One Dimensional Resampling with Inverse and Forward Mapping ...

0 downloads 0 Views 204KB Size Report
Separable resampling algorithms are useful in casting image warping into a ... Resampling requires a mapping function to govern the geometric relation-.
F_\ % >_ #* !!°##

>]T3X\T]bX^]P[ ATbP\_[X]V fXcW 8]eTabT P]S 5^afPaS Ug I_b[

8 = CeUi\\Q] = 1 9c]QY\ ; = 1X]UT 1\UhQ^TbYQ E^YfUbcYdi

VAR„s{ 7‚}s„sAj‚ „‚Rs8}j$t sjB„$Y8R R$t$h{stjk „‚IZ{‚ Y‚ {B8}j‚-$k BP $8s‚ bs„}$t 3st }„‚R‚t‚I s R‚}s„sAj‚ sjB„$Y8 Ys $R b‚jj RZ$‚I PB„ Ys„IT bs„‚ $8}j‚8‚ts$Bt qYs 8‚YBI YBb‚%‚„ $R $tY‚„‚tjk R‚„$sj stI s}}j$‚R Btjk bY‚t Y‚ $t%‚„R‚ 8s}}$t $R $%‚t GBjA‚„ }„‚R‚t‚I stBY‚„ sjB„$Y8 Ys $R j‚RR RZ$‚I PB„ Ys„Ibs„‚ $8}j‚8‚ts$Bt stI s}}j$‚R Btjk bY‚t Y‚ PB„bs„I 8s}}$t $R $%‚t qY$R }s}‚„ I‚8BtR„s‚R Y‚ ‚JZ$%sj‚t{‚ BP Y‚ bB sjB„$Y8R $t Y‚ R‚tR‚ Ys Y‚k }„BIZ{‚ $I‚t${sj BZ}Z R{stj$t‚R G‚ I‚„$%‚ s %s„$s$Bt BP 3st:R sjBT „$Y8 Ys s}}j$‚R bY‚t Y‚ PB„bs„I 8s}}$t $R $%‚t stI s %s„$s$Bt BP GBjA‚„:R sjB„$Y8 Ys s}}j$‚R bY‚t Y‚ $t%‚„R‚ 8s}}$t $R $%‚t yt‚„s‚I Ys„Ibs„‚ $8}j‚8‚ts$BtR Ys }‚„PB„8 Bt‚TI$8‚tR$Btsj „‚Rs8}j$t ZtI‚„ ‚$Y‚„ PB„bs„I B„ $t%‚„R‚ 8s}}$tR s„‚ }„‚R‚t‚I PB„ ABY sjB„$Y8R AsR‚I Bt Y‚$„ RBPbs„‚ I‚R{„$}T $BtR qY‚ 3st sjB„$Y8 YsR Y‚ sI%sts‚ BP A‚$t R$8}j‚ bY‚t $8}j‚8‚t‚I $t Ys„Ibs„‚ bY$j‚ Y‚ GBjA‚„ sjB„$Y8 YsR Y‚ sI%sts‚ BP A‚$t }s„sjj‚j$9sAj‚ stI Ps{$j$s‚R s PsR‚„ RBPbs„‚ $8}j‚8‚ts$Bt qY‚ GBjA‚„ sjB„$Y8 sjRB YsR Y‚ sI%sts‚ BP I‚{BZ}j$t Y‚ „BZtIB& ‚„„B„R 8sI‚ s8Bt $t‚„%sjR R$t{‚ $ IB‚R tB s{{„Z‚ ‚„„B„R Y„BZY Y‚ $t{„‚8‚tsj {sj{Zjs$BtR „‚JZ$„‚I Ak Y‚ 3st sjB„$Y8

d

yt„BIZ{$Bt

7‚}s„sAj‚ „‚Rs8}j$t sjB„$Y8R s„‚ ZR‚PZj $t {sR$t $8s‚ bs„}$t $tB s P„s8‚bB„, Ys $R s8‚tsAj‚ B Ys„Ibs„‚ $8}j‚8‚ts$Bt p„Bb$t $t‚„‚R $t Y$R s„‚s YsR s$t‚I $8}‚ZR P„B8 Y‚ b$I‚R}„‚sI }„Bj$P‚„s$Bt BP sI%st{‚I !!

— 1 ; @UdUbc GBjA‚„ (H G‚ ‚-‚tI $ B bB„, b$Y $t%‚„R‚ 8s}}$t sR b‚jj

""

Z_eb^Q\ _V WbQ`XYSc d__\c

;d

GVNpU 3B„bs„I s}}$t

yt Y‚ PB„bs„I 8s}}$t PB„8Zjs$Bt BP GVNp st $t}Z }$-‚j $R „‚s‚I sR s Zt$Tj‚tY s„‚s Rs8}j‚ Ys {st A‚ „stRPB„8‚I $tB st BZ}Z $t‚„%sj Ys 8sk j$‚ PZjjk ‚8A‚II‚I $t st BZ}Z }$-‚j B„ 8sk R„sIIj‚ R‚%‚„sj BZ}Z }$-‚jR yt Y‚ h„R {sR‚ Y‚ $t}Z $t‚tR$k $R b‚$Y‚I Ak $R }s„$sj {BtT „$AZ$Bt B Y‚ BZ}Z }$-‚j stI Y‚t I‚}BR$‚I $tB st s{{Z8ZjsB„ qY‚ s{{Z8ZjsB„ b$jj Zj$8s‚jk A‚ RB„‚I $t Y‚ BZ}Z s„„sk Btjk bY‚t Y‚ $t}Z $t‚„%sj }sRR‚R s{„BRR Y‚ „$Y8BR ABZtIs„k BP st BZ}Z }$-‚j sRRZ8$t Ys Y‚ sjB„$Y8 }„B{‚‚IR P„B8 j‚P B „$Y yt Y‚ R‚{BtI {sR‚ Y‚ $t}Z }$-‚j s{Zsjjk {„BRR‚R B„ R„sIIj‚R s j‚sR Bt‚ BZ}Z }$-‚j ABZtIs„k V R$tj‚ $t}Z }$-‚j 8sk $%‚ „$R‚ B s Xj‚P R„sIIj‚" $P $ B{{Z}$‚R Btjk s }s„$sj BZ}Z }$-‚j A‚PB„‚ $ {„BRR‚R $R h„R BZ}Z ABZtIs„k P„B8 Y‚ j‚P R$I‚ VR jBt sR Y‚ $t}Z }$-‚j {Bt$tZ‚R B PZjjk {B%‚„ BZ}Z }$-‚jR $ $R Rs$I B A‚ $t Y‚ X{‚t„sj $t‚„%sj" 3$tsjjk Y‚ jsR }s„$sj {Bt„$AZ$Bt B st BZ}Z }$-‚j Bt Y‚ „$Y R$I‚ $R {sjj‚I s X„$Y R„sIIj‚" V RBPbs„‚ $8}j‚8‚ts$Bt $t ] $R $%‚t A‚jBb ;dd 7BPbs„‚ y8}j‚8‚ts$Bt dClBƒQdIwICYBl Q?H %v %v?H %v CY?H %v %vlv %v CYlvD Z %v Y ]~ %vI0 %vC %v}Y %9u 0 ]~ %vI0 %vC CY}Y %9u Yl ]~ %vI0 CQ X lQ9CR %v}Y }%0l Yƒ ]~ %vI0 CQ X ƒ%X9CR %v}Y }%0l %0+ ]~ %vI0 CQ X lQ R%I CQ %vƒ'ul %0g" ]~ %vI0 CQ X ƒ%XR%I CQ %vƒ'ul ICYBl 0+ ]~ %vI0 CQ X lQ R%I CQ %vƒ'ul 0g ]~ %vI0 CQ X ƒ%XR%I CQ %vƒ'ul Iy" ]~ %vvR%m %v|ƒ9v C'ƒ %vƒ'ul

~] ~] ~] ~] ~] ~] ~] ~] ~]

]~ |luƒ CY}Y]u||Y9YluCƒ uƒƒum ~] QCƒ w0,+" 0^CYlv" 0KKD CY?0H , +" ]~ |X|/ %Q vC %v}Y R|uvl%v }%0l }ƒCb|R C ?+CYlvH ƒuv ~] %QwQ?%vlvH ^ + (( Q?+H h CYlvD ƒYƒv" ]~ g++2 |l%}}%v ~] ]~ %v% Yl X lQT0v CQ X %v}Y R|uvl%v ~] QCƒwY,+" Q?YH^+" YKKD" ]~ uI'uv| Y ~] Yl , Y" ]~ %v% Yl ~] ]~ }ƒC|RR Q%ƒR %vƒ'ulU |l%} lQ RƒuIIl ~] %QwY h +D Z Y , Yl T g" 0+ , Q?YH" 0g , Q?YKgH"

G_\RUbW Ud Q\* ?^U4Y]U^cY_^Q\ BUcQ]`\Y^W

"#

%0+ , 0+ T g" %0g , 0g" ]~ |vƒul %vƒ'ul" d%ll B |l%}}I QCƒ 0^+ ~] Iy , w%v?YKgH T %v?YHD ] w0g T 0+D" QCƒw0,+" 0^%0g oo 0^CYlv" 0KKD CY?0H , %v?YH K Iy~w0T0+D" ]~ ƒ%X RƒuIIl ~] %Qw%0g ,0g oo %0g^CYlvD CY?%0H , w%v?YH K Iy~w%0gT0+DD ~ w0gT%0gD"

e ]~ %v% Yƒ X ƒ%XT0v CQ X %v}Y R|uvl%v ~] QCƒwY,%vlv" Q?YHhCYlv" YTTD" ]~ uI'uv| Y ~] Yƒ , wY ,, %vlvD 4 %vlvTg U Y" ]~ %v% Yƒ ~] ]~ |X|/ %Q Cvlm Cv %v}Y }%0l |C'ƒR R|uvl%v ~] %QwY ,, YlD ƒYƒv" ]~ }ƒC|RR luR %vƒ'ulU |l%} ƒ%X RƒuIIl ~] %QwY ^ %vlvD Z %0+ , 0+ , Q?YH" ]~ %vT uvI ƒulT'ulYI lQ %vI0 ~] %0g , 0g , Q?YKgH" ]~ %vT uvI ƒulT'ulYI ƒ%X %vI0 ~] ]~ lQ RƒuIIl ~] CY?%0+H K, %v?YH ~ w%0+T0+KgD" ]~ |vƒul %vƒ'ulU d%ll B |l%}}I QCƒ 0h,CYlv ~] Iy , w%v?YKgH T %v?YHD ] w0g T 0+D" QCƒw0,%0+Kg" 0^%0g oo 0^CYlv" 0KKD CY?0H , %v?YH K Iy~w0T0+D"

e ]~ 9u%v lCC} ~] QCƒwY,Yl" Y^,Yƒ" YKKD Z %0+ , 0+ , Q?YH" %0g , 0g , Q?YKgH"

]~ %vT uvI ƒulT'ulYI lQ %vI0 ]~ %vT uvI ƒulT'ulYI ƒ%X %vI0

~] ~]

]~ |X|/ %Q %vƒ'ul %R 9BIII %v Cv CY}Y }%0l %Qw%0+ ,, %0gD Z CY?%0gH K, %v?YH ~ w0gT0+D" ]~ u||Y9Ylu }%0l |Cv%vY" ]~ v0 %v}Y }%0l e

~] ~] ~]

]~ lQ RƒuIIl ~] CY?%0+H K, %v?YH ~ w%0+T0+KgD"

]~ uII %v}Y Qƒu9v ~]

]~ |vƒul %vƒ'ul ~] Iy , w%v?YKgH T %v?YHD ] w0g T 0+D" QCƒw0,%0+Kg" 0^%0g" 0KKD CY?0H , %v?YH K Iy~w0T0+D"

]~ QCƒ l%vuƒ %vƒ} ~] ]~ '%R% ull }%0lR ~] ]~ %v% CY}Y }%0l ~]

]~ ƒ%X RƒuIIl ~]

"$

e

Z_eb^Q\ _V WbQ`XYSc d__\c

e

%Qw0g , %0gD ]~ CY}Y }0l Qƒu9v~] CY?%0gH , w%v?YH K Iy~w%0gT0+DD ~ w0gT%0gD"

y $R {j‚s„ P„B8 Y‚ sAB%‚ I‚R{„$}$Bt Ys Y‚ }„B{‚RR$t BP s R}‚{$h{ $t‚„%sj $R $tI‚}‚tI‚t BP Y‚ }„B{‚RR$t BP BY‚„ $t‚„%sjR qY‚ }„B{‚RR$t BP st $tI$%$IZsj $t‚„%sj Btjk „‚JZ$„‚R Y‚ }BR$$Bt BP $R j‚P stI „$Y ABZtIs„$‚R qYZR Y‚ sjB„$Y8 YsR }B‚t$sj PB„ }s„sjj‚j$R8 WB‚ Ys Ztj$,‚ 3VNp $t‚„}Bjs$Bt BP Y‚ $t}Z $t‚tR$k $R tB }‚„PB„8‚I Ztj‚RR $ $R t‚{‚RRs„k $‚ bY$j‚ }„B{‚RR$t Y‚ {‚t„sj $t‚„%sj stI Y‚ „$Y R„sIIj‚ G‚ {st IB Y‚ Rs8‚ $t 3VNp Ak sII$t Y‚ ‚R inseg == sf B Y‚ $t‚„}Bjs$Bt Rs‚8‚t stI R‚$t Y‚ $t‚tR$k B 7z>`H $P Y‚ {BtI$$Bt $R „Z‚ B„ R‚$t $ B Y‚ $t‚„}Bjs‚I %sjZ‚ BY‚„b$R‚ VjRB tB‚ Ys Y‚ 9‚„B {k{j‚R s„‚ ‚j$8$ts‚I $t Y$R s}}„Bs{Y qYZR GVNp $R PsR‚„ Yst 3VNp bY‚t $8}j‚8‚t‚I $t RBPbs„‚ qY‚ R‚„$sj RBPbs„‚ $8}j‚8‚ts$Bt BP Y‚ sjB„$Y8 {st A‚ PZ„Y‚„ s{{‚j‚„s‚I Ak sIB}$t $t{„‚8‚tsj {B8}Zs$Bt PB„ Y‚ {‚t„sj $t‚„%sj qYZR $t Y‚ 8s$t jBB} sR b‚jj sR $t Y‚ }„‚}„B{‚RR$t Y‚ bB j$t‚R PB„ {B8}Z$t Y‚ {‚t„sj $t‚„%sj QCƒw0,%0+Kg" 0^%0g" 0KKD CY?0H , %v?YH K Iy~w0T0+D"

{st A‚ „‚b„$‚t sR %Qw%0gh%0+KgD Z CY?%0+KgH , %v?YH K Iy~w%0+KgT0+D" QCƒw0,%0+K3" 0^%0g" 0KKD CY?0H , CY?0TgH K Iy" e

qY$R „‚}js{‚R Y‚ 8Zj$}j${s$Bt B}‚„s$BtR b$Y sII$$Bt (, L`0qzH $R B sRRB{$s‚ BZ}Z sRR$t8‚tR $tR$I‚ Y‚ 8s$t jBB} b$Y Zs„I {BtI$$BtR qY$R $R RjBb‚„ bY‚t $8}j‚8‚t‚I $t RBPT bs„‚ AZ $ $R 8B„‚ RZ$sAj‚ PB„ s Ys„Ibs„‚ $8}j‚8‚ts$Bt V RBPbs„‚ $8}j‚8‚ts$Bt $t ] PBjjBbRU dClBƒQdIOYuƒIRwICYBl Q?H %v %v?H %v CY?H %v %vlv %v CYlvD Z %v Y ]~ %vI0 %vC %v}Y %9u ~] 0 ]~ %vI0 %vC CY}Y %9u ~] %0+ ]~ %vI0 CQ X lQ R%I CQ %vƒ'ul ~] %0g" ]~ %vI0 CQ X ƒ%XR%I CQ %vƒ'ul ~] ICYBl 0+ ]~ %vI0 CQ X lQ R%I CQ %vƒ'ul ~] 0g ]~ %vI0 CQ X ƒ%XR%I CQ %vƒ'ul ~]

G_\RUbW Ud Q\* ?^U4Y]U^cY_^Q\ BUcQ]`\Y^W Iy"

]~ %vvR%m %v|ƒ9v

"% C'ƒ %vƒ'ul ~]

]~ |luƒ CY}Y]u||Y9YluCƒ uƒƒum ~] QCƒ w0,+" 0^CYlv" 0KKD CY?0H , +" ]~ 9u%v lCC} ~] QCƒwY,+" Y^%vlv" YKKD Z %0+ , 0+ , Q?YH" %0g , 0g , Q?YKgH"

]~ %vT uvI ƒulT'ulYI lQ %vI0 ]~ %vT uvI ƒulT'ulYI ƒ%X %vI0

]~ |X|/ %Q %vƒ'ul %R 9BIII %v Cv CY}Y }%0l %Qw%0+,,%0g oo %0+h,+ oo %0+^CYlvD Z CY?%0gH K, %v?YH ~ w0gT0+D" ]~ u||Y9Ylu }%0l |Cv%vY" ]~ v0 %v}Y }%0l e

~] ~] ~]

~] ~]

]~ lQ RƒuIIl ~] %Qw%0+h,+ oo %0+^CYlvD CY?%0+H K, %v?YH ~ w%0+T0+KgD" ]~ uII %v}Y Qƒu9v ~] ]~ |vƒul %vƒ'ul ~] Iy , w%v?YKgH T %v?YHD ] w0g T 0+D" ]~ QCƒ l%vuƒ %vƒ} ~] QCƒw0,%0+Kg" 0h,+ oo 0^%0g oo 0^CYlv" 0KKD ]~ '%R% }%0lR ~] CY?0H , %v?YH K Iy~w0T0+D" ]~ %v% CY}Y }%0l ~]

e

e

;1

]~ ƒ%X RƒuIIl ~] %Qw%0gh,+ oo %0g^CYlv oo 0g , %0gD ]~ CY}Y }0l Qƒu9v~] CY?%0gH , w%v?YH K Iy~w%0gT0+DD ~ w0gT%0gD"

GVNpU yt%‚„R‚ s}}$t

yt Y‚ $t%‚„R‚ 8s}}$t PB„8Zjs$Bt BP GVNp st BZ}Z }$-‚j $R „‚s‚I sR s Zt$Tj‚tY s„‚s Rs8}j‚ Ys {st A‚ „stRPB„8‚I $tB st $t}Z $t‚„%sj Ys 8sk j$‚ PZjjk ‚8A‚II‚I $t st $t}Z }$-‚j B„ 8sk R„sIIj‚ R‚%‚„sj $t}Z }$-‚jR yt Y‚ h„R {sR‚ Y‚ $t}Z $t‚tR$k $R {B8}Z‚I s Y‚ j‚P ABZtIs„k BP Y‚ ‚8A‚II‚I $t‚„%sj 7$t{‚ Y$R }BR$$Bt 8sk tB t‚{‚RRs„$jk {B$t{$I‚ b$Y st $t}Z }$-‚j ABZtIs„k $t‚„}Bjs$Bt 8sk A‚ t‚{‚RRs„k B k$‚jI Y‚ %sjZ‚ BP Y‚ {Z„„‚t BZ}Z }$-‚j yt Y‚ R‚{BtI {sR‚ s R$tj‚ BZ}Z }$-‚j 8sk 8s} B st $t}Z $t‚„%sj Ys {BtR$RR BP s j‚P R„sIIj‚ s {‚t„sj $t‚„%sj stI\B„ s „$Y R„sIIj‚ 3B„ Y‚ j‚P R„sIIj‚ Y‚ $t}Z $t‚tR$k $R $t‚„}Bjs‚I s Y‚ j‚P ABZtIs„k BP Y‚ j‚P R„sIIj‚ stI Y‚t R{sj‚I Ak Y‚ j‚tY BP Y‚ j‚P R„sIIj‚ qY$R $t‚tR$k {Bt„$AZ$Bt $R I‚}BR$‚I $t Y‚ s{{Z8ZjsB„ sRRB{$s‚I b$Y Ys BZ}Z }$-‚j 3B„ Y‚ {‚t„sj $t‚„%sj tB $t‚„}Bjs$Bt B„ R{sj$t $R t‚{‚RRs„k

"&

Z_eb^Q\ _V WbQ`XYSc d__\c

R$t{‚ Y‚ {‚t„sj $t‚„%sj Rs„R Bt $t}Z }$-‚j ABZtIs„$‚R stI {B%‚„R bYBj‚ $t}Z }$-‚jR qYZR Y‚ $t‚tR$k BP Y‚ $t}Z }$-‚jR $t Y‚ {‚t„sj $t‚„%sj s„‚ R$8}jk sII‚I B Y‚ s{{Z8ZjsB„ 3B„ Y‚ „$Y R„sIIj‚ tB $t‚„}Bjs$Bt $R t‚‚I‚I AZ R{sj$t Ak Y‚ j‚tY BP Y‚ „$Y R„sIIj‚ $R „‚JZ$„‚I A‚PB„‚ sII$t Y‚ htsj $t‚tR$k {Bt„$AZ$Bt B Y‚ s{{Z8ZjsB„ WB‚ Ys Y‚ s{{Z8Zjs‚I RZ8 t‚‚IR B A‚ I$%$I‚I Ak Y‚ $RP ‚t„k BP Y‚ {Z„„‚t BZ}Z }$-‚j B k$‚jI Y‚ {B„„‚{ BZ}Z $t‚tR$k %sjZ‚ qY$R I$%$R$Bt $R tB t‚{‚RRs„k bY‚t Y‚ BZ}Z }$-‚j $R ‚8A‚II‚I $t Y‚ $t}Z }$-‚j Ztj‚RR b‚ R{sj‚ Y‚ $t‚„}Bjs‚I $t‚tR$k Ak Y‚ j‚tY BP Y‚ ‚8A‚II‚I $t‚„%sj sR $R IBt‚ $t Y‚ Ys„Ibs„‚ $8}j‚8‚ts$Bt V RBPbs„‚ $8}j‚8‚ts$Bt $t ] PBjjBbR G‚ {YBR‚ Y‚ $8}j‚8‚ts$Bt b$Y }„‚}„B{‚RR$t BP %sjZ‚R BP 8s}}$t BZR$I‚ Y‚ sjjBbsAj‚ „st‚ >(, 7zqzH Vt $8}j‚8‚ts$Bt b$Y Zs„I {BtI$$BtR {BZjI A‚ {BI‚I sR $t Y‚ }„‚{‚I$t R‚{$Bt dClBƒ%v'wICYBl Q?H %v %v?H %v CY?H %v %vlv %v CYlvD Z %v Y ]~ %vI0 %vC %v}Y %9u ~] 0 ]~ %vI0 %vC CY}Y %9u ~] 0l ]~ %vI0 CQ X lQ9CR CY}Y }%0l~] 0ƒ ]~ %vI0 CQ X ƒ%X9CR CY}Y }%0l~] %Y+ ]~ %vI0 CQ X lQ R%I CQ %vƒ'ul ~] %Yg" ]~ %vI0 CQ X ƒ%XR%I CQ %vƒ'ul ~] ICYBl Y+ ]~ %vI0 CQ X lQ R%I CQ %vƒ'ul ~] Yg ]~ %vI0 CQ X ƒ%XR%I CQ %vƒ'ul ~] ]~ |luƒ CY}Y]u||Y9YluCƒ uƒƒum ~] QCƒ w0,+" 0^CYlv" 0KKD CY?0H , +" ]~ |X|/ %Q vC CY}Y R|uvl%v }%0l }ƒCb|R C ?+%vlvH ƒuv ~] %QwQ?CYlvH ^ + (( Q?+H h %vlvD ƒYƒv" ]~ g++2 |l%}}%v ~] ]~ %v% Yl X lQT0v CQ X %v}Y R|uvl%v ~] QCƒw0,+" Q?0H^+" 0KKD" ]~ uI'uv| 0 ~] 0l , 0" ]~ %v% 0l ~] ]~ }ƒC|RR Q%ƒR %vƒ'ulU |l%} lQ RƒuIIl ~] %Qw0 h +D Z 0 , 0l T g" %Y+ , Y+ , Q?0H" ]~ %vT uvI ƒulT'ulYI lQ %vI0 %Yg , Yg , Q?0KgH" ]~ %vT uvI ƒulT'ulYI ƒ%X %vI0 ]~ |vƒul %vƒ'ul" d%ll B |l%}}I QCƒ 0^+ ~] QCƒwY,+" Y^%Yg oo Y^%vlv" YKKD CY?0H K, %v?YH" ]~ ƒ%X RƒuIIl ~] %Qw%Yg ,Yg oo %Yg^%vlvD CY?0H K, w%v?%YgH ~ wYgT%YgD"

~] ~]

G_\RUbW Ud Q\* ?^U4Y]U^cY_^Q\ BUcQ]`\Y^W

e

"'

]~ vCƒ9ul%: u||Y9YluCƒ ~] CY?0H ], wQ?0KgH T Q?0HD"

]~ %v% Yƒ X ƒ%XT0v CQ X %v}Y R|uvl%v ~] QCƒw0,CYlv" Q?0Hh%vlv" 0TTD" ]~ uI'uv| 0 ~] 0ƒ , 0" ]~ %v% 0ƒ ~] ]~ |X|/ %Q Cvlm Cv CY}Y }%0l |C'ƒR R|uvl%v ~] %Qw0 ,, 0lD ƒYƒv" ]~ }ƒC|RR luR %vƒ'ulU |l%} ƒ%X RƒuIIl ~] %Qw0 ^ CYlvD Z %Y+ , Y+ , Q?0H" ]~ %vT uvI ƒulT'ulYI lQ %vI0 ~] %Yg , Yg , Q?0KgH" ]~ %vT uvI ƒulT'ulYI ƒ%X %vI0 ~] ]~ lQ RƒuIIl ~] CY?0H , w%v?%Y+H K wY+T%Y+D~w%v?%Y+KgHT%v?%Y+HDD ~ w%Y+TY+KgD" ]~ |vƒul %vƒ'ulU d%ll B |l%}}I QCƒ 0h,CYlv ~] QCƒwY,%Y+Kg" Y^%Yg oo Y^%vlv" YKKD CY?0H K, %v?YH" ]~ vCƒ9ul%: u||Y9YluCƒ ~] CY?0H ], wQ?0KgHTQ?0HD"

e ]~ 9u%v lCC} ~] QCƒw0,0l" 0^0ƒ" 0KKD Z %Y+ , Y+ , Q?0H" %Yg , Yg , Q?0KgH"

]~ %vT uvI ƒulT'ulYI lQ %vI0 ]~ %vT uvI ƒulT'ulYI ƒ%X %vI0

]~ |X|/ %Q %vƒ'ul %R 9BIII %v Cv CY}Y }%0l %Qw%Y+ ,, %YgD Z CY?0H K, %v?%Y+H K wY+T%Y+D~w%v?%Y+KgHT%v?%Y+HD" |Cv%vY" ]~ v0 %v}Y }%0l e

~] ~] ~]

~]

]~ lQ RƒuIIl ~] CY?0H , w%v?%Y+H K wY+T%Y+D~w%v?%Y+KgHT%v?%Y+HDD ~ w%Y+TY+KgD"

e

e

]~ |vƒul %vƒ'ul ~] QCƒwY,%Y+Kg" Y^%Yg" YKKD CY?0H K, %v?YH"

]~ '%R%

]~ ƒ%X RƒuIIl ~] %QwYg , %YgD CY?0H K, %v?%YgH ~ wYgT%YgD"

]~ CY}Y }0l Qƒu9v~]

CY?0H ], wQ?0KgHTQ?0HD"

ull

}%0lR ~]

"(

x

Z_eb^Q\ _V WbQ`XYSc d__\c

(, L`0qzH PB„

3$Z„‚ d yt‚„s‚I 3VNp „‚Rs8}j$t sjB„$Y8

G_\RUbW Ud Q\* ?^U4Y]U^cY_^Q\ BUcQ]`\Y^W

")

3$Z„‚ 1 qY‚ $t‚„}Bjs‚ AjB{,

PB„bs„I 8s}}$t qY$R {j$}}$t sR b‚jj sR Y‚ $t$$sj$9s$Bt BP $tR‚ stI BZR‚ s Y‚ Rs„ BP Y‚ }„B{‚RR s„‚ tB RYBbt $t 3$Z„‚ d B ,‚‚} Y‚ I$s„s8 R$8}j‚ x1

GVNpU 3st MEH €s„j  3st XV WBtsj$sR$t i‚sjTq$8‚ 7}s$sj q„stRPB„8 q‚{Yt$JZ‚" yeee ]B8}Z‚„ p„s}Y${R stI V}}j${s$BtR EwdDU duM( wFstZs„k dMED 7‚‚ sjRB XN‚‚„R B Y‚ eI$B„" $t EwnDU EETE ws„{Y dMED stI EwDU n M wFZjk dMED >78$Y MH Vj%k isk 78$Y X_jsts„ 1T_sRR q‚-Z„‚ s}}$t stI Gs„}$t" ]B8T }Z‚„ p„s}Y${R w_„B{ 7yppiV_< :MD 1dw;DU 1Enu11 wdMD >G$jj$s8R MnH Nst{‚ G$jj$s8R X_k„s8$Isj _s„s8‚„${R" w_„B{ 7yppiV_< :MnD dwnDU dudd wdMnD

]B8}Z‚„ p„s}Y${R

>GBjA‚„ (H p‚B„‚ GBjA‚„ *$$sj y8s‚ Gs„}$t NBR Vjs8$BR ]VU yeee ]B8}Z‚„ 7B{$‚k _„‚RR d( >GBjA‚„ BZj MH p‚B„‚ GBjA‚„ stI q‚„„st{‚ e BZj Xy8s‚ Gs„}$t b$Y 7}s$sj NBB,Z} qsAj‚R" ]B8}Z‚„ p„s}Y${R w_„B{ 7yppiV_< :MD 1nwnDU nEunM wdMD G‚A ytPB„8s$BtU Y}U\\bbbs{8B„\`\}s}‚„R\GBjA‚„eVj(( p‚B„‚ GBjA‚„ *‚}s„8‚t BP ]B8}Z‚„ 7{$‚t{‚ ]$k ]Bjj‚‚ BP W‚b OB„, W‚b OB„, WO d((nd wbBjA‚„o{R{{tk{Ztk‚IZD

Suggest Documents