Robust Matching by Partial Correlation

(1)

HAL Id: inria-00074047

https://hal.inria.fr/inria-00074047

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- lished or not. The documents may come from teaching and research institutions in France or

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires

Zhong-Dan Lan, Roger Mohr

To cite this version:

Zhong-Dan Lan, Roger Mohr. Robust Matching by Partial Correlation. [Research Report] RR-2643, INRIA. 1995. �inria-00074047�

(2)

)

(3)

a p p o r t

d e r e c h e r c h e

1995

Robust matching by partial correlation

Lan, Zhong-Dan / Mohr, Roger

N RR-2643

Août 1995

PROGRAMME 4

Robotique, image et vision

(4)

(*),+-/.1023+4,576)8+:9<;=230>?-@234BA?>

CED7F8G3DH8IIJLKNMPOF3QRF,STVUXWBJ8YTZI[H?G8J\J]S ^3TV_TVF3`

CEDaF,bcJ]Sdfe g'h'ikj]F3I[INF3`[SlFnm oO pYqhroO htsuYhroCEvwH8`Bxzy#{8|E}

O H8~R~F3DaSxRJDaJ]j]BJDajBJ`'3O#O&c8?K3NMsF*WBS8,'M R~RH?G,J]_

<]q?8gT_WRH?j]F3DlDaJ]_~RFB`BxRJ`Bj]J~RDaF3QBVJI itI[H?Sj]BTZ`BG3}]Y TV_!H8`:I[H?baF3DT_l_WBJfTZ`^BTV_TVF3`dfH?Sj]BTZ`BG

jH8`!QRJxRT^BTVxRJ]xTZ` #" #]¡ 3 #¢H8`Bx #"?¡ 3 #¢[I[H£SjBTZ`BGqhr`¤H8DaJHcQRH?_lJ]xqI[H?Sj]BTZ`BGqYj]F3DDaJ]ZH?SlTFB`¥TV_H

j]F3I[INF3`¦SF3F,§¨F3DSBJu^BTV_WRH?&j]F3DDaJ]_~F3`BxRJ`Bj]J<~RDaF3QBVJI<n©WBSIF,_S'j]ZH?__TVjH?&j]F3DDaJ]ZH?STVF3`¤IJ]SBFBxR_'§rH?TV

`BJH8DSBJ<xRTV_~RH8DaTVSaª«xRTV_j]FB`8STZ`BWBTVScª8Y#¬LBTVjF3j]jWRD7_®H?SSBJzQF3WR`BxqH8DaTVJ]_<F?§'F3QBbaJ]j]S_«h¯`°SBTV_®DaJ~F3DaSY&¬J

~RDaF3~F8_JH ""$#% & '[SJ]j]R`BTVUXWBJ§±F3D_lF8V^3TZ`BG<SBTV_~RDaF3QBVJI<²fJWB_J[H[DaF3QRWB_lSL_SH?STV_STVj]_SFBF81SlF

³

`Bx!SBJ %¢ " *SlF®QJuj]FB`B_TVxRJDaJ]x!§±F3DLH,~R~BªBTZ`BG¥j]F3DlDaJ]ZH?STVF3`Y²fJRH^,Juj]FBI[~RH8DaJ]x¦F3WRD'IJ]SBFBx¥¬ TVS

SBJ'_SH8`BxqH8Dax¥H8`Bx¥`BFB`<_SH,`BxqH8Dax<SJ]j]R`BTVUXWBJ]_´"µR~RJD7T¶INJ`8SH£*DaJ]_WBVS_^·H?VTVxqH?SJ\SBJH8~R~RDaFBH?j

¸<¹Bº1»a¼½?¾8f^BTV_TVF3`YI[H?Sj]BTZ`BGqYBj]F3DDaJ]ZH?STVF3`YDaF3QRWB_lS`BJ]__YBFBj]j]¶WB_lTFB`

¿¨ÀÁ

ÂaÃaÄÅ

Á

Â"Æ"Ç¶ÃcÈkÉÊ

Ë

Unité de recherche INRIA Rhône-Alpes

46 avenue Félix Viallet, 38031 GRENOBLE Cedex 1 (France)

(5)

¹X ¹ H,~R~RH8DaTVJIJ`,SJ`,SDaJ[xRJWBµfTZI[H£G8J]_J]_SWR`BJ[j]J[xRJ<`BF3IQRDaJWBµf~RDaF3QBJIJ]_'xRJ®~JDaj]J~BSTVF3`Y

J` ~RH8DaSlTjWBVTVJDj]J]¶WBT#xRJ<¶H!~JDaj]J~BSTVF3` _lSJDJ]F8_j]F3~BTVURWBJ8*mJ<~RDaF3QBJIJnJ]_lSuJ]_l_J`8SlTJ]VVJIJ`,S¥H8QRFBDaxJn~RH,D

xRJWBµ[SaªR~RJ]_xH8~R~RDaFBj]BJ]_Y8j]J]VVJuQRH?_J_WRD&WBSTVVT_H?STVF3` xRJ]_jH8DH?j]SJDaTV_STVURWBJ]_Ej]F3IIJLVJ]_j]F3`,SF3WRDa_Y8J]SEj]J]VVJ

QRH?_J_WRD"ZHINT_lJLJ`j]FBDDaJ]_~F3`BxqH8`Bj]JxWR`BJL~RH8DaSlTJ#xqW[_TVG3`RH£¨1H'j]FBDDJ]ZH?SlTFB`J]_lSEF3WBSTVJ'~BZWB_j]F3I[IWR`

~RFBWRD"ZH'_J]j]FB`Bx[jH?SJ]G8F3DaTVJ8d H£T_"VJ]_ H8~R~RDaFBj]BJ]_Ej]ZH?__TVURWBJ]_xRJ ZH'j]F3DDJ]ZH?STVF3`F3`8S"xRJ]_&xRTnjWBVSJ]J]_ ~RDJ]_*xRJ]_

xRTV_j]F3`,STZ`3WBTVSJ]_ URWBT1_J~RDJ]_J`8SlJ`8SH\ZHVT¶INTSlJuxRJ]_#F3QBbaJ]S_F3j]jWBVSH8`,S_H8`B_j]JDH8~R~RFBDaSYR`BF3WB_L~RDaFB~RF8_FB`B_

WR`BJSlJ]jR`BTVURWBJnQRH8~BSTV_J]J " # & # &#L~RFBWRDLDJ]_F3WBxqDaJ'j]J~RDaF3QBJINJ8qo FBWB_ WBSTVVTV_F3`B_WR`<F3WBSTV1xRJ

ZH _SH?SlT_lSTVUXWBJ[DaF3QRWB_lSJ[~RF3WRDSD7F3WB^8JD#¶H # " '#xRJ]_§¨J` J]SDaJ]_!H j]F3DlD"J]VJD]o FBWB_ H^8F3`B_j]F3I[~RH,D"J

`BF8SD7JNI#J]SBFBxRJ[H^,J]juVJ]_I$J]SBFBxRJ]_'_SH,`BxqH8DaxR_'J]S'VJ]_[I$J]SBFBxRJ]_'~B¶WB_[DaFBQRWB_SJ]_%'J]_'J]µR~&JDaTZIJ`,SH?SlTFB`B_

^·H£TVxRJ`,S'ZH[I#J]SBF3xRJ8

' ½q »)(*¹ =^BT_lTFB`YH8~R~RH,DaTVJIJ`8SYRj]F3DDJ]ZH?STVF3`YqDaFBQRWB_SJ]__J8YBFBj]jWBVSH?STVF3`

(6)

:' $

½1¾ %?½

¹(R]¹R¾:¼½

R mFBDDaJ]ZH?STVF3`<H8`Bx<TZI[H£G8JSDlH8`B_a§±F3DI_

R O H,`nH8`Bx¦j]J`B_WB_SDH8`B_a§±F3DI8

R sIFBxRT³ jH£STVF3`<F?§1H8QBTZ%_H8~R~RDaF3H?j]

q ( ?½?¹(ZR½

R e'WRD ~RH,DaSTZH?1j]F3DlDaJ]ZH?STVF3`<IFBxRJ]

R OFBQRWB_S J]_STZI[H£SF3D&§±F3D&VT¶`BJH,D'DaJ]G3DaJ]__lTFB`

RRZ BJ\jRH£VJ`BG8J\F?§"F3WBSVTVJDa_!

RR OFBQRWB_S D7J]G3DaJ]__TVF3`" ,

#%$'&

¹R(!¹

] (¹R*(Z

¾:¾'k%½ )

Kq ´/µXH8I~BJ]_*

Kq pBSH£STV_STVj]_LDaJ]_WBVS_

Kq 'TV_jWB__lTFB`B_+

,½

(1½

¾.- *%¹¦¼u½

)/

(7)

1

BJ^BT_WRH?Ej]F3DlDaJ]_~RFB`BxRJ`Bj]Jn~RDaF3QBVJI<YT±J8I[H?Sj]BTZ`BG¥QRJ]Sa¬J]J`¥Sa¬F T¶IH?G8J]_'TV_uH8`!I[H£bcFBDSH?_ TZ`!^3TV_TVF3`

Z]KcY cY cY3H?_&TVS WR`BxRJD7TVJ]_ SBJLj]F3I~RWBSH?STVF3`F?§*IF8STVF3`¦i±IF8STVF3`I[H?Sj]BTZ`BG3}EH8`Bx SBJj]F3I[~RWBSH£STVF3`F?§

_SJD7J]F'xRJ~BS¥ik_SlJDaJ]FI[H?Sj]BTZ`BG3}]8vT^,J`Sa¬ FTZI[H?G8J]_"F£§%H'_H8IJ_j]J`BJ8Y3H'~BTVµBJ]qTZ`F3`BJ#T¶IH?G8J j]F3DlDaJ]_~RFB`BxR_

SF¥H<~BTVµBJ] TZ`!SBJ[F8SBJDF3`BJT§ SBJ]ªfH8D7JN~RD7F8baJ]j]STVF3`B_uH?VF3`BG¦VT¶`BJ]_F?§_TVG3,SF?§SBJ[_H8INJN~R,ªB_TVjH?E_j]J`BJ

J]VJIJ`,S*h¨§ SBJ]ª H,DaJ[SJI[~F3DH?VVª!j]F3`B_J]jWBSTV^8J8YSBJ` SBJ[j]F3I[~RWBSH?STVF3`¦F?§ j]F3DDaJ]_~RF3`BxRJ`Bj]J xRJ]SJDITZ`BJ]_

IF8SlTFB`qhk§"SBJ]ª<H8DaJ'_~RH?SlT¶H£Vª<_J~RH,DH?SJ]x¥QRWBS_TZIWBSH8`BJ]F3WB_YRSBJ`<SBJ'j]F3I~RWBSH?STVF3` F?§"j]F3DD7J]_~RF3`BxRJ`Bj]J

xRJ]SJDINT¶`BJ]__SJD7J]F[xRTV_~RH8DaTVSaª8

dfH?SljBTZ`BG[jH8`<QJxRT^BTVxRJ]x!T¶`¦H8DaJH[QRH£_J]xzI[H£SjBTZ`BG<H8`Bx §±JH?SWRDaJQRH?_lJ]xzI[H?SljBTZ`BGfik_J]J§±F3DTZ`B_SH8`Bj]J

H8`Bx TZ` SBJ<jH?_J<F?§L_lSJDaJ]F?r^BTV_TVF3`R}] RD7J]J<ScªR~RJ]_F?§ IJ]SBFBxR_nRH^8J¥QJ]J`«WB_J]x=§±F3DH8DaJHfQRH£_J]x

I[H?SljBTZ`BG

F3~BSTVjH?qF?¬

|qF3WRDaTVJDSDH8`B_a§±F3DI[H£STVF3` 8

j]F3DDaJ]ZH?STVF3`

hr`¤SBTV_[DaJ~RFBDaSY1¬J[TZ`,^8J]_STVG3H£SJnFB`Bª¤SBJ[SBTZDax IJ]SBFBx1*CJ]F3~BVJ<TZ`,SJDaJ]_SJ]x=TZ`fSBJ[Sa¬ F!~RDaJ]^BTFBWB_uFB`BJ]_

ITVG3,S RH^,J H\VF3F TZ`<SBJ'DaJ§±JDaJ`Bj]J]x¥~RH8~RJD7_ BJWB_J'F?§1j]F3DD7J]¶H£STVF3`<H?_ H\_TZITV¶H,DaTVScª<IJH?_WRDaJQRJ]Sa¬J]J`

Sa¬Fn_TVG3`RH£_\TV_uH ¬J]V3`BF?¬L`¦SJ]j]R`BTVUXWBJ8h±S'TV_j]F3IIF3`BVªfWB_J]xfTZ`!_SJD7J]Fn^BTV_TVF3`!§±F3D#SBJ[^BTV_WRH?"j]F3DD7J]_a

~RFB`BxRJ`Bj]J ~RD7F3QBVJI H,`Bx J]µ3SJ`B_lT^,J¥j]F3I[~RH,DaTV_F3`«RH^8J¥QJ]J`«I[H£xRJ §¨F3DNSBJ<J]^·H?ZWRH?SlTFB`«F£§ xRT1JDaJ`,S

j]F3DD7J]¶H£STVF3`<jDaTVSJD7T¶H Z c

s_ TZ`BxRTVjH?SJ]xfTZ` Z cY (H8`Bx cYRFBj]j]¶WB_lTFB`f~BZHªB_'H8` TZI[~RF3D7SH8`,S DaF,J\TZ`<_SJD7J]FnI[H?Sj]BTZ`BGqhr`

hr`,STVVVJnWB_J]_vD7F3WR`BxzmFB`8SD7F8*CF8TZ`,S_Ni }SlF[j]F3`B_SDlWBj]SLSBJ[QJ]_SLxRTV_~RH,DaTVScª!~RH?SSBTV_IJ]SBFBx¥G8J]Sl_

TVS_QRJ]_lSDaJ]_WBVS_'T§ H8D7JJ1J]j]STV^8J]Vª¥^8JD7ª¥j]VF8_JSF JH?j]¥FBj]j]ZWBxRTZ`BGzQRFBWR`BxqH8DaªzH£_'SBTV_'T_'SBJND7J]G8TVF3`

TZ`<¬LBTVj]¥H?V*INJ]SBF3xR_#§rH?TV¨

²¤JujH,IJSFnSBJ[j]F3`Bj]ZWB_TVF3`!SRH£S'F3`BVªzSBJNWB_lJuF£§ H # ¢ LjH8`¦F?^8JDaj]FBIJSBJ[I[H?Sj]BTZ`BG

~RDaF3QBVJI_\J]^8JDaª!IJ]SBFBxzJ`Bj]FBWR`8SJD7_H?SLSBT_\F3j]j]ZWBxRTZ`BG!j]F3`,SF3WRDa_ BTV_DaJ~F3DaS'TV_xRJ]^8F,SJ]x!SFnxRJ]_ljDaTZQRJ

H[IJ]SBF3x¦¬LBTVj!~RDaF?^BTxRJ]_G8FBF3x!I[H?Sj]BJ]_ TZ`¦SBJ]_JH8DaJH?_YR~RDaF?^BTVxRT¶`BG<SBJDaJ§¨FBDaJuHSlF3F8%§¨F3D

³

`BxRT¶`BG<G,F3FBx

z~F8TZ`8S_¬LBJDaJ&SBJ]ª'H8DaJEDaJH?VVª`BJ]J]xRJ]x1?|qFBDqSBT_"~RWRD~F8_J8Y?H `BJ]¬fj]F3DD7J]¶H£STVF3`H?VG8FBDaTVSRI:TV_*xRJ]^,J]FB~RJ]x

¬LBTVj]¥¬F3D 8_J]^8J`¦¬LBJ` SBJFBj]j]ZWB_TVF3`!H8DaTV_J]_ BJ £J]ª<TxRJHTV_'SFnWB_JHnD7F3QRWB_S J]_SlT¶IH?SF3DSlF ³ `Bx!SBJ

%¢ " 8F3`¬LBTVj\SBJj]F3DlDaJ]ZH?STVF3`'_BF3WBVxnQRJ~RJD¯§±F3DIJ]x1Y8H,`BxSBJ`\SF jH,DDaª'F3WBSSBJ " ' j]F3DDaJ]ZH?STVF3`

F3` SBTV_'~RH8DaS

O F3QRWB_S J]_SlT¶IH?SF3D¬JDaJH£¶D7JH?xRª¥WB_J]x<§±F3D_lF8V^3TZ`BG<I[H?Sj]BTZ`BGn~RDaF3QBVJI_|qFBDJ]µXH,I[~BVJ8YqTZ`<SBJ~RH8~RJD

F?§uexRF3QJH8`Bx©&F3WBSBJI\ª Z cYH $ #F3~BSTVjH?qF?¬ IJ]SBFBx QRH£_TZ`BG F3`8rJ]_SlT¶IH?SF3Da_T_¥WB_lJ]x SlF

J]_SH,QBTV_°SBJ!IF8STVF3`=j]FBDDaJ]_~F3`BxRJ`Bj]J8 1H8QBTZ 8 WB_J]_<H # " # ¢¥SF¤j]F3I[~RWBSJ¦SBJ

^BT_WRH?qj]F3DlDaJ]_~RFB`BxRJ`Bj]J §±F3D"_lSJDaJ]F?r^BTV_TVF3`8²fJ#_RH?Vqj]F3INJLQRH?j SlF'SBJ 1H8QBTZ%_&j]F3DDaJ]ZH?SlTFB`nIJ]SBF3xR_H8`Bx

_BF?¬_FBIJ'j]F3I[~RH8D7T_lF3`<QRJ]Sa¬J]J`<BTV_ IJ]SBF3xR_YF3WRDa_LH8`Bx¥INF3DaJ'_SH,`BxqH8Dax¥IJ]SBFBxR_

(8)

#BJ ~RH8~JDT_"FBDaG3H8`BT]J]x[H?_ §¨F8VVF?¬ TZ`BGq?|"TZDa_SVª\¬ J&TZ`8SD7F3xqWBj]J _lF3IJ D7J]¶H£SJ]x¬ FBD qY SBJ`\¬ J&J]µX~BZH?TZ`FBWRD

IFBxRJ]§¨F3D&SBJ " ' " # & H8`Bx<TZ`8SD7F3xqWBj]J'SBJD7F3QRWB_SJ]_STZI[H?SlF3Da_xRJ]^8J]VF3~RJ]x¦TZ` $ '

Z8 aY1J]_~J]j]T¶H£Vª:SBJ £rJ]_STZI[H?SlF3D]Y1¬BTj] TV_nWB_lJ]x T¶`F3WRDH?VG8F3DaTVSRI SF ³ `Bx SBJ %¢<~RH8DaSF?§

SBJ\j]F3DDaJ]ZH?STVF3` F3` ¬LBTVj]¥SBJ" ' ""$#% & '[_BF3WBVxfQRJ\xRF3`BJ8s S SBJ\J`Bx¥¬J'_BF?¬J]µR~RJDaTZIJ`,SH?

DaJ]_WBVS_'H8`Bx¥~RDaFB~RF8_J'_lF3IJ§rWBSWRDaJ'¬F3D

$& $

"!#%$ &'"(*)+$ (

gT_WRH?Ej]F3DlDaJ]_~RFB`BxqH8`Bj]JnF£§ Sa¬F<^8J]j]SFBDa_'TV_NWB_WRH?Vª¤xRJ

³

`BJ]x«Q8ª!j]F3DD7J]¶H£STVF3`' BJD7JnH8DaJnIH8`8ª!xRT1JDaJ`,S

xRJ ³ `BTVSTVF3`B_§¨F3D\SBTV_n~RWRDl~RF8_Ji¨_J]J<SBJ! *H8QBVJf<TZ`Z §±F3D\T¶`B_lSH8`Bj]J}]E´/µX~JDaTZIJ`,SH? j]F3I~RH8DaTV_F3`¤¬JDaJ

~RJDc§¨F3D7JIJ]x¥H8`BxzH,DaJ D7J~RF3DaSlJ]x<T¶` Z *H8`Bx<TZ` aRs INF3`BGSBJI<YR¬JRH^8JjBF8_lJ` SBJ]JDaFnIJH,` _WRIF?§

_URWRH8DaJ]x!xRT1JDaJ`Bj]J]_[QRJ]jH8WB_JF?§ TVS_DaJ]ZH?STV^8J[_TZI[~BVJ§±F3DIH,`BxzTVS_\G8FBF3x!J]µR~RJDaTZIJ`,SH?~RJD¯§±F3DI[H,`Bj]JuSlF

^·H,Daª3TZ`BG VTGB8STZ`BG j]F3`BxRTVSTVF3`B_

1pRpni-,/.0,2143,f}6587 9;:=<*>

ii@?

)

i-,A1CB[}EDGF? )

i-,f}}=D i@?IHi-,A1CB 143,f}=DJF?IHi-,G1K3,f}}}

H

i±L#1}itMN1:}

¬BJDaJO,P5[email protected]} YB25 i@T=.+UB}]YWV TV_LSBJ¬ TZ`BxRF?¬ xRJ ³ `BJ]x Q,ª/XXi@T=.+UB}ZYID;LN[\T/[ L H8`Bx]D^M [

U'[_Ma`3Y3,N5 i@3Q=.+3bR3} T_'SBJuxRTV_~RH,DaTVScªfH8`Bx

F

?Sci-,f} TV_'SBJ[IJH,`!G3DHª<VJ]^8J]"^·H£¶WBJF?§ TZI[H?G,Jed T¶` SBJ

¬ TZ`BxRF?¬ i@d5 .8}

sVSJD`RH?SlT^,JuH8~R~RDaFBH?jBJ]_'RH^8JuQJ]J`!~RDaF3~RF,_J]x!¬LBTVj¦_WBG8G,J]_S SF<WB_JuHSDH,`B_a§¨FBDIJ]x¥^,JDa_TVF3`<F£§ESBJ

F3DaTVG8TZ`RH?_TVG3`RH£¨/s _SH8`BxqH8Dax=SDH8`B_7§¨F3DlITV_[SF!WB_J<SBJ 1H8~BZH?j]TZH8`=F£§LSBJ<TZI[H?G8J8"h¯`=_F3IJ ¬ Hª!SBTV_[TV_

J]URWBT^?H?VJ`8S'SlFN`BFBDI[H?VT]TZ`BG<SBJ'TZI[H?G8JH?_TSTV_LxRFB`BJQ8ª SBJ]_l_x¥IJ]SBFBx1

f#F?¬J]^8JD"SBJ]_lJIJ]SBFBxR_ H,DaJL_lSDaF3`BG8Vª[j]FBDDWR~BSJ]x¥Q,ª[VF3jH£_lSDaF3`BG[`BF8TV_J'F3DQ,ª[SBJ'~RDaJ]_J`Bj]J\F?§*VF3jH£

~RJD7SWRDQRH?STVF3`¤F?§ SBJ F3DaTVG8TZ`RH?_TVG3`RH?¬LBJ`¤FBj]j]¶WB_lTFB` H8DaTV_J]_"hr`¤F3DaxRJDSFzD7J]xqWBj]J<_WBj=H% ' &

H8WBSBFBDa_'VT¶INTSlJ]xSBJT¶` WBJ`Bj]J F?§SBJn`BWRIJDaTVjH?E^?H?ZWBJ]_uQ,ª!SH ,T¶`BG<TZ`,SFzH£j]j]F3WR`8S'FB`Bª!SBJ_TVG3`!F?§SBJ

1H8~BZH?j]TZH8` ?KZ cY,F3D&SBJLFBDaTVJ`8SH£STVF3`[F£§*SBJG3DH?xRTVJ`,S R cBhr` _WBj]nH\jH?_lJ8Y3SBJLj]RH8`BG8J'TZ`,SDaFBxqWBj]J]x<T¶`

SBJ'j]F3DlDaJ]ZH?STVF3`¥H,`B_¬JD Q8ª VF3jH£*~RJDaSWRDQRH?STVF3`B_¬ TVVQJTZ`<xRTZDaJ]j]S'DH?STVF[¬#TS<SBJ'_T]J\F?§SBJu~RJD7SWRDQRJ]x

H8DaJH3s _TZITVZH8DTVxRJH[TV_J]µX~BVF8TVSJ]x¦TZ`<SBJDH8`[H8`Bx¦j]J`B_WB_SDH8`B_a§±F3DI~RDaJ]_lJ`8SJ]x<TZ` SBJu`BJ]µBS _J]j]STVF3`

g h/"i j!8kW"(mlj("(*)+$ noqpr

1H8QBTZ!RH?_'xRJ]^8J]VF3~J]xH8`!H8~R~RDaFBH?j ¬LBTVj¤DaJ]VTJ]_\F3`<VFBjH?"SDH,`B_a§¨FBDI_LQRH?_lJ]xzFB`z`BFB`,c~RH8DH8IJ]SDaTVjNINJH

_WRDaJ]_ BJ]ªnH,DaJ xRJ]_TVG3`BJ]x<SF\SF8VJDH?SlJ" &Bo F3` ~RH8DH,IJ]SDaTVj _SH?STV_STVj]_ TV_xRTV_STZ`BG3WBTV_BJ]x!Q8ª

SBJWB_J\F?§"F3DaxRJDaTZ`BG[TZ`,§±F3DI[H?SlTFB`<H8IF3`BG[xqH£SHRYRDH?SBJD SRH8` SBJ'xqH?SH^·H?ZWBJ]_SBJI_J]V^8J]_

(9)

¬ F#FBjH?R`BF3`,c~RH8DH,IJ]SDaTVjEVFBjH?BSDH8`B_a§±F3DIN_¬JDaJ&TZ`8SD7F3xqWBj]J]x1 BJ ³ Da_S1FB`BJ8YjH?VVJ]x "Y

TV_uH<`BF3`,c~RH,DH8IJ]SD7Tj IJH?_WRDaJF?§VF3jH?"TZ`,SJ`B_TVSaª81s'`BxfSBJ[_lJ]j]F3`Bx!F3`BJ8Y1jH?VVJ]x #% "uYTV_H

`BF3`,c~RH8DlH8IJ]SDaTVj'_WRII[H8Daª F?§"FBjH?1_~RH?STZH?1_SDWBj]SWRDaJ8

%J]S QJH=~BTµBJ]±Y ?i'} TVS_<TZ`8SlJ`B_TVScª8Y H,`Bx L i'}SBJ!_J]S<F?§[~BTVµ3J]V_¥TZ`:TVS_¥`BJ]TVG3BQRFBWRD]sLV`BF3`

~RH8DH,IJ]SDaTVj¥SDH8`B_a§±F3DI_ xRJ~RJ`Bx WR~RF3`°SBJ!j]F3I[~RH,DaTV_F3` F£§ ?i'} H8`Bx:SBJ!TZ`8SlJ`B_TVScª°F?§SBJf~BTVµ3J]V_¦T¶`

L i'}] 'J ³ `BJi . }SlF QJ &T§ ?iZ}K?i'}*H,`Bx #F8SBJD7¬ TV_J8 BJ `BF3`,c~RH8DH,IJ]SDaTVjEVFBjH?RSDH,`B_a§¨FBDI_

xRJ~RJ`Bx!_F,J]Vª<F3` SBJ'_J]S F?§E~BTVµ3J]j]F3I[~RH8D7T_lF3`B_YR¬LBTVj]<TV_SBJ'_J]S F?§"F3DaxRJD7J]x¥~RH?TZDa_

5

<

i

.i .

}}

#BJ SDH8`B_a§±F3DI TV_ xRJ ³ `BJ]x¥H£_ SBJ `BWRIQRJDF?§*~BTVµBJ]_TZ` SBJFBjH?1DaJ]G8TVF3` ¬BF8_JT¶`,SJ`B_TVSaª T_VJ]__

SRH8` SBJ'T¶`,SJ`B_TVSaª<F?§"SBJ'j]J`,SJD ~BTVµ3J]±|F3DI[H?VVª8YRSBJDlH8`[SDH8`B_a§±F3DI[i'}TV_

[i'} 5#YYX

L i'}ZY?i

}K?i'}S` YY

|F3D#SBJnDH8` SDH8`B_7§¨F3DlI<YqSBJ!

)

j]F3DlDaJ]ZH?STVF3`«i±INT¶`BTZITH?SlTFB`fF?§SBJ_WRIF£§ H8QB_F,¶WBSlJu^?H?ZWBJnF£§ xRT§

§±JDaJ`Bj]J]_}F3`¦SBJSDH,`B_a§¨FBDIJ]x¥TZI[H£G8JT_WB_lJ]xzFB`¥FBDaxRJDSF<~RDaJ]_JDa^8J[H DaJ]_~F3`B_J[SRH£SLxRTV^8JDaG,J]_'TZ`BJH8D7ª

¬ TVS SBJ`3WRIQJDF?§"F3WBSVTVJDa_

#BJ "# SDH8`B_a§±F3DI"$#3i'}#TV_H<I[H8~R~BTZ`BG §tD7F3I SBJuVFBjH?E`BJ]TVG3BQRF3WRD_WRDDaF3WR`BxRTZ`BG¥H<~BTVµBJ] SlF

H<QBTVS_SDaTZ`BGzDaJ~RDaJ]_lJ`8STZ`BG¦SBJ[_J]S'F?§ `BJ]TVG33QF3DaTZ`BGf~BTVµ3J]V_¬LBF8_JT¶`,SJ`B_TVSaª!TV_VJ]__SRH8`!SRH?S'F£§% %J]S

L i'} 5&$')(¬LBJDaJ*'wTV_SBJd!TZ`?F?¬ _ ,T*_WRI H8`Bx+( T_H[_lJ]S'F?§ExRTV_~BZH?j]JIJ`,S_Y*H,`BxzVJ]S-,xRJ`BF,SJ

j]F3`BjH?SlJ`RH?STVF3` BJ'j]J`B_WB_LSDlH8`B_a§±F3DIwjH8`<SBJ`<QRJ_~RJ]j]T³ J]x1Y

$#3i'} 5 .

/

c1023

<4

i .C1d0.65 ±}

¬ F<~BTVµ3J]V_[F£§ j]J`B_WB_\SDH8`B_a§±F3DINJ]xzTZI[H£G8JnH8DaJj]F3I[~RWBSJ]x!§±F3D_TZITVZH8DaTVSaªWB_TZ`BG¦SBJfH8I[ITZ`BG¥xRTV_a

SH8`Bj]J8YBT±J8BSBJ'`3WRIQJDF?§*QBTVS_ SRH?S&xRT%JD T¶` Sa¬FQBTVS _SD7T¶`BG,_ BJ H£G,F3DaTVSRIwj]F3I[~RWBSJ]_SBJ'j]FBDDaJ]_~F3`,

xRJ`Bj]JuQ,ª<ITZ`BT¶INT]TZ`BG¦SBJ fH8I[ITZ`BG[xRTV_SH8`Bj]JuH§±SJDH8~R~BVªBT¶`BG<SBJ'j]J`B_WB_LSDH8`B_a§±F3DI<

-p 7 $ !"8 kW%\):9 ;"6<>=-( ??jk@<

s'`Bx¥QRH?_J]x¥FB`<BT_#TxRJHYq¬J'RH^,J'xRJ]^8J]VF3~RJ]x!HVF3jH? SDH8`B_a§±F3DI ¬LBTVj jH8~BSWRDaJ]_IF3DaJ'TZ`,§±F3DI[H?SlTFB`<H8`Bx

SBJDaJ§±F3DaJ[QJ]j]F3IJ]_uINF3DaJj]F3I[~BVJ]µ*hr`B_lSJH?xfF?§j]ZH?__T§±ª3TZ`BG ig?i'}) ?iZ}}Q8ª F3D,Yq¬J[DaJ~BZH?j]J SBJ

QBTZ`RH8Daª<^?H?ZWBJuQ,ª®H[~RD7F3QRH8QBTVVTSaª¦F?§ i@?i'}K?i

}}]YRIF3D7J ~RDaJ]j]TV_J]Vª

G,T^,J`nH~BTVµ3J]AH8`Bx®H`BJ]TVG3BQRF3D7T¶`BG<~BTVµ3J]AB'd0.C5 cY?SBJLG3D7JH?SJD&SBJ ?i'}=D ?i+'.d0.65 ±}]YSBJ IFBDaJ

j]F3` ³ xRJ`Bj]J ¬J RH^8JSRH?S ?i*' d0.C5 ¨}DK?i'}]·e#§j]F3WRDa_J8YSBJ j]FB` ³ xRJ`Bj]J xRJ~RJ`BxR_H?V_F'F3`\SBJ_SH8`BxqH,Dax

xRJ]^BT¶H£STVF3`<F?§"?i'}6D^?iE'd0.65 ¨}]

(10)

%J]S'SBJn~RDaF3QRH,QBTVTVSaª!F?§ SBJ ?i ' d0.65 ±}>8?i'}SF®QJ®i1}¬BJDaJ[TV_SBJuFBQB_JDa^8J]xf^?H?ZWBJ[F?§

?i'} DK?i ' d0.65 ¨}]Y TV_[SBJ J]_STZI[H?SlJ]x_SH8`BxqH8DaxfxRJ]^BTZH?STVF3`=F?§ ?i'} D4?i ' d0.C5 ¨} YH8`Bx T_SBJ

vH,WB__TZH8`!xRTV_SD7T¶QRWBSlTFB`¤§tWR`Bj]STVF3`°*pBF¦SBJ FBjH?&SDH8`B_a§±F3DI xRJ~J`BxR_nH?V_F!WR~RF3`¤SBJ[J]_SlT¶IH?STVF3`¤F?§ SBJ

_SH,`BxqH8Dax<xRJ]^BT¶H£STVF3`<F?§"?i'}6D^?iE'd0.65 ¨}]8h±S#¬ H£_ J]_STZI[H?SlJ]x<T¶` SBJ§±F8VF?¬ TZ`BG ¬ Hª

J]_STZI[H?SJ

)

5SBJ'_SH8`BxqH8D7x<xRJ]^3TZH?STVF3` F?§"?i'}

J]_STZI[H?SJH 5SBJ'_SH8`BxqH8D7x<xRJ]^3TZH?STVF3` F?§"?iE'd0.C5 ¨}

J]_STZI[H?SJ 5 SBJ]TZD#j]F3DDaJ]ZH?SlTFB` j]F3J nj]TVJ`,S

SBJ'_SH8`BxqH,Dax<xRJ]^3TZH?SlTFB`<F?§"?i'}D;?iB' d0.65 ±}jH8`¥`BF?¬QRJ\j]F3I[~RWBSJ]x!H?_ H) 1

H

D

) H

|DaF3I F3WRD#F3QB_JDa^?H?STVF3`Y¬JuRH^8J[~RWBS'SBJ

)

H,`BxHSF¥QRJj]F3`B_lSH8`,S RY SF®QJ c

2

Y¬LBJDaJ¬J

~RWBS

5

5 R

e#§j]F3WRDa_J!SBTV_¥IJ]SBF3x:TV_zIFBDaJ qJ]µBTZQBJ=SRH8`°SBJ 1H,QBT¶%_<F3`BJ8Y QRWBS<TVS¥jH8`R`BF8S<QRJ¤J`Bj]F3xRJ]x H£_

J nj]TVJ`,SVª H?_TVS¬ H?_xRF3`BJ§±F3D\SBJnj]FBI[~RWBSH?STVF3`¤F?§ SBJfLH,I[ITZ`BG!xRT_lSH8`Bj]J8|DaFBI FBWRD'J]µR~RJDaTZIJ`,S_Y

¬J'J]_STZI[H?SlJ]x¥SRH?SSBJ\j]F3I[~RWBSH£STVF3` STZIJ'§±F3D&SBTV_'IJ]SBFBx¥TV_LH8QF3WBSu \STZIJ]_LZH8D7G8JDSRH8` SBJ ³ `BJ]Vª

SWR`BJ]x!IJ]SBFBx<xRJ]^8J]VF3~RJ]xfQ,ª 1H,QBT¶

l !" 1$E

J]S _'_J]VJ]j]SuTZ`!SBJ ³ Da_S'TZI[H?G,JnH SJI[~BZH?SJF?§ ³ µBJ]xf_T]J8"pRWR~R~RF8_lJ[SRH?S'SBJD7JnH8DaJ_J]^8JDlH?"jH8`BxRTVxqH?SJ]_

F?§ESBJ_H,IJ_T]J81mJD7SH?TZ`BVª8Y¬ J\jH8`!WB_JSBJ # & " ' 1H8`Bx¥F,SBJDj]F3`B_SDlH?TZ`8SSFnDaJ]xqWBj]JSBJ

H8IFBWR`8S"F?§1SBJ#jH8`BxRTVxqH?SJ]_B²RH?S"¬JLWB_J]xnH·§¨SJD&H8DaJ SBJ # ' a ' # # Bj]F3`B_SDlH?TZ`8SEH8`BxSBJ# &

" ' ± #BJ]_J[Sa¬F<j]F3`B_SDH£T¶`,S_H8D7J[xRTV_~BZHª,J]xTZ`¤SBJ[|"TVG3WRDaJ¥ SBJ[¬ TZ`BxRF?¬ jH8`BxRTVxqH?SlJ®RH?_\SF¥QRJ

j]J`,SJDaJ]x¥FB` SBJ'j]F3DDaJ]_~RF3`BxRTZ`BG J~BT¶~F8ZH8DVTZ`BJNH,`Bx<_SHª[¬ TVSBTZ`¦SBJDaJ]G8TVF3` F?§*TZ`,SJDaJ]_S

p l" ?"m% kW $ !j

d!F8_S j]FBDDaJ]ZH?STVF3` SJ]jR`BTVURWBJ]_uRH^8J'xRTnjWBVSaªf`BJH8D xRTV_~RH,DaTVScª<xRTV_j]FB`8STZ`BWBTVSTVJ]_Y1F3D#TZ`!~B¶H£j]J]_'¬LBJDaJuBTVG3,

VTVG38Sl_'F3j]jWRD]Y1H£_LSBJ¬ TZ`BxRF?¬WR`BxRJD'j]F3`B_TVxRJDH£STVF3`¦T_'VFBjH?VVª~RH8DaSTZH?VVªzQRWBSRH,DaxRVª¥j]F3DDlWR~BSJ]x!T¶`¦_IH?V

H8DaJH BJD7J§¨F3D7JuTZ`!_WBjfH jH£_JSBJ[~BTµBJ]V_T¶`¤H FBjH?EDaJ]G,TFB`fDaJ~RDaJ]_J`,S'_j]J`BJ[J]VJIJ`,S_§tDaFBI Sa¬FnxRTV_a

STZ`Bj]STZ`8SJ`B_lTSaªn~F3~RWBZH?STVF3`B_pBF3IJ F?§SBJL~BTVµ3J]V_ j]FBDDaJ]_~F3`BxnSlFSBJSJI[~BZH?SJ'WR`BxRJD&j]F3`B_TVxRJDH?SlTFB`<H8`Bx

_F3INJ§tDaFBI H8`BF8SBJD~RH8D7S_ F?§"SBJ'_j]J`BJ8sL_#¬ JH£¶D7JH?xRª¥IJ`,STVF3`BJ]x1YRSBTV_JH£xR_LSF H[~RDaF3QBVJI §¨F3DI[H,`8ª

j]F3DD7J]¶H£STVF3` SJ]j]R`BTVUXWBJ]_YE_TZ`Bj]J!SBJ¦_SH8`BxqH8D7x j]F3DDaJ]ZH?STVF3`SJ]j]R`BTURWBJ]_¥H8DaJ¥WB_WRH?Vª:QRH?_J]x°F3`=_SH8`BxqH,Dax

_SH£STV_STVj]_[IJ]SBFBxR_Y¬LBTVj H8D7J®QJ]_S_WBTVSJ]x SFfH¦_TZ`BG8VJ¥~RF3~RWBZH?STVF3`/²fJ<_RH?VjH?VSBTV_n~RBJ`BF3IJ`BF3`

/ " &J]^8J`TSITVG3,S RH^8JF8SBJDE~R,ª3_TVjH?_FBWRDaj]J]_ H?_BTVG3BVTGB8S_YXH,`Bx[¬JL~RDaF3~F8_J SBJ

" #% 'TVxRJH[SFF?^8JDaj]FBIJLTVS

m F3`B_TVxRJD"SBJ#Sc¬F'¬ TZ`BxRF?¬ _&F?§1SBJ |"TVG3WRDaJLY?SBJ]ª[I[H?Sj]J]µBj]J~BS"§±F3D"SBJDaTVG38S7cWR~[~RH8DaS&T¶`SBJ TZI[H£G8J

? )

H,`Bx? H ?²¤JLRH^8JSFuDaJ]j]F?^8JDSBT_&j]F3DDWR~BSlJ]xn~RH8DaS?²¤J H£__WRIJ SRH?S"VF3jH?VVª SBJ_TVG3`RH?qFBQRJ]ªB_ H8`[H ®`BJ

(11)

x

y

ROI, S(x,y)

template

epipolar line

I (x,y) the second image

I (x’, y’)

2 1

2ulen+1 2vlen+1

|"TVG3WRDaJ[ ´E~BTZ~RF8ZH8D#j]F3`B_SDH?TZ`8SH8`Bx¥DaJ]G8TVF3` F?§*TZ`8SlJDaJ]_Sj]F3`B_SDH£T¶`,S

|"TGBWRDaJ qej]j]ZWB_TVF3`%J§¨S?

)

YqDaTVG3,SW? H

(12)

DaJ]ZH?STVF3`®§tD7F3IwF3` TZI[H?G8J\SFSBJF8SBJD i¨_J]J|"TVG3WRDaJ,}

?IHi.a} 5W?

) i "1C3bQ.q1C3bR3}1b1

¬LBJDaJi@3Q=.+3bR3} TV_ESBJ#xRT_~RH8DaTVSaªuF£§%SBJL~RF8TZ`,S i@Q=.+RB}]Y 5 Qj1T. 5 R61U[H8`Bx

XmQ D L %Q"1L `

X R DKM %R 1 Ma`3Y"L]1<H8`Bx«M 1¥H,DaJnSBJn¬ TVxRS°H8`Bx=SBJ¥BJ]TVG38SF?§LSBJ<SJI~B¶H£SJ<¬ TZ`BxRF?¬

DaJ]_~J]j]STV^8J]VªzH8`Bx #TV_ Hv\H8WB__TZH8` T¶IH?G8J`BF8TV_J8

pRWBj] H8`nH ®`BJDaJ]ZH?STVF3`TV_ SDWBJTZ` SBJL¬#T¶`BxRF?¬J]µBj]J~BS&§¨FBDESBJ ~RH8D7S_ " &3¢#¢i±H?_SBJ'DaTVG38S7cWR~n~RH8D7S

TZ`BxRTVjH?SJ]x!TZ`<SBJ'|"TVG3WRDaJ}

s _TZI[~BVJDIF3xRJ] ¬ FBWBx!H?VVF·¬b7WB_SH_BT§¨STZ`<TZ`,SJ`B_TVSaª8YRT±J8qSBJ'_jH?VJ'§rH?j]SF3D TV__J]S SF<

?IH?i .c} 5 ?

)

i"1K3bQ.1K3bR3}1W1

I2

I1 50

100 150 200 250

50 100 150 200 250

|"TGBWRDaJ Rs ®`BJDaJ]ZH?STVF3`¦QRJ]Sa¬J]J` ? )

H,`Bx ?IH]YRSBJ'_I[H?V1j]TZDaj]VJ]_H8DaJ'FBWBSVTJD7_

h¨§1SBJ j]J`,SJD&F?§1SBJ ¬ TZ`BxRF?¬«¬ TVSj]FBF3DaxRTZ`RH?SJ]_i@Q=.+RB}1TV_ F3j]j]ZWBxRJ]x1YqH8`H?xRxRTVSTVF3`RH?j]F3`B_SDlH?TZ`8S&jH8`

QRJ_SH?SJ]x RTVS'¬ TVVEQRJ\jH?VJ]x¤SBJ3i "# #% " Z} BJDaJ[H§±SJD]h±S&b7WB_S_SH£SJ]_ SRH?SSBJ\j]J`8SJD#F?§

SBJ'¬ TZ`BxRF?¬RH?_ SF_H?SlT_7§¨ª SBJu~RD7J]^3TVF3WB_LH ®`BJF3D&SDlH8`B_ZH?STVF3`RH? j]F3`B_SDH£T¶`,S

? H igQ.+RB}N5 W?

)

i@Q 1K3bQ.SR 1C3RB}1 i±H ®`BJ'jH?_J}

?IHigQ.+RB}N5 ? )

i@Q 1K3bQ.SR 1C3RB}1 ikSDH8`B_ZH?STVF3`jH?_J}

#BJ'F3j]j]ZWBxRJ]x~RH8D7S TV_ §±F3WR`BxzWB_lT¶`BG # ¬LBJDaJH8DaJ'xRJ]SH£TVJ]xfBJDaJH§¨SlJDSBJ'_J]j]STVF3`

R3s'~R~BVTVjH?STVF3`¦F?§"SBTV_ SJ]j]R`BTURWBJ_RH?V*QJTVV¶WB_lSDH?SJ]x!TZ`<_lJ]j]STVF3`<K

fH^3TZ`BG\§±F3WR`BxnSBJ " &3¢#¢~RH8DaS_Y,SBJ'j]F3DD7J]¶H£STVF3`[TV_LD7J]_SDaTVj]SJ]x F3`SBJ D7JI[H?TZ`BTZ`BG®~RH8D7S_EF?§SBJLSa¬F

¬ TZ`BxRF?¬ _²fJjH?V"SBTV_SJ]j]R`BTVUXWBJ " # & 1hr`¦§rH?j]S " ' " #% ' T_H _~RJ]j]TZH?&jH?_JF?§

# #¢ # & YqH?_¬J'JH^8J [email protected]}=5nikTZ`BVTVJD}F3D i@T=.+UB}5 ¥i¨F3WBSVTVJDa_}]

|F3D&J]µXH,I[~BVJ8YqSBJ'¬J]TVG3,SJ]x ( jH8`<QJJ]µR~RDaJ]__J]x!H?_§±F8VF?¬ _

(13)

("i-, .S3,f}5

7 9 :<Z>

ilii@?

)

i-,G1CB[} DGF? )

i-,f}}D:i@?IHi-,G1CB[} DGF?IH?i-,f}}}

H

d i@B[}l}

9;:=<*>

d ]i@B[}

ia}

p g h/ ;jl"( ( %$ )+'%%j W&(m(

BJTZ`8SJ`B_lTSaª F?§*H\¬ TZ`BxRF·¬:j]F3DlDaJ]_~RFB`BxRT¶`BGSFuH\SJI[~BZH?SlJLTV_xRJ ³ `BJ]x¥Q8ªF3`BJLFBDESa¬F~RH8DH,IJ]SJDa_&xRJ~RJ`,

xRTZ`BG!T§¬ J j]F3`B_TVxRJD\SBJ<H ®`BJ[FBDSDH8`B_ZH?STVF3`RH£"SDH8`B_a§±F3DIH?STVF3`!F?§ VTVG3,SuTZ`,SJ`B_TVSaª8"´"_STZI[H£STZ`BGzSBJ]_J

~RH8DH,IJ]SJDa_TZ` ~RDaJ]_J`Bj]J<F?§F3WBSVTVJDa_®H,`Bx H?SSBJ<_H8IJ STZIJ §¨FBWR`BxRT¶`BG¤SBJ<F3WBSVTVJDa_[TV_[xRJ]_jD7T¶QJ]x BJDaJ

WR`BxRJD#SBJ'G8J`BJDH?%§tDH,IJ]¬F3D F?§"DaF3QRWB_S J]_lSTZI[H?STVF3`

¹f

((Z¹

¹!½ -½ (¹R·

s_ TZ`¥I[H8`,ªnDaJ]J] ¬ FBDaVx<_TVSWRH?STVF3`YRFBWBSVTJD7_Lj]F3DlDWR~BS SBJ'xqH?SHuH,`Bx<SBJDaJ§±F3DaJ'SBJIJ]SBF3x<F?§"VJH?_SLINJH8`

_URWRH8DaJ]_§tH?TV± BTV_T_¬L,ªf¬J[_BFBWBx¤§±F3DIWBZH?SJ[SBJ<H?VG8F3D7TSRI_uWB_TZ`BGINJ]SBF3xR_\j]F3ITZ`BG¦§tD7F3I

a

²¤J_WR~R~F8_JSRH?S^3TV_TVF3` T_'H<~RDaFBj]J]__J]_SF ³ SL_FBIJ^3TV_WRH?"IFBxRJ]V_'SFn_lF3IJuWR`RD7J]TZH8QBVJ xqH?SHRf#JDaJ

WR`RDaJ]VTZH8QBVJ`BJ]__'IJH8`B_SBJLH8~R~JH8DH8`Bj]JF?§1_F3INJ # 3]3OJ]G3D7J]__TVF3`<H8`RH?VªB_TV_i³ SSTZ`BGuH\IFBxRJ]SlF`BF8TV_ª

xqH?SH,}"TV_LH8`TZI[~RF3D7SH8`,S _lSH?STV_STVj]_SFBF8qTZ` ^BTV_TVF3` BJ'WB_WRH?VVª¥WB_J]x<DaJ]G3DaJ]__lTFB`<IJ]SBFBx1Y3jH£VJ]x<SBJ'VJH?_lS

IJH8`N_UXWRH,DaJ]_EDaJ]G3DaJ]_l_TVF3`TV_EF3~BSlT¶IWRI ¬LBJ`NSBJL`BF8TV_J TV_vH8WB__lT¶H,`f#F·¬J]^8JD SBTV_ INJ]SBF3xT_`BF8SEDaF3QRWB_lS

SF[FBWBSVTJD7_qpBJ]J|"TVG3WRD7J'K§¨FBD H8` J]µRH8I[~BVJ Z aqhr` SBTV_ ³ G3WRDaJ8YqH,` F3WBSVTVJD j]F3DlDWR~BS SF8SH?Vª SBJDaJ]_WBVS

y-axis

x-axis y-axis

x-axis

|"TVG3WRDaJK"ikVJ§¨S}'e'DaTVG8TZ`RH?"xqH?SH¬ TVS ³ ^8J[~F8TZ`8S_H,`BxzSBJ]T¶DVTZ`BJ<Q8ª<SBJVJH?_SINJH8`¦_UXWRH,DaJ]_DaJ]G3DaJ]_l_TVF3`

i±DaTVG3,S}pRH8IJ\xqH?SHQRWBS ¬ TVS¦H8` F3WBSVTVJD#T¶` SBJ'xRTZDaJ]j]STVF3`/Q

d!F3D7J I[H£SBJI[H?STVjH?VVª8YHVT¶`BJH,DLDaJ]GBDaJ]__TVF3`¦IF3xRJ] F?§*F3DaxRJD!TV_LDaJ~RDaJ]_J`,SJ]x!Q8ª SBJJ]URWRH?STVF3`

R c 5

) Q c) 1

H Q cH 1+1

Q c

(14)

§±F3D&SBJOd

~F8TZ`8SF?§"SBJ'xqH?SHR

c"TV_LSBJ\J]_STZI[H?SlTFB`<F?§ESBJ~RH8DH8INJ]SJDa_ c"F?§ESBJuINF3xRJ]± BJ[DaJ]_TVxqWRH? §¨F3D JH?j¦~RF8TZ`,S'F?§"SBJxqH?SH

TV_ *cq5 R cD Rcc

h¯`!SBJ[VJH?_lSuIJH8`¦_URWRH8DaJ]_DaJ]G3DaJ]_l_TVF3`YSBJn~RH8DlH8IJ]SJDa_ J]_STZI[H?STVF3` F?§ SBJ IF3xRJ]"TV_\F3QBSH?TZ`BJ]x Q8ª

SBJITZ`BTZITH?STVF3` F?§*SBJ\_WRIF?§"SBJ'_URWRH8DaJ]x¥DaJ]_lTxqWRH£_

ITZ`

c

)

Ic

H

#BJ #" ·¢

' RF?§*HDaJ]GBDaJ]__TVF3` IJ]SBFBx1Y3`BF8SlJ]x Y,T_SBJ_I[H£VJ]_S H8INF3WR`8S&F?§1F3WBSVTVJD&j]F3`8SH

ITZ`RH?STVF3` SRH?S I[Hª§¨FBDaj]J'SBJ'^·H£¶WBJ\F?§*SBJ'J]_lSTZI[H?SJF3WBS_TVxRJH8`nH,DQBTVSDH8Daª<DH8`BG,J8XpBJ]J §±F3D&TVS_LIFBDaJ

I[H?SBJI[H?STVjH?xRTV_jWB__TVF3`B_

|F3D&SBJVJH?_lSLIJH8` _UXWRH,DaJ]_LIJ]SBFBx1YR¬JRH^8J 5 )

H8`Bx<TZ`¦SBJ'VT¶INTSl_ 5 R RH£S TV_LSF_Hª

TVS TV_ `BF,SLDaF3QRWB_SH?S H?V¨

½ % n¹

¹RZ½

|qFBDaSWR`RH?SJ]Vª8Y"_lF3IJzD7F3QRWB_SnDaJ]GBDaJ]__TVF3`°IJ]SBFBxR_n¬JDaJ<xRJ]^8J]VF3~J]xTZ`«DaFBQRWB_Sn_lSH?STV_STVj8"s'IF3`BG¤¬LBTVjY

SBJQRH?_lTjD7F3QRWB_SJ]_STZI[H?SlF3Da_ H,DaJLj]ZH?_l_T³ J]xzH?_ d¦rJ]_SlT¶IH?SF3Da_Y3O&rJ]_SlT¶IH?SF3Da_ H8`Bx rJ]_SlT¶IH?SF3Da_Z, Z c

pBJ]^8JDH£LDaF3QRWB_SJ]_STZI[H?SFBDa_[RH^BTZ`BGSBJ¥QRDaJH ,xRF·¬`«~RF,T¶`,S[j]VF8_J¦SF !¬JDaJ<xRJ]^8J]VF3~RJ]x Z ah¯` SBTV_

~RH8~JD]Y1¬J¬ TVV WB_J[SBJ[VJH?_SIJ]xRTZH8`¤F?§ _lUXWRH8D7J]_ni #¢X} DaJ]GBDaJ]__TVF3`!SlF ³ `BxfSBJ &'#%'~RH8DaS'F?§SBJ

j]F3DD7J]¶H£STVF3`

h¯` SBTV_ INJ]SBF3x1Y¬ JINT¶`BTZIT]JSBJIJ]xRTZH8`<F?§"SBJ'_URWRH8DaJ]_#F?§SBJDaJ]_TVxqWRH?

INT¶`

INJ]x

cH

pBJ]J]TZ`BG SRH?SSBJ #¢[J]_lSTZI[H?SF3D&TV_'BTGBBª¥WR`,cH,`RH?Vª3STVjH?±Y¬JWB_J'SBJ\d!F3`8SlJ m H,DaVF[SJ]j]R`BTURWBJSlF

TZI[~BVJIJ`,SLTVSpBJ]J'SBJ H8QBVJn §¨F3D&SBJH£G,F3DaTVSRI<

#BT_ IJ]SBF3xnRH£_ESBJ'QRDaJH ,xRF?¬L`[~RF,T¶`,S <8pBJ]J|"TVGuRBhr`SBTV_ ³ G3WRDaJ8Y8SBJLDaJ]_WBVSTV_ `BF,SEj]F3DDlWR~BSJ]x

Q,ªnSBJ'FBWBSVTJD

F ³ `Bx SBJF3WBSVTVJDa_YB¬JLWB_JSBJ

F3QBSH£T¶`BJ]x<Q,ª[SBJ #¢J]_STZI[H?SFBD"H8`Bxnj]FBI[~RWBSJJ]^8JDaª[DaJ]_TVxqWRH?

c RsL_#T_xRJ]_jDaTZQJ]xzTZ` Z cYR¬J'jH8` J]_SlT¶IH?SJ'SBJ'_SH8`BxqH8Dax<xRJ]^BTZH?STVF3`<F£§/`BF8TV_JH?_

Wc5 K 88qia1

D

} IJ]x

Ic

H

(15)

s__WRIJ'SRH£S SBJDaJH8D7J !xqH?SH~RF,T¶`,S_'H8`Bx ¥~RH8DlH8IJ]SJDa_TZ`<SBJVTZ`BJH8DLINF3xRJ]±

, m BF3F,_J ¥~RF,T¶`,S_LH£SLDH8`BxRF3I §tDaFBI SBJ'_J]S F?§ !xqH?SH~F8TZ`8S_

mF3I[~RWBSJD&SBJ ³ S F?§"SBJIFBxRJ]1SFSBJ ¥~RF8TZ`,S_

mF3I[~RWBSJD&SBJIJ]xRTZH8`<F£§SBJ'_lUXWRH8D7J'F?§SBJDaJ]_TVxqWRH?V_

BJ

³

SSTZ`BG¥TV_[DaJ~JH?SJ]x WR`8STV H

³

S\TV_§±F3WR`Bx=¬ TVS¤_W nj]TVJ`8Slª=_I[H£IJ]xRTZH8`¤F?§ _UXWRH,DaJ]x D7J]_TVxqWRH?V_uFBD

WR`,STV1_F3IJ~RD7J]xRJ]SJDITZ`BJ]xf`3WRIQJD F?§"DaJr_H8I[~BVTZ`BG<_SJ~B_

H8QBVJn BJ\JH£_SLIJ]xRTZH8` _UXWRH,DaJ]_LDaJ]G3D7J]__TVF3`<H?VG8F3D7TSRI

y-axis

x-axis y-axis

x-axis

|"TVG3WRDaJ 3i¨J§±S}"e'DaTVG8TZ`RH?RxqH£SH ¬#TS ³ ^8J ~RF,T¶`,S_EH8`Bx\SBJ]TZDVT¶`BJ'Q,ªDaJ]G3DaJ]__lTFB`F£§qSBJEVJH?_SEINJ]xRT¶H,`_lUXWRH8D7J]_

i±DaTVG3,S}pRH8IJ\xqH?SHQRWBS ¬ TVS¦H8` F3WBSVTVJD#T¶` SBJ'xRTZDaJ]j]STVF3`/Q

(16)

f#JDaJ °T_ SBJ<xqH?SHz`BWRIQRJD H8`Bx TV_[SBJ¥~RH,DH8IJ]SJD`BWRIQRJD] #BJ<§rH?j]SF3D K 88<TV_§±F3Dj]FB`B_TV_SJ`,S

J]_STZI[H£STVF3`=TZ`=SBJ¥~RDaJ]_J`Bj]J¦F?§ vH,WB__TZH8` `BF8TV_J8Y"H8`Bx SBJ<SlJDI

TV_nDaJ]j]F3I[INJ`BxRJ]x Q,ªOF3WB__lJ]JW8¬

xRJ]^BT¶H£STVF3`<J]_SlT¶IH?SJQBTZ`RH8Daª<¬J]TVG3,S_ jH8`<QJuH?VVF3jH£SJ]x¥SFSBJ'xqH?SH[~F8TZ`8Sl_Z

cq5

[«

$"1 $ %$& 7 ul&

hr`¤SBTV__lJ]j]STVF3`Y ³ Da_S'_F3INJ[TV_F8ZH?SJ]x=J]µXH,I[~BVJ]_NH,DaJ_BF?¬L`!TZ`fKZ[H8`Bx=SBJ`!_SH£STV_STVj[j]F3I[~RH,DaTV_F3`B_uH,DaJ

I[H?xRJ'¬#TS<_SH,`BxqH8Dax¥H8`Bx¥`BF3` _lSH8`BxqH8Dax¥INJ]SBF3xR_#T¶` Kq

"$ ?"(

Fn~RDaF?^8J'F3WRD H,~R~RDaF3H?j]YB¬ J)^8J'SJ]_SJ]x<TVS FB` _F3IJ~F8TZ`8S_SH £J`§tDaFBI *¬LBJDaJ\SBJ'j]ZH?__TVjH?"IJ]SBFBx

§rH?TV_Xh¯` |"TVG3WRDaJ'RYBSc¬F'J]µRH8I[~BVJ]_LH8D7JLxRTV_~BZHª8J]x1 BJSa¬FuDaJ]j]SH,`BG8VJ]_ TZ` SBJ'DaTVG3,ST¶IH?G8J'H8DaJ SBJD7J]G8TVF3`

F?§ETZ`,SJDaJ]_S'j]BF8_J`1pBSH,`BxqH8Dax!j]F3DDaJ]ZH?SlTFB`¥SlJ]jR`BTVURWBJ]_'§rH?TVJ]x¤SF

³

`Bx¤SBJj]F3DDaJ]j]Sj]F3DDaJ]_~RF3`BxRTZ`BGz~F8TZ`8S

TZ`fFB`BJnjH?_lJ®H¦3WBG8J FBj]j]¶WB_lTFB`=F3j]jWRDa_[H8`Bx=TZ`=SBJ[_J]j]FB`Bx jH?_J[SBJ _WRD¯§rH?j]J TV_NH£¶INF8_SSH8`BG8J`,SSF¦SBJ

^BTJ]¬#T¶`BG xRTZDaJ]j]STVF3`!H8`Bx<SBJ\¬ TZ`BxRF?¬ _ xRF3`BS ³ S#j]F3DDaJ]j]SVª8

´&~BTZ~RF8ZH8DVTZ`BJ]_nH8D7JnxRTV_~BZHª8J]x«H?_H8DaJ xRT_~B¶Hª8J]x SBJn¬LD7F3`BGzI[H£SjBJ]_§¨FBWR`Bx Q,ªfSBJ _SH8`BxqH,Dax ]_l_x

IJ]SBFBx1qC"H8D7STZH?1j]F3DD7J]¶H£STVF3`<_WBj]j]J]J]x¦TZ`¥JH£j F?§"SBJ]_J\jH?_J]_|qF3DTZ`B_SH8`Bj]J8YqFB` SBJuC"H?F,F _ ³ `BG8JD]YSBJ

~RH8DaSlT¶H£*j]F3DlDaJ]ZH?STVF3`fIJ]SBF3x ³ `BxR_SBJuj]FBDDaJ]j]S'I[H?Sj]¦F3`<SBJ DaTVG38SYq¬LBJD7J ]_l_x ³ `BxR_SBJ\§rH?V_J[I[H?Sj]

F3` SBJ'VJ§±S

h¯`¦SBJ|"TGBWRDaJ RYSBJF3WBSVTVJD~F8TZ`8Sl_H8DaJxRTV_~BZHª8J]x!§±F3D#JH?j]¥SlJI[~BZH?SJ8Y¬LBJ`¦SBJj]F3DDaJ]j]S'I[H?Sj]<TV_

§±F3WR`Bx1

|DaF3I SBJ]_JSc¬F\J]µXH8I~BJ]_Y3¬J_J]JSRH?SEFBWRD INJ]SBF3x<ITVG3,S¬ FBD \¬LBJDaJ'SBJj]ZH?__TVjH?F3`BJ#§tH£TV_²fJ

H8DaJ'G,F8TZ`BG[SF[URWRH8`,ST§¨ª SBTV_ Q,ª j]F8VJ]j]SlT¶`BG<_lSH?STV_STVj]_ FB` ¶H,DaG8J'J]µR~RJDaTZIJ`,S_

g 6 %( %kW( ( lj@(

hr` FBDaxRJD&SFj]F8VJ]j]SSBJJ]µXH£j]S D7J]_WBVS F?§I[H£SjBTZ`BGqYBJ]µR~RJDaTZIJ`,S_¬JDaJLj]FB`BxqWBj]SJ]x<F3` ~B¶H,`RH8D ~RH?Sj]BJ]_Rhr`

_WBj]<HjH?_J\SBJ'J]µRH?j]SLI[H?SljBJ]_jH8`¦QRJj]FBI[~RWBSJ]x¥Q,ªnJ]_SlT¶IH?STZ`BG®~RD7J]j]T_lJ]ª¦SBJBF3IF,G3DH8~R,ªnI[H8~R~BTZ`BG

F3`~RH?Sj]\F3`'SBJ F,SBJD]?²fJ RH^8JEFB`BªSJ]_lSJ]xSBJ IJ]SBF3xnWB_lT¶`BG'SBJ SDH8`B_ZH?STVF3`DaJ]ZH?SlTFB`[H8`BxSBJj]J`8SlJD

~RF,T¶`,S'j]F3`B_SDH?TZ`8SR²fJjH?V*TVSD ]_l_xRj[BJDaJ8Yq¬BTj]¦_SH8`BxR_#§±F3D #% #%$#¢"¢,qD ]__xRjTV_'j]F3I[~RH,DaJ]x

¬ TVSSBJ _lSH8`BxqH8Dax ]__lx1Y?SBJLDH8`\IJ]SBFBx[H8`Bx[F3WRD"IFBxRT³ J]xnTZI[~BVJIJ`,SH?SlTFB`F?§SBJ j]J`B_WB_ SDH8`B_a§±F3DI<

(17)

|"TVG3WRDaJ' RC"H?F8VFq ¬FuI[H?SljSlJ]_S_,F3`BJLFB`[SBJ ³ `BG,JD H,`BxnSBJF8SBJD&F3`SBJJH8D] BJL_I[H?V_UXWRH,DaJ]_T¶`

SBJ'VJ§±SLTZI[H?G,JH8DaJ'SBJ'SJI~B¶H£SJ]_

|"TVG3WRDaJ ·e'WBSVTVJD~RH8DaS_Li¨¬LBTVSJ}§±F3WR`Bx\§¨FBDSBJ Sa¬FLJ]µRH8I[~BVJ]_Bhr`SBJVJ§±SETZI[H?G8J#T_&xRTV_~BZHª,J]x[SBJ F3WBSlTVJD

~RH8DaS §¨F3D&SBJ ³ `BG,JDLH8`Bx<TZ` SBJuDaTVG3,S F3`BJ'TV_xRTV_~BZHª,J]x¥SBJ'F3WBSlTVJD~RH8DaS§±F3DSBJ'JH8D]

(18)

¬ F[~RH?TZDa_#F?§TZI[H£G8J]_LH8DaJWB_lJ]x<§±F3DSBTV_ SJ]_lS BJ]ª¥H8DaJ'xRTV_~BZHª8J]x¥TZ` |"TGBWRDaJ [H,`Bx<|"TGBWRDaJR

|"TVG3WRDaJ pBSJDaJ]Fn~RH?TZD' #% #%

|"TGBWRDaJ qpBSJD7J]Fn~RH?TZD V¢

(19)

©&F8S<F?§ESBJI RH^8JuH ~BZH8`RH8DQRH?j 8G3D7F3WR`BxfQRWBSLSBJ]_lJNQRH£j ,G3DaF3WR`BxR_'H8DaJ\_J]S¬ TVS<xRT1JDaJ`,S8TZ`BxR_'F?§

SJ]µBSWRDaJ8?|F3WRD"SJ]_lS_"¬JDaJxRJ]_TVG3`BJ]x1B|"TGBWRDaJxRTV_~BZHª3_Sa¬FL_lJ]S_EF?§1~RF8TZ`,S_"§±F3DSBJ #% # QRH?j 8G3D7F3WR`Bx

§±F3D'¬LBTVj]fSBJ[j]F3DDaJ]_~RF3`BxRTZ`BG~F8TZ`8S_\¬JDaJ[_F3WBGB8S |"TVG3WRDaJ¥8xRTV_~BZHªB_SBJ SJ]_S¥H,`BxK¦¬LBTVj¤¬JDaJ

~RJDc§¨F3DlIJ]x[¬ TVSSBJ

" V¢'~B¶H,`RH8DQRH?j ,G3DaFBWR`Bx §¨F3D/SBJ SJ]_lS 'SBJ SJI[~BZH?SJ~RF8TZ`,S_ H8DaJ _jH£SSJDaJ]xnH£FB`BG

SBJ'FBj]j]ZWBxRT¶`BG¦j]F3`,SF3WRDRHxRTnjWBVSSJ]_S jH?_lJ8

|"TVG3WRDaJ[ X©H?j ,G3DaF3WR`Bx #% #% qRCF8TZ`,S__J]VJ]j]SJ]x ikTZ`<QBZH?j 3} §¨F3D&SJ]_lS'H8`Bx¥RJ§±SRJ]µRH8I[~BVJ8'j]F3DD7J]_a

~RFB`BxRT¶`BG<SlF H8QBVJu qOTVG3,SRJ]µRH8I[~BVJuj]FBDDaJ]_~F3`BxRTZ`BGnSF H8QBVJu

#BJ xRT%JD7J`8S IJ]SBFBxR_E¬JDaJDWR`[FB`SBJ]_J#§¨FBWRD"SJ]_Sl_ BJjH8`BxRTVxqH?SJ]_¬JDaJ j]F3`B_SDH?TZ`BJ]xnSlF_SHª\F3`

SBJJ~BTZ~RF8ZH8D#VT¶`BJH8`Bx<SF[RH^8JSBJLxRTV_~RH,DaTVScª VJ]__ SRH,`n R8|F3D&JH?j<INJ]SBF3x1YB¬Jj]F3I[~RH8DaJSBJ'DaJ]_WBVS_

§±F3WR`Bx¥¬ TVS SBJ'J]µXH?j]S#^·H?ZWBJ[~RDaF?^3TVxRJ]x!Q8ª SBJBF3IF,G3DH8~R,ª8

#BJ DaJ]_WBSl_LH8DaJ'DaJ~RFBDaSJ]x<TZ` SBJ H8QBVJRYRRY8K[H8`Bx¥RB|F3D&JH?j IJ]SBFBxikT±J8RDH8`YBj]J`B_WB_YqD ]_l_xRj

H8`Bx ]__lxq}LH8D7JLTZ`BxRTVjH?SJ]x

ESBJ`3WRIQRJD F?§/H£j]jWRDH?SJI[H£SjBJ]_ XWR~ SFF3`BJu~BTVµBJ]*JDlDaF3D'ikG8FBF3x¥IH?Sj]R}]Y

ESBJ`3WRIQRJD F?§/IH?Sj]BJ]_ TZ`¥HxRTV_SH,`Bj]JuQRJ]Sa¬J]J` F3`BJH8`Bx¦Sa¬ F[~BTVµBJ]_JDDaFBDi±`BJH8D INT_l_}]Y

ESBJ`3WRIQRJD F?§/IH?Sj]BJ]_LH?S HxRTV_SH8`Bj]J\F?§"Sc¬FSFSRDaJ]J~BTVµ3J]V_[i±QRH?x¥I[H?SljBJ]_} Y

ESBJI[H?Sj]BJ]_¬LBTVj TVJ[IF3D7J'SRH8` SRDaJ]J~BTVµBJ]V_H¬ Hª§rDaF3IwSBJ]TZD#J]µXH?j]S~RF8_TVSTVF3`=i§rH?V_JI[H?Sj]BJ]_}]

-p (mkWl"(m(m%j(

|D7F3ISBJ[~RDaJ]^BTVF3WB_'SH8QBVJ]_Y¬J_J]J\SRH?SSBJuD ]_l_xRj[IJ]SBFBxz~RDaF?^BTxRJ]_'SBJuQRJ]_lS DaJ]_WBSl_Y¬ TVS<VJ]__'SRH8`

¬LDaF3`BG!I[H?Sj]BJ]_1mJ`B_WB_[IJ]SBF3x=G8J]S_\SBJ[_J]j]F3`Bx QRJ]_lSND7J]_WBVS_[QRWBSNH,`BxDaJH?j]BJ]_[QRJ]Sa¬J]J`f!H8`Bx

8 ¬LDaF3`BG[I[H?SljBJ]_H?_LH?ZDaJH?xRª<IJ`,STVF3`BJ]xzQ,ª!1H8QBTZYqSBJDH8` IJ]SBFBx¥TV_LJ]^,J` J]_l_LG8FBFBx1 BJ]_l_x

(20)

" ¢,1CF8TZ`8S__J]VJ]j]SJ]x«ikTZ`!QBZH?j B}#§±F3D SlJ]_S H8`Bx¦Kq %J§¨S J]µXH,I[~BVJNj]F3DD7J]_a

~RFB`BxRT¶`BG<SlF H8QBVJK qOTVG3,SRJ]µRH8I[~BVJK[j]FBDDaJ]_~F3`BxRTZ`BGnSF" *H8QBVJ

$

X R 3TZ`,§¨Saª

?K3 ,

#%

X R 3TZ`,§¨Saª

8 , R

"]¢

X R 3TZ`,§¨Saª

R ,

"]¢

X R 3TZ`,§¨Saª

?K

*H,QBJ +

Â"!?ÂÇZÇ$#!

$

X R 3TZ`,§¨Saª

R 8

#%

X R 3TZ`,§¨Saª

8 , K8K

"]¢

X R 3TZ`,§¨Saª

88 £K

"]¢

X R 3TZ`,§¨Saª

8 R

H8QBVJu

%&

+'

()

+

*

Â"!?ÂÇZÇ+#!

(21)

$

X R 3TZ`,§¨Saª

K K3

#%

X R 3TZ`,§¨Saª

8 8

"]¢

X R 3TZ`,§¨Saª

8

"]¢

X R 3TZ`,§¨Saª

8 ?K

H8QBVJK

(

+

#

$

X R 3TZ`,§¨Saª

8 8

#%

X R 3TZ`,§¨Saª

8 8

"]¢

X R 3TZ`,§¨Saª

8?K ,

"]¢

X R 3TZ`,§¨Saª

R ?K

*H8QBVJ

&

+'

(

+

)

#

R R 3TZ`,§¨Saª

8?K3 8R 8, 8

"#

R R 3TZ`,§¨Saª

88 88 , K38

"]¢

R R 3TZ`,§¨Saª

8?K3 8 , 8

"¢

R R 3TZ`,§¨Saª

R]K ?Kq 8 8

*H8QBVJ Bs ` J]µXH8I~BJ§¨FBDSBJ'G8J`BJDH£1jH?_J'F3` SBJ'T¶IH?G8J

" V¢

TV_ SBJ¬F3Da_JTZ` _WBj xRTnjWBVSj]F3`BxRTVSTVF3`B_LH8`Bx<TVS__j]FBDaJ]_ QRJ]Sa¬J]J`<8H8`Bx ,wF?§*¬LDaFB`BGNIH?Sj]BJ]_ BTV_

J]µR~RJDaTVJ`Bj]J!^·H?VTVxqH?SJ]_ SBJ §rH?j]STVF3`RH?VTV_I F?§LSBJ<j]J`B_WB_nIJ]SBFBx1YEH8`Bx«~RDaF?^8J]_SRH£Su¬#TS«H8`=H?xRxRTVSTVF3`RH?

j]F3I[~RWBSH?STVF3`RH?1J1F3D7S SBT_#jH8`<TZI[~RDaF?^8J]x<¬#TS SBJu~RH8D7STZH?j]F3DDaJ]ZH?STVF3`¦IJ]SBFBx1

f#F?¬J]^8JD]Y "!$#&%'%)(+* ,-./*&01"234(25#!6#75 7*)0

"3,5#78(903!$:5 :7!<;=>%B H8QBVJu ~RDaF?^3TVxRJ]_SBJuD7J]_WBVS_ §±F3DSBJ'§±F3WRD ~RDaJ]^BTVF3WB_IJ]SBFBx¥SJ]_lSJ]x

F3`¦H¥,9? 8[H8D7JHRo#F8STVj]JSRH?SH?V"F8SBJDIJ]SBFBxR_LxRF<`BF8S'QRJRH^8JSFBF®QRH?xRVª¦SF3Fqd!F3DaJ'SRH8`

I[H?SljBJ]_LH,DaJ'¬ TVSBTZ`¥[~BTVµBJ]V_§¨F3D&JH?j]¥INJ]SBF3x1

#BJDaJfH8DaJ!_J]^8JDH£'J]µX~BZH8`RH?SlTFB`B_<§±F3D J]µX~BZH?TZ`BTZ`BG:SBJ]_JfZH?_lS¥DaJ]_WBVS_|"TZDa_SlªH?_<j]J`B_WB_zH8`Bx ]_l_x

j]F3`B_TVxRJD&SBJ¬LBF8VJ¬ TZ`BxRF·¬\Y8SBJ_WR~R~RFBDaS&§¨F3DSBJ]T¶DH8`B_l¬ JD/TV_ ZH8D7G8JDH8`BxnIF3D7JLDaF3QRWB_S&SFu`BF,T_lJ8XC"H,DaSTZH?

j]F3DD7J]¶H£STVF3`fITVG3,S_J]VJ]j]SuH<¬DaF3`BG¥¬#T¶`BxRF?¬w¬ TVS~JD¯§±J]j]Su~RH8DaSlT¶H£ I[H?SljBJ]_\T¶`B_lSJH?xfF?§ j]F3`B_lTxRJD7T¶`BG¤SBJ

_TVG3`RH? G8VF3QRH?VVª<¬LBJ`<TVS_BF3WBVxzQJxRF3`BJ8 #BT_TV_ TVV¶WB_lSDH?SJ]x!TZ`<|"TVG3WRD7J[F3`<H<xRT¶INJ`B_TVF3`RH?_TVG3`RH?±