First steps towards automatic building of anatomical atlases

HAL Id: inria-00074454

https://hal.inria.fr/inria-00074454

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,

First steps towards automatic building of anatomical

atlases

Gérard Subsol, Jean-Philippe Thirion, Nicholas Ayache

To cite this version:

Gérard Subsol, Jean-Philippe Thirion, Nicholas Ayache. First steps towards automatic building of

anatomical atlases. [Research Report] RR-2216, INRIA. 1994. �inria-00074454�

a p p o r t

d e r e c h e r c h e


   !"
#%$&
(')
(*,+-/.

%*, 0
#1'2&"'3

Ge´rard Subsol, Jean-Philippe Thirion, Nicholas Ayache

N˚ 2216

Mars 1994

PROGRAMME 4

Robotique,

image

et vision


  ! "#$"$%%&(') "#*"#+,-"/.0 132-456.7  8+9;:<9>=?@?BADC-EGFH:I5:JLKNMO APQKR?S=<A3A0JUTK#VWKX:Y 8+9:ZA0JH[]\K#^ =O 9;A F_=\ \5:9JD^A`9;Abac A09>ac A3Y`d6ee fbg-Eihj=9>VkfbllC-Eieem\5=n<AbV oqpsr0tbuwv5xty{z!cK#Vm9A0\5:9;Jm\ 9;AbVLA0Y6J>V-=|<A0Y A09>=w}UV;a;c A0?BAS~1:9-J;c ASI OK}#^KXY <€:~=Y5=J:?mK#a0=w} =JL}N=VAbV0‚|ƒ„A(\ 9:\5:6VLA(J;:|O5VAqV\5AbaK†…a‡=nY5^ˆVJ*=I}XA@~/Ab=J;O 9;AbV7P‰Jc A‹Š0a*9AbVJ-}KXY AbV;Œ‹:9`9K#^<A }†KXY AbVqUcK#acŽ=9A‡=O J;:?(=nJK#a0=w}†}RA*‘ J;9>=a*J;Ab^~19:?“’”•KX?(=<AbV@I–^K†—A09;A0YJK#=w}3<A0:?@A0J;9 :\˜A09>=J;:9>V0‚-ƒ„A@c5=wTA@^A0TA*}X:\5Ab^Y :Y ™/9KX<K#^9;A0<K#VJ;9*=JKX:Y„J;Abac YK#a0V`=Y5^‹<:J)A0Y5a*:O 9>=<KXY < 9;AbVLO}RJ*Vš~1:9›Jc A3I OK}#^KXY <q:~œ=k…59>VLJH=nJ}#=Vš:~‰J;c A`a*9;AbVLJ}†KXY AbV_:~‰J;c A`VžO}†}‰I5=VAb^B:Y‡VA0TA09>=w} Ÿ zH™ 6a0=YqKX?(=<AbV!:~^K—A09;A0YJU\5=JLKRA0YJ>V0‚ ¡£¢6¤¥¦m§u¨sry©=Y5=J;:?mK#a0=w}ª=J}#=V7PbJ;9LKN^KX?@A0Y5VKR:Y5=w}?@Ab^K#a0=w} KX?(=n<AbV0Pa*9;AbVJ&}KXY AbV0PY :Y ™/9LKR<nKN^ 9;A0<nKNVLJ;9>=JKX:YPQ\5:}XY :?mK#=w}+J;9>=Y5VW~/:9;?S=JKX:Y5V «1¬m­ ®¯°b± ­ ®+²+³R¯´$µb¶

1*  0
,, 

¢ªr ¢(y ”3=Y5Va*A9*=\ \5:9JbP*Y :O5V\ 9AbVA0YJ;:Y5V˜O Y a0=^9;A<A0YA09>= } \5:O 9}#=)a*9Ab=JLKR:Y=O J:™

?(=nJK#MO A3^=J}#=Vš=Y5=J;:?mK#MO AbV0‚_:O5V+\ 9:\5:6VL:Y5V!^O JK†}†KNVLA09D^AbV!a0=9>=a*JA09K#VJK#MO AbVVJ>=nI}RAbV7P

}XAbV`Š}†KX<Y AbVU^A3a*9A0J;AbŒ`MOK‰V:YJ›=O J;:?(=JK#MO A0?@A0Y6JšA*‘ªJ9>=wKXJ;AbV!^AbV]KR?S=<AbVš?Ab^K#a0=w}XAbV!J9K#^KR™

?@A0Y5VKR:Y Y A*}}XAbVm\5=n9^AbV):\A09>=J;A0O 9*VU^Am<A0:?A0J;9KXA`^K†—A09;A0YJKXA*}†}XA‚U:O5V3=wT:Y5VU^ A0TA*}X:\ \A

O Y(= }R<:9KXJ;c ?@AU^AU?mK#VA_A0Y(a*:9;9;AbVL\5:Y5^ =Y5a*A_Y :Ym9KX<K#^AUA0J+:I J;A0YO(^AbVs\ 9;A0?mKXA09>V]9AbVLO}RJ*=J>V

A0Y5a*:O 9*=<Ab=YJ>V_\5:O 9_}#=qa*:Y5VJ;9;O5a*JLKR:Y ^O Y„=J}#=V)^AbVH}KX<Y AbV-^A a*9A0J;A`^O„a*9!=Y A#"=@\5=9JKX9

^KX?(=n<AbVDVa0=Y Y A09D^A`\}XO5VWKXA0O 9>V)\5=nJKXA0Y6J>V7‚

$ §˜tbr0¥;x!%¢„y(=J}#=V+=nY5=J;:?mK#MO AbV0PKX?(=n<AbVs?Ab^K#a0=w}XAbV]J;9K#^KX?@A0Y5VWKX:Y Y A*}†}#AbV0P}†KX<Y AbV!^ADa*9A0J;AP

  */ ) # "
 * WY‡:9>^A09_J;:mKX?@\ 9;:TA3J;c A`^K#=<Y :6VWK#VD=nY5^qJ;c A3J;c A09*=\6S\}#=Y YKXY <5P˜J;c A`\ cªVKNaK#=Y|Y A0Ab^ V)J;: a*:?B\5=9;A@’” ?@Ab^K#a0=w}+KX?(=<AbV3a*:?mKXY <S~19;:? Ÿ :?@\ O J;Ab^jz&:?@:<9>=\ cP5hj=<Y A0JK#amF!AbV:™

Y5=Y5a*A ?(=<A09;q:9 UO5a}XAb=9`h|Ab^K#aKXY A)6=l’ W‚5ƒ„A-!K†}†}›Y :J3^K#V;a*O5V;V)c A09;AmJ;c Am\ 9;:I}XA0?

:~`?mO}XJKX?@: ^ =w}†KXJ9A0<K#VJ;9>=JLKR:Y I O JS›AqHK}†}`VJK†}†}k^K#VJLKRY <OKNVLc I5A0J!A0A0Y J;c 9A0A‡žKRY5^ VB:~

a*:?B\5=9K#V:Y5V  ! a*:?@\5=9LKNVL:Yq:~sKR?S=<AbV!:~+J;c A`V;=n?@A3\5=JKXA0YJDJ;:@VJO5^(J;c A-A0T:}XO JKX:Y|:~œ=@^K#VAb=VLAP ! a*:?@\5=9LKNVL:Y‡:~sKX?(=<AbV_:~›^K†—A09;A0YJD\5=JLKRA0YJ>V_J;:(a*:YJ;9>=VJD=mc Ab=w}XJ;c =nY5^‡=m\5=Jc :™ }X:<K#a3\˜A09>V:YP ! 9;A0<K#VJ;9*=JKX:Yq:~sKX?(=<AbV!HKRJc‡=Y =Y5=nJ;:?mK#a0=w}‰=J}#=V7‚

z!c A =wKX? :~›=Y5=J:?mK#a0=w}œ=JL}N=VUI˜:6:ž V#"/~1:9UA*‘Q=n?@\}XAP 8sA09%$’&('+K#V)J;:(a*:?B\K}XAm?@Ab^K#a0=w}

:I5VLA09;T =JLKR:Y5V@=Y5^€<KXTA‡=„MO5=w}†KXJ>=JKXTA‡^AbVa*9KX\ JKX:Y a*:Y6TA0YKRA0YJm~/:9@=„VžK†}}XAb^ \ cªVWK#aK#=Y‚

WY–V:?@A(a0=VAbV7PJ;c A0ˆa0=nY„\ 9;:TK#^ASO5V-!KXJ;c–VL:?@A(MO5=YJKXJ>=JKXTAmKXY~/:9;?(=nJKX:Y–=nI5:O J-J;c A

T=9K#=JKX:Y5Vq=?B:Y <„\5=JKXA0YJ>VS=V0Ps~/:9BKRY5VLJ>=Y5a*APšJ;c A =JL}N=V@:~3J;c A|I 9>=wKXY©:~kzs=w}#=wKX9>=ac*)

z&:O 9;Y :O‘+zUz$,$&‚+z!c A|Y A*‘ªJqVJ;A0\€K#VBJ;:„O5VA|J;c :6VAqT=9K#=IK†}†KRJ \5=9>=?@A0JA09>VmJ;:ˆ^A0JAba*J

\5=Jc :}X:<KXAbV0‚

’” ?@Ab^K#a0=w}+KX?(=n<AbV3=9;Am=SJ;9;A0?@A0Y5^:O5V_:\ \˜:9;J;O YKXJ‡J;:BKX?@\ 9;:TAmJ;c :6VLA =J}#=VLAbV3=Y5^

J;:jI 9;:=^A0YˆJc A V;a*:\5Aq:~DJc A*KR9S=\ \}†KNa0=nJKX:Y5V0‚.-_:›A0TA09bP?@Ab^K#a0=w}!KX?(=<AbV@a0=Y€I5AqcO <A

"/~/:9mKXY5VJ*=Y5a*AP›=

Ÿ

z!™ 6a0=Y :~Jc A VžO}†}DKXY5a}XO5^KXY < f0CC/10Qfbe/20 fbejT:b‘ A*}#V-K#Vjf $„h|:

}#=9;<A3'54›A3?mO5VJ!J;c A09A*~1:9A^A0TA*}X:\j=O J;:?S=JK#aUJ:6:}#VšJ;:m?(=Y5=n<AVLO5a;c‡MO5=YJKXJS:~œ^ =nJ>= ‚

6QO 9;J;c A09;?@:9;APw~ =n9+I5A0J;J;A09+\ 9AbaKNVKR:Y a0=YBI5AD=acKXA0TAb^m!KXJ;cS’”KR?S=<AU\ 9;: a*AbV;VWKXY <-J;Aba;c YK#a0V

J;c5=nYq!KXJ;c‡?(=nY6O5=w}:Y AbV7‚

 …59>VJ@=J;JA0?@\ J`J;:„=acKXA0TA‡VO5ac–=nYˆA*}XAba*J;9;:YKNa|=J}#=Vk~/:9`J;c A‡’” TK#VO5= }K87b=JLKR:Y :~

:9<6=Y5Va0=nY@I5A_~1:O Y5^mKXY† 9-D8;:+l’& ‚ƒ©c5=J+!AU\ 9:\5:6VLAUK#VšJ;:3A*‘ J;A0Y5^@Jc ADO5VA_:~J;c :6VAD=nJ;™

}#=VAbV]J;:3J;c AD=nO J;:?(=JLKNa!MO5=YJK†…a0=JKX:YS:~J;c A_T =9K#=JLKR:Y5V+UcK#ac(a*:O}#^m}XAb=^ J;:`=O J;:?S=JK#a

^K#=<Y :VWK#VD=Y5^|VO 9;<K#a0=w}s\}N=nY YKRY <˜‚

Y J;cK#VS\5=\˜A09bPU!A|\ 9;AbVA0YJ‡:O 9q\ 9;:ZAba*JS:~@=Y =O J;:?(=nJK#a0=w}I OK†}#^KXY < =Y5^©O5VAj:~

=„MO5=YJKXJ>=JKXTA‡=nJ}#=Vk~19;:? ’”{?@Ab^K#a0=w})KX?(=<AbV7‚ _~/J;A09(=|\ 9;AbVA0YJ>=JKX:Y:n~DJ;c Aq<A0Y A09>= }

V;ac A0?@AP&›A@^A0J>= K}Jc A J\5A@:n~+~1Ab=JO 9;AbV)O5VAb^„=Y5^j=w}#V:j^AbV;a*9KXI5AS\ 9;AbaK#VA*}Xˆ=SY :Y ™/9LKR<nKN^

9;A0<nKNVLJ;9>=JKX:Yj=w}X<:9KXJ;c ?|‚UJš}#=VJbP !A`Vc : VL:?@A3TA09;SA0Y5a*:O 9>=n<KXY <(9;AbVLO}RJ*VU:~+J;c A`=O J:™

?(=nJK#amI OK†}N^KXY <j:~U=Y„=J}#=V):~!J;c A@a*9;AbVJ)}†KXY AbV`A*‘ J;9>=a*J;Ab^£~19;:? ’” Ÿ zH™ 6a0=Y|KR?S=<AbV):~

  ! "# %$&$(')! * "+, *-.!#/1032/-!

4 5

 * 1' 3#6, !

7 O 9)\ 9;:ZAba*J!?(=w(I˜A ^Aba*:?B\5:6VAb^ KXY6J;:BJ!:m\5=9;J*V"VA0A3…5<O 9A@f3'5

Average

Statistical Analysis

Registration

Data 1

Registration

Comparison

Atlas

Data 2

Diagnosis

3D Visualization

BUILDING

USE

6&KX<O 9;A(f 8 9:9;&<=-.!>? !A@"!B.! "#  "!C s^ =J>=fmK#Vm= VLA0J`:~U9;A0\ 9;AbVLA0Y6J>=nJKXTA(:I ZAba*J*V "/~/:93KXY5VJ*=Y5a*AP+V;=Y AS\5=™

JKXA0Y6J*V%'`UcK#acŽ=9;AS9;A0<K#VJA09;Ab^‚Dšˆ?S=žKXY <ˆa*:?@\5=9K#V:Y5V I5A0J!A0A0Y J;c A‡^ =J*= PsJ;c A

9;A0<K#VJ;9*=JKX:Y(=w}X<:9KXJ;c ? VA0A0ž Vs~/:9›V:?@Aš~1Ab=JO 9;AbV+J;c5=nJ=9;AUVc5=9;Ab^ I6mJ;cK#V+9A*~1A09;A0Y5a*A

}#=V0‚  VLJ>=JK#VJK#a0=w}=Y5=w}X VWK#VU^A0J;A09;?mKXY AbV_J;c A@Š0=a0a*A0\ J>=I}XA`^K†—A09;A0Y5a*AbŒ-KXY‡9A*}N=nJKX:YqJ;:

J;c A`=J}#=V7‚

!A@"!?

J;c A39A0<K#VJ;9>=JLKR:Y =w}X<:9KXJ;c ? \5A09;?mKXJ>V_J;:ma*:?@\5=9;A3Jc AVAba*:Y5^qVA0JU:~œ^ =nJ>= P

^ =J>=e "/~/:9SKXY5VJ>=nY5a*APD=€\5=J;c :n}R:<K#a0=w} \5=JLKRA0YJ '(=Y5^ J;c Aˆ=J}#=V7‚Uz!c AˆVJ>=nJK#VJK#a0=w}

\5=9>=?BA0J;A09>Vš<KXTA`\ 9AbaKR:O5V!KXY~/:9;?(=JLKR:Y‡=I5:O J_J;c A3}XA0TA*}‰:n~_Š0=nI Y :9;?(=w}†KXJªŒQ‚

Yˆ= }X:Y <™/J;A09;? \˜A09KX:ª^PsVO5acˆVJ>=JLKNVLJK#a0V3a*:O}#^jI5A(VLA0Y6J)J;:‡=q^K#=<Y :6VKNV)?B:ª^O}XASJ;c5=J

a*:O}#^€^A0J;Aba*J VL:?@Am\5=J;c :}X:<nKRAbV7‚ 6 :93Y : -P5!A@\}#=Y„J:SKRYJ;A0<9*=J;AmJ;c A(’” TK#VO5=w}†K87b=JKX:Y

:~)J;c A‡a*9;AbVJ-}†KXY AbV@:~)J;c A VLž6O}†}=Y5^J;c A‡=JL}N=V3KXYJ;c Aqa*9>=YKX:~=aK#=w}VLO 9;<A09;ˆVKR?mO}#=JKX:Y

J;AbVLJ;I5Ab^|^A0TA*}X:\5Ab^ KRY|J;c A`[+\K#^ =O 9A`\ 9;:ZAba*J ”-  Ÿ
lC3PKRY|:9>^A09UJ: c A*}X\|J;c A3\ c6 VWK#aK#=Y J;:B\}N=nY‡:\˜A09>=JKX:Y5V0‚   6 -"'" # "      

FU=w ?@Ab^K#a0=w}sKR?S=<AbV)=9;A VLJ;:9;Ab^BKXY„=@^K#V;a*9;A0J;A@’” ?S=J;9K†‘ " "!"# '*‚!DšqJ;c 9;AbVc :n}R™

^KXY <PK#V:6VO 9L~ =a*AbVH:~‰:9;<=Y5V!=9;A`a*:?@\ O JAb^"/~1:9KXY5VJ*=Y5a*AP J;c A`VO 9L~ =a*A3:n~‰J;c A`VžO}†}‰~/:9

Ÿ zH™ 6a0=YP:~J;c A_I 9>=wKXY(:9+J;c A!~=a*A!~/:9›hjF  '>‚6z!c A_\ 9;:I}XA0? KNV]J;c A0Y@J;:ma*:?@\ O J;A)V\5AbaK†…a

~/Ab=J;O 9;AbVH:~œJc AbVA`VO 9~=a*AbV0‚ A0TA09>=w}‰?@A0Jc :ª^ V!c5=wTA3I˜A0A0Y‡\ 9;:\5:6VAb^£J;:@=acKRA0TA`J;cK#V 

! = %$=-&$=@ ;.

Jc A@?@Ab=Yˆ=nY5^('3=O5V;VWK#=Y€a*O 9;T =JO 9;AbV`=9A O5VLAb^„J;:‡VLA0<?@A0YJ3J;c A

K#V:6VO 9~=a*A_KXY6J;:B\5=J>ac AbV:n~œV:?@A_~/O Y5^ =?@A0YJ>=w}J\5AbV0‚˜ O5ac‡=m^Aba*:?@\5:VWKXJKX:Yq\5A09;™

?mKXJ>V)J;:‡VJO5^‡J;c A(^A*~/:9;?S=JKX:Y5V_:~›J;c A }RA*~/J3TA0YJ;9K#a}XA 6+hj8 le +:93J;: ^AbVa*9KXI5A

J;c A)~ =a*AbV D Ÿ FUl’3 ‚

!A# * )$=@ ;.

 -U:V;=ž =-_:6V;le&9;A0\5:9;J>V=-!K#^A)9>=Y <A):~‰ac5=9>=a*J;A09LKNVLJK#a!}†KXY AbVUI5=VAb^

:Y@^K†—A09A0Y6JK#=w} <A0:?BA0J;9;‚z!c AU’” h|Ab^K#=w}_‘6K#V+z&9>=Y5VW~/:9;? <KXTAbVs=w}#V:`VA0J>V&:~5}†KXY AbV0P

a;c5=n9;JKXY <m~/:9!KXY5VJ>=Y5a*A-J;c A3<9>=w}‰=Y5=J:?mmKXY † !D+* : le&‚

! $ ":@)$@ !.

&J;c AˆŠ*A*‘ J;9;A0?(=w}!\5:KXYJ>V;Œ2z!cK#l’& PsI5=VAb^€:Y€<A0:?@A0J9K#amKXYT =9K#=YJ>V

=9;A3O5VAb^£J;:m\5A09~/:9;? ’” 9KX<K#^q9;A0<nKNVLJ;9>=JKX:Y‚

 …59*VJA*‘5=?@\}XA):~‰=`a}†KXYKNa0= }œ=\ \}†K#a0=JKX:Y‡a0=Y@I˜AU~/:O Y5^ KXY

Ÿ O JJKXY <`A0J›= }‚ Ÿ D - :sl’& Uc A09Am}†KRY Aq=Y5^j\˜:KXY6Jk~1Ab=nJ;O 9;AbV3=9;ABO5VAb^|KXY„:9>^A09-J;:‡a*:?@\ O JA£Š7=Yˆ=wTA09>=<AbŒ(VžO}†}‚ Y J;c5=nJDVJ;O5^Sc :›A0TA09bP:Y}X‡VA0?mKX™=O J;:?S=JK#a0=w}†}XqA*‘ªJ;9*=a*J;Ab^B~/Ab=J;O 9;AbVU=n9;A3O5VAb^‚

  ! "# %$&$(')! * "+, *-.!#/1032/-!


     

ƒ„Aq^AbaK#^Ab^€…59>VLJ`J;:|O5VA(:Y}R‹}KXY A£~1Ab=JO 9;AbV Jc A Š0a*9;AbVJ-}†KXY AbV;Œ|KXYJ;9;: ^O5a*Ab^KRY z '3l’&‚

z!c A0S=9;AD^A*…5Y Ab^S=V+Jc ADVO5a0a*AbV;VWKXTA_}X:ªaK:~=`VO 9L~ =a*A_Uc :6VA!}#=9<AbVJ\ 9LKRY5aKX\5=w}+a*O 9;T =JO 9;A

KXY=I5V:}XO J;AST =w}XO ABK#V3}X: a0=w}†}X„?(=w‘KX?(=w}KXY€J;c A(^KX9;Aba*JKX:Y€:~!KXJ>V3\ 9LKRY5aKX\5=w}3^KR9Aba*JKX:Y "VA0A

…5<O 9A e '>‚A0J )I˜A`J;c A3\ 9KXY5aKX\5=w}a*O 9;T =nJ;O 9;A`_c :6VA`a*O 9;T=J;O 9;A)K#V_?(=w‘KR?S=w}KXY =I5VL:}XO J;A

T=w}XO A =nY5^ jJ;c A`=VV:ªaK#=JAb^q\ 9KXY5aKX\5=w}^KR9Aba*JKX:YP5Ab=a;cq\˜:KXY6J):~=@a*9;AbVJ!}†KXY AmTA09K†…5AbV 

    

t

₁

t

2

n

k

₁

maximal

curvature

direction

principal

normal

crest line

6&KR<O 9;A e   @ *)-!-9@  @ "-  $  !%$- ? @"  -9@# * 

z!c AbVA|}†KRY AbVq=n9;A =O J:?(=JK#a0=w}†}X A*‘ J;9>=a*J;Ab^€~/9;:?“=nYK#V:6VO 9L~ =a*AjIJ;c A–Š?(=9>acKXY <

}†KXY AbV;Œq=w}X<:9LKRJc ? z '3l’&‚

6 O 9;J;c A09?@:9;APa*9;AbVJ)}†KXY AbV`=9A =nY5=J;:?mK#a0=w}†}Xj?@Ab=YKXY <~/O}›=V_A0?@\ c5=VWK870Ab^‹KRY D Ÿ $,$&‚

6Q:9UKXY5VJ*=Y5a*AP˜KXY„J;c A-…5<O 9;AmC5P5a*9AbVJ)}†KRY AbVk9;A0\ 9;AbVA0YJ3J;c A@V;=w}†KXA0YJ)}KXY AbVk:~J;c A@VžO}}"WJ;c A

:9IKRJ*V0PJ;c A)Y :6VAPJ;c AU?(=nY5^KRI}XAP Jc AUJ;A0?@\}XAbVš:9Jc Aac A0A0ž6I˜:Y AbV%'=Y5^m:Y(J;c A_I 9>=wKXYPJ;c A

 6 -+
"
 * 1'+1/"
 6

      

z!c A`’” a*O 9;TAbV9A0<K#VJ;9>=JLKR:Y‡=w}X<:9KXJ;c ? K#VU=-žA0S\5:KXYJU:~‰:O 9UV;ac A0?@A,<KXTA0YqJ!: VA0J*V

=Y5^ 5a*:?@\˜:6VAb^B:~J;c Aa*9AbVJš}KXY AbV=Y5^ 



A*‘ªJ;9*=a*J;Ab^-~/9;:? KX?(=<AbVš:~J!: ^K†—A09;A0YJ

\5=JLKRA0YJ>V0PQ›A)U=YJ›J:`…5Y5^S_cKNacS}†KXY AbV  :~ 2"W:9!\5:9;JLKR:Y5V  ']a*:9;9;AbV\˜:Y5^SJ;:mUcK#a;c

}†KXY AbV  " :9›\˜:9;JKX:Y5V  'š:~ "VLA0A)…5<O 9;A`’ '>‚

P

1,1

2,1

P

3,1

3,2

P

P

P

P

1,2

2,1

4,1

4,2

1,1

4,1

3,1

P

’

_P

’

1,1

P

’

P

’

P

’

P

’

2,1

1,1

1,2

5,1

2,1

3,1

3,2

4,1

3,1

4,1

4,2

5,1

C

1

C

C

C

C

C

C

C

2

3

4

’

’

C

2

’

3

4

5

C

’

1

’

C

C

5

6&KX<O 9;A`’  ' !3;C& @@ *&(%C *@" > !/ @ : @"  $@ *           $-@  !9#2 @"! #"$ $@ "  $ %  *-. - $ @(@"!& "'$ $@ *  $   : ! "- (!9 = z!!:`^K*)qa*O}RJLKRAbV_=9K#VA,J;c AUYO ?mI5A09š:~}KXY AbVš:~Ab=a;cSVA0J+K#VMOKXJ;A_KR?B\5:9;J*=Y6J "~19;:? VA0™

TA09*=w}5J;A0Y5VsO \mJ;:`VA0TA09*=w}ªcO Y5^9;Ab^ V%'+=Y5^-J;c A!9;A0<K#VJ;9*=JKX:YmI5A0J!A0A0Y =Y5^+  K#Vš^A*…5YKRJA*}R

Y :J_9KX<K#^‚

!

KXY D_     9$g3=Y5^ † 6h$# P’” a*O 9;TAbVk?(=J>acKXY <q\5A09;? KRJ*V3J;:S9;Aba*:<YK870A@9LKR<nKN^€VY ™

J;c A0JK#aB:I ZAba*J>V0‚6&KX9>VJbP&I5:O Y5^ =n9;„a*O 9;TAbVm=9;A@V?@::J;c Ab^=Y5^„Jc A0Y„?(=J>ac Ab^!KXJ;c

\ 9;AbVJ;:9;Ab^S?@: ^A*}NV_I O JUJ;c A-9;A0<K#VJ;9*=JKX:YSK#V!:Y}Xq9KX<K#^‚

!

KXY ' 3le&PJc A =w}X<:9LKRJc ? V?B:6:Jc AbV(a*O 9;TAbV@I O5VWKXY <Y :Y ™/O YK†~/:9;? Dš™ \}†KXY AbV0‚

z!c A0YSJ;c ADJ!:`VA0J>Vš:~‰a*O 9;TAbV›=n9;AU?(=J*a;c Ab^B!KXJ;cq=Y(c5=VcKXY < J*=I}XAUKXY5^A*‘ Ab^qI A0O ™

a}†KN^Ab=nY‡^K—A09;A0YJK#=w}˜KRYT =n9K#=Y6J*V0‚6F!AbVLO}RJ*V›=n9;AUTA09;m<:: ^  'z:sl’&5AbVL\5AbaK#=w}†}Xq!KXJ;c

VA0J>V]:~a*9;AbVLJ+}†KXY AbV!I O JJ;c A_?@A0J;c : ^m:Y}X(VO5a0a*A0Ab^ V]KXY@…5Y5^KXY <(=)9LKR<nKN^S^K#V\}#=a*A0?@A0YJ =Y5^qa0=Y Y :J_I5A`<A0Y A09>=w}†K870Ab^‡Ab=VWK†}RqJ:@J;c A3Y :Y ™/9KX<K#^ja0=VA‚ !-, c5=Y <|KXY* , c5=le= U=Y5^  ,

c5=leI ›=Y5^KXY5^A0\˜A0Y5^A0Y6J}X DAbV}#D›hjle&šKXY6J9;:ª^O5a*Ab^

  ! "# %$&$(')! * "+, *-.!#/1032/-! ~1:9UAb=acq\5:KXYJ
‰:n~ !P…5Y5^£J;c A`a}X:6VAbVJ)\5:nKRYJ
  :~  ‚ a*:?@\ O J;AmJ;c Am9KX<K#^j^K#V\}#=a*A0?@A0YJ`I˜A0J!A0A0YjJ;c AmJ!:(VA0J>V):~?S=J>ac Ab^q\5:nKRYJ>V "
   
 '›=Y5^"
    
  'Iq=-}XAb=VJ;™ V;MO5=9;AbVHJ;Aba;c YK#MO A‚ =\ \}XqJ;cK#VU?B:JKX:YqJ;: –=nY5^BKRJA09>=J;A3O YJK†}œJc A3?@:JKX:YSK#VmŠ0V?(=w}†}#Œ ‚

D:J;c`=O J;c :9*VO5VAJcKNVs=w}X<:9LKRJc ? J;:U9;A0<nKNVLJ;A09~/9;A0A0™$~1:9;? a*O 9;TAbV&I O Js:Y5a*A=<6=wKXYk~1:9&J;c A

9KX<K#^ja0=VA‚_A0TA09;J;c A*}XAbV;V7P5!A`a0=YSKX?@\ 9;:TAm=Y5^S<A0Y A09>= }K870AmJ;c A3?@A0Jc :ª^£J;:m:O 9U\ 9;:I}XA0?

=Y5^£:O 9D=w}X<:9KXJ;c ? ~/:}†}R:DVHJ;c A`VJ;A0\5V_:~‰J;c AqŠKXJ;A09>=JLKRTA`a}R:VAbVJU\˜:KXY6J>ŒB?@A0J;c : ^‚


        

[š=a;cq\˜:KXY6J!:~ jKNV›}KXY žAb^£!KXJ;cSKXJ>VUa}X:6VAbVLJ›Y A*KX<cI5:O 9UKXY  =a0a*:9>^KXY <@J;:mJ;c A3A0O5a}†K#^Ab=Y

^K#VJ>=nY5a*A‚ƒ„A!\}N=nY = }NVL:3J;:UKXY5a}XO5^A_KRYmJ;c AU^K#VJ>=nY5a*AHa*:?@\ O J>=JKX:Y@^K†—A09;A0YJK#=w}5\5=9>=?BA0J;A09>V

VO5ac =VSa*O 9;TAjJ>=Y <A0YJbP+Y :9;?(=w}P!a*O 9;T =JO 9;A„=Y5^ J;:9>VWKX:Y ' 3le&):9 VLO 9~ =a*A‡Y :9;?S=w} P

\ 9KXY5aKX\5=w}›^KX9;Aba*JKX:Y5V)=Y5^£\ 9KXY5aKR\5= }]a*O 9;T=J;O 9;AbV)=VU^AbVa*9KXI5Ab^£KXY 6 3lC W‚

z!!:‹a*:A ) aKXA0YJ>Vq=9;A‡a*:?B\ O J;Ab^€!KXJ;c Jc AbVA a*:O \}XAbVB:~3\5:KXYJ>V 

  =Y5^    UcK#a;c

=9A‡J;c A|\ 9;:\5:9;JKX:Y :n~J;c Aja*O 9;TA`:n~ ?(=J>ac Ab^!KXJ;c J;c A a*O 9TA€:~  =nY5^TKNa*A

TA09*V;= ‚z!c6O5V7P5I‡J;c 9AbVc :}#^KXY <5P    =Y5^     P5!A@a0=Yj^A0J;A09;?mKXY A@J;c A@a*O 9;TAbV Š*9A0<K#VJ;A09;Ab^ Œ@=nJ  \˜A09>a*A0YJ 4~/:9šKRY5VLJ>=Y5a*AP˜J;c A`a*O 9;TAœKNV_a*:Y5VWK#^A09;Ab^qJ:@I5A`^A*…5YKXJKXTA*}X 9;A0<nKNVLJ;A09;Ab^qHKRJcqJ;c A a*O 9;TA(_c A0Y     0-:9     0 ‚                 !     3V!J;c A)9;A0<K#VJ;9*=JKX:YBKNVHY :J!9KX<K#^‡=Y5^BA0TA0YqY :JU= )(Y AP!A3J;9;mJ;:m9;A0<nKNVLJ;A09 „=Y5^  !KXJ;c

=@en™/:9>^A09U\˜:}X6Y :? KN= }œJ;9*=Y5VW~/:9;?(=JLKR:Y =V›KRY h DF : l f%‰=nY5^ '):6VC$,$ 

" #$    %  & '% & !(& '%*) #!& '%!+ ! '%-, ! # '%*. # '%-/  '%!0 ! '%*1 # '% 2 !   3  & '3 & !(& '34) #!& '34+ ! '35, ! # '34. # '35/  '340 ! '341 # '3 62 #   7   & '7 & ! & '74) # & '74+ ! '75, ! # '74. # '75/  '740 ! '741 # '7 62

VšJ;c AbVA_\5:}XY :?mK#=w}#VU=9;A_}†KXY Ab=9!KXY(Jc A*KR9Ua*:A ) aKXA0Y6J*V0P›A)a0=Y(O5VLADJ;c A_}XAb=VJ;™VMO5=9AbV

?@A0Jc :ª^ 8.6+z98 $,$  PD&Z5::6l f%J;:(a*:?@\ O JA%  P3  =Y5^;7  ‚

ƒ„AUJ;9KXAb^BJ;:`O5VLADcKX<c A09!:9>^A09š\5:}XY :?mK#=w}#V!I O Jš}#=9;<A_O Y A*‘ª\˜Aba*J;Ab^qO Y5^O}#=JKX:Y5VHJ;c A0Y

: a0a*O 9@=V3A0?@\ c5=VWK870Ab^KRY Dš9;:6le W‚‰e™/:9*^A09`\5:n}RY :?mK#=w}UJ;9*=Y5VW~/:9;?(=JLKR:Y5V)<KXTA(=a0a*O 9>=nJ;A

9;A0<nKNVLJ;9>=JKX:Y I O Jq!A =9;A|Y :Jq=I}XA J:ˆ^Aba*:?@\˜:6VAjJ;c A0? KRYJ;:VO5ac KXYJ;OKXJKXTA„\ cªVKNa0= }

?@Ab=nYKRY < J;9>=Y5V~1:9?(=JKX:Y5VS=VS9;:J*=JKX:YPšJ;9>=Y5VW}#=JLKR:YŽ:9 V;a0= }KXY <5‚ U:JK#a*A„J;c5=Jq=JqAb=ac

KXJ;A09>=nJKX:YP!!A‹a*:?@\5:6VLA„J;c AjJ;9>=Y5V~1:9?(=JKX:Y !KXJ;c =e™/:9>^A09q\˜:}X6Y :? KN= } =Y5^ V:5Pš!A

:I J*=wKXY =w~/J;A09<|KXJ;A09>=JLKR:Y5VU=@e



 
  

z!c AmJ;9*=Y5VW~/:9;?(=JLKR:YqK#V3=\ \}†KXAb^PJ;c A0YjJ;c A@=w}X<:9LKRJc ? KRJA09>=J;AbV)=<6=wKXYj:93VJ;:\j=a0a*:9>^KXY <

J;:SVA0TA09>=w}‰a*9KXJ;A09LKN= 

! $ ":@ - *@ 9 "

VL:?@A VLJ>=JK#VJK#a0V-=9;A a*:?@\ O J;Ab^„=I˜:O J3J;c A@^K#VJ>=Y5a*AS^KNVLJ;9KXI O JKX:Y

I5A0J!A0A0Yj?(=J>ac Ab^|\5:KXYJ>V0‚ a0a*:9*^KRY <£~1:9DA*‘5=?@\}XAmJ;:SJ;c Am?@Ab=YjT =w}XO A@:9UKXJ>V)T=™

9K#=JKX:YP!AU?(=w@^AbaK#^A3J;:3KXJ;A09>=nJ;AU:9šJ;: VJ:\‚ _A0TA09;J;c A*}XAbV;V7P6JcKNV!a*9KXJ;A09LKR:Y@K#Vš:Y}X }X:ªa0=w}D=Y5^<A0:?BA0J;9K#a34KXJ-K#V`Y :J`9;A0\ 9;AbVLA0Y6J>=nJKXTA(:n~HJc A(9;Ab= }›9;A0<K#VJ9>=JKX:Y€I5A0J!A0A0Y a*O 9;TAbV0‚ !A-  !9(- *@ 9 " ›A@a0=Y„a*:?B\5=9;A@J;c AmA0T:n}RO JLKR:Y„:~›Jc A@9;A0<K#VJ;9*=JKX:Y„a*:6A )qaKRA0YJ>V    =Y5^    =Y5^SVJ;:\BJ;c A!KXJ;A09>=JLKR:Y5V_c A0Y(J;c A0@=9AVJ*=I}XA,J;c A3a*O 9;TAbV]9;A0<K#VJ;9>=nJKX:Y K#VUJ;c A0YSKXYj=-}X:ªa0=w}s?mKXYKR?mO ?‡‚

!A@$=& > -9 "@  *&

!A@a*:?@\ O J;A@Jc A ?S=J;9K†‘ Y :9;?



 ˜Uc A09;A  K#VkJ;c A

J;9>=Y5V~1:9?(=JKX:Yj=Y5^  J;c A-K#^A0Y6JKXJj?(=J;9LK‘‚z!cK#V3\5=9>=n?@A0J;A09)A0T =w}XO5=J;AbVkJ;c A(^™

Y5=?mK#a0V_:~œJc A)KRJA09>=JKX:Yq\ 9;: a*AbV;V0‚

6 O 9;J;c A09?@:9;APISKRY5a*9A0?@A0Y6JLKRY <SJ;c A-J;c 9;AbVc :}#^£T =w}XO A 

=nJUAb=acSKRJA09>=JKX:YP~/:9!KXY5V™

J>=nY5a*AP~/9;:? qJ;: ‚0£I6ˆVLJ;A0\ˆ:n~ Q‚e,0q=Y5^I„J>=žKXY < :Y}R‹KRY =a0a*:O Y6J-J;c AS?(=J>ac Ab^

\˜:KXY6J`a*:O \}XAbV "

'!I5A*}X:Y <KXY <|J;:@9;A0<K#VJA09;Ab^ja*O 9;TAbV)=J  \5A09*a*A0Y6JbPJc A =w}X<:9LKRJc ? J;A0Y5^ VHJ;:mKX?@\ 9;:TA)J;c A39;A0<K#VJ9>=JKX:Yq:~+=w}X9;Ab=^S?(=J>ac Ab^qa*O 9;TAbVU=nY5^SJ;:@^KNVa0=9>^BK#V:}#=J;Ab^ :Y AbV7‚      6&KX9>VJwP5!A`=\ \}†KXAb^jJ;cK#V)=w}X<:9KXJ;c ? J;:SJ!:@VA0J>V_:~+J;c A3}X:Y <AbVJa*9AbVJU}†KXY AbV3=O J;:?(=JK#a0=w}†}X

A*‘ J;9>=a*JAb^S~/9;:? ’” KX?(=<AbVU:~Jc A VžO}†}NVk:~+J!:(^K†—A09;A0YJ3\5=JKXA0YJ>V0‚˜ƒ„A3KXYKXJK#=w}†K870Ab^€J;c A

Y :Yj9KX<K#^j9A0<K#VJ;9>=JLKR:Y‡I V;a0=w}†KXY <‡Jc A`J!: VžO}†}#V`=J)J;c A V=?@Amc A*KX<c6J`=nY5^‡I‡=w}†KX<YKXY <

J;c A*KX9`a*A0YJ;9;:K#^ V0‚˜ƒ„Ama0=Y‡Y :JLKNa*A-KXYq…5<O 9;A0 "/}XA*~1J '›J;c5=nJUJ;c A`YO ?mI5A093:~s}†KXY AbV3:~+J;c A`J!:

VA0J*V " C 0(=Y5^|’e }KXY AbV%'D=nY5^qJ;c A*KX9`Vc5=\˜A " Y :JK#a*APQKRYj\5=9JK#a*O}N=n9bPJ;c A`Y :VA3'H=n9;A ^K†—A09;A0YJ

=Y5^£J;c5=J!J;c A-J!:mVž6O}†}#V3=9;A`MOKXJ;A VLcK~/J;Ab^‚

7 Y A‹VLA0J(:~3}†KXY AbV K#VSJ;c A0Y©^A*~1:9?@Ab^ J;:„I5Aj9;A0<nKNVLJ;A09;Ab^ !KXJ;c©J;c A VLAba*:Y5^



‚!z&:

A0T=w}XO5=J;ASJ;c A@9;AbVO}XJbP&!A(^K#V\}#=b‹KRY…5<O 9;A 0" 9KX<cJ 'UJ;c AB9;A0<K#VJ;A09;Ab^ }KXY AbVm:n~›J;c A(VLA0J 

=Y5^B:~J;c ADVLA0J „=w~1JA09›^A*~/:9;?(=JLKR:Y‚z!c AD?S=J>ac Ab^m\5:KXYJ>V!=9;A!}†KXY žAb^SI@VA0<?@A0YJ>V0‚z!c A

9;A0<nKNVLJ;9>=JKX:YqJ*=žAbVš}XAbV;V_J;c5=YqJ;c 9A0A3?mKXY6O J;AbV_:Y‡=@”3[ Ÿ ™(_}R\ c5= ›:9;žªVLJ>=JKX:Y‚

z!c A =w}X<:9KXJ;c ? ^A0J;Aba*J>VS=Y5^?S=J>ac AbV(VWKX?mK†}#=9S}†KXY AbV">f&0|}†KRY AbV ' =VBJ;c A‡:9;IKXJ>V0PšJ;c A

  ! "# %$&$(')! * "+, *-.!#/1032/-!

Yq…5<O 9;A g PQ›A`VLc :  "/}XA*~1J 'šJ;c A`9;A0<nKNVLJ;A09;Ab^S}†KXY AbV):~+J;c A VLA0J



=Y5^S:~+J;c AmVA0J ˆY :J

J;9*=Y5VW~/:9;?@Ab^ KXYq:9>^A09UJ;:@ac Aba;žSJ;c A3=a0a*O 9>=a*S:~‰Jc A`=w}X<:9KXJ;c ?‡‚ƒ„A3^K#V\}#=w" 9KX<cJ '+J;c A

^A*~/:9;?(=nJKX:Y‡=\ \}†KXAb^‡J:(=m9;A0<O}#=9_?@AbVc‚

z!c A0YP!A@=\ \}†KXAb^„J;cK#V-^A*~1:9?(=JKX:YjJ;:qJ;c ABUc :}XA(VA0J( :n~Ha*9;AbVJ)}†KXY AbV" 0C6’B}†KXY AbV%'

=Y5^B!AU9;O Y(=n<6=wKXY(Jc AD=w}X<:9KXJ;c ? !KXJ;cSJ;c AUUc :}XA3VA0J  " 0C6’_}†KXY AbV%'>‚ z!c A)9;AbVO}XJ+K#V!MOKXJ;A

KX?@\ 9;AbVVWKXTA"VLA0A)…5<O 9;A(,'5Y A0 VKR? K}#=9H}KXY AbV3=\ \˜Ab=9D=VšJ;c A`ac A0A0žI5:Y AbV0PQJ;c A3J;:\S:~+J;c A ?(=nY5^KRI}XA‚z!c A3\˜:KXY6J*VU?(=nJ>a;cKXY <mK#V)=w}#V:(=a0a*A0\ J*=I}XA‚  -  !
             z!cK#V3=w}X<:9KXJ;c ? K#V!KXJ;A09>=nJKXTA@=Y5^‡a*:YTA09;<AbVUJ;:U=9>^ V_=m}X: a0=w}œ? KRYKX?mO ?‡‚s :5PQKXJ^A0\˜A0Y5^ V :YJ;c AmKXYKXJK#=w}D\5:VWKXJKX:Y–=nY5^P˜KRY€\5=9;JLKNa*O}#=9wPK#VkTA09;„VA0Y5VWKXJKXTASJ;:q9;:J*=JKX:Y5V0‚{V:}XO JKX:Y =V-\ 9;:\5:6VAb^I„I5:JcADAbV}_=nY5^ , c5=nY <‡K#V-J;:jJ;AbVJ-J;c AS?(=J>acKXY < HKRJc =‡VA0Jm:~UKXYKXJK#=w}

\˜:6VWKXJKX:Y5V):~‰Jc A Vc5=\˜A`=Y5^qJ: J*=žA3J;c A3I˜AbVJb‚

ƒ„AUa0=Y@=w}#V:`O5VA!J;c AšKXY A09;JK#=k?@:?@A0YJ>VsJ;:3^:`=_…59>VJa*:6=n9>VA9A0<K#VJ;9>=JLKR:Y›AUa*:?B\ O J;A

J;c A)KXY A09;JLKN=B?(=J9K†‘(:~‰J;c A3J!: VLA0J>V!:~œa*O 9TAbV0PJ;c A0Y‡^K#=<:Y5= }K870A-KXJ!J;:-…5Y5^qJ;c A3\ 9KXY5aKX\5=w}

=w‘K#V0‚3V)!A@c5=wTAm:Y}X„^KR9Aba*JKX:Y5V0Ps!A :I J>=wKXYˆVA0TA09*=w}I5=VWK#V0‚z!c A0Y›AB9;A0<K#VJ;A09`=w}†}!J;c A

I5=VKNVB:~DJc AqJ!:„VA0J>Vm=Y5^€!A‡ac :6:VAqJ;c Aq?(=J*a;cKXY <jUcK#a;c ?mKXYKX?mK870AbVSJ;c A‡^K#VJ>=Y5a*AbV

I˜A0J!A0A0Y|\5:KXYJ>V0‚5z!cK#V_?@A0J;c : ^BK#VUc :!A0TA09UVJK†}†}]VLA0Y5VWKXJKXTA`J;:SVA0TA09;A3: a0a}XO5VWKX:Y5V0‚

ƒ„AUa0=Y@=w}#V:3O5VA!J;c A!Y5=J;O 9>= }QV?@?@A0J9;3:~5:9;<=YK#a:I ZAba*J*V+=VJc AHVLž6O}†} ‚ƒ„AU^A0TA*}X:\

=m?BA0J;c :ª^£J;:-…5Y5^‡=O J:?(=JK#a0=w}†}XqJ;c A`V?@?@A0J9;(\}#=Y AbV 

!

=\ \}X‡=@V?@?@A0J;9 ˆJ;:BJ;c A3:I ZAba*J "/~/:9!A*‘Q=n?@\}XAP  



 '>P

!

9;A0<K#VJ;A09!J;c A3:I ZAba*JU=Y5^ KXJ>VUV?@?@A0J9K#a)!KXJ;cqJ;c A3=w}X<:9KXJ;c ? =nJJ;c A3:9*^A09 "Jc A0YP

KXJ!K#VUTA09 a}X:6VA-:~+J;c A 

Ÿ

8?@A0J;c : ^ '›=Y5^ …5Y5^qJ;c A39KX<K#^£J;9>=Y5VW~/:9;?S=JKX:Y `‚

!

~19:? =Y5^ ›P!^Ab^O5a*A„J;c A„V?@?@A0J9;\}#=Y A‚  Y …5<O 9;A $ Pš!A„Vc : c : J;c A

V;=<KXJ;J*=w}\}#=Y " J;c A)TA09;JK#a0=w}‰V?@?@A0J;9@\}#=Y':~‰Jc A`Vž6O}†}K#VU=nO J;:?(=JLKNa0= }}XB~1:O Y5^‚

D@=w}†KX<YKXY <@J;c A)V6?B?@A0J;9;m\}#=Y AbVš:~Jc AUJ›:3:I ZAba*J*V=Y5^m? KRYKX?mK87*KXY <SJ;c AD^K#VJ>=Y5a*A

I˜A0J!A0A0Y|J;c A3J›:@a*A0YJ;9;:K#^ V0PQ›A3:I J>=wKXY =mMOKRJA`<::ª^BKXYKXJK#=w}†K87b=JKX:Y‚

 
            !    

ƒ„Amc5=wTAmVJ;O5^KXAb^|J;c A@=a0a*O 9>=a*q:~Jc A`J;9>=nY5VW~1:9;?(=JKX:Y‡=a0a*:9>^KXY <qJ;:SJ;c A`:9*^A09b‚WYjJ;c A

7 9>^A09 hqKXY hj=w‘ h|Ab=Y  J>=Y5^ =9*^q”)A0TK#=JKX:Y h‡Ab^K#=Y

 "FšKX<K#^ '  ‚ ’’l 0  ‚e fbe’e f Q‚,0g,0 $# Q‚’,$g ,0  ‚C’g,0#

f "  )(Y A3'  ‚ ’ fbeQf  ‚e  nC6gl Q‚CC9$ 0 Q‚egeeg  ‚’ $ fbg’

e  ‚ ee fwl  ‚Xfb’ll,0g Q‚’ fbel f Q‚e f 3$ f  ‚eeC6’g

zs=I}XA(f, ”_K#VJ>=Y5a*A-I5A0J!A0A0YqJ;c A`?S=J>ac Ab^S\5:KXYJ>VU=a0a*:9*^KRY <SJ;:@Jc A3:9>^A09b‚

=a0a*:9>^KXY < J:`J;c AU:9>^A09  "9KX<K#^(a0=VA3'>P5f#"= )(Y A)a0=VA3'œ=nY5^(e ‚zHc A=I5VaKNVV;= @9;A0\ 9AbVA0Y6J*V

J;c A„^K#VJ>=nY5a*A„I5A0J!A0A0Y©J!:„?S=J>ac Ab^\5:nKRYJ>V" J;c A a*::9>^KXY5=JAbVS:~`J;c AjJ›:€Vž6O}†}#V‡=n9;A

a*:?B\ 9K#VAb^|I5A0J!A0A0Y‡™;f`=Y5^f3'>‚5zHc A`:9>^KXY5=JA !BK#VUJc A`\5A09*a*A0Y6J>=n<A3:~\5=wKX9>V_:~+?(=J>ac Ab^

\˜:KXY6J>V_Uc :6VLA`^KNVLJ>=Y5a*A3K#VHKXY~1A09KX:9)J;: ‚

z!c A3:9>^A09Ue-K#Vš~ =9!I5A0J;JA09UJ;c5=YqJ;c A3:J;c A09>Vš!KXJ;cqJ;cK#V!9;AbVL\5Aba*Jb‚5zHcKNV›KNV)a*:Y…59;?BAb^SI6

J;c A …5<O 9;AbV3:n~›J;c A@J*=I}XA‡f‚z!c A@?BAb=Y„T = }RO ABK#V3J;c A0YC6’
}X:›A09)~/:93J;c AB:9>^A09 eSJc5=Y

:9*^A09DfU=Y5^$Qf J;c5=YmJ;c AU9LKR<nKN^Ba0=VA‚6zHc ADVJ>=Y5^ =n9>^m^A0TK#=JKX:Y KNVš9;AbVL\5Aba*JKXTA*}X(e  =Y5^

 }X: !A09UJc5=YqJ;c A3:9>^A09-f`=Y5^  ‚

   
        

ƒ„A?(=^A„A*‘ \5A09KX?@A0YJ>V|J;:J;AbVLJqJ;c A„9;:I O5VLJ;Y AbV;Vq:n~ :O 9j=w}X<:9KXJ;c ? =a0a*:9>^KXY <ŽJ:J;c A

^K†—A09;A0Y5a*A@:~›V=?@\}†KXY <5‚ƒ„AmV;=?@\}XAmJ;c A@a*O 9;TAbV):n~  IqJ>=žKXY <‡=JD9*=Y5^:? f 0 "'$ =Y5^ ff  "'$ :~›\˜:KXY6J*V0‚ƒ„A(=\ \}XjJ;c A0Y„Jc A 9A0<K#VJ;9>=JLKR:Yˆ=w}X<:9KXJ;c ?|‚ƒ„A@VA0AmKXY„J;c Am…5<O 9;A@l J;c5=nJUJ;c A39;A0<K#VJ9>=JKX:Yq9;A0?S=wKXY5VDa*:c A09A0Y6J!KXYjV\KXJ;A`:~sJ;c A`Y :Y ™/9A0<O}#=9D^AbaKX?(=JKX:Y‚   2'(
# "
 *,  
# 2  '('(
(* +

'_KRTA0Y <VA0J>V!:~+}†KXY AbV0P!A`a0=Y|9;A0<K#VJ;A093=w}†}œJc A VA0J>V_J!: IqJ!:5‚ z!c A0YP5!Ama*:Y5VJ;9;O5a*J)=

Š0VKR? K}#=9LKRJ|<9>=\ c5Œ ! J;c A3Y : ^AbVD=9ADJ;c A)}†KXY AbV   Uc A09;AsK#V_J;c A3YO ? I˜A09U:~+J;c A`VA0JU=Y5^@J;c A)KXY5^A*‘‡:~ J;c A)}†KXY A`KXY|J;c A`VA0J  P ! J;c A3TA09;JLKNa*AbV_9;A0\ 9;AbVLA0Y6JUJc A39;A*}#=JKX:Y–Š>KNV_9;A0<K#VJA09;Ab^S!KXJ;c5Œ ‚ U:`P˜!A(VAb=9>ac|~1:93J;c A@a*:Y Y Aba*J;Ab^\5=9;J>V):~!J;cK#V3<9*=\ c„Vc5=9KXY < =nJU}XAb=VJm=B}†KRY AS:~

Ab=ac‡VA0Jb‚ -UA0Y5a*APQ›A3^A0J;A09;? KRY A-J;c A3VO I5VA0J>Vš:~œVKR? K}#=9_}†KXY AbVUJ;c5=nJ›a*:?@\˜:6VA3J;c A@Š0=JL}N=V;Œ ‚

ƒ„A@c5=wTAmA*‘ª\˜A09KXA0Y5a*Ab^J;cK#Vk?@A0J;c : ^j!KXJ;c„J;c 9A0A(VA0J>Vk:~Ha*9;AbVLJ3}†KXY AbV`A*‘ J;9>=a*J;Ab^|~/9;:?

  ! "# %$&$(')! * "+, *-.!#/1032/-!

VWKX?mK†}#=9_}†KRY AbV3=nY5^q=Vš›A)}#=I˜A*}†}RAb^jV:?@A)}†KRY AbV_:~‰:Y A`VA0JbP!A`a0=YqAbVJKX?(=JADJ;c A39A*}RA0T=Y5a*A

:~sJ;c A`VO I5VA0J>V]KXYS…5<O 9;Amf  ‚_:JK#a*A)J;c5=JU=mVO I5VA0J!?(=w@I5A`a*:?@\5:6VLAb^@:~+VA0TA09>=w}˜}†KRY AbV_:~

J;c AmV;=?@A`VLA0J "/~/:9!A*‘Q=?B\}RAPQJ;c 9;A0A3}†KXY AbV_?(=žA3O \|J;c A39KX<cJUJ;A0?@\}XA`:n~œJ;c A)…59*VJDVžO}†}'*‚

 * # '( 
*

WY JcKNV_\5=\˜A09bP5!A-c5=bTA`\ 9;AbVA0YJ;Ab^|V:?@A-TA09;SA0Y5a*:O 9>=<KXY <q9;AbVLO}RJ*VD=I˜:O J)J;c A =O J:?(=™

JK#a0=w}†}XqI OK†}#^KRY <j=Y5^BO5VA3:~œ=Y‡=nY5=J;:?mK#a0=w}‰=JL}N=V0‚U:`P›A3=9;A`VLJ;O5^KXY <@Jc A`=bTA09>=<KXY < =w}X<:9KXJ;c ? KRYS:9>^A09šJ;:`\ 9:ª^O5a*A3=)…59>VLJ›=J}#=V]:~J;c A3a*9;AbVJ+}†KXY AbV!:~J;c A)Vž6O}†}!KXJ;cq=)}#=9;<A09 ^ =J*=I5=VAS:~V;=nY A‡=Y5^„\5=nJ;c :}X:<K#a0=w}D\5=nJKXA0Y6J>V7‚‰ƒA(U=YJ@=w}#V:jJ;:„^A0TA*}X:\ =„VJ>=nJK#VJK#a0=w} =Y5= }R VWK#V-:~J;c A@T=9K#=JKX:Y5V-=V_KXY  Ÿ -)z-)l’& ‚z!c A@Y A*‘ J`VJ;A0\jK#V3Jc A`KXYJ;A0<9>=nJKX:Y„:~J;cK#V

=JL}N=V)KXY6J:‡J;c A(a*9*=YKX:~ =aKN= }HVO 9;<A09;„VWKX? O}#=JLKR:YˆJ;AbVLJ;I5Ab^:~›:O 9`\ 9;:ZAba*Jb‚ƒA@\}#=Y–= }NVL:

J;:|O5VA@J;c ABUc :}XA Va;c A0?@ABJ;:qI OK†}N^=nYˆ=J}#=V):~UJ;c ASa*:Y6T:}XO JKX:Y5V3:~UJ;c ABI 9>=wKXYˆ=Y5^J;:

a*:?B\5=9;A)KXJDHKRJcqJ;c A =JL}N=VI˜:6:ž 

7

* l 3 ‚

 #
,*  '+  */

z!cK#V]›:9;žDU=V&\5=9;JLKN= }}X@VO \ \˜:9;J;Ab^-I ”_KX<KXJ>=w}5[MOKX\ ?@A0Y6J Ÿ :9;\˜:9>=JLKR:Y =Y5^-J;c AU[VL\ 9KXJ

[]O 9;:\5Ab=nY@\ 9;:ZAba*JD9*=™ 8UKXT= ‚ƒ„AUJ;c5=nY ž 'DA0Y A09>=w}X™[œ}RAba*J9K#aD=Y5^D9O5a*A &=JKX?@A09bP”_KX9;Aba*J;:9

=J+Jc A Ÿ }RA0TA*}N=nY5^@h|O5VA0O ? :~ )=J;O 9*=w} -HKNVLJ;:9;P Ÿ :O 9;J Ÿ O J;JKXY <5P”3=wTK#^-”)Ab=Y@=Y5^ DY5^9A

')OA 7*KXAba!~/:9+J;c A

Ÿ

z!™ 6a0=nY(^ =J>=k:~J;c A3VžO}†}NV7‚ =a0MO AbV;6 A*}#^?(=9!<6=wTAU=-VO I5VJ>=YJK#=w}c A*}R\

.  * # 

 'z : l’3 -‚?)6=ac AP.m‚+')OA 7*KXAbaP ‚8s‚›z!cKX9KX:YP;m‚ '):O 9>^:YP=nY5^ ‚+*)Y :\}†KX:ªac‚

[]T =w}XO5=JLKRY <„’”•F!A0<K#VJ;9>=nJKX:Yˆ:n~ Ÿ z!™ 6a0=Y ?S=<AbV
)VWKXY < Ÿ 9;AbVJ ˜KXY AbV0‚Y ”3=wTK#^ Ÿ

‚ ƒ K†}NVL:Y =Y5^£ƒ K}#V:Y :6VLA0\ c -‚XPAb^KRJ:9>V0P

@" >?@ "-   @"  / "    "-  >?C& * C  

P˜\5=<AbV)el6CC5P˜ 6=Y ”_KXA0<:5P Ÿ =w}†K†~1:9YKN="
3 , '>P

O}R„fwll’ ‚˜ 68?[U‚

)6=l’3 HK#a;c :n}N=V?)6=ac A‚8+:}XO ?@A ?(=<AH8]9;: a*AbV;VWKXY <5‚6FHAbVO}XJ>V!=Y5^mF!AbVAb=9>ac Ÿ c5= }R™

}XA0Y <AbV7‚zAbac YK#a0=w}F!A0\5:9Je  0  P  )F  mP& A0\ J;A0?mI5A09mfbll’ ‚

D Ÿ $ $3 6Q9;Ab^ +‚Dš::ž VJ;A*KXY =Y5^ Ÿ :O 9;J D)‚ Ÿ O J;JKXY <5‚3€\ 9;:\˜:6V;=w}~1:9J;c A=n\ \ 9;A0c A0Y5VWKX:Y

:n~a*O 9;TKXY < a*9*=Y :~=aK#=w} ~1:9;? KXY(J;c 9A0AD^KX?@A0Y5VWKX:Y5V0‚WY *m‚8_KX< =nY5^  ‚DšO 9>^KP

Ab^KXJ;:9>V0P   $=&- "   $ ! C&:.=  &:  29>? $ ! C&:.=  P\5=<AbV@fwe# f7C ‚fbl,$,$Q‚

D Ÿ F_l’3 8_K#a;žK D9O5a*AP DY Y A Ÿ :6:?mI˜AbV0P =nY5^ FH:IKXY FšK#a;c5=n9>^ V0‚ ”)AbV;a*9LKRIKXY < J;c A

VLc5=\5AbV):~+~ =a*AbV_O5VWKXY <‡VO 9~ =a*A`\ 9LKR? KRJLKRTAbV0‚

 >?C& : 8  *  &> $<!@ "!C P ff3"g '5’,0’ª’g’QP3DO <O5VLJ`fbll’Q‚ D&Z5::6l f  d

 D&Z ::9*a;ž‚ U}X<:9LKRJc ?(V&~1:9 ˜KXY Ab=9 Ab=VJ! 6MO5=n9;AbV+8+9;:I}RA0?SV0‚ Y@[]?mK†}KX:S \5A0™

^K#a0=J:5PAb^KRJ:9bP

> $  @  0,%C *@" > )$ !9 * C ": 0,%C . *- /

@ "  @"!?<@@ ? $ @"! 0,@

P\5=<AbV0 ªle ‚˜ \ 9KXY <A09™ 8+A09}#=<5Psfbll f‚

D!hjle3 8+=nO} ‚DšAbVW}`=Y5^ _A*K†}k”m‚!hja *3=w‚  h|A0J;c : ^€~/:9(F!A0<nKNVLJ;9>=JKX:Y :~`’™”

 c5=n\5AbV0‚

  0





P5f0C"e '5e’lªe30,0 P,6QA0I 9;O5=9;jfblleQ‚

Dš9;:le3 KNV= 'D:J;JAbVW~1A*}#^ Dš9;:UY‚   O 9;TA0 :~  ?(=<A F!A0<K#VJ9>=JKX:Y z&Abac YKNMO AbV0‚

0

 !

&> $<!@ "!C   !29

P eC" C'%’e,0 ’# g P”)Aba*A0?mI5A09mfblle ‚

D_     9$g  Ÿ ‚5hj=9>a D!=VLJ;O5V;ac Aba;žP[š^KXJ;c€ 6a;c :YI5A09<5P =a*:Ijz3‚& 6a;cU=9;JC7P5=nY5^ h£K#ac5=

 c5=n9KX9b‚ 7 I ZAba*JU9;Aba*:<YKRJLKR:Y‡I(J;c 9A0A0™ ^KR?BA0Y5VWKX:Y5=w}›a*O 9;TA3?S=J>acKRY <˜‚  :@9   @ ":    8 $" :@9*# #C @ <29=@ 9>  Pf,Xf  0fb’eQP fbl,$g ‚ Ÿ D -:

l’3 Ÿ :O 9;J,DD‚ Ÿ O J;JLKRY <˜P6 9;Ab^ +‚ Dš:6:ž VJ;A*KXYP DšA0J>V-D=^ ^ =^P”3=wTK#^‡”)Ab=nYP=Y5^

”3=wTK#^(*)O ?‡‚ V\}†KXY A0™/I5=VAb^ =n\ \ 9;:6=acj~/:9@=bTA09>=<KXY <‡Jc 9;A0A0™^KX?@A0Y5VWKX:Y5=w}

a*O 9TAbV!=Y5^(VLO 9~ =a*AbV0‚WY‡”3=bTK#^ Ÿ ‚6ƒ K†}#V:Y‡=Y5^Sƒ K†}#V:Y :VA0\ c`‚NPAb^KXJ;:9>V7P

 @"!9> &@ *-  @"  / "    *-> 9C "!C#$   P!\5=n<AbV(el6CC5PH 6=Y ”_KXA0<:˜P Ÿ

  ! "# %$&$(')! * "+, *-.!#/1032/-!  Ÿ -Dz-)l’3‡zk‚6!‚ Ÿ ::J;AbV7Pm‚.-!K†}†} P Ÿ

‚ ‚+z‰=w}X:9bP+=Y5^ ‚.-)=VW}#=?‡‚€z!c A
)VAq:~ a*JKXTA

 c5=n\5Ah‡: ^A*}#V 6 :9 : a0=JKXY <  J;9;O5a*J;O 9AbVqKXY h|Ab^K#a0=w} ?(=n<AbV0‚ WY --‚--‚

D!=99;A0J;J(=Y5^  ‚6!‚ 'D?mKXJ;9;:˜PAb^KXJ;:9*V0P

  $>?@ *&  - * C "



  "- 

> 9C "!C

Ps\5=<AbV(’’ 6C6P?6&}#=<6VJ*=w—P )9K870:Y5= "%
k , '>P OKXY fwll’ ‚?8hl’ P

 \ 9LKRY <A09;™8+A09}#=<5‚

”-  Ÿ+ lC, -_A09;T Am”)A*}KXY <A0JJ;AP)'A09>=9>^| O I5V:n} P] JA0\ c5=nY A Ÿ :JLKRYP=nY5^ 8œKX<Y :Y A09 :?@A‚

 Ÿ 9>=YKX:~ =aK#=w}+ O 9;<A09;£ KR?mO}#=JKX:YjzAbVLJ;I5Ab^‚+z&Aba;c YK#a0=w}œFHA0\5:9;J)e fbll P3 U™

F  mP :\ cK#=™()Y6JKX\˜:}†KNV " 6 9*=Y5a*A3'>P6 A0I 9;O5=n9;„fbllC˜‚

6 3lC, =a0MO AbV6 A*}#^?(=9@=Y5^HK#a;c :}#=V D6=a;c A‚„FšKX<K#^ =Y5^ )SY A F!A0<nKNVLJ;9>=JKX:Y

:n~› ?@::J;c O 9~=a*AbVUO5VKRY <‡”_K†—A09;A0YJK#=w}œ8]9;:\5A09JKXAbV0‚WY     P J;:ªažc :}X? " ›Ab^A0Y'*Pªhj=wjfbllC5‚[ ŸUŸ 8 ‚z&:(=\ \˜Ab=9b‚

6+hj8 3le3 ”)A0YK#V 6Q9KXI5:O}XA0JbP#V;=I˜A*}†}RA [_‚hj=<YKRYP#DY5^9;Ab=V„8s:?@?@A09JbPD=Y5^ h£K#ac A*}

)?mKXA*} ‚q’” Ÿ O 9;T=J;O 9;A6QAb=J;O 9;AbVk:~UJ;c A A*~/J8+A0YJ;9K#a}XA@~/9;:? Ÿ z 8+:}XO ?mK#a

W?(=<AbV7‚Y   $> &@ *  -= "!C *    *- > 9C "!C P˜\5=<AbV-f $e fble ‚ 8hle PfblleQ‚

' le3 m‚ 'DOA 7*KXAba„=Y5^ -‚)6=ac A‚  ?@::J;cKXY <Ž=Y5^ h =nJ>a;cKXY < :~ ’™ ”  \5=a*A

Ÿ O 9;TAbV0‚WY  = # 
@ " * ">?  "-  &> $<!@ "!C P\5=<AbV+e 0lªe#’ P Ÿ c5=™ \˜A*} -HK}†} P_:9;J;c Ÿ =n9;:}†KXY5= "%
k , '>P 7 a*J;:I5A09-fblle ‚˜ 68 [U‚

'):6VC$,$  )9>^AbVcKX9'D:Vc6J*=VI‚ ?S=<A(F!A0<nKNVLJ;9>=JKX:Y€I :ªa0=w} D\ \ 9:b‘KX?(=JKX:Yh|A0™

Jc :ª^ V0‚  >?C&?:   "  &> $<!@ "!C P5g " C'%e,0,0 eg fP!U:TA0?mI˜A09`fbl,$,$Q‚ -_:6V;le3 h€‚-_:6V;=nž = ‚  9 # "!C  $    !9   $- "  0  0 j‚! \ 9KXY <A09;™ 8+A09L}N=n<5Pfblle ‚

h )F : l f  ')A09>=w}#^`‚3hj=<OKX9;AP)h =n9K†}RY [U‚ _:,7P -_A0Y 9; F!O5VWKXY A0žP O5^KXJ;c =A0<A09wP

[œ}†KNVV;=+‚)*)9>=?@A09wP :6VA0\ c ‚+ 6=nY <A09bP=Y5^ 'D!A0Y Y€ ?mKXJ;c‚ 'D9>=n\ cKNa0V#D\ ™

\}†KXAb^jJ;:‡h|Ab^K#a0=w}.W?(=<A@F!A0<K#VJ9>=JKX:Y‚   > $  @ $: *-. 0 $: $<I "-@ *& P\5=<AbV_e ªe#Pªhj=9*a;cjfbll f‚

7 * 3l 3 h£K#acKR: 7 Y :˜Ps J;A*~ =nY *)O IKXžP=Y5^ Ÿ c5=^j”m‚ DI˜A09;Y5=J;c A0‚

0,@#/  $ @"!   /  #- ‚')A0:9;<(zHcKRA0?BA8+A09}#=<5P&fbll  ‚ 8sA09%$’3 [š^O5=9>^q8sA09;Y ž:\~L‚ 0,@#/  @ >? "  !>? ": ‚›8œKNa0aKXYPsfbl,$’Q‚

8;6+z98 $,$3 ƒ K†}†}†KN=n? -`‚8+9;AbVV0PDš9K#=Y 8s‚ 6&}N=nY Y A09;P˜ 6=O} m‚6z&A0O ž:}#VžP =Y5^mƒ K†}}†K#=? zk‚

8+A0JJ;A0YKXY <5‚ +  >? *- - $. "   ' ! 0,@, $ <- " @  - &> $<!@ "!C ‚ Ÿ =?mI 9K#^<A
UYKXTA09*VWKXJ‡8]9;AbV;V0Pfbl $,$ ‚

† !D+* :+le  'm‚s ,7 A0žA*}XP Ÿ c‚ D9Aba;cI :O c}XA09bP 7 ‚ *:O I}XA09bP+F3‚ 7 <YKXA0!K#a%7P=nY5^„z3‚8DšO5^KXY ™

<A09b‚‰hj=\ \KXY <SJ;c A3c6O ?S=Y a*A09A0I 9>=w}œa*:9J;A*‘(O5VWKXY <q’” ?BAb^KN= }‰?(=YK†~/:}#^ V0‚?Y

F›KNac5=9>^ m‚ F!:I IP Ab^KXJ;:9bP

8 = #
=@ " *  ">?  *-



> $  @ "!C P\5=<AbV

fw’ f0CC5P Ÿ c5=\˜A*} -HK†}} PU:9;J;c Ÿ =9:}†KRY5= "%
k , '*P 7 a*J:I5A09mfblleQ‚5 68 [_‚

† 9-)8

:

l’3 Fk‚ 6ac6O I˜A09;JbP *m‚ --‚,-::c Y AP3 ‚8s:?@?@A09JbP h€‚FšKXA0?@A09bPz!c‚ 6acKXA0?(=Y YP=Y5^

-‚zšKXAb^A‚& \5=JK#=w} *)Y :!}XAb^<A)F!A0\ 9;AbVA0YJ>=JKX:Y ~1:9 8_K#VO5=w}†K87b=JKX:Yq:~-UO ?S=Y

)Y5=J;:? 3=Y5^ 6 O Y5a*JKX:Y‚WY --‚--‚ D!=9;9A0J;J‰=Y5^ m‚6!‚ 'D? KRJ9;:5P0Ab^KXJ;:9*V0P  $ 

>?@ "? -= "!C "



  "-   >?C "!C

P0\5=<AbVšfbg,$f $ fP 6&}#=<6VJ*=w—P D9LK70:Y5=

"
3 , '>P O Y A(fwll’ ‚ 8šhl’QP5 \ 9LKRY <A09;™8+A09}#=<5‚

† 6h$#& =a*:I`z3‚ 6acH=n9;JC7=Y5^- c5=9LKR9+h£K#a;c5= ‚ ^A0YJK†…a0=JKX:Ym:~58+=9;JK#=w}†}X

7

I5V;a*O 9;Ab^

7

IQZAba*J>V›KRYjz!!:@=Y5^‡z!c 9A0A ”_KX?@A0Y5VWKX:Y5V_I6qhj=J>acKXY < U:nKNVL

Ÿ c5=9>=a*JA09K#V™ JLKNa Ÿ O 9TAbV0‚ ')! :@ :&@ * <    $ ! @ *- .=- P5g "e '%el6CC5P  O ?B?@A09`fbl,$ 6‚

z 'l’3 ‚8s‚z!cKX9KX:Y =Y5^2m‚&'D:O 9>^:Y‚Žz!c A„hj=9>acKXY < KRY AbV _}X<:9KXJ;c ? šY A0

9AbVO}XJ>VU=Y5^£\ 9;:6:n~V0‚+z&Aba;c YK#a0=w}F!A0\˜:9;J`f $ $ fP  )F mPh =n9>a;c„fwll’ ‚

zHcKNl’3 ‚8s‚z!cKX9KX:Y‚ _A0 ~/Ab=J;O 9A \˜:KXY6J*V)I5=VAb^j:Yj<A0:?@A0J;9K#akKXY6T=9K#=YJ>V)~/:93’”

KX?(=n<A39;A0<K#VJ;9*=JKX:Y‚+zAbac YK#a0=w}F!A0\5:9J fbl  fP  )F mPh =w‡fwll’ ‚ z_z$,$3 Ab=Y zs=w}#=wKX9>=acq=Y5^@8sKXA09;9Az&:O 9;Y :O‘‚ / #  <@@
"- 0,@#/1 $ @"!   > &   " ‚ 'DA0:9;<(z!cKXA0?@A 8+A09}#=<5Pfbl $,$ ‚  , c5=le=3 , c A0Y <:O , c5=Y <5‚WJ;A09>=JLKRTA`8s:KXY6J!h =nJ>a;cKXY <m~/:9!F!A0<K#VJ;9>=nJKX:Yq:~~19A0A0™$~1:9? a*O 9TAbV0‚+zAbac YK#a0=w}F!A0\5:9J fbg 0,$ P  )F  mP D\ 9K†}›fwlle ‚  , c5=leI , c A0Y <:O ,

c5=Y <5‚ 7 Y :ªa0= }khj=J>acKXY <:~ 6Q9;A0A0™ 6 :9;? Ÿ O 9;TAbV0‚ WY ”3=™

TK#^-U:<< =Y5^qFH:<A09 Dš: }XAPAb^KRJ:9>V0P

  "@    -.! ":$ = "   $=9:- P

\5=n<AbVD’nCª’,0g P A0Ab^ V "%
UYKXJ;Ab^ *_KXY <6^:? '>Ps A0\ J;A0?mI5A09Sfblle ‚ D9LKRJLKNVLcˆhj=™

Unite´ de recherche INRIA Lorraine, Technoˆpole de Nancy-Brabois, Campus scientifique,

615 rue de Jardin Botanique, BP 101, 54600 VILLERS LE

` S NANCY

Unite´ de recherche INRIA Rennes, IRISA, Campus universitaire de Beaulieu, 35042 RENNES Cedex

Unite´ de recherche INRIA Rhoˆne-Alpes, 46 avenue Fe´lix Viallet, 38031 GRENOBLE Cedex 1

Unite´ de recherche INRIA Rocquencourt, Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex

Unite´ de recherche INRIA Sophia-Antipolis, 2004 route des Lucioles, BP 93, 06902 SOPHIA-ANTIPOLIS Cedex

E

´ diteur

INRIA, Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex (France)

ISSN 0249-6399

6&KX<O 9;A0   $=@
')! #!C&@-9;.=@ # *   $?@"! @ % (
 ",.$ "> $/  IC !@
;C&  @@ "  $, "> "#,# * , $@ ,@"! & $ >?@ "  6&KX<O 9;Ajg  $@
C =@ @ "A $(= ">? *#(# ": * @"!9 *( #C ": $/ *@ "  IC !@
' ! C =@ @ "  $>?@ *&B=$$ # * (@ (;C #,>? 

6&KX<O 9;A+9 ;C& @@ *&B $ @ %  % !#?@"  $ -.=@ I ":.  $@ & $ >?@ "  +,@ *- @"!

Graph 1: Distribution function of the distance between matched points

Order 2

Order 1: (Affine)

Order 0: (Rigid)

Y

-3

X x 10

0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

80.00

90.00

100.00

0.00

50.00

100.00

150.00

200.00

6&KX<O 9;A|f  0, @>?@ "-(I  9*# "!C( $ @"!   1 @ 
 * 
  $@ =. *@"  IC !@  "@"  '   $@3':> $ # ,' #C/!@':> $ #      '  $@ @, $ @"  >?  #  @@ &>  $
/    ' IC !@   @  $ @"!(>?:  #  @@ &> $
      $@  !      IC !@  !   :.  >?9 -- $ *@&I.8+ +,/=