HAL Id: inria-00072552
https://hal.inria.fr/inria-00072552
Submitted on 24 May 2006
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub-
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non,
A Robust Technique to Recognize Objects in Images, and the DB Problems it Raises
Laurent Amsaleg, Patrick Gros
To cite this version:
Laurent Amsaleg, Patrick Gros. A Robust Technique to Recognize Objects in Images, and the DB Problems it Raises. [Research Report] RR-4081, INRIA. 2000. �inria-00072552�
ISRN INRIA/RR--4081--FR+ENG
a p p o r t
d e r e c h e r c h e
INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE
A Robust Technique to Recognize Objects in Images, and the DB Problems it Raises
Laurent Amsaleg , Patrick Gros
N˚4081
Novembre 2000
THÈME 3
,/0 2143 5768:9;+-#< ,
=?>A@BDCFE&GIHJLKD>NMOCFPQSRUTV>AGDBDWYX[Z]\^B`_aKcb
dfehgjiklmonqpsrtk`uwvFxyrwz|{FpIeh{Fi}ikj~Oi%vx<ez|phkF
zi%vFk` `h{phph`k` `hx{Fphpvz w tvpxkD
'uw{kjrw dkjizxj kjr;?z r<v
;vhA{Fur;k8uwk`x<ekju<x<ehkpsm;{[Fkjiutk8Fm0FvFk`
I ¢¡`£j¤[¥h¦£§ nqp¨rtehk%x{Fpsrtk©r{ªfx{psrwkjpsr~«v tk`^z|i%vFk¬uwkrwutzkj[v®ª¯uw{i°vuwkhv[r<vvF kD jNrwuwvFz±~
rwz|{Fpv t² rtk`i% ;r²hzxjv|²Sx{ih³hrtkvI tz|phF|kkD txjutzrt{Fu?NkjuzivkAv tk`Sª¯{Fu´kj©hvihk{p¨x{{u
ez rt{Fu<vi% jµdfehkuwk` t³h±rf{ªv¶F³kjuw²%z fzp:kjpkju<vArtehk8zi%vkD ·eh{F tkVhk` wxuwz|rw{u< vutk´rtekx{F tk` r
rw{}rtehk8kD txjutzrt{Fuf{ª&rwehk¶s³hkjuw²%z|i%vkµ'¸² rtk`i h³z||rrtehz f·fvc²¹vuwkVvh|kVrw{¬uwkrw³hutpzivkD ºrwev[r
vutkI{v|²» tzi}zvurw{^rwehk¶s³hk`ut²»zivkF¢³rx`vp¼p{r¬uwkrw³huwp¼z|i%vk` rtevr}xj{psrwvz|p¾½j¿ÀÁS¿Â
Ã¯Ä Á¿ÅÇÆjÁwÈ
Ã
½?rteAv[rvuwk?zp¹rtekV¶s³hk`ut²Fµ¢kDxk`pFrvhcvpxkD 'zpIzi%vk´huw{xjk` w zph8rwk`x<ehpz¶s³hkD jeh{[· kjFkjuD
i%vÉkVrtehz ;N{F w tz|hk8²xj{ih³rwz|ph%{xjv®k` wxuwzrt{Fuw rwev[r?vutk8· kj® t³hz±rwk`ª¯{u´krwk`xyrwz|pI ziz|vu
{Fk`xrw 8zpÊzivkD jµ^Ë´sz{³A ²^N{[·k`uª¯³hOrtehz 8Ìpk~«u<vzp¨zi%vk%uwk`xj{Fphz±rwz|{FpÊv {Sx<evphkD rtehk
·fvc²}rtehkVuwkrtuwzkj[vahuw{xk` w z Nkjutª¯{uwi}kDÍ¢z|p rtkDvI{ª¢ t³hhiz|rrwz|phv} zphk¶F³kjuw²¬rw{¬uwkrwutzkjFk´ tz|i}~
zvu;zi%vkD jAi³h|rtzhk¶s³hkjuwzk` ;i¬³ r?Ak¬ ³hi}z|rrwk`Nrwehkjzu?vurwzv&uwk` t³h±r< ;N{F r~«huw{xjk` w kDINkª¯{Futk
hkjz|Fkjuwz|phrtekvp t·k`u`µ}dfehz vNkjuVÌu< r8huwk` tkjpsr< VvªÇvi}z²^{ªf|{x`vUk` wxuwzrt{Fuw ´rteAv[r ³hA{Fur
ÌAphk~«u<vzpÊz|i%vkIuwk`xj{Fphz±rwz|{Fp&µ¼Ë´³hurwk`x<ehpz¶s³hkz }uw{h³A rD͹z±r%kjrtk`xrw tz|izvu¬{Fk`xrw ¬z|pÎx{{u
zi%vFk` hk` thz±rwk{Futzkjpsr<v[rtz{p¼x<eAvphFk` ϯuw{rwvrtz{pÊ{ª?{kDxyr< wÐUrtu<vp tv[rtz{pA juwk` t{³rtz{p¼x<evphkD j
z|³hizpv[rwz|{Fp^[vuwzvrtz{p `vpSvurwzv®{xjxj|³ tz{p `µ;Ñ^vp²i³h|rtz|~qz|ik`p z{pAv®zpkj©k` ;eAvckNkjk`p
ut{FA{s kDrt{: NkjkD~O³^rtek¬uwkrwutzkj[v¢huw{xk` w `µVdfehkD k}zpk©kD jaeh{[· kjFkjuDAevcFkNkjkjp»i{F rt²Sk~
tzphkD%ª¯{ufvpAIk`cv|³Av[rtkDIvFvzp rzi%vkVhv[r<vvF kD º·ekjuwk´kDvx<eIzi%vFk?z hk` wxuwz|Nk`Is²v¬ tz|pk
hk` wxuwz|rw{uDµ;Ò¾ehz|krtehz VvNkjuV{k` ´ph{rVhuwk` tkjpsr´vp²:phk`·z|phk©z|p wx<ehkjikNz|rV teh{[·; rwev[rVrtehk
rwehuwkjki{F r'kÓ¹xzkjpsr'zpkj©zphrwk`x<ehphz¶s³hk` Éph{[·p}rw{vc²vuwk rwz|hrw{s{ t{[·¼rt{8Nk³ tk`}zp%huwvFxyrwzxjk
·z|rte:{xjv&hk` wxuwz|rw{u< AkDxjv³A k{ªrtehkx<eAvphFk` fzpIrwehk8utkjrtuwz|k`[vhuw{xk` w `µ
ÔSÕsÖa×wØÙ ¤[Ú¢¡§ uw{h³A r;ÌAphk~«u<vzpSz|i%vkuwk`xj{pz±rwz|{Fp&hi³±rwz|ik`hzvIz|phk©z|pNi³h|rtzzi}k`p tz|{Fpv
zpkj©z|phAz|i%vk8hv[r<vvF kD jxj{psrtk`pFrt~OAv tk`¹uwkrwutzkj[vY{xjv&hk` wxuwz|rw{u<
ÛÜÝtÞ«ß`àfÝá¢âÞ«ãOäå
æºçAèjécêìëíUîíïêìðñòDó¯ô&óÇõ`ö¨÷aøù¢ôõ
ú
çAèjécêìëíûêìñYüOýDòcó¯ô&óÇõ`öþ÷øù¢ôõ
Unité de recherche INRIA Rennes
/#j+-, .: (96¢8:9;+- :,®#/2/ #2 9,
¨
¡ § k` U t² rtg`ik` ¢Ak`utikjrrwvpsrvVutkDx<ehkju<x<ehk zi%vFkvu|kx{Fpsrtkjp³}xjvx³|k`pFrUFjph`uwv|kj~
ik`pFr³hp tkj³hFkr®³hpz¶s³hk k` wxuwz|hrtkj³u&vu®z|i%vFkDvuk©kjihkº tkj{p8³hp8ez rt{Fu<viik'kºx{F³hkj³hu< jµ
v:ut`A{Fp tkS³hphkIz|psrtk`utuw{sv[rwz|{Fp¨kD rr²hz¶s³hkjik`pFr}x{iN{F tjk¹kD zi%vkD kIvSAv tk¹{psrk`
hk` wxuwz|rwkj³hu< {FpFrk` h³ tz|izvz|uwk` k8xk`|³hz&hkVz|i%vFk´uwk`¶s³jrtkFµkVr²NkhkV t² rwgjikAk`utikr
hk8utkjrtuw{³hFkjufv³S k`z|pS³hphk8FuwvpkVv tk|kD zivkD ¶F³z® {FpsrfF|{Fvkjik`pFr; tz|izvz|uwk` zi%vFk
uwk`¶s³jrtkFi%vz %phkþAk`utikr¹Av ¹kþutkjrtuw{³hFkju%k` ¹z|i%vFk` i{psrwuwvpFr¹xjkjutrwvzp %{Fkr< ¹x{Fpsrtkjp³
vp 8z|i%vFkutkD¶F³rtkFµd{³rwkª¯{Fz `®k` vc[vpx`k` uw`xk`psrtk` k`prtu<vz|rtk`i}k`psrzi%vFk%utk`pkjpsrxjkjv
N{F w tz|hk¹zvS|kxjvxj³hki³h|rtzhk` }k` wxuwzrtk`³huw |{x`v³©Ê¶s³hz t{psrz|k`p vhvrtD :ªÇvz|uwkIkv
uwk`xj{phpAvz t wvpxjk}{Fkr< k¹Fuwvz|p»Ìp®µ k¹r²sNkIkIutkDx{ppvz t wvpAxk%x<evpk%hzkjpÊ`szk`i}ik`pFr
k` xjvAvxz|rtD k%utkDx{Fphpvz w tvpxk³hpÊ ² rtgjikF®i%vz x<evphk%v³A t tzUhuw{ª¯{pAjikjpsr8v:ivphzgjuwk
h{psr|kD futkDx<ehkju<x<ehk` f k"!NkDxyrw³hkjpsr®Í'v³z|k`³Sk8phk8 {F³hikrtrtuwk¶s³³hphk tkj³|kuwk`¶s³rwkkr?v[rtrtkjpAutk
¶s³hkfk; ² rtg`i}kfuwkrw{³huwphkf|kD z|i%vk` U tzi}zvzutkD jki¬³h|rtzh|kD Uuwk`¶s³rwk` Uxj{p t`xj³rtzkD ¢h{zkjpsr#rwutk
t{³i}z tk` `skjr;³hphkhevF k8k8 t²pFrwehg` tk8k` fuw` t³h|rwvrw vutrtzkj {Fz±r$rwutkk"!NkDxyrt³jk8vc[vpsr;kutk`puwk
³phk¹uwjN{p tkµ%kr¬vurwzxj|k%huw` tkjpsrwkvA{Fuw»³hphk¹ªÇviz|kIkIkD txjutzrwkj³hu< |{x`v³©¶F³zºNkjuwi}kjr~
rwkjpsr¬kIªÇvzutk¹hkIvSutkDx{Fphpvz w tvpxk}ut{Fh³ rtkI{Fkr< k¹Fuwvz|p»Ìp8Í}z ¬utkjrtuw{³hFkjpsrk` {kjrw
tzi}zvzutkD 8i%vz {FpFr¬vþA{s z|rtz{p&{Futzkjpsr<v[rtz{p®®z|³hizpv[rwz|{Fp&U|kIªÇvxrtkj³u¬`x<ehk`|kIz&!agjuwkjpsr`µ
Uvufvz|kj³hu< jkph{Fihuwkj³ tk` ºrtkDx<ehphz¶s³hk` fz|pAk©hv[rwz|{FpIi¬³h±rwzhz|ikjpA z{phpkj|kD f{psr jrthuw{N{F tjkD
N{³uvFxjxjjjuwkju¢|kD utkDx<ehkju<x<ehk` ³u'z w¶s³hkµ#k` zpkj©{psrrtfi%v[{Futz|rwvz|uwkjik`pFrx{Fp'³ ¢kjr`[v³h`
vp k%x{psrwk©rtk%k%vF kD 8z|i%vFk` :k` wxuwzrtk`³hu8³hphz¶s³hkµ)( zkjp¶F³k¹xkrvurwzxj|kphk%huw` tkjpsrwk
Av fkVph{³hFk`v³I tx<eji%v¬zpkj©vrtz{p&zi{psrtuwkV¶s³hkVk` flik`z||k`³huwk` rtkDx<ehphz¶F³k` fz|phk©hv[rwz|{Fp
i¬³h|rtzz|ik`p z{pphkj|kD *ekj³huwk?vxrt³hk`|k? t{psr'kjpAx{uwkhzkjp%rwut{F|k`pFrwk` º|{Fuw w¶s³k`|k` º {FpFr'³hrtz|z `k`
xj{p[{Fz|psrwkjikjpsr;vckDx´kD ;kD txjutzrtk`³hu< {xjv³©µ
+ Ù £D¡ × ¦-, § uwk`x{Fphpvz w tvpxk´zi%vFk` u<vzp¹Ìp®z|phk©hv[rwz|{FpIi³±rwz|i`hzvz|phk©hv[rwz|{Fpi¬³h±rwzhz±~
ik`p z{pphkj jAv tk` z|i%vk` `utkDx<ehkju<x<ehkVvuk8x{FpFrwkjp³&hkD txjutzrwkj³hu< f|{x`v³©
Ã Ã Ã Ã¯Ä Ã
!
)N¬ ®6%/º
nqi%vk hut{xjk` w zph´vp}hv[r<vvF krtkDx<ehphz¶F³k` Uvuwkrt{Fkrwehkjuuwk`¶s³hzutkD8rt{h³z|}vutFkx{Fpsrtkjpsrt~OvF kD
uwkrwutzkj[v´ t² rtk`i% jµ nqi%vk¨huw{xjk` w zphÊrwk`x<ehpz¶s³hkD vutk¨phkjkDk` rw{Lkj©rtu<vxyr³ kjª¯³h"Á½jÈ#$ % Ã
¿<½
ª¯uw{izivkD jµ'&´k` wxuwz|rw{u< vutkr²hzxjv|²¨Fk`xrt{u< 8{ªfuwk`vºp³hi¬Ak`uw ¬kÌpz|phþA{Fz|psrw ¬zp¼vSehze~
hz|ikjpA z{pv´ tvxjkµ(&´k` wxuwz|hrt{u< %k`px{k¨z|pª¯{Futi%vrtz{p ª¯{³p¾zp¾z|i%vFk` `;vp¾rtehk`²Îvutk^³A kD
h³hutzphrtek¹ kDvu<x<eþhuw{xk` w `µdfek¹ ziz|vuwz±r²S{ªr· {:z|i%vk` Vz v w t³hik`þrt{:Ak%ut{FA{Furwz|{Fpv¢rt{
rwehk ziz|vuwz±r²:{ªUrtehk`z|u8kD txjutzrt{Fuw `N·ehzx<e¨z Vik`vF ³utkDSv ?rtehkSÏr²hzxjv|²*)'³xj|zk`vpAдz rwvpxk
Nkr· kjk`prtehk´A{Fz|psr< ºkjÌphk`¹s²¬rtek´kD txjutzrt{Fuw `µ¢¸z|izvutz|r²} tk`vuwx<ez Urwehkjuwkª¯{Futk;zihkjikjpsrtkD¹v
v}phkDvuwk` r~«phkjzeN{uf kDvu<x<eI{Fu;v v,+c~Ou<vphFk´ tk`vuwx<e·z±rwehz|p:rwehkVª¯k`vrt³huwk AvxkFµ
duwvFz|rtz{pv?ikrweh{h ª¯{u:x{ih³hrtzphLkD txjutzrw{u< %z|pAx³kx{{uehz rw{u<vi% ¹vp]xj{uwutk`|{~
Fuwvi% -¸h¸/.h10328Ñ546.s87Oµ:dfehk` tk¹ wx<ehkjik` `®³A kD¨zp:9 ( n;-< (=<>46.7«´z|u<vFk®{Fu?)U©hxjv|zh³hu#@c
r²hzxjv|²¹x{Fih³rtk8vI½$ AB|ÁkD txjutzrw{ufAk`uz|i%vkµºË´phkkD txjutzrt{Fu rtehk`utkjª¯{uwk´k`px{kD zpª¯{Futi%v[~
rwz|{Fprtevr¬z F|{Fv'rt{^{FphkIzi%vkFµSnqprtehz }x{psrwk©r`Ux{Fpsrtkjpsrt~OvF kD»utkjrtuwz|k`cvºz Nkjutª¯{uwik`Êv[r
vSxj{Fvuw tk~«u<vzpþkjFkjOÍrtekI ² rtk`i uwkrw³hutpA rtehkIz|i%vFk` rwev[r}vuwkC|¿FÅEDÊ tz|izvu8rt{:rwehk¶s³hk`ut²
zi%vFkµdfehk´ t² rwkji#xjvp¹ph{rfkrwk`xr`eh{[· kjk`u`rtevrºr· {zivkD ºx{Fpsrwvzp¹ tz|izvuº{hk`xyr< jsh³rv[r
hz!akjuwkjpsr{xjvrtz{p `Fzp¹ª¯uw{psr {ª®z&!Nk`utk`psr vFx<Éuw{³hp j[ª¯uw{i#z&!akjuwkjpsr zkj·N{zpsrw {uhz!akjuwkjpsrt²
z|³hizpv[rwk`µ¨d®{þvFhuwk` w rtez ¬huw{hkji:i{hkjuwpÊz|i%vFk%huw{xjk` w zph:rwk`x<ehphz¶s³hk` evckIutkDxkjpsrw|²
ª¯{xj³ kD¹{FpIÌpk~«u<vzp¹z|i%vkVutkDx{Fphz|rtz{p&µF<¢z|phkj~OFuwvz|pHG{Fu {Fk`xrIG¹uwk`xj{pz±rwz|{Fp¹z|pzivkD 'r²~
zxjv|²Suwk`¶s³hzutkD ;rw{xj{ih³rwk}i%vps²^hk` wxuwz|rw{u< ?Nkju8zi%vFkµdfehkD kkD txjutzrt{Fuw Vvuwk}{ªrtk`p¨x`v|kD
¿`È6Á½jÈ#$ % Ã
¿<½¬Nk`x`v³ tk{pkk` wxuwzrt{Fu;kjpxj{k` ?z|pª¯{Futi%vrtz{prtevr´z ;{xjv®rt{IvþÏÇ tiv|ÐvutkDv
{ª¢vpzi%vFkµnqpFkjphk`uwvYhvp{Fk`xrz|p:{pkVzi%vFkVz fuwkjhuwk` tkjpsrtkDI²I tkjFkju<vkD txjutzrt{Fuw `µ
dfehk?Ìu< rxj{psrtuwzh³rtz{p%{ªartehz ºAvNkjuºz Urwehk´hk` wxuwz|rwz|{Fp{ª®v8ikrweh{¹kD zphkD}ª¯{uUÌAphk~«u<vzp
zi%vFk%utkDx{Fphz|rtz{p¨rtevrz k`ut²¨ut{Fh³ r8rt{þx<evphkD z|pÊzi%vFk` `µdfehz ikjrteh{Êx{Fih³rtkD {xjv
hk` wxuwz|rw{u< Urwev[rvuwk?· kj ³hz|rtkD%ª¯{Fu kjrtkDxyrtzph ziz|vu {hk`xyr< ºzpxj{{u z|i%vk` kD hz|rtkV{uwzkjpsrwv~
rwz|{Fp¨x<evphkD ¬ÏÇut{rwvrtz{p^{ªº{kDxyr< wÐartu<vp tvrtz{p `autkD {F|³hrtz{pþx<evphkD jaz|³hizpv[rwz|{Fpþ[vuwzvrtz{p
vp}vutrtzv{x`x³ z{pA jµÒ¾z±rwe%utkD Nk`xrUrt{rtekutk`z{p~«v tk`z|i%vkfutkDx{Fphz|rtz{p tx<ekjikfhut{FA{s kD
²»?v[r< k`a;vF rw{zUvpʸehziJ-??¸/.B.K7«{F³hu8ikrweh{z 8uw{³ rrw{Si}{Futk%x<evphkD %ϯkFµAµ|®rtehk`z|u
vhhuw{FvFx<ez Uph{r'uw{³ rUrw{8ut{rwvrtz{p ¢{uºz||³i}zpvrtz{p%x<evpk` <Ðyz Up{r'vF kD¬{Fpi³h|rtzhk; zhz|ph
·zp{[·; vpz fph{r;v tk`{p·fvckjkr< ·ehzx<eª¯{Fuwxjk?rwehk` tk8·z|pA{[·; rt{Nk t¶s³vutkj~« tevNk`&µ
nqpÊFkjphk`uwvYz|Fph{uwz|pS{³huhk` wxuwz|rw{u< j®Ìphkj~OFuwvz|p»z|i%vk¹uwk`xj{pz±rwz|{Fp¨zivxrw 8rwehk¹uwkrwutzkj[v
x<eAvzp%·ehkjpI tk`vuwx<ez|phª¯{Fu tzi}zvuºzi%vFk` `µ><¢zuw r`sz±r z|pAxuwk`v tk` 'rtehkV zMLjk´{ªrwehk´hvrwvv tkÍnqp rwk`vF
{ª¢ rt{Futzph{phk8kD txjutzrw{ufAk`uz|i%vki%vps²I{ª¢rtehk`i(i³A rNk rw{uwk`Iª¯{uk`vFx<ezi%vFkµUdfehk8 zMLjk
{ªArwehk;hvrwvAv tk z r²hzxjv|²zpxuwk`vF kD²r· {{u<kjuU{ªNi%vphz|rt³hkµU¸k`xj{pFz±rºx<eAvphFk` ¢rtek· vc²
tzi}zvuUzivkD Uvuwkf tk`vuwx<ek`Í&nqpA rwk`v¬{ª tk`vu<x<ehzph´rtehk?hk` wxuwz|rw{u< rtevrºvuwkfxj|{s kfrw{Vrtehk;³phz¶s³hk
¶s³hk`ut²k` wxuwz|hrt{uÏYv z|r?z frtekxjvF k8·z|rte:{Av®kD txjutzrw{u< wÐrtehk t² rwkji r<vutrw f²xj{ih³rwz|ph
v|rtehk´k` wxuwz|hrt{u< ¢rteAv[r hk` wxuwz|NkfrtehkV¶s³hkjuw²zi%vk;vp}rtekjpI¶s³hk`utzk` rwehk?hvrwvv tki%vp²rwz|ikD j
kDvx<e%rwz|ikV³ tz|ph}vz&!akjuwkjpsr {xjvA¶s³hkjuw²%k` wxuwzrt{Fu`µ>)ºvx<e¨Ï¯vurwzvÐvp t· kjuºz Ékjhrfvut{F³hp%vpA
{Fpxkv|¢¶s³hkjuw²hk` wxuwz|rw{u< fevck8Nkjk`p^³ tk`Nvp t· kju< ;vuwkxuw{F w ~qx<ehkDx<Ék`vprwehk tkrV{ª' ziz|vu
zi%vFk` ´z ´kjFkjpsrt³v|²:utkjrt³huwphkDSrt{Irtehk³ tkjuDµ?<h{Fu´kj©vih|kFz|pþrtehkx{Fpsrtk©rV{ªº{F³hu´kj©Ak`utzikjpsrw
N
óO8PQ$RÇï;ýwüOêSQ$O ýTQyéDü0üVUcíñOí ñVW`ñYüYíïñðtýO TíXPQyéKOKY ýwüZUjüÇüOë\[]$]_^1^`^baèTcêìð$aýcìï;ýYcídOAaêSTcïaðdQyïe]`ò
UjüÇüOë\[]$]_^1^`^baf`êSROýgyí$aðdQyïe]fýOKYhUüÇüOëA[]$]_^`^`^baíjiDðýcìêSTAaðdQyïe]a
ÏY k`k¸k`xyrwz|{FpIAµlsÐy kDvu<x<ehzph8ª¯{u rwehk´zi%vFk` x{psr<vzphz|p{hk`xyr< rtevrfvutkV ziz|vu rt{¬rtek´{Fphk` zp
rwehk¬¶s³hk`ut²z|i%vk8r²hzxjv|²Fkjphk`uwvrtkD Akjr·k`kjp%vp%xj{p tk`xj³rtzk¶s³hk`utzk` ;rtevrV tk`vuwx<e:zp
vIhv[r<vvF k8rwev[rVz rw{F}rtzik` ´vutFkjuDµ;dfehz ´k`i%vpzph¹ut{xkD t ?z|pAxuwk`v tk` rtehk¬z|ivFxyr´{ª
rwehk8Nkjutª¯{uwivpxkVhuw{hkji% rwuwvFz±rwz|{Fpvi¬³h|rtz|~«zikjp tz{pvz|phk©¹rwk`x<ehphz¶s³hk` t³ !akjuª¯uw{i:µ
dfehk kDx{Fpx{psrwutzh³rwz|{Fp8{ªrtehz vNkjuz vp8zphz±rwzvkj©|{Fuwvrtz{p{ªrtekx{Fp tk`¶s³hkjpAxk` &{ª³ tz|ph
{xjv'k` wxuwz|hrt{u< Vrt{Fkjrtehk`u8·z±rweʳh~Ort{~qhvrtk¹hvrwvAv tk}i¬³h|rtz|~«zikjp tz{pvUz|phk©z|p^ rwuwvrtkjFz|kD jµ
Ò¾ez|kºrwehz ®vAk`u=F¿`Á½=N¿
à % tÁ½jÁ#
Ã
D3aÁ FÁ\ V½jÈ
Ä
ÁÀ%Áz±rk©Nkjuwz|ikjpsr<v|²8 teh{[·; rwev[r¢rtehk
rwehuwkjki{F r'kÓ¹xzkjpsr'zpkj©zphrwk`x<ehphz¶s³hk` Éph{[·p}rw{vc²vuwk rwz|hrw{s{ t{[·¼rt{8Nk³ tk`}zp%huwvFxyrwzxjk
·z|rteI|{xjvkD txjutzrt{Fuw `µ´ zph8rw{hvc² & (Lz|pAk©zph8rtkDx<ehphz¶s³hk` º·z±rwe¹|{x`vAhk` wxuwz|rw{u< utkD¶s³hz|uwk`
rw{ B\j8%7rtehk»uwk` tA{Fp k:rwz|ik¨{ªk`vFx<e¾z|pAz|z³vV¶s³hk`ut²F·ehzx<e ivÉkD rtehk¨{v?uwk` tA{Fp tk
rwz|ikªÇvu?vA{[Fk8·ev[r?{Fphkizesr;rt{F|k`uwvrtkFµ Ò»krwehkjuwkª¯{Futk8z rVhut{Fhkji% ;vpA:kjp³hikju<v[rwk k`k`uwv
N{rwkjpsrtzv t{³rtz{p &ª¯{u¢h³hzhz|phVkÓ¹xjz|k`pFrx{FpFrwkjpsr~«vF kDutkjrtuwz|k`cvF t² rwkji% t³hhN{utrtzphÌAphk~«u<vzp
zi%vFkVuwk`xj{Fphz±rwz|{FpvF ³hFkD rwk`¹²¹i{k`utp:zivkVhuw{xjk` w zph¬rtkDx<ehphz¶F³k` `µ
dfehk¬utk`i%vzpkju´{ªrtez ´vNkjuVz ? rtuw³xyrw³hutkD^v ;ª¯{|{[·; `µ?¸kDxyrtz{p»%k` wxuwzAkD ?vpASkj[v³vrtk`
{F³hu%{x`v?hk` wxuwz|rw{u< ¬rwvz{uwk` ª¯{u¹uw{h³A r%{hk`xyr¹uwk`xj{Fphz±rwz|{Fp&µ ¸kDxyrtz{p¾l»zkD %vp {[k`utzkj·
{ª?rwehk:i³h|rtz|~«hz|ikjpA z{pvz|pAk©zphþrwk`x<ehpz¶s³hkD ³ kD zp hv[r<vvF kD jµ ¸k`xrtz{pΨk`cv|³Av[rtkD }rtehk
Nkjutª¯{uwi%vpxjkI{ª;rtehkrteutk`ki{F rkÓ¹xzkjpsr}rtk`x<ephz¶s³hkD Éph{[·p rt{hvc²{pÎv^vuwkv tkI{ª?ehze~
hz|ikjpA z{p:hv[r<vzprtehk8x{Fpsrtk©r{ª¢|{x`vk` wxuwzrt{Fuw `µ¸k`xyrwz|{Fp¬huwk` tkjpsr< t{ikV{Nkjpz w t³hk` fvpA
vpzphz|rtzv® tkr{ª t{³rtz{pA fAkjª¯{uwkxj{pxj|³Az|pµ
%,9Ê14®6¢ 86[68 !#%$&º ( <
dfekhk` wxuwz|rw{u< º· khuwk` tkjpsr zprtehz tk`xyrwz|{Fpvutkvpk©rtk`p tz|{FpIrw{xj{{u z|i%vk` {ª®rtek´ÌAphk~«u<vzp
uwk`xj{Fphz±rwz|{FpÎ wx<ehk`i}k:ª¯{Fu¹uwkj²s~«|k`k` zi%vFk` {uwzzpv|² hut{FA{s kD ² -<r0?2h.7vpÎk©rwkjp~
tzkj²S³ tk`¨vp¨kj[v³vrtk`þ² -¸hÑ5.s7«µ}Ò¨kh³hz|r{Fpþrwehz 8 tx<ehk`ik¬Nk`x`v³ tk¬z|r8z ez|Feh|²þut{Fh³ r
rw{:uwkj²s~OkjFkj¢z|i%vk}rtu<vp ª¯{uwi%v[rwz|{Fp jÍ´z±rkjrtkDxyrw ziz|vukjkjik`pFr< z|pzi%vkD k` thz|rtk%{uwzkjpsrwv~
rwz|{FpÎx<eAvphFk` Sϯuw{r<v[rwz|{Fp wÐ'rwuwvp v[rwz|{Fp `ºuwk` t{³rtz{pÎx<evphFk` `ºz|³hizpv[rwz|{FpÎ[vutzv[rwz|{Fp jvutrtzv
{x`x³ z{pA jx<evphkD ?{ªvFx<ÉsFut{F³hph ?{uVz|k`·A{Fz|psrw `kr<xµµ|µ {hzph·z±rwe»xj{{uVz|i%vk` ´zp rwk`vF
{ªUuwkj²s~OkjFkjazivkD ev ?v%kjk`Sz|ivFxyr?{Fp:rtehk·fvc²%rwehk¬kD txjutzrw{u< fevph|k¹ÏÇzYµkµNv t{uwAÐrtehk
[vutzv[rwz|{Fp ;{ª'z||³i}zpvrtz{p&µdfehki%vz|p¨{Fv®{ªUrtehz ´ tk`xrtz{p^z ´rt{hutkD k`psr;rtehk}{uwzzpvutkDx{Fphz|~
rwz|{Fp» wx<ehk`i}khuw{N{F tk`þ² -<r0?2h.7vp^{F³hu8k©rwkjp tz|{Fpþrw{Sx{{uVzivkD jµ<¢z|u< rD&eh{[· kjFkjuD
· k%huwz|k²þutkD k`pFrvp»zpsrtk`utkD rwz|phSkj©hvihk%{ªvS ² rtkji ³ tz|phS{xjv'k` wxuwz|hrt{u< h³h|z ek`zp
rwehk & (]z±rwkju<v[rt³utkFµ
nqpÒvut³ -??¸/.B.7«&kDvx<e»z|i%vFk¬z huw{ÉFkjp~q{[·p^zpsrt{S t¶s³vutk t|zzph:·z|ph{[·; ´{ª[vuw²z|p
tzMLjk` `µdfehk zpAv[rt³utk¬{ªv·z|pA{[· z Vxj{ih³rwk`þs²S³A zphrtehk}xj{kÓ¹xzkjpsrw ´ª¯uw{irtek}{[· k` r
ª¯uwk`¶s³hk`px²SAvp¨{ª'rwehkH0?vFvu· vcFkjkr´rtu<vp ª¯{uwiª¯{urtek}·zp{[·8µ¬dfehk` tk% zpvrt³huwk` Vvuwk¬xj|³A ~
rwkjuwk`vp¨rtekxjkjpsrtuw{z¨{ªkDvx<ex³ rtkju8z Vrtekjp³ tk`v ´rtek¹k` wxuwz|hrt{uVª¯{Furtehk%uwkjFz|{Fp&µ}dfez
ikjrteh{»huw{[szkD z|p[vuwzvpxk}rw{[· vuwh ´rwuwvp v[rwz|{Fp `® tx`vz|pk"!NkDxyr< j¢vutrtzvU{x`x³ z{pA 8vp¨rt{
xj{{u' tehz|ªrw `FzOµkFµ|s·ehk`prtehk;[v|³hkD '{ªArwehk?hz|©kj 'vuwk; tehz±ªrwk`ª¯uw{i "!# %$&¢rt{'()*+ ,!-)/.0 %$1)23&y
·ekjuwk4*º5.þvpA62:vuwk;x{Fp r<vpsr'[v³hk` `µ{{uº tehz|ªrw `Feh{[· kjFkjuD{8ph{rx{Futuwk` tN{prt{vp²pvrt³~
u<vcvutzv[rwz|{Fp{ªNrtehk´z||³i}zpvrtz{p¹x{Fpz|rtz{p ?ϯ[vuwzvrtz{p{ªz|³hizpv[rwz|{Fp%z|psrtk`p tz±r²hÐyµnqp¹vFhz|rtz{p&
·fvck`|kjrw ´ª¯{u<xkrwehkI t|zzphS·zp{[·; rw{SAkI w¶s³vuwk~q tevNk`®·ehzx<e»ª¯{Futhzh rwehkjzu wx<ehkjikrw{^Ak
Ã Ã Ã Ã¯Ä Ã
zp[vuwzvpFrrw{Iuw{r<v[rtz{pA jµ
v r`hrwehkjzu tx<ehk`ikkj[v³vrtk` ´ ziz|vuwz|r²{Fp^vIx{Fii}{Fp^vuwk`v%xjutz|rtk`utz{p&
³rº{k` ph{rºx{Fp zk`urwehk;k`uwkjkf{ªa ziz|vuwz±r²{ªNrtehk;vutkDv `µ®dfehkjuwkª¯{FutkFcrtehk`z|u tx<ehk`ik ·zªÇvc{Fu
vuwkVuwkjz{pA ºrwev[r?vutkVuw{³hFeh|² ziz|vu rt{¹ ti%vutk`z{p rwev[r?vutkvi{F rfzk`pFrwzx`vOµ
!"#$%$&
nqp:-<r0?2h.7«`<¢|{FuwvFx<ÉkjrvYµkD txjutzNk`^vphkj·ikjrteh{{F|{F²ª¯{ux{Fi}³rtzphehz|Feh²Sut{Fh³ r
hk` wxuwz|rw{u< ª¯{Fu&Ìphkj~OFuwvz|p8Futk`²s~OkjFkjzi%vkutkDx{Fphz|rtz{p&µ (kjª¯{uwk'{Fz|p?zpFrw{´kjrwvz| jDrwehkjzu¢ wx<ehk`i}k
x`vpAk8uw{³eh²%{³rw|zphkDvF ª¯{|{[·; `µ
{Fi}³rtzphrtehk%{xjvhk` wxuwz|rw{u< ´rtevrk`px{kzpª¯{uwi%v[rwz|{Fp¨vN{³hr8v: tz|pk¬zi%vk}z 8{phk
zp:rteutk`k rwkj `µ <¢z|u< rDN tNk`xz|ÌAx8N{zpsrw ?z|pSrwehkzi%vkFAx`v|kD:z|psrtk`utkD r< N{zpFr< jNvuwk tkjk`xyrwk`µdfehk
p³hi¬Ak`u{ªfN{zpFr< 8zp»{Fphk%zivk[vuwz|kD j¢ zpxjk%z±r¬hkjNkjph {p»rtehk evAk%{ªrwehk¹ tz|Fpv'{ªrwev[r
zi%vFkµÎ¸k`x{FpUrwehk^ tz|Fpvvuw{³pÊk`vFx<e zpsrtkjuwk` r%A{Fz|psr%z }x<eAvu<vxyrwkjuwzL`k`ʲ¼z|rw %xj{p{F|³hrtz{p
·z|rteSv('v³A t tzvp¹ª¯³hpAxyrtz{pSvpIz|rw ?kjuwz|[vrtzk` ³hrw{¬rwehkrtez|u<{u<kjuDµ¢dfez|u<rwehk` tk8kjuwz|[vrtzk`
vutkiz|©kD¨rt{Skjphª¯{u<xkz|p[vuwzvpxjk}ut{FAk`urwz|kD 8vpþrt{Si%vÉFk%k` wxuwz|hrt{u< uw{h³ rrt{:rwehk¹x<evpk`
ik`pFrwz|{Fphk`vN{[kµ*)LkD txjutzrw{u®z r²hzx`v|²v;Fk`xrt{u{ªuwk`vp³hi¬Ak`uw evcz|pf{Fu .´z|ik`p z{pA jµ
&´k` wxuwz|hrt{u< ¹vutk:rwehkjp¾zp tkjutrtk` zpsrt{¼vp¾z|phk©µ d{¼Éph{[··ehzx<e¾z|i%vFk^vÊk` wxuwzrt{Fu¹ev
Nkjk`pxj{ih³rwk`%ª¯uw{i:zivk;zk`pFrwz±ÌAkju< vutk´ rw{uwk`rw{kjrtehk`u·z|rteIrtehkkD txjutzrt{Fuw `µ{ih³rwz|ph
hk` wxuwz|rw{u< f{[k`ufv|®rtehk8zi%vFk` z ;{Fphk{ !N~«|zphkµ dfehk tz|izvutz|r²¹uwkrwutzkj[v®hut{xjkjk` v fª¯{F|{[·; jÍ
zpsrtk`utkD rA{Fz|psr< UvuwkºÌu< r¢zkjpsrwz±ÌkD}z|p¬rtehk¶s³hk`ut²8zi%vkFvprtekfxj{uwutkD N{pAz|p?{x`vhkD txjutzrw{u<
vutkrwehkjpLx{ih³hrtk`&µ')ºvx<e¼kD txjutzrw{u{ªrtehkI¶s³hk`ut²»z ³ tk`»rw{þhuw{Nk%rtek¹z|pAk©µþdfehkIz|phk©
uwkrw³huwp f ziz|vukD txjutzrt{Fuw ª¯{F³hpz|prtekv[rwvv tkϯ·z|rte:utkD Nk`xrfrt{%v}phk`vutkD rt~Ophk`z|FeA{Fuº{uv,+
tk`vuwx<eNÐyª¯uw{i ·ehzx<e%z|r z 'N{F w zhk;rw{¬kjrtkjuwiz|pk;rtek?z%{ªrwehk´vF t t{xzv[rtkDz|i%vkµ¢n«rz ºrtehk`utkjª¯{uwk
kDv t²¹rw{Ix{F³hpsr;rtehkps³iNkju?{ªrtzi}k¬k`vFx<ezi%vFkz:z ;uwkrw³huwphk`:²¹rwehkzpkj©:h³hutzph%rwehk·eh{F|k
uwkrwutzkj[vNut{xkD t `µ) rrtehk8k`p{ªrtehz huw{xk` w 8ϯzOµkµh{pxjk8vartehk8{xjv&hk` wxuwz|rw{u< {ª¢rtehk¶s³hk`ut²
eAvck%NkjkjpL³ tk`rw{^huw{Nk¹rtekIzpk©Ðrtehk:x{F³hpsrtkju< v|{[· rt{þu<vpÉþrwehkx`vpzhvrtk¹zi%vkD ²
hk`xuwk`vF zph ziz|vuwz|r²µ
Ò»k8ph{[· utkD k`pFrzp:i}{Futk8kjrwvz| rtehkxj{ih³r<v[rwz|{Fphuw{xkD t {ª{³u;k` wxuwz|hrt{u< `µ
+,.-/,.- 01
£`¤c¥¦£3254*68794a£ Õ ¤ Õ ¡j£(: Ù 2.4a£D¡
nqpsrwkjuwk` rN{zpsrw vutk%kjrtk`utizphk` t³x<e»rtevrz±rz 8k`ut²þ|zÉk`|²Srwev[rv:N{zpsr8ª¯{³hpA¨zp{phk%zi%vFk
·zAkv {¬ª¯{³pIzpvph{rwehkjufzi%vk´rteAv[r; zesrt²%z!akju< ª¯uw{i rtek´ÌAuw r {Fphkµ'¸x<ei}z·eh{}k©~
rwkjp tzkj²³ tk`C<¢{u<vx<É 'ikrweh{x{ivutkD¹ tkjk`uwvN{zpsr kj©srwuwvFxyrw{u< 'zp-ì¸Ñ (=.K7&vp¹ teh{[·kD
rwev[rrwehkk©rtu<vxrt{uVzpFrwut{³Axk`þ² ( z|<;hp -('VÒ .h$7ºvpþzihuw{[k`^s²50´vuwutz -0V¸7'evþrtehk
Nk` r;Nkjevcz{uDµ
dfehz ;kj©rtu<vxyrw{uf{s{FÉ fª¯{u´B& tz|phF³hvuwz±rwz|kD fz|p:rwehk zpAvOvpz ;vF kDI{Fp:rtehkxj{ih³r<v[rwz|{Fp
{ª®rwehk8kjzk`ps[v|³hkD f{ªrtehk8i%v[rwutz|©
k>=?@BA<C@
@ED
@GF HJI
K I K
I9L
I K
I9L I LNM
·ekjuwk I K
vp
I9L
vuwk'rwehkx{FpsF{³rtz{p{ªrwehk zpAv·z±rwerwehk r·{k`utz[v[rtzkD %vp
{ªv 'v³ w zvpª¯³hpxrtz{p&µ nqp:kjpkju<vOrtehk`utkvutk8i%vp²¹N{zpsrw ?z|p:k`vFx<e:z|i%vFkr²hzxjv|²INkr· kjk`p
¬vpFhµ
&´³ª¯{³utpv³'-&V¸/0?7NN{zpsrtkD~O{F³rºrwev[rfk` wxuwzrt{Fuw 'xj{³h%ph{rºNk´zpcvutzvpsrUrw{¬ wxjvkªÇvFxyrt{Fuw
z|ªrtehkA{Fz|psrw ;k©rtu<vxrtk`· kjuwkph{r;zpcvutzvpsrrw{¹ tx`vz|phAµºdfehk`utkjª¯{uwkhehk8ut{FA{s kDIrw{%k©rtu<vxrrtehk
N{zpsrw v[rfz!akjuwkjpsrf tx`vk` '²[vuw²z|phrtehkV[vuwzvpxk;{ªrtehk 'v³ w tzvp%ª¯³hpxrtz{p¹³ tk`&µdfez v|{[·;
rw{%x{Nk8·z|rteS tx`vk?ªÇvFxyrw{u< f³hrt{Iu<v[rwehkjufrwevp:³hrt{I}v ª¯{Fufrtehk8{FutzzpvNikjrteh{µ
+,.-/,+ Ù ®£ 2.4#6 Ù ¦¥, Õ ¡`¦¤>2¢£ Ù ¤c¡Ù ¤¤ ÕFÖa× ÕAÕ ,7 ¥6 Õ ¡
Ë´pAxk¬rtehkN{zpFr< vuwk¬kj©srwuwvFxyrwk`arwehk}hk` wxuwz|rw{u< ´vutkx{Fih³rtkDþ³A zphrtehk% tz|Fpvvuw{³hpA^k`vFx<e
{ªrwehk%N{zpFr< jµdfehz x{ih³hrwv[rwz|{Fpz h{phkzpr·{S rtkjA jµC&´³huwz|p:rtehkÌu< r rwkj&rtehk¹ tzpvUz
xj{p{F|³hrtk`»·z|rte v 'v³ w zvpª¯³hpAxyrtz{p¼vpz|rw .:Ìu< r¬hkjuwz|[v[rwz|Fk` ¹Ï¯rtehkkjuwzcvrtzkD 8³hrt{þrtehk
rwehzuwS{FuwhkjuyÐyµdfehk` tk¬ ti{{rtek`Sk`utz[v[rtzkD huw{[zk¬v%v tzxk` wxuwzrtz{pS{ª¢rwehk¬ tzpvYµ&´³huwz|ph
rwehk¬ tk`xj{p: rtk`&Nrtehkhkjuwz|[v[rwz|Fk` ´vuwk8i}z|©k`:rw{Fkrtekjurw{Ikjphª¯{u<xk8zps[vutzvpxjk8huw{Nkjutrtzk` ?vprt{
i%vÉkk` wxuwz|hrt{u< ut{Fh³ r rw{rwehkx<evphkD ºikjpsrwz|{Fphk`vN{[kFµÒ»kk` wxuwzAkVAk`|{[· rtehk·fvc²rtehkD k
hkjuwz|[v[rwz|Fk` fvuwkiz±©k`&µ
¥%2.4#2.4#6º¤[¥4¢¡ ,Ç¥£ 2Ù 4¥,%¥%4Ú IÙ £`¥£ 2Ù 4¥,7 4 ¥¤>2Ç¥4¢¦ Õ ,
duwvp tvrtz{pv zp[vuwzvpxk:z %{~
r<vzphk`²¹rwehkªÇvxr rwev[rrwehkkD txjutzrt{Fuw fvutk8x{Fih³rtkDvut{F³hpk`vFx<ezpsrtkjuwk` rA{Fz|psrDµ
dfehkvpk;{ª®uw{r<v[rwz|{Fp%{ª&zivkD ºxjvp¹NkVv|Fkjhu<vzxjv|²k`|ziz|pvrtkD%ª¯uw{i rtehk?rtk`pk`utz[v[rtzkD j
ut{[zz|pphzphkutkD ³±rwz|ph%¶s³vpFrwz±rwz|kD z|p[vuwzvpsrrw{}uw{r<v[rwz|{Fp jµ¢n«ª®rwehk ti}{{rtehkDI tz|Fpvaz kjph{rtkD
²
I
vpIz|rw ?kjuwz|[vrtzk` ²
I K I L I
K3K
µ|µµrtehkD k?.}zps[vutzvpsr;¶s³vpsrtz|rtzk` vutkFÍ
I
I I
I I I
I!"
I I #
+
I $&%5II!$ I%' I($$<I5I%.I&%
&
I)* I I!$>I+$,'I $<I5I-3I!$
' +
I $-%I I $ I %
I * $ I I I $
ÏDÐ
dfehkª¯³hpxrtz{p'+
z VkÌAphk`S² + K L/.0'
+ L K .21
+
K K . + L9L3.54
µ?dfehk)ºz|p rtk`z|p Vph{rwv[rwz|{Fp
³A kDzp}rtehk ª¯{uwi³vF ¢xj{uwutkD N{pAh rt{8v ³hii%v[rwz|{Fp¬{[Fkju¢k`vFx<e¬zpkj©aÍ®ª¯{uUzp rwvpAxk
I .76
I .
I K ) I L
vp
I!* I-#8. 6 6
I* I #8. I K K I K K
):9
I K L I K L ) I L9L I L9L
µ
¥%2.4#2.4#6 :<; Ù £ Ù Õ £j¤>2Ǧ 794 ¥¤>2Ç¥%4¦ Õ ,
dfehkSk` wxuwz|hrt{u< }vuwkzpcvutzvpsr}rt{¨rtehkS[vutzv[rwz|{Fp {ª
z|³hizpv[rwz|{FpIrwev[r?vutki{kjk`²
I3=>@? I ) $cµUdfehz i{kjOhv|rte{³hFe tz|ihkAk` wxuwz|Nk` ¶s³hz|rtk
vFxjxj³huwvrtk`|²»·ev[revhAk`p }·ehkjp rtehk{Av z|psrtk`p tz±r²{ª?rtehk:z|³hiz|pAv[rtz{pL[vuwz|kD t|zesrt²µÊn«r
z N{F w zhkrw{·z|rteAuwvc· rtehkD k}r· {phk`· vuwvikrtk`uw
?
vp$¬vpA^rw{{Frwvz|pÊIut{rwv[rwz|{FpvvpA
Ã Ã Ã Ã¯Ä Ã
eh{rw{ikrwutzx;zpcvutzvpsr< jÍ><zu< r ·z±rweu<vc· rtehk´r·{Ìuw r¶F³Avpsrtz|rtzk` {ªºÏDÐvp¹hz|zk´kDvx<e%{ª&rtehk
tkjFkjp¨vF r8{pk` ²Srtek¹vhhuw{utzv[rwkN{[·k`uV{ª I I
t³x<ev Vrw{{Frwvz|p»u<v[rtz{F V{ª k`uwkjk%I·z|rte
uwk` tNk`xyrfrw{
I
vpz|rw k`utz[v[rtzkD jµ
¥%2.4#2.4#6®¦¥,Õ 794 ¥¤>2Ç¥%4¦ Õ ,
nqps[vutzvpxjk:rt{Î tx`vk^z vx<ez|k`k` ² v{Frtzph v i³h|rtz|~q tx`vk
vhhuw{FvFx<e&Írwehkxj{ih³r<v[rwz|{FpÊ{ª;zps[vutzvpsrw z ¬uwkjNk`v[rwk`»ª¯{Fu¬[vuwz{³ 8[v|³hkD {ªrtehk[vuwzvpxk¹{ª
rwehk'v³ w tzvp&svpIv|arwehkVutkD ³h|rtzph}[v³hk` fvuwkV³ kD%rw{}kD txjutzNk?rwehkz|i%vFkµUdfehkV[v³hk` {ªrtehk
[vutzvpxjk´³A kDIehk`utk8vutkVutk`vrtkD¹rw{¬rwehk8{pk` f³ tk`³huwz|p¬rwehk8k©rwuwvFxyrtz{p{ªrtehk8zpsrtkjuwk` rA{Fz|psr< jÍ
rwehk;[vuwzvpxjk ³A kD}rt{kj©srwuwvFxyrºvN{zpsrºzkD rtehk?cvutzvpAxk rt{xj{ih³rwkrtek?v w {xjzvrtk`}kD txjutzrt{Fu`µ
+,.-/, 01 £ Õ 4¢¡ 2Ù 4L£ Ù Ù ,Ù ¤ 7 ¥6 Õ ¡
dfek¬ikrweh{þ³A kDSrt{Sxj{ih³rwkrwehk|{xjv¢hk` wxuwz|rw{u< ;ª¯{Fuuwkj²s~OkjFkjz|i%vFk` Vz ´Fkjuw²:ut{Fh³ r`&v
k`[v³v[rwk`:² -ì¸Ñ5.7«µ;Ò¨krtehk`utkjª¯{uwkk©rwkjpkDrtehz ´i}kjrteh{:rw{Ix{FAk¬·z±rweþx{F|{Fu;zivkD jµ=)ºvFx<e
z±©kjf{ª´v¨xj{{u¬z|i%vFkz kÌAphk` s²¼l¨[v³hk` }·ehzx<eLx`vp¼NkSx{kD¼zp i%vp²Ê·fvc² -¢{[² .7OÍ
'(V0V¸ v&Vdfehk'(7 ² rtk`iz ´x<e{F tkjpSNk`xjv³ tkz±r´ªÇvxjz|z±r<v[rwk` ?rtehk¬k©rtk`p z{pS{ªUrtehk
hk` wxuwz|rw{u< rt{%x{F|{Fu zi%vFk` `µ
)U©rwkjpzph´rtehkf{xjvkD txjutzrt{Fuw {k` ph{rUx<evphkUrwehkf· vc²´rtekzpsrtkjuwk` rN{zpsrw vuwkºkj©rtu<vxyrwk`µ
Ò»kf rwz|F³A k=0?vutuwz ®kjrtk`xrt{Fu`µ¢dfehk tz|FpvOceh{[· kjk`u`Dz ®ph{[·¼x<eAvu<vxyrwkjuwzL`k`V²l;hkjuwz|[v[rwz|Fk` ÏD
Nkjux<eAvphphk`е{hzph:·z|rteÊx{F|{Fuhkjkj|²þx<eAvphFk` ´rtehk%·fvc²:rtek` tk¹kjuwz|[vrtzk` Vi¬³ rNk%iz±©kD
rw{þsvzpÊz|p[vuwzvpxk¹rt{[·fvu<h uw{r<v[rtz{p¼vpÊz|³hizpv[rwz|{Fp¼[vuwzvrtz{p `µ^Ò»kkjrwvz|rtehkD kx<evpk`
Nkj{[·8µ
¥%2.4#2.4#6 Ù £D¥£32Ù 4¢¥, 794 ¥¤>2Ç¥%4¦ Õ , {r<v[rtz{pAvaz|p[vuwzvpxjk´z {hrwvzphkDI²¹·z|rtehuwvc·zph}rtehk
vphkI{ª´uw{r<v[rtz{p®µ þzpcvutzvpsr< ¬x`vp NkSx{Fi}³rtkD¼·z|rteÎk`¶s³v[rwz|{Fp :ÏcÐvhhz|kD {Fp k`vFx<e
x<eAvphphk`Yvp¹r· {}{rtekjuf{phkD fvuwkVx<eh{s k`pIvi{FphrwehkVrtehuwkjk´ª¯{{[·z|ph¶s³vpsrwz±rwz|kD Vϯª¯{up³hikjuwzxjv
uwk`vF {Fp `Fz|r;z ;·z tkVrt{%Ék`kj:vartehuwkjk[v³hkD z|phu<vxrtzxkDÐÍ
K K )
L L
K K )
L L
K K ):
L L
ÏYÐ
¸hxjvkfz|p[vuwzvpxjkz {r<vzphk`¬²vVi³h|rtz|~q tx`vk vhhuw{Fvx<e} ziz|vu¢rw{´rwehk{pk ³A kD·z|rteuwkj²s~«|k`k`
zi%vFk` `µ
¥254*254*6(:<;
Ù £ Ù Õ
£j¤>2Ǧ 794
¥¤>2Ç¥4¢¦
Õ , ºeh{rw{ikrwutzxUzps[vutzvpxjkUz &i}{Futkx{ihk©V·z±rwex{F±~
{Fuw aNk`x`v³ tk'z&!Nk`utk`psr&z||³i}zpvrtz{p8i{kj &xjvpAkºxj{p tzkjuwk`µ)¼kjpkju<v[i{kjz ( (
&
.
#
& ) ·ehk`utk z v }i%v[rtuwz|©Ivp v¬Fk`xrt{u {ªzi}k`p tz|{FplµË?rtehk`u i{k`
vutk {hrwvzphkD¬²³A zph8v8zv{Fpv{Fu' tx`vvui%v[rtuwz|©ª¯{u vp}²N{F w zh²utk`i{[szph´rtehkFk`xrt{u
¹µ )x`x{Fuwzph%rw{¹rwehkp³hi¬Ak`u´{ª'vu<vikrwkju< ;{ªUrtehk}i{hkjOArwehkz|ik`p z{pþ{ªUrtek}kD txjutzrw{u<
[vutzk` Nkr· kjkjpD¬vpS.hµ
)7Fkjuw²¹x{ii{pi{kj&z f{hrwvzphkDI·ehk`p0z zv{FpvOµnqpIrwehz ?xjv tkrwehkrteutk`kx<eAvphphk`
uwkji%vz|p¹zpk`Ak`pk`pFr;·ekjp¹rwehkz|i%vk?z rtu<vp ª¯{uwik`µUdfehkkD txjutzrt{Fuw xjvp¹rwes³A Nk8x{Fi}³rtkD
{Fp^k`vFx<e¨x<evphphk`z|ÉFkrwehkj²S· kjuwkzp^rwehk}uwkj²s~OkjFkj¢xjv tkvp^²^vz|p¹r· {Ii{uwk¬zikjp tz{p
³A zph}rtehkª¯{Futi¬³hv z|pÊÏOÐyµ'dfez ut{[zk` fkD txjutzrt{Fuw {ª¢zikjp tz|{Fp^[µ
)?ph{rwehkjux`v tk¬z Vrtevr{ªfv¹ª¯³h'u<vphÉ i%v[rtuwz|©þ·ehkjp»ph{:uw{rwvrtz{pvzp[vuwzvpxk}z pkjk`hk`µ
nqp¹rtehz fxjv tkrtehkVkDxyrw{u< 4 #
&3 K #
K K
&y
L
L L
&yµµ|µUvutk?v|a t³hk`xrw ºrt{rtehk tvik
zphk`vu8{uv[Ó%phkrwuwvp ª¯{uwiµ%dfehk%Fk`xrt{u x`vp»AkI·z±rweu<vc·p¨²þp{rx{Fp zk`utzphrtehk%Fk`xrt{u
#
&yµkji%vz|p &rtehk|zphkDvu®Avutr`µdfekºvF zxUzps[vutzvpsr®zp8rtez ¢xjvF kºvutk'rtehk x{{u<zpv[rwk` &{ªrtehk
Fk`xrt{u< ·z±rweuwk` tAkDxyrfrt{}rwehutk`k´{ª®rwehkji(x<e{F tkjpvF vuwkª¯k`utk`pxk´ª¯u<vikµn«ª· k8x<eh{{F tk¬Ï¯ª¯{uuwk`v t{pA
{ª t²ii}kjrtuw²hЬrtehkSrwehuwkjkSkDxyrw{u<
K3K #
K K K K
&y
K L #
K L K L
&fvp
L9L
# L L
L9L
&%v
uwkª¯k`utk`pxk´ª¯u<vikrwehkjprwehk8z|p[vuwzvpsrw fvuwkÍ
K L
L9L
K L
L9L
K L
L9L
K3K
K L
L9L
K K K L
L9L
K3K K L
L9L
K K L L
K K
L9L
K K L L
K K K L
L9L
K3K
K L
L9L
K K K L
L9L
K K K L
K3K
K L
K K K L
K K K L
L9L
K K K L
L9L
K K K L
L9L
·ekjuwk &%z utkD Nk`xrtzk`|²Lk`¶s³v?rt{ K #
K K
&6 L #
L L
&6
K3K K
K3K K K K3K
&µ|µµ
dfekz|p[vuwzvpsrw ¢rt{A{rte%uw{rwvrtz{p Uvpvheh{rt{ikjrtuwzxfi{kjA·z±rweª¯³hu<vphɬivrtuwz±© eAvckfph{r
Nkjk`pSkjuwz|Fk`I²krDv ªÇvu;v f· kÉsp{[·8µ
5 "$ # !& & % %&
nqpFkjphk`uwvY&k`[v³v[rwz|phrwehk%utkDx{Fphz|rtz{pxjvvhzz±rwz|kD {ªk` wxuwz|hrt{u< Vz z±Ó¹xj³h±rDµC)U©Nkjuwz|ik`pFr<v
uwk` t³h|rw VkjNkjpA^{z{³ t|²{pþrtehk¬z|psrtuwzp zxN{[· kjuV{ªUrtek}kD txjutzrw{u< jAh³r8v {{pSrwehk¬xj{psrtk`pFr
{ªrtehkhv[r<vvF kFµ<h{Fukj©vih|kFUz±r}z ¬uwk`v²¨evuw»rw{þuwkrwutzkjFk¹{ph² ³hpA ehzphkD ·ehk`p ¶s³hkjuw²z|p
·z|rteÎvþ t³hp tehzphkzi%vFkIv¨v[rwvv tkIxj{psrwvz|phzphþ t{kj²Ê ³p ez|phkD ¬vp t³hphuwz kD IÏrwehkj²¼vutkph{r
t{¹z&!Nk`utk`psr`av[ªrtk`u?vÐyNh³r;rwehz ´z ;vi{F r;rtuwz|zv&·ekjp:rtek¬hvrwvAv tkxj{psrwvz|pA {ph²z|i%vFk` {ª
t³hp tehzphk` ´vp^{ªºhvutÉrtuw{hzxjv&ª¯{FutkD r< jµ?dfekzi}AvxyrV{ªUrwehz V t³hrtk¬ tzk~«k!ak`xrVxjvp^Nkz|iz|rtk`
·ekjp¾rwehk¨hvrwvv tk^ rw{uwk` Iz|i%vFk` Nk`xjz±ÌAx`v|² x<eh{s k`p rt{L rtuwk` w ¹v vutrtzx³hvuv tAkDxyr{ª8rtehk
hk` wxuwz|rw{u< jµ><h{Fu'k©hvihkFrtek;ut{Fh³ rtphkD t Urt{z|³hizpv[rwz|{Fp¹[vuwzvrtz{p U{ªartehk?hk` wxuwz|rw{u< 'xjvp%Ak
utkDxz k`|²:kj[v|³vrtkD^z|ªºrtekv[rwvv tk}z|pxj|³Ak` v k`utzk` V{ªzk`psrtzxjvzi%vkD ´rtevr8hz!akju{p|²S²
rwehkjzuz|³hizpv[rwz|{Fp»x<evuwvFxyrwkjuwz rtzxj `µ%dfehk%hv[r<vvF k· k}³A kDþrw{Skj[v³vrtk{³huxj{{ukD txjutzrw{u<
xj{psrwvz|pA t³x<e:zivkD zpSvhhz±rwz|{FpIrw{%{rtekjuuwk`v|~«|z|ª¯k´p{p~q Nk`xjz±ÌNx´zi%vFk` `µ
+,+,.- 0 ¥,¥h£32 Ù 4 Ø 2¯£ ; ¤ ÕsÖa× ÕAÕ ,7¼¥6 Õ ¡
¸hx<ehizÊkj©rtkjpA zk`|²»kj[v³vrtk`»rwehkhk` wxuwz|rw{u< 8huw{N{F tk`² <{u<vx<Éaµ50?kjuk`[v³v[rwz|{Fp teh{[·
xj|kDvuw|²Irtehk}uw{h³ rtpk` w ;{ªrwehk}hk` wxuwz|rw{u< zpSrtehkx{Fpsrtk©r?{ª'uwkj²z|i%vk` `µ;dfehk}hv[r<vvF k³A kD
ª¯{Fuehkjukj©Ak`utzikjpsrw f·fv fi%vhkV{ª¢vA{F³r`F¬z|i%vFk` `ͬhzk`xkD {ªvutr`D}vkjuwzvaz|i%vk` f{ª
rwehk{[·psrt{[·p{ªUÑ^vu< tkjz|k` Ï<uwvpxkcÐyhvp^¬zivkD {ªl\&7{kDxyr< jµ
dfehkvkjuwzv'zi%vkD vuwkrtek¹i{F r¬x<evkjphFz|phAµdfekj²{{Év|i{F r¬ tz|izvuIϯuw{{ªÇ h{^ph{r
hz!akjuf {i³x<eAÐ'vp%zi%vFk` ºxj{iN{F tk`{ª®l\&]izxuw{ rwut³Axyrt³utkD ?ÏÇx<ez|iphk`² `vpsrtk`phpv `xjvu< ' tkjk`p
î`Ucêìñ`Y[ýwüOýT[ý<ñOí'ðýOTí6TKRQ_^®ñOídYVýwü
UjüÇüOë\[]$]_^1^`^baêSOKRÇêýcìëíñ aPMR ]wï Q_f`ê]wëcéKT]! ¢íï Qyñj]<ô&íðdQ$OKOcý<êìñOñ«ýODðí"øQ$R Ycídcìêý#]wí O]RYíðdQ$OKO[ý<êüVROí"`Q$T$#Çíqü«ñ aUjüYï c
Ã Ã Ã Ã¯Ä Ã
ª¯uw{ivA{[Fkckr<xµìÐyµ¢nqpehkju¢rwk` rw `crtehkf¶s³hkjuw²´zi%vFk` ·k`utk'p{rvutr{ªhrtehkfhvrwvAv tkµ®dfehkD kz|i%vk`
· kjuwk;r<vÉFkjph³hutzph%v} ³hA kD¶F³kjpsr Av w {[Fkjurtehk8xjz±r²Fµdfez x<evphkD 'rwehkz|k`·A{Fz|psrÏrwehkVªÇvxjvFk`
{ªh³hzzphs 8AkDx{Fi}kIsz tz|hk¹{Fuz tvhAkDvuyÐvp»rwehkIxj{iA{s z|rtz{p{ªfzi%vFk` ¹ÏY {Fi}kxjvu< evcFk
i{[Fk`е'dfehkhvphkeh{[·k`k`u`srt{{FÉIvrtek8z|i%vFk` fzpSv} teh{Furfrtzikª¯uwvikhi%vÉzph³hpx<evphkD
tevF{[·; jµ
9´³hk`ut² ( k` r)?p t·k`u 9´³hk`ut² ( k` r );p t·k`u
<¢z³huwk:Íd·{S¶s³hk`utzk` Vi%vk%·z|rtezi%vk}ª¯u<vFi}k`psrw 8vpA^rwehk%i{F r ziz|vu8zi%vkD ´ª¯{³hp»²
rwehk8uwkrtuwzkj[v t² rtk`i:µ
d{:z||³A rwuwvrtk¬rtehkuwk`x{Fphz|rtz{p¨A{[· kjuV{ªrtehk%kD txjutzrw{u< j· k¬zp tkjutr8ehkjuwkr· {k©hvihk` Vk©~
rwuwvFxyrwk`ª¯uw{i ¸x<ehiz · {uwÉaµ1<¢z|F³huwk; teh{[·; &rtehk AkD rUvpA · kjuutkjrt³huwphk`s²Vrwehk t² rwkji#ϯzOµkµ[rtehk
i{s r? tz|izvuz|i%vkDÐ ·ekjpS¶s³hkjuwz|kDs²v i%v&zi%vkVª¯u<vFi}k`psr`µ )´ ; r<v[rwk`:vN{[kFszkj·N{zpsrw
hz!akjuNkr· kjk`p¶s³hkjuw²¹vpAhvrwvv tk?zi%vkD jµI9´³hk`utzk` ³ tzphª¯u<vFikjpsrw huw{[zk´{{¹uwk` t³h|rw v
{pIv frwehk¬ tzMLjk{ªrtehkª¯uwvikjpsr´ rwvc² ;vA{[Fk%` {ªrwehk¬ tzL`k{ªUrwehk{Futzzpv&z|i%vkµ?¸iv|kju
ª¯u<vFikjpsrw fk`u<vk´rtehk8uwk` t³h|rw fu<vhz²µ
<¢z³huwkIz|³ rwuwvrtkD vph{rtehk`u8z|psrwkjuwk` rtzphSutkD ³±rDµ¸k`kju<vUzi%vFk` 8{ªfvSzph{s tv³hu k`kjp»ª¯uw{i
Fkjuw²Êz!akjuwkjpsrA{Fz|psr< ¬{ª?z|k`· · kjuwk rt{uwk` z|p rtehkShvrwvv tkµÊl»z!akjuwkjpsr%¶s³hkjuw²Êz|i%vk` ¬· kjuwk
rwehkjpx{{ÉFk`~«³h¹³A zphv¬xj{ihk©¹vFx<ÉsFut{F³hp{FpI·ehzx<ev¬z|k`· Ïrwev[rfz ph{rz|pIrtehk?& (fк{ªrtehk
hz|ph{s tv³huf· vF ³Ak`utziA{s kDµnqp:vFhz|rtz{p&rwehk8kªr;vur{ª¢rtekrtehzuw:¶s³hk`ut²%zi%vk·fv k`|kjrtkD
ÏÇ{ph²^rwehk¹r<vz'{ªfrwehkIzph{F wv³uutk`i%vzp z tz||kcÐyµSdfehkI t² rwkji4·fv 8rtehk`p¼v tÉk`¨rw{Sutkjrt³huwprtehk
i{s r; tz|izvuz|i%vFkVª¯{u;kDvx<eI{ªrwehk` tkl¶s³hkjuw²¹zivkD jµb<{u;v&¶s³hkjuwzk` `rtehk8Nk` r´vpA · kjufz frtehk
zi%vFk{ªºrtehkzph{F wv³hu?rtevrVz V{pSrwehkutzesrV{ªUrtek<¢z³huwkÏÇz±rz ?rwehk}A{Fz|psr{ªºzkj·zp^rtek& (
rwev[rVz ´rwehk}xj|{s kD r?rt{¹rwehk}{phk¬z|p¨k`vx<e^¶s³hk`ut²hеVdfehz VutkD ³±rVkjihevF zMLjkD rtek¬uw{h³A rwphk` w ;{ª'rtehk
ikjrteh{:xjv³ kDI²%rwehk8{x`vz±r²I{ª®rwehkkD txjutzrt{Fuw fvprtehk8²%rwehkx{F³hpsrtzphhut{xjk` w jµ
+,+,+ 0 ¥,¥h£32 Ù 4 Ø 2¯£ ; Ù ,Ù ¤ 7¼¥6 Õ ¡
d{Vkj[v³v[rwk rtehkfuwk`x{Fphz|rtz{pA{[· kju{ªN{³hukj©srwkjp tz{prw{8x{{u¢zivkD j[· k³A kD¬vhvrwvAv tkºi%vk
{ªartehk[zikjp tz{p¹kD txjutzrt{Fuw ºkjuwz|Fk`}ª¯uw{ihutkDv|~Oz±ª¯k;xj{{u'zi%vFk` `µF zivkD 'x{Fi}k
ª¯uw{i ^ kDx{Fph {ª?v^zkj{Aµ¨dfehkutk`ivz|pz|phþz|i%vFk` ¬x{ikIª¯ut{Fi2v¨hv[r<vvF k%{ª´ rtz| z|i%vk`
9´³hk`utzk` )?p t·k`u
<¢z³huwkÍdfeutk`k ¶s³hk`utzk` ¢·z|rtex³rrwkjuwk`}x{ihk©} txjkjphkD ¢vp8rwehkuwkrtuwzkjkD8zivkϯ{Fprwehkfutzesr<Ð
ª¯{F³hpI{p%rwehk´· kj[µ'dfehk;rw{r<vNps³iNkjuf{ª®kD txjutzrw{u< ºx{Fih³rtkDª¯uw{i rtek` tk?zivkD 'z A`lAD
vpIrtehkhvrwvv tk´{x`x³hhzk` ?vN{³rFÑS:{Fpz tÉNµ
dfehk¹ rtzUz|i%vFk%hv[r<vvF k}z 8xj{iN{F tk`^{ªf tkjFkju<v kD¶s³hkjpxjk` V{ªfzivkD ´·ekjuwk}{Fphk}{ur· {
Avu<vikrwkju< [vuw² t|{[·²µh<h{Fu?zp r<vpxjkNrtekjuwk¬vuwk tk`¶s³hk`pxkD ;·z|rte¨vI[vuwzvrtz{pS{ªUrwehkzpsrtk`p z|r²
{ªartehk;zesr t{³hu<xkFF tk`¶s³hkjpAxk` UrwvÉFkjp%²v8ut{rwvrtzph8{uºv8rtu<vp tvrtzph8xjvi}k`uwv ºdfehz ºv|{[·; rt{
rwk` r; Nk`xjz±ÌAx`v|²¹rtehk8uw{h³A rwphk` w {ª®rwehk8k` wxuwzrt{Fuw fvpAI{ª®rtek8utkjrtuwz|k`cvai}kjrteh{rt{[·fvu<h ºrtehkD k
Avu<vikrwkju< jµnqpIvrwehk´Ì³huwk` ºAk`|{[·8srwehk?p³hi¬Ak`u{ª®k` wxuwz|hrt{u< Urwev[rfx<evu<vxrtk`utzMLjkkDvx<eI¶s³hk`ut²
zi%vFk¬z 8zpzxjv[rwk`þrt{Fkrwehkju8·z|rte»rwehk¹¶s³hkjuw²Sz|i%vkµnqpÊvz±rwz|{Fp&rwehk%p³hiNkju8{ªfkD txjutzrw{u<
rwev[r;i%vrwx<ehkDz zpzxjvrtk`rw{kjrtehk`u·z±rweSk`vFx<ezi%vkuwkrw³hutpk`²¹rtek ² rtkji:µº?{rwkrtevr;rtehk
vcFkju<vFkph{z kVkjk`¢ÏÇzYµkµrtekVp³hi¬Ak`u{ª®i%v[r<x<ehk` ·evrtkjFkjurtehk¶s³hkjuw²%z wкz Nkr· kjk`p/¬vpþ`hµ
9´³hk`ut² );p t·k`uw <Av k8?kjµ
h` l lA lFs B.
<¢z³huwk8lhÍU{Fh³ rtphkD t rw{[· vuwh [vuwzvrtz{p{ªz||³i}zpvrtz{p&µ )?pkj©hvihk´·z|rtertek¶F³kjuw²¹z|i%vk
rwehk8kjzesri{F r; ziz|vuzi%vkD futkjrtuwz|k`kDvpv¬ªÇv k8phk`Fvrtzkµ
UüYüYëA[]$]_^`^`^baêSOKRYêýcìëíñ_aPR]wï Q_f`ê]wëcéKT]wóï;ýgyíñj]wêSO8Ycíji\aUüOï c