆA+×+='Õ5F 9 ?ØB@S Æ(S:E= 9 ?MA+BË ÅIFIB@=H{FÔB 9 =EH=kÊ 9 FÔB 9 ?<=HGACÆ(=u >ÐS+FÔB 9 H== Ð×CP@EG=uË+A Ó Ã ?@=B Ö<9 ?<= HSCÅIP 9 FISCB È}SCE FIHHGFÔÆ>@Å J ×CF¡ÒC=BRÄ J 2 3 3 ] 3 Ó . . ñ.
(38) . N. . P B UWV Q VX P G Y S[Z U WQ Y1\. . ä`È 9 ?<=WSCÄÉ =kÊ 9 ÅIFIB@=HACE=WÊSC>@ÅIACB@A+E 9 ?<=B 9 ?<=WEA+BMêSyÈ FIH°SCB<Å J A A+B@L 9 ?<=]ACÄMS¬ÒC=]HSCÅIP 9 FISCB Ê&A+BMB<S 9 ÄÐ==B:ÒFÔHGA+×+=L²A+B J ÆSCEG=+Ó = 9 H ÊS:B@HGFIL<=kE 9 ?@=><ÅIACB<=aÈ}S:EGÆ=L3FÔB 9 ?<FÔH ÊA+HG=ÙÄ J 9 ?<=S:ÄÉ =Ê 9 ÅIFÔB<=HACB@LØÅ¡= 9 ÄM= 9 ?<= P@B<F 9 Ò+=kÊ 9 SCE{SCE 9 ?@S+×+S:B@AyÅ 9 S 9 ?<FIH><ÅIACB<=+Ó 1=Ê 9 SCEH J A+B@L A+B@L(=ÚP<FIÒ¬AyÅI=B 9 Å J J ? ACB@L ? Ê&ACB(ÄÐ={ÕEF 99 =BA+H1AuHP@ÆíSyÈA'Ò+=Ê 9 S:E!ÄÐ=&ÅISCB@×+FÔB<× 9 S 9 ?<K FÔH >@ÅIACB<='ACB@LA Ò+=Ê 9 S:EW>Ð=E>M=kK B@L<FÔÊ&P<ÅÔA+E 9 S 9 ?<FÔH{><ÅÔA+B<= Ö BMA+Æ=&Å J 2 J 3 J 5 ACB@L 3 5 Ó K KJ HP@Ä@H 9 F 9 P 9 FIB@× 9 ?<=HG==ë@>@EG=HHFISCB@HÈ}SCE J ACB@L FÔB 9 SR=ÚHÓ A+B@L ñ E=kHG>Ð=ÊÍ 9 FIÒ+=&Å J =ÚHÓ > ACB@L â È}SCE5>@ACEGAC>M=kEGH>Ð=Ê 9 F¡ÒC= qÖ ACB@LOK Ä J B<S 9 FÔÊFÔB<× 9 ?@A 9 > 3 ACB@L 3) Ó > 3 Ö@9 ?@= H J H 9 =Æ ÆA J ÄM= EG=&ÕEGF 9G9 =kBØACH 2 à ?<= EA+BMêuSyÈ FÔH A F¡ÈYÕ ={?@A¨Ò+= A 9 Å¡=kA+H 9 Ï4FÔB@L<=>Ð =BML<=B 9 FÔB 9 =E>@EG= 9 A 9 FISCB(><ÅIACB<=H Ö F[Ó =+Ó ÕW=Æ(P@H 9 ?@A¨Ò+=AHP@Ä@HG= 9 S+ÈÏ Å¡FÔB<=H©FIB 9 ?<=FÔÆA+×+=5Õ5F 9 ?aB<S(Æ(S:E= 9 ?@A+BË'ÅIFÔB<=H]FIB 9 =kEGHG=Ê 9 FIB 9 ?<= HA+Æ=>ÐS+FÔB 9 H== Ð×CP@EG= ËyÄ Ó Ã ?<=uÒ+=Ê 9 S:E FÔH{SCE 9 ?@S+×+S:B@AyÅ 9 S J ACB@L K CÖ<9 ? P@H > J 3 A+B@L > K 3 ACE= 9 ÕWSÆ(S:E=FIB@L@=>Ð=B@L<=kB 9 =kÚP@A 9 F¡S:B@ H]ACB@ L 9 ?<=' ÆÙA 9 EGFoë FIH5S+È!EA+B@ê > Ó Ã ?P@H{Õ =SCÄ 9 AyFÔBØHGS+ÅÔP 9 FISCBMH È}SCE J ACB@L K 2 3 3 ] 3 Ó ä BÙSCEL<=E 9 S =H 9 FÔÆÙA 9 = J A+BML A+B@L=ÚP<FIÒ¨A+Å¡=kB 9 Å J J@? A+ BML K ? S:B<=FÔH]ÅI=È 9 Õ5F 9 ? 9 ?@= 9=H FÔÆA 9 FISCBØSyÈ 9 ÕWSaHÊ&A+ÅIACEGH Ö A+B@K L Ó ä BÕ =ACêa>M=kEGH>M=kÊ 9 F¡ÒC=4Ê&ACH= Ö ÄM=kEGê¨A+ÆÙ>È Ö Î'=Æ=B 9 ?<SCB Ö ACB@LÎuA¨ÒFIH ß A ã >@ES¬ÒFÔL<=LOA HSCÅIP 9 FISCBRP@HFÔB<× 9 ?<= ÊS:B@H 9 EGA+FIB 9 H J 3 K ACB@L J> K 3 Ó ä BÝ>MA+EA+>Ð=EHG>Ð=Ê 9 FIÒ+=OÊA+HG= Ö QS:EGACP@LÛA+BML-AyÅÓ ß ñ ã >@ES¬ÒFÔL<=L-A²HGS+ÅÔP 9 FISCBÝP@HGFIB<× 9 ?@= ÊS:B@H 9 EGA+FIB 9 HWS:B 9 S J ? ACB@L K ? Ó . . .
(39) . . . . . . . . . . . . . . Q V QBS Q(Z Y Y \ P U WQ Z *Q Z Y U Y V X \ \ Y . N. . B<=²ÆA J B< S 9 FÔÊ= 9 ?@A 9 FIB 9 ?<=²ÊA+HG=³SyÈ 9 ?@=Õ =A+ê 9 9 9 9 ¨ Ö 9 >M=kEGH>M=kÊ F¡ÒC= F =kEGA FIÒ+=5AyÅI×+S:EF ?MÆ ?<=ÆÙA 9 EGF¡ë S:E È}S:E1ÊSC>@ÅIACB@A+E$ÆS<L<=&Å L<S=HB 9 L<=>Ð=B@L²SyÈ A+B@L Ó Ã ?P@H 9 ?<=Ù>@HG=P@L<SRFÔBCÒC=EH= SyÈ 9 ?<FIHÆÙA 9 EGFoë³EG=ÆÙAyFÔB@H 9 ?<=aHA+Æ= A 9 =ACÊq?F 9 =kEGA 9 FISCB3H 9 => Ö ACB@L 9 ?<=kE=&È}SCEG=ÙB@=&=LMH 9 SÄM=Ê&SCÆÙ>@P 9 =L3SCB@Å J S:B@Ê=CÓhä 9 H B<S 9 9 ?<= ÊA+HG=4È}S:E5>@A+EA+>Ð=EH>M=kÊ 9 FIÒ+=CÓ OCP X VU V Z!WP?Q à ?<= 9 ÕWSÛF 9 =kEGA 9 FIÒ+=3AyÅI×+SCEGF 9 ?@ÆÙHOHGS+ÅIÒ+=²AÛÅIFIB<=kA+EØH J H 9 =Æ/A 9 =kA+Êq? F 9 =EA 9 FISCB H 9 =>hÓ MS:EOBP@Æ=EGFÔÊ&AyÅuEG=A+HGSCBMH Ö ÕW=3?@A¨Ò+= 9 SÝB<S:EGÆÙA+Å¡FIÜ&=²=A+Êq?èÅIFÔB<=²S+È 9 ?@= ÆA 9 EGFoëOH J H 9 =Æ7ÄÐ=ÊA+P@HG= 9 ?<=B<SCEÆìSyÈ 9 ?<='Ò+=Ê 9 S:EGH ACB@L ÆÙA J ÄÐ=uÒ+=kE J L<F Y=kE=kB 9 ÄM= 9 ÕW==B3=ACÊq?²ÅIFÔB<=+Ó é SCEG=&S¬Ò+=kE Ö È}S:EAÊSC>@ÅIACB@A+EÆS<L<=&Å ÖÑ9 ?<=Ò+=kÊ 9 SCE Æ(P@H 9 A+ÅIHGS³ÄÐ= B<SCEÆÙAyÅIF¡Ü=LhÓ . !. . . . . ". #%$. /*ѸM½ (. *°¶]·. ä B 9 ?@= ÐEH 9 ÊÅÔA+HH©S+È=ë@>Ð=EGFIÆ=kB 9 H Ö Õ =4H 9 P@L Ja9 ?<=u>M=kE È}S:EGÆÙA+BMÊ=S+È 9 ?<=4F 9 =EA 9 F¡ÒC=Õ =A+ê A+B@L(>@A+EA+>Ð=EHG>Ð=Ê 9 FIÒ+= AyÅI×+SCEGF 9 ?@ÆÙH°SCB HGFÔÆ P<ÅÔA 9 =L FÔÆÙAy×C=HÓ Ã Õ S 9KJ >Ð=H!S+ÈÐ>M=kE È}S:EGÆÙACB@Ê=kH A+EG=uH 9 PML<F¡=kL 2 9 ?<=(>@E=kÊFÔHFISCBRS+È1>ÐSCHG= ACHAÙÈ^P@B@Ê 9 FISCBS+È1>ÐSCHGF 9 FISCBA+BMLØS:EFI=B 9 A 9 FISCBRS+È 9 ?<= S:ÄÉ =Ê 9 Õ5F 9 ?E=kHG>Ð=Ê 959 S 9 ?<= ÊA+Æ=EA(FIB 9 ?@= >@E=kH=kB@Ê=uS+È°FÔÆA+×+= >@Foë<=&Å B<SCFIHG= Ö ACB@L 9 ?<= Ê&SCB:Ò+=kE×C=B@Ê&=S+È 9 ?<=F 9 =EA 9 F¡ÒC=u>ÐSCHG=AyÅI×+S:EF 9 ?@ÆÙHÓ A.
(40) Ã <? = FÔB 9 EFÔB@HGFIÊ Ê&A+Æ=kEGAÙ>@ACEGACÆ(= 9 =kEGH5ACE= ' 33 Ë ñ A Ö 3 3 ø Ó 'ACP@HGHGFÔA+B B<S+FÔH=aÕ5F 9 ?-H 9 A+B@L@ACEGLçL<=ÒFIA 9 FISCB
(41) 3 ø >@Foë<=&Å ?@A+H ÄM==BÛACL@L<=L 9 S 9 ?<=OFIÆÙAy×C=OÆ=AyÍ HGP@EG=Æ=kB 9 H]ACB@L 9 ?<=kE='A+EG= ñ 9 EGFIA+ÅIH©È}SCE©=kA+Êq?Ù=&ë<>Ð=EGFÔÆ(=kB 9 H 9 ?<='SCÄ<É =Ê 9 FIHWES 9 A 9 =LaA 9 ñ EGACB@L<SCÆ¿SCEGFI=B 9 A 9 FISCB@H 9Ó !FÔB@A+Å¡Å J+ÖY9 ?<=ÙϬÍ`ÎìÆ(S<L<=Å!EG=>ME=kH=kB 9 HAØHFÔÆ P<ÅÔA 9 =L³?@SCP@HG= A+B@LØFIHÆACL<=uSyÈ ø > ÅIFIB<=kH&Ó PRQ X QBS ä BeA+Å¡Å 9 ?<=kH=OÊA+HG=H Ö ÄMS 9 ?ÛA+Å¡×CSCEGF 9 ?@ÆÙH?@A¨Ò+=aÊ&SCB:Ò+=kE×C=L²FIB ø SyÈ 9 ?<= Ê&SCY B M×:Y P@EA 9 Y FISCBMH Ö ÄÐ= 9 Õ =&=BRÏaA+BML ñ F 9 =EA 9 F¡S:B@HÓ S Z!WP?Q Z! $ F 9 ?-B<S³S:> 9 FÔÆF¡ÜkA 9 F¡S:BeA 9 A+Å¡Å Ö =&ë<=Ê&P 9 FISCB 9 FIÆ=OFÔH Ó HG=ÊS:B@L >M=k E5Y F 9 =EA 9 F¡S:BSCBAY Å 9 EA 8 >@A+EÊ ø ø à È}SCE ø > Å¡FÔB<=H Ó P V X P?Q îÊ&Ê&SCEL<FÔB<× 9 S M×:P@EG=Ï Öy9 ?<= 9 Õ SF 9 =EA 9 FIÒ+=5A+Å¡×CSCEGF 9 ?@ÆÙH1?@A¨Ò+= 9 ?<=HA+Æ= \ J J à A+Ê&ÊP@EA+Ê Ó ?<=SCB<Å L<F =EG=BMÊ=(ÄÐ= 9 Õ =&=kBÕ =A+êR>Ð=EHG>Ð=Ê 9 FIÒ+=(ACB@L³>@ACEGAC>M=kEGH>Ð=Ê 9 F¡ÒC=FIH 9 ?<=BP@Æ(ÄM=kE1SyÈF 9 =EA 9 F¡S:B@H$Õ?<FÔÊq?(FÔH1×C=B<=kEGA+Å¡Å J SCB<=5S:E 9 ÕWSuÅI=HH1Õ5F 9 ? 9 ?<=4>@A+EA+>Ð=EHG>Ð=ÊÍ 9 FIÒ+=AyÅI×+S:EF 9 ?@Æ HG=&= M×CPME= Ó. . . . . . . . . . . 0.3. 1.5 weak perspective paraperspective. weak perspective paraperspective 1.25. Mean orientation error (deg.). 0.25. 0.15. 0.1. 0.05. 1. 0.75. 0.5. 0.25. 0. 0 2. 4. 6. 8. 10. 12. 14. 16. 18. 20. 2. 4. 6. 8. 10. 12. 14. 16. 18. M f l m l q©lKKik j n i¨p ikj t p t xCjG ikj-i zCl n f j n Klqp`lwj:lØi 'o t ¥l T t x pKp ¡t jOje j:i p`l jÙ f l ¥ f q:lwKKik jaik lwj¬ t ikj t p tu xCjG ikjai zCl n f j n Klqp`lwj:l i o t ¥l T t xpKp ¡t jaj:i p`l ¦ îB =ë@A+ÆÙ><ÅI=eSyÈaA+>M><Å¡FÔÊ&A 9 FISCB SyÈÝS:ÄÉ =Ê 9 >MS:H=0FIH 9 ?<=7×CEA+H>Í FIB<×¢S+ÈÙAè>ÐS+Å J ?<=L@EAyÅS:ÄÉ =Ê 9 Ä J A¿>@ACEGA+Å¡ÅI=&Å¡ÍIÉA¨Õ ×CEGFI>@>Ð=E M×CP@EG= ñ A Ó S 9 ? 9 ?<=èFÔÆÙAy×+=¢ACB@L 9 ?<= Æ(S<L<=ÅA+EG=L<=HÊ&EGFIÄÐ=LÄ J AçB<= 9 Í ÕWS:EGê(SyÈ°H 9 EAyFI×C? 9 ÅIFÔB<=H{A+BMLÉP@B@ÊÍ 9 FISCB@H Õ?<FIÊq?eACE=aÆÙA 9 Êq?<=LePMHFÔB<× AOÆ= 9 ?<S<L³L<=HÊ&EGFÔÄM=kLFIB ß ã Ó Ã ?<= È}S+ÅIÅ¡S¬Õ5FÔB<A × Ð×CP@EG=HRE=k>@EG=HG=B 9O9 ?<= K 9 J Ú:PMAyÅIF S+ÈMSCÄÉ =kÊ 9 >MS:H={ÊS:ÆÙ>@P 9 AyÍ 9 FISCBS:Ä 9 A+FIB<=kLÕ5F 9 ? 9 Õ S4L@F =EG=B 9 AyÅI×+SCEGF 9 ?@ÆÙHÓ Ã ?<=uϬÍ`ÎÇS:ÄÉ =Ê 9 ?@ACH -- 8 >M==L³S+È]ÊS:BCÒC=EG×+=kB@Ê=A+H4AaÈ^P@BMÊ 9 FISCB³SyÈ ÄM==B EG=>MES+É =Ê 9 =LFÔB 9 S 9 ?<={FÔÆA+×+= L<=k> 9 ?ÑÓ 9 SHG=&= 9 ?<==kEGEGSCEWSyÈ 9 ?@= >MS:H=CÓ G6HJI . Distance to camera / Object size. Distance to camera / Object size. 6. mean number of iterations (weak perspective) maximum number of iterations (weak perspective) mean number of iterations (paraperspective) maximum number of iterations (paraperspective). 5. 4. Number of iterations. Mean position error. 0.2. 3. 2. 1. 0. 2. 4. 6. 8. 10. 12. 14. à. Distance to camera / Object size. 16. 18. 20. 20.
(42) !FI×CPME= ñ ÄRHG?@S¬ÕH 9 ?<=E=kHGP@Å 9 SCÄ 9 AyFÔB<=kLOÕ5F 9 ? 9 ?@='F 9 =kEGA 9 FIÒ+=u>@A+EA+>Ð=EH>M=kÊ 9 FIÒ+=uAyÅI×+S+Í E F 9 ?@Æ FIB 9 ?<=aÊA+HG=(S+ÈWÅIFIB<=kH Ö L@=HÊ&EGFIÄÐ=L²FIB 9 ?@FIH>@AC>M=kE ä B M×CPME= ñ Ê Ö ÕW=ÙP@HG=L3AØB<S:B Å¡FÔB<=ACE5Æ= 9 ?@SL =&ÒC=BÄÐ=EG×yÍ é A+EÚP@A+EL 9 A+Å¡×CSCEGF 9 ?@Æ È^EGSCÆòÅ¡FÔB<= ÊS:EGEG=H>ÐSCB@L<=kB@Ê=kH&Ó . M ® t yq± V j(l t n+m l i Ñt n:nCm«ª j:¥' f l{ik+lwG n ikp`l t m ¥ki f p ¦. G6HJI . ½ ¼h» ½ ¹]¶¾1¶º /*Ѹ /*°¼Y·<½
(43) * ä B 9 ?@FIH{>@AC>M=kE Ö Õ =4L<=Ò+=&ÅISC>Ð=L 9 ÕWS(F 9 =EA 9 F¡ÒC=4AyÅI×+S:EF 9 ?MÆH F 9 =kEGA 9 FIÒ+='ÕW=kA+ê>M=kEGH>M=kÊ 9 F¡ÒC= A+B@L F 9 =EA 9 FIÒ+={>@ACEGAC>M=kEGH>M=kÊ 9 F¡ÒC=WAyÅI×+S:EF 9 ?MÆH 9 S'L@=AyÅÕ5F 9 ?ϬÍ`Î 9 S˨Í`ÎÅIFÔB<=5ÊSCEEG=H>MS:BÍ L<=B@Ê&=H Ö È}SCE'AOB<S:BÊS:><ÅÔA+B@ACESCE'ÊS:><ÅÔA+B@ACESCÄ<É =Ê 9 ÆS<L<=&ÅÓ Ã ?<= 9 Õ SØA+Å¡×CSCEGF 9 ?@ÆÙH?@A¨ÒC= 9 ?<=aHA+Æ=aA+Ê&ÊP@EA+Ê J ÓÐQ4S¬ÕW=Ò+=kE Ö F !9 HÄÐ= 9G9 =kE 9 SP@HG= 9 ?<=ÙÕW=kA+ê>Ð=EHG>Ð=Ê 9 FIÒ+=ÙAyÅI×+S:EF 9 ?@Æ È}SCEÙÅIFIB<=Ê&SCEE=kHG>ÐSCB@L@=B@Ê&=HÙÄM=kÊ&ACP@H=ÊS:ÆÙ>@P 9 A 9 FISCBÊS:H 9 FÔHÙÅ¡S¬Õ =EÓ $ =S:B<Å J B<=&=kL 9 S ÊSCÆÙ>@P 9 =ÙSCB<=FÔBCÒC=EH=ÆÙA 9 EGF¡ë³Õ?<FIÊq?²E=kÆÙAyFÔB@H 9 ?<=aHA+Æ=A 9 =kA+Êq?F 9 =EA 9 FISCB 9 SHSCÅ¡ÒC= 9 ?<=ÙÅIFIB<=kA+EuH J H 9 =kÆ =kÚ:PMA 9 FISCB ø Ó é SCEG=&S¬ÒC=E Ö Ã ?<=ÙS:EFI=B 9 A 9 FISCBS+È 9 ?<=aÊ&A+Æ=kEGA Ö G Ö D FIHÆS:E=u=ACHFIÅ J ÊSCÆÙ>@P 9 =LRÕ5F 9 ? 9 ?@=ÕW=kA+ê>Ð=EHG>Ð=Ê 9 FIÒ+=AyÅI×+S:EF 9 ?MÆØÓ * *¸ *¶? ¼* . .
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(49) &P4E=D4F KUF^RK2Fy"M=z,{wJ0P?D }&KUG?KM=F&|lZ E=JilZITI"E=F&V
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(58)
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