HAL Id: inria-00070621
https://hal.inria.fr/inria-00070621
Submitted on 19 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 abroad, or from public or private research centers.
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 publics ou privés.
The Quality vs. Time Trade-off for Approximate Image Descriptor Search
Rut Sigurðardóttir, Hlynur Hauksson, Björn Pór Jónsson, Laurent Amsaleg
To cite this version:
Rut Sigurðardóttir, Hlynur Hauksson, Björn Pór Jónsson, Laurent Amsaleg. The Quality vs. Time Trade-off for Approximate Image Descriptor Search. [Research Report] RR-5382, INRIA. 2004, pp.19.
�inria-00070621�
ISRN INRIA/RR--5382--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
The Quality vs. Time Trade-off
for Approximate Image Descriptor Search
Rut Sigurðardóttir , Hlynur Hauksson , Björn Þór Jónsson , Laurent Amsaleg
N˚5382
Novembre 2004
Systèmes symboliques
& "%('*))+"-, ./01 2435687+)9/";:6 %7+
<>=+?A@/BDCE=FHGEIJFHKL?H?MBDFMNOQP9RDS8TU=F9PIJ=+V8WWHXETNYO
Z-[\EFT^]-LJF_JLJTWHWXET`NOQabI=FHcdTU?9eAfgWHIJRhcdC1i
jlknmporqsutm6mrkvsxwydz|{~}vtm
Q y to6/tlsut
- y o-lt t#t tdv-ydtsw t%d%¡ ¢ #£ tm
¤9¥+¦§¨©ª§« ¬ ttvo>kt m®yddo¯tvop°±w mptHg{²s £ t to {|t z6 m9wtHyds³t´suy t #µsuy t
{²s y o vo{²¶s nk z²{² o¯{|yd t m·¸jl{|su{²z{|o k to {²t zQ{²m{|#t tvorz²k t kYts #{| £
# yltHmrmQ{² or{~zu¹ t t rºy su{| £¼»¯½v¾d¿À mrt tHm·Á®t t ºy td`ort t¸{~m g{|# t mr{| £
{²vort tHm o6{² t rºy su{| £´¾ÂÂEÃrĽdÅÇƾÀÈ» mrt #tm ¹ #t t tHmpz|o-}v z²{Éo k £ ¯ do¯ttHm tÊo ¯ lt ºy
t#tHA}vt k>tltor{²yAor{²s³td·
®t £ y zy ºË#yMl{²s ort to {|t z`mpklmportsum.mry#z²Ywt³o¯yydwlo {|ortuwJtmpo yvmrmr{²wz|t tmrzÉo
}v z|{|o k9{²orts³{²{²ss suydvo-y º or{²sut·®Ìbm u tmrz|oo k {~ zU{²#ltl{² £ mpo ort £ {²tm6l{²n{²t%ort
o mpto{²do¯ys nk o nÍlm·`δ{|#{|su{²Ï{² £ o¯tÊmrt ³o¯{|sut.mp £d£ tHm omory £ t#t ortb{ºy s³z²k
mr{²ÏtYnÍlmÐory¸wtHm o%ydt z ¬rÑÒ ydmpo¯m ¹ {Éo¯ÔÓ ÖÕ ydmpo¯m·xÎ l{|su{²Ï{² £ }d z²{Éo kd1yo¯tyo¯t
#1mr £d£ tmpo¯mËo¯ym o yd £ z²kz|{²su{Éo6o¯t%{²do ¯ °±n#Í>l{²m¯mr{|su{²z {|o k>y º o ·
®t # t ` tm¯mrtm8ort6}vtmpor{²yory ¹ o`tvo¯tvo £ ¯ do¯tt{| £ ort6}vt k yltm¯mr{| £ or{²sut
mp{²
£
#{
ºy
snÍ×mp{²ÏtHm`yds
ydsu{²mrtm.o¯t9}v
z|{|o kYy
º
ort
tHmpz|o¯m
#×n{~tAt
m · Õ mr{|
£
z
r£
tyz²z²to¯{|yd´y
º
usu{²z|z²{²yY°Èl{|sut#mp{²ym6z|yl
z/tm¯
{ o¯y
m-yds
lortH´yt
suy
t%or
Y
o¯ym
#
t z/z|{
º
t³{|s
£
tm
¹
t³mpy
¹
o¯
o.su{|{²su{|Ï{|
£
o¯t³}vt
k
yltm¯mr{|
£
or{²s³t³s
k¸{|
ºØ
o
z²t >o¯yuwtoport }v z²{|o k>y º ort%{²vort sut{ ort tHmp#zÉom·
Ù´ÚvÛEܯÝÞ ¨ß+¦« yMl{|s o¯tÊmrt #tmn}vt k yltm¯mp{² £ or{²s³td#}v z²{|o k>y º ort tmrz|o¯m
à~á1ârã±äå®â6æ+ç²ã±èhéê
ëUìMíïîµðMñØòóØô õ öµíïîµð÷ñøö¼òùöDìMôúdû-üðHñDòóØô õÈö¼òý*úvþ9ÿ ç
údû ±ÿ ç è
å
á
ç
è
îDô ô
ìöØöhð÷¯ö±÷÷ñ !íïî"¯ô$#!%'&" ëUìMôúvû ü ðMñDò¯óDô õÈöÊíïîb÷³õ òòðôpñD÷¯öDíïòý(ôÈö*)1ô ô ý¸ñØôpîDôp÷ñDõ±ìHôpñØî÷¯ö-öhìHô,+.-/+10324÷òñh÷5
öhòñ.6%íïý7-Uô ýMýMô î8:9ñD÷ýMõ ô'8v÷ý;,-Uô<63=póh÷<>@?A=CB/ýMí>ô ñØîhíö*6'8:+Çõpô<÷ý;8n÷ý;%íïî/ð÷ñøöhí÷A6ÊîDMðMðòñøöhô<,E6C-8÷ýMý;?ïîëlô õ±ìMýHíïõr÷
-8ô îhôp÷ñØõ±ìGF+ñD÷ýöIHJH%KHHHLb÷ý;7MNFI+.OQPSR;ïô îUTôpñØýMôQëlñD÷>ô<VF+ñh÷ýö L5.%HHJ@
ë8ìHíïî/)Eòñ =bñDô õ ô í>ô<.ð÷ñøöhí÷lî MðMðòñØö8ù|ñDòWÔöhìMôQ÷õ ôX.ô<Mí÷+Çýöhô<YñD÷¯öhô<ðMñØòóDô õÈö8Z9V[N\5.HH@]^\_@
`
-8ô$63=róD÷>3?A=aB/ýMí>ô ñØîhíö*6'8b/ù~÷ý@ïôpíöDíc%@8@+10E5"]HJ-Uô$6@=póD÷>3?A=:8Z+Çõ ô<÷ý;!/drñ ö"H@]edrì;6ýEMñDH@]edóDòñØý:ef+ñ1!íïî
g
+.-h+1032/i@jUkI- 0:8:j1÷W6ð;Mî/MômlEôp÷;ïíïô<!8J_HL'%n-Uô ýMýMô î8;9ñh÷ýMõ ôo÷MñDô ýö÷W6îh÷ïô<YEf+íïñDíïîh÷@ù²ñ
Unité de recherche INRIA Rennes
& "%('*))+"-, ./01 2435687+)9/";:6 %7+
¦ « t s³topo t>lt tHt t tm{²s £ tm # z²t yvortn¶tmpot>tHmrmr{|o y
#ydsw tx yd{²m¯m voÐ z²{~ o¯{|yd#m·8t yltHmrmr#mbt tt #t # mr{|su{²z {|o HmbtHm o%lt ºØ yd
{² tvort¸o qm9yortE®mr o¯ylo>z²y m¯}d#tzyµtEtorttm tt #tm »r½n¾d¿ÀÈ» · Ì-#m¯mr{D ºØ { t
z|looltHm tHt tm ¾¯ÂdÂJÃrÄH¿» mr#m¯{|ortu{|vo o £ #{²m¯m vo· 1z }d z²{Éou mrz|o o
tHm o-l{²su{|nt y"!obt t#t tbw{²t z²#m {²ltd·
8tmUmrklm o¯qsutm1sutopo vo8t$#% ttm t#t tm # yltmEtHmrm ktdoEw{²t%tdo¯t#.%ydwlort{
tm mrz|o omltz sut{²z|z²t t>}v z²{|o ydm¯mp{²wz²t> m%z|tsu{²{²sslto¯ts m·'&Ð yd 8z²tmm °
o ¯ o £ {²tm6o ¯ l{|or{²ytz|z²tsutdo.ts z²yktm yd tz l{|n{~mptvoÐz²tb tltulydtHmbt to¯{Éom%mpyd#m °
t#mrtsw#z|tHm·Qδ{²{²su{²mrt
z²t.orts
m6su{²m
#
z
u
tHt
t.mp
££
q t.lt
t
ltHm-mpyd#mp°ht#mptswz²tm®lt
o {²z|z²t#{
ºy sut
y
s³{²t
ºØ
{ tmrt
tHyd
{ z|tHm-tdo
tmp°±mry
or{²tmËtoÐz²tmb
z~z~m·ËÎ
l{|su{~mpt
z
}v
z|{|o tm
mrzÉo
om#%
lo
t%o#mr
£d£
q
t.ltydvo
{²#
tbo
qHm
ºy
ortsutdo-z
l{~mrmr{²s³{²z
{Éo
tm6lydtHm
¸mpt{|´lt
}vt.mpyd#m °±tmptswz²t·
Óto
o¯{²z|tmpt¸ly#t
y
ydwl tor{
º
or#{|t
#mu}vtz²z²t9sutmr
t
£d¯
vor{
Ôorts
mult
o
¯
{Éo¯tsutvo
ºØ
{²wz²t%(
Åؾ
ltHm6mpyd#m °±tmptswz²tmËltÊo
{|z²z|t.#{
ºy sut%yds
#
yds³toËz
}d
z²{Éo.tm
mrzÉ°
o omvto®n{²t°±top°±t m ·) * t+ltmortHm omÖt,JtHo¯mËmp s³{²z²z|{²y#mËltÐtort mlt.l{|sut#mp{²y#
#y#msuyvo y#m}vtÐsu{²{²s³{~mrt z|tHmÖo¯ts m®lt yd#mpt tlo-!# z|ts³tvoËyd#l{ t+tm Hmp#zÉo o¯m
{²vort s.{ { tm®lt%sut{²z²z|t t%}v z|{|o d·
/ Þ
§H¦
Ü
ª0
«
t#t
tm
#
yltmo¯ts
m-%t1Hlo¯{|ydU#}v
z|{|o %ltHm
Hmp#zÉo
o¯m
0x8" A7Ö/"
¬ tHtdokt myvortdor°hw mrt%{²s £ t to {|t zv m+wJtydsutsuy t #s³y t{|s y o do{²xs nk
!tz~mJmp m6sutl{~{²td £ ty £d¯ nk ¹ t o¯t 6ºy tH m o¯{| £ #¸mptH {Éo kd·6Óydvortvor°hw mptH9{²s £ t
to {²t z1{²mËo k {~ z|z²k>{²s z|ts³tvort¸wnk>s {² £ ort%{²s £ tmËoryusxzÉo¯{É°Èl{²sut#mr{|yd zUtm¯ { o¯y m
¹ #{² t%ortYmptH´{|×mr{|su{²z {|o kmrt #tm6o¯ytort su{²t ¹ {²Y{|s £ tmb{|Yor#t³yz²z|tHor{²y t
suyvm o-mr{|su{²z ory }d#t k>{|s £ t·
Ðt k yltm¯mp{² £ {|ydvortvor°hw mptHmr{|su{²z {|o k to {²t zl{~m{²t tvo¯z|k dt klts #l{² £ °
z|{~ or{²yU· ¼{²z|t.s nk l #t9sz|or{|°±{|sutmp{²y zE{|#tl{| £ sutorylm®tn{~mponor#tk>{²n { w#z|k
g{|voryYor#t{² ºØ s³yd#m ¿lû´Ä!"ÅÇÆ»$#ÅØÄ%#J¾%ÅÇÀ¸¹ t ºØ tH ¹ {|orÁzr£ tAydz|z²tor{²y#m³y º {£ l°
{|sutmp{²y
z-ltm¯
{ ory
m'&^j)(®¢l*((+% -,±·
¬
Áort¸wJtmpo9
mptdÖo¯t{
t
pº y s
#t´lt
£
ltHm
£d¯
t
º
z|z²kuoryuo¯
o6y
º
mrt}vtvo¯{
zUmr
y
º
o¯tydz|z²tor{²yU·
¬ Ys
nk¸
mrtm{|o%
mÐwJttYyw#mrt
tHor
oÊsuyvm oÊy
º
o¯txttdo¯
z8ory
tmrzÉom
t º y{²
o¯tt
z²kmpo
£
tmÊy
º
or#t>}d#t
k
yltm¯mp{²
£¸
#Yor
o%suydmpoy
º
o¯t>mrt
o¯{|sut{~m.{|
ºØ
om
tdo
yd
#¾Ã¯¾##ÀÈ»»Å.#
o¯
o6o¯t
tHmp#zÉo-y
º
o¯t}vt
k>{~m6{|lttHort%wJtmpo
tHmp#zÉo6o¯
ob
¸wt%ydwlo
{|#t1·
(ËtH mpty º or#tx{²t tdo%l{0/>z|o k´y º ydwlo {|#{| £ mp 9£ vo¯tt#ort t³ m ttvorz²k¸wtt
mr ¯£ t.y º {²do¯t tmpo-{| yMl{|s o¯t%}d#t k yntm¯mp{² £ z£ y {|or#sum ¹ {~o lt.o¯t £ vorttÊy º
wJtmpo tHmp#zÉo ºy 6 t#tHA}vt k # yltHmrmr{² £ o¯{|sut1&2(®l ) l ) ¬Î¢¢lJÓ l3(®Ì ).d ,±·
Ò tut s z|tuy º mr# mrt mr#tsutu{²mÊo¯t54pz|m o¯t {| £Aºy {²#ltl{| £%6³#¯ l{£ s¸ ¹ {~
¹® my {£ {² z|z²k y ydmrt³{²"&Ó-).Î" d7,±· ¬uor{~m y umrysut6sut {²mrs {~mQmptHo¯yl{²n{²lt
o¯t>ltHmr { ory yz²z²to¯{|yd×{|vory´nÍlm.y º mr{|su{²z o ·>Ìb yMl{|s o¯t³mrt z£ y {|ors;{²m
o¯t³#mrtor o6 78 £ z²yw z|z²k Ílm/ort6 o nÍlmw mrtyxort6l{~mpo t ºøyds ort-}vt k y{²vo
98 t m # # yltHmrmrtmQort. o n#Ínm{²>or#tÐy lt y º ort £ z²yw z ¯ Ín{| £ #>:8 z²{|tHm
££d
tHmrmr{|dt
ÀÈįÂÈÃ;)²»
orytort
su{²t
¹
ttyd
£
xor{²sut-
mQwtt>m
tdoQyd³ortb}vt
k
yltm¯mp{²
£ ·
Ì*mp{²s
z²t
¶
o¯
zmpory
z|tA{²mory
yntm¯mydz|kYor#t=<¼t
tmpoxnÍlm
#×o¯t
to¯
o¯t
tmrzÉo.o¯
o
mÊwtt×ywlo
{²t
o%o¯
o%o¯{|sut
mÊo¯t.!#
z tmrzÉo%y
º
or#t>}d#t
k·Ök
{~
z|z²k
wnk
yltHmrmr{|
£
ydz|k
xº t ¹ y º
ort
o
nÍlm
z|yvmpt
#
yMl{²s
or{²y>y
º
o¯t.ttvor
z tmrz|o6{²m
ydwlo
{|#t1·
>@?!> ACBD EGFIH%JLKNM?POQFGRTS
)Ê{²tor#tÐmpory 9 z²tÐtm¯ {|wJt wydtort £ y z#y º ort # yMl{²s ort to {²t zmrknmportsmpydz~wt
o¯yuywlo {²9o¯t%wtHm o ydm¯mp{²wz²t tHmpz|o-}v z²{Éo kQUÇo k {~ z²z²k>sut mr t9#mp{² £u t{²mr{|yd # Ñ y ® tH z²z.8
{²¸or#tsu{|{²s#s s³ydvo-y º or{²sut·®Ì {|to k9y º suto¯ylm6o¯y ºy s o¯tnÍlm6y º o s kAwt
U
#>
t-wJttV8#mrt1vwloËor{~mo
lty"¸wto
¹
tto¯t.}d
z²{Éo k
tHm
ympt6o¯{|sutÊ
myoËwJtt
mporl{|tH{|´lto
{²zh·
jn{²#tÐo¯t.nswJt
y º
v#ÍlmÖo¯y
t
{~m !lt1vo¯t
tHm
y#mrtÐor{²s³tÊy
º
ort%mrt
>{~m
{|s
{²z|k
tort
su{²twnko¯txÓ
ÖÕ
ydmpo®y
º+#
yltHmrmr{²
£
o¯tltHmr
{ ory
m®y
º
o¯tnÍlm·W¼#{|z²t%or#{²m-ydmpo6{²m
o k
{~
z|z²ku}d#{Éo¯tÊmr{
£
{!
doHdtd·
£ · ¹
t9#mr{²
£
or#tÊysusuyXQz²{²lt
9mr{²s³{²z
{Éo k³sut
mr
tv{Éo®
yo¯tvor{ z²z²kAwJtydt z tH ¹ {Éo¯ ¬rÑÒ ydmpo·-Ìbm > tmrz|oort ¹Ë k9ory £ ¯ do¯tt%su{²{|s z+}vt k
# yltHmrmr{² £ yvm oÐ{²mÐory yn#tx{ºy s³z²k´mp{²ÏtHnÍlm#o¯y9w z #tort ¬rÑÒ YÓ ÖÕ ydmpoÐy º
o¯tmrt U·
Õ
{
ºy
suz²k mr{²Ïtn#Ínm%y
¹
tdt
Ðs
k m
#
w{Éo
¯
{²z²k z
r£
t y o¯{|yd#m´y
º
o¯t s#zÉo¯{É°
{|sutmp{²y
zUm
td#lt
t#l{²
£
yo¯tlt#mp{|o kA{²mpo
{|w#lor{²y¸y
º
or#t
o
ydz|z²tor{²yU·Ö®#t
t ºy t
mrysuty
º
o¯tA}vt
k
yntm¯mp{²
£
or{²sut9s
kwJtAm
tvoy
yltHmrmr{|
£
ltm¯
{ ory
mÊor
o
t>}v{|ort
{Et tvo ºø ys o¯t.}d#t kutm¯ { o¯y ·/®tÊwJtmpo ¹® ko¯y £ vo¯tt tmrz|oË}v z²{|o k³{~mÖort t ºy t-ory
z²{²s³{|o6or#t%{|vo °ÈnÍ>l{~m¯mp{²su{|z {Éo kwJto ¹ tt´ltm¯ { ory mnmry³or o6y#t o nÍ9 m®wJtt
tort su{²t9orywJt%t ort}vt kAltm¯ { ory z²zUy º {Éom-ydvortvom tÐz²{|Ídtz²korywJtz²ydmrt m ¹ tz²zD·
Óz²t z²k+wyorÔ}v z|{|o k # tm yd#mptuo¯{|sutAttHorywJtAy#mr{²t t1 ¹ tÔ{|n{~l{| £ ortAlt°
m¯ { ory yz²z²to¯{|ydµ{|vory n#Ínm·#y t s z²t®wnkÁl{~mpo {|wor{² £ ltm¯ { ory m³o¯yÔnÍlm{²
y##n° ydw{|Ys t nÍlm.y º {ºy s mr{²Ït tywo {²tH18woort>}v z|{|o k ¹ {²z²zmr Jt · Ò
o¯t³yor#t #U { {² £ t tm¯ { o¯y й {Éo¯y#ty .9ºt ¹ y º {ÉomÊz|yvmptHm oÊt{£ nwJy m ¹ {²z|z £ {|dt
dt kAz²y ¹ {|vo ¯ °±nÍl{~mrmr{|su{²z {|o kJwloÐortxor{²suto¯y £ z²yw z²z|k ¯ ͸mp#mrs z²z+n#Ínm ¹ {|z²zwt
ttm¯mr{|dt·
>@? HVFBNH F M 1HNSDPS
®#t%s {| tmrt }d#tmpor{²yAor o6or{~m # t - tHmrmrtmË{~m®ort ºyz²z|y ¹ {² £5Ä #¾À6»r½dÀÈ»$#À dÄ»
#¾Ã¯¾##ÀÈ»»Å.#À» #»Ã;³ÂEÃrÄ¿»Å.#ÀhÅÇÆ»"! 1Å.#")#ÅÄÃÆ ¿))## Å%$H»&!.¿ÄÆbÂJïÄƳŻAÀ» $#¾%ÅÇÀ
Ä!À»9Ãr»;)À!.¾%# ( ÅØ¿» ( »Ã¾(' ¬¶y lt o¯y m¹ t o¯{²mx}vtmpor{²yU ¹ t>ys # t³o¹ yl{Jt tdo
y tmo¯y ºy su{² £ o¯t. o nÍlmÖor o ºylmyd £ vortt{² £ tm yd#mpt-or{²s³t # tmrzÉo
}v z|{|o k tm to¯{|dtz²k·
#y #{ºy s nÍ.mp{²Ïtd ¹ tQ dt`{|m o sutdo¯t j °ho ttQ{²#lt &+jl¢*)7,ory £ t#t ortQn#Ínm
y º #{ºy s(mp{²ÏtdlwvkA kv{² £ ortmr{²Ït.y º ort%z²t dtmËy º ort.o tt # £ tt o¯{| £ ydt%v#Í ºø ys
t
¼z²t
º
· ®tj
°Do
tts
ÍtHm>mrysuttEy
o9o¯y Ítt
mr{|su{²z
ltHmr
{ o¯y
muory
£
to¯t
®wloort
ts
mr{~m®{²m6m¯}v
tz²kyor#tv#Í9mr{|Ït·
/y6su{|{²su{|ÏtQ{²do
¯
°±n#Íbl{~mrmr{|su{²z
{|o k
¹
t`
t#mrtÐortz²#m o¯t
{|
£-
z£ y
{|ors y º &(®Ì ).
,h·
®#{²m
z£ y {Éo¯s
º
ylmptHm%y
£
vortt{²
£
o¯ts
l{²ss4l{
sutort
y º or#t
£
tt
o¯tz²#m o¯t
m
¹
#{|z²t-s
Ín{²
£
wJtmpot,Jy
oÖyduortÊnÍxmr{²Ït-wnk
z²z|y
¹
{²
£
or#tb#mrt
y º ort
z£ y
{|ors oryyvo
yz
o¯t%nswJt y º z|m o¯t m·
®t´s {|¼ydvo {|wor{²yÁy º or{~m # t {²m to {|z²tÁt t {²s³tvo z-mporlkÔy º o¯t´o ty"
wJto ¹ tt¼}d z²{Éo k #µ}vt k yltHmrmr{| £ o¯{|suty º o¯tmrt¸o ¹ y {Et tvo # y tHmxory ºy su{| £
n#Ínm·5tu#mrt z¯£ tu o mrto.y º 9su{|z²z²{|yd×°Èl{|sut#mp{²y zltm¯ { ory mU t o¯t#mp{² £ yt
y º o¯tsuydmpo #tHÁÍv#y ¹ Á{²s £ tltm¯ { or{²y¼mr#tsutm"&Ì ). $,h· ®t tmrzÉom>mry ¹ o¯ o
86o¯tul{Et tt³wto ¹ tto¯t}vt k yltm¯mp{² £ o¯{|sut }v z²{|o ky ºÖ tmrzÉomÊ#mp{² £ ortHmptxo ¹ y
y tm+{~mQz²tm¯mor t to¯t1 >8 ºylmp{² £ yuo¯tb}vt k yltm¯mp{² £ or{²sutbs k or z²z|k
£ {|dt + »ÀDÀȻà t z|k tmrzÉomÐor ºyl#mr{| £ yd}v z²{Éo kd· Ò wlo {|{² £ {ºy s5v#Í´mp{²Ïtx{²m z~mry ºØ
t mr{|t
or
£
vo¯tt{²
£
{|vo
°ÈnÍ>l{~m¯mp{²su{|z
{Éo kd·
®tHmpt
tmrz|o¯m`{²#l{~
ort®o¯
o ºy
Ö#
yMl{²s
ort®mr{|su{²z
{|o kxmrt
U#{
ºy s nÍmr{²ÏtmÖmpydz~
wJtuor#t.!
mpo
{|y
{|o k
¹
{|z²ts
Ín{²
£
tEy
o%ory
{|tt
£
ynyl
£
y
{²
£ m ¹
{|or#{|or#t9nÍlm·
)Ê{²tÊortQtno
tsutz²kbz²y
£
o¯{|sut
t}v{
tH-o¯y
£
tt
o¯t{
£
%}d
z²{Éo kÊv#Ílm
ºy yd
ydz|z²tor{²yUor#{²m
{~m
t
k ºy or
ort
tmrzÉoH
m t
rº y
s³{²
£
mpAz²#mport
{²
£xº y
t
kuz
¯£
t.ltm¯
{ ory
ydz|z²tor{²y#m
¹ y#z²mp{²s z²k>wt%{²s yvmrmr{²wz|td·