HAL Id: tel-00349464
https://tel.archives-ouvertes.fr/tel-00349464
Submitted on 31 Dec 2008
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.
De la résolution numérique des EDP à l’extraction de caractéristiques linéiques dans les images : application à
la détection multi-échelles d’un arbre vasculaire
Benoit Tremblais
To cite this version:
Benoit Tremblais. De la résolution numérique des EDP à l’extraction de caractéristiques linéiques
dans les images : application à la détection multi-échelles d’un arbre vasculaire. Traitement du signal
et de l’image [eess.SP]. Université de Poitiers, 2002. Français. �tel-00349464�
!#"$%&!'
(')+*-,/.1032546.87:9;=</>@?+.A2CB&>D,/E846.GFH)I>@,3>J.A2CB
KL
%:MNOPQ!RTSUMNVMWR
L
!X%&YZ[%:RHW\]!@V^U!PNR`_
Ka
VbYZdce%fV X%&1gh\]ikjWP'!mlnpom%&iRQq[r:rts:_
uwvyx{z}|3~xvJx{ z}| UW!3:e&V
|yvJ|[h|3w|yvy ¡|¢vy ¡| &£A¤¡¥i[¦§[:¥H¨! kV:¤¡AW¥¨©@¦ª¤«:
¬®¯°±²N³¯k±h´¡µ
¶¸·t¹»º1¼¾½#¿ÁÀd©ÃÅÄTÆwÇÉÈkÊ
Ë Ì ÍÎ Ï3ÐÒÑwÓ=ÍÔÖÕ/×W ØÔÚÙ ÐÏ/×ÛÜÔÝÌ Þ ÌTÑ Ë ß à
ÍUáÌâÕãÏ6Î=äIÕã×W ÞÝÌ äHÎdÏ6Î=äIÕãЩÏ3×ÑAÕ/×ÛÜÔ ÌTÑ ÍW×Ø Ðe×ÛÜÔÝÌÒÑ
ÞmÎ=ØÚÑ ÍWÌTÑ ×Ù Îdå=ÌTÑ æ#ÎdçÚçmÍW×äHÎèÕ/×W à ÍÎ Þ Ð©ÕãÌTähÕã×WÓ§Ø
Ù Ô Í Õã×`éXÐÒä»êÝÌÍWÍWÌTÑ Þ8áÔÚØ ÎQÏ3ëÝÏ3Ì ìdÎ=ÑãäHÔ ÍÎd×Ï3Ì
í/î}±kï³¢±kð«ãñf±»òôófõ°±
oÝ@M`ö!/÷
EXøh2ã4
ùAú`û ±²fïiµ`ñf±ü±²N³Cñf±»òôófõ°±
ý
%&mþ
0ãÿh.12ã.Xø30
! "$#$#% &')(*$))+,-+'$ .0/132$) 4)5$,-687
9;:5<>=
++56?*$'$ A@
<
BC,-,-@DE +%,-+F6%+@GIH
9KJ-J:::L::::L:::::L::::L:::::::::::::::::::CM
$5$-
9 ) J, 58?N'O= @ < BC,-,-@01>PQ < +,@5Q& JR:L::::::::::::::::::::::::::::L::::L:::::L:::::::SM $5$-
9;:5T
$,-6HE'$S@
<
$BU,-,-@5D +',-+F
<
$++,@VW+'+'
=X ,-+FV$+
::::L:::::L:::::::::::::::
1>2)+'
9;:09 +
=
9
WVY@
9
WZ'-[6(*$ BU ,@5\]
M
@DE +%,-+F6"GI
M
O
=
@5GA^
J)::::L::::L:::::
1>2)+'
9;:09 +
=
AGAWVY@
<
BC,-,-@5DE +%,-+F
<
+F+,@
J_M (a`
94b J(
:::::::::::::::::::L::::L:::::
1>2)+'
9;: ?*L--V$ 4HEcA@ 9 WZ'-[6(*$ BU ,@5D +%,-+F < $+F+'L,@ JdM (a` 94b J( :::L::::L::: 1>2)+'
9;:
])+ .(*$+,- @
9
+ e,a\
X
+FV$20@5(*\
M
Df
<
+F+,
::::::::::::::::::L::::L:::::L::::L::::::::UJ +F
{6|~}3W%l%KSl% &5 3lWOWOO|3|kl|Ye%Sl.Y%K3SSS}3}.Y a¡¢0S
OO%}3W£ 3;W%SSW;O%W>OW%4 a¡F%|¥¤%W;lO}3}W% 3W¦§¨©¢0%Wl|«ª>|kl 3O¬£%SW
£%|>£ªk%l£¬ 3.l% 3)lO% 3WeWORW%|AS¢0%R 3.l% 3W)W%©WA >O)}3W£O%l% >WO¦3®Y.l%|>W%%W%l%
lR6W¯°OW% 36®05W£±Y0²E¬ a¡¢0S!OO%}3W£R a¡F¤%WR}3W£Ol 3%|Y! ³ . 3´S|>>A >Rµ«l>%*¶¸·>²E¹aº6
»el%|½¼eE¾d¿&ÀÁ%µf%lK¹aþ_¿Ä a¡F¤%W¬¢0%|A >4WWlW%Å}3W£OW%|Yl|Æ 3eOe¢S¦
®Y.¢0 > ³l)W%%W%l%)W 3)}kl% 3Sl%W%%|YKÇ!%|> ȱ¬É¨ÊÀk¹aÀ³²É½Y 3È¡ ³SSË0£.W 3R
l|3Ë© 3eOORWl|3|>£OOR 3.>OW5¦>L&W 3W£%W£e ³l}*|3S3l5N¡F£OO 3W¬ 3.O)|>3W% >O
A >Ol|>³%¡FO!W 3WS|AW£%WOWW£e;¡O¢5|>O£OK 3KO!O¢5 ³Ìa¦I§¨O|>3W% >WOR ³l% >Wl|>
A >|> >¬O¢0|>¬% >O;S|>6Y >WOeO|>%Sl¬O¢IlW£O¬W|Ae}* 3. >O 3}½ >|>elW£O 3S.ª>|k
3OO¢5S¦a{|³ª>|&&O4|>;3W% >WO¬W%lO% 3WO%.OWO%l|>;V´ISllA >Oe%eW%l%|YCªkA >O¬ 3
O%We>O¬|Y£%W£¬WO}3}3W£O%Å3lO¦*Í!%W¬>OWeS 3& 3SR >O 3}&¦
®YÎW%%W%lÁµ«l>%4Ï6·³²E¹aºÐ a¡O¢0SOÑV%|> ³W£ÈOÒ¢SR 3Î>OW5¦"LÈ¡«W 3 a¡W
}%l a¡S|AW£%Ë5W%¡F£OA 3S}*ÔÓIÍp ³ ¥ÅWSW©ÕRÍ)ÖKµ×%|¥}3W}*5|A 3|½ %¬WOeS|AW£Ñ
WOW$|Ya}3 3leS[ÎW 3e¯-SWO|³ªN|>OÔ%eÅlWW%e 3|>%|Al%WSS*%W£}* 3¬l%|AW%¬O
¢ ³ÌÈ 3eWO>%WW>5¦
®YW%%W%lØ >WW >~lO~%3WOÆ ³ rË5W 3}*%%|A¥ÙES 3l 3OfL©Ë0%l¸ÓASË5|kÍW ³lÑ
¢5W% 3ÅSW~Ú°Ù"Ó3Í)ÛeO¢0OÔY 3&%¡[% l}3ÅlS 3} 3¢0S¢SSl%¨|>%|Y"µ~lW>%¶¸·IÜ
²¹aº>ÝKS|>O%|Y¼.É&¹aÞNÉ&0²YßØ%R»el%|¥¼.¾_¿&À¦
®YÔW%%W%lÒÅ«W£%Ë5l|ØESW ³ÑÍ8kW%|AWO© a¡O¢0S©OO%}3W£Î 3©ª>|k|>O%OO;Wl|3|>£OO 3
¢S¦
®Y¬l%|>.W%%W%l%4W 34}kl% 3Sl%W%%|Ye®5 3Sl%|&*àSS|>5kÙ3|>áOlW%3SSS}3}¬} 3l% 3
W%lO% 3WOW%|AS¢0O 3Ô}klO t 3ÔÅÁWSSW£ÒO©£%SW5¦Ll;|A;}kl%S}£ÒÈÅ«A kSSW£
>Ë5}33lA >;%)W£O >%l|3|>%Sl 3eOe©|A >W%S¦
®YÎW%%W%lÁ£%ËYl%%|YW >lO>£OW 3Ë5ÅSWO%}*%©|>%|AW© ³ ¸Å*WSWÎ} 3
ÅÒ|3|>3Å|>O 3¢S©le£%ËYl%%|A¬}* 3elOK|>;3W% ³ÌÆ|>.%|YW¬}kWW£Oe%|³Ñ
W%;3lO¦3{|AW 3WOR§¨ 3W%|ANâK 3SSÅ 353®5 3Sl%|&>63SSS}3}*5kÍ8kã0%3à4|3|>ÑÓI33Ù3WO a>Ç%|>S
l%W5Í83lÅ|&à|3|>ÑVµÆl5µf ³¨®YOA >OE{l5¨äeO¢Il%¦O¦O¦L8|>Ô¡Ë5SS}k a¡F 33Sl%
|>5¬O%W£%SWO¬}3W£¯-£%W£OO¬Ù3|>áOlW%;ÓA´IS¢Il;} 3el% 3´I}k3l%el% 3¬ ³l}|3S3SSSW£©ÒW£Ñ
Ë5l%elOe}%SW.}3W3l%O ³S|3lC¯-¦EÓ³|>.l% 3e¢0l|AW£|> >e|&¡ 3l|>e}k% ¥ 3|A 3
%WlW$|YW.%4}kS|>e ³Ì«>AOÅWe©Å}k >W¯°£5¦*LlR¢0|Y.}% 34¤%W¤%W;W 3}3lÚdS|Y.}3S ³Ñ
Wå;¡k3S > 3ÒA >¡F|æW}3ÅSË5|>Ô a¡F% ³Ì>Û¬©l)l%|> >W8ÈW%%W%l%{6l©%;µÆ|Y &ElO
³S|3lW% 3WW£OW æ ³ ½ÅWSW©} 3¬©È}k³|&¡[W%|>O|YW£ÒA >WO¬}% 3
}3W3l%O4S|³¯°©lA >O ³ 3|A4OO)Wl4|3|>£OO 3.>OW5¦
{6|³ª>|&5e|>eW%%W%l%N©lW%çà4SS|>e}* 34W|«W 3l%|&>$}kl%|>O%OR%|>O 3Ñ
òÒóAôóYõöY÷dóAôóAø*ùú û
ü ý ø*ùõþaÿEö5ù÷dþNø
Èþ>ù³ù÷dþNøEú ü
Òk:V¥:Öt¦ªN{ è¨T®:eV$¥¤¡O¥¦ª¥H¨V¦ª¤f&
Èþ>ù÷dþNøEúúEõdóÈùõ>÷_ùóAô½óIø*ùÔô_ù÷Yö Eó!"dóYú
aü
# ¦%$ &4lWlY > ¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦e¦¦e¦¬¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦ #'#
# ¦# àÌIl©ll|~ ³ ÈSW%%|YK 3O)S©Ë0OR¦¬¦e¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦ #'(
# ¦# ¦%$ §&O4̳lOW3SWO% 3 ³Ì ¦¬¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦ #'(
# ¦# ¦#
§&O4̳lO)Ë0£O£%lA >O%R}3>lË5lA >O ¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦
# è
# ¦# ¦( ) >£OW%O4 3£OO 3Å|A4 3O̳lOe¦¬¦e¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦ #'*
û +-,/.106þ2¨õ354%>ô6!°÷dþkõ³ù÷_þ*ø ÿ74l÷dô68kóAú:9;Yù³ù©ÿó<4%3õù
( ¦%$ §alW$Ë0.}k{6». ¦e¦¬¦e¦¬¦¬¦e¦¬¦e¦¦e¦¬¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦ #'=
( ¦%$5¦%$ ÙSSË0e 3SCÑV£O>%SlO4SS|>£SW~¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦ #'=
( ¦%$5¦# ÙSSË0e 3SCÑV£O>%SlO4|>|«SS|>£SW ¦e¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦ ('>
( ¦%$5¦( ÙSSË0e}kR©lO 3e ³@? >l| ¦¬¦e¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦ è >
( ¦%$5¦è à}3}3WIW>O}kRË0£O£%l ³@?a£%W%|Yl%Sl ¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦ è (
(
¦%$5¦BA »K@?* >l|«¢0O%Wl%Sl ¦¬¦e¦¦e¦¬¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦ è *
( ¦# Õ%k >W%%|Y%4{6».DCIª>SWO 3e>A ¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦ è!E
( ¦(
Í!3S|kl|~ ³ ÈSlW$Ë0e% ³ ÁW%k >WW%%|Aצ¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦ è!E
( ¦è »KlW%W£%ll|« 3O{6».v¦¬¦¬¦e¦¬¦e¦¦e¦¬¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦FA (
( ¦è>¦%$ ÓIW>£%©©ÌI}3Sl%SW©Ú° ~{ 3l%4O¢5|Y$Û¦¬¦e¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦FAè
( ¦è>¦# ÓIW>£%©©W%CÑS}3Sl%SW ¦e¦¦e¦¬¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦FAè
( ¦è>¦( ÓIW>£%©S}3Sl%SWÔÚ° È{ 3l%4W£%WË5 3Û¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦FAè
( ¦è>¦è à 3WOR£%>A 3O4 3¬ ³lW%W£%ll|Á¦¬¦e¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦FA'A
( ¦è>¦BA Í8>CÌÈ a¡ 3|«WW>£%©|Y 3£%lA >¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦FA'A
G H õYúþ2I¨ù÷dþNø ÿEóAú+J,/. LK
è>¦%$ Í!|> ³Sl|> 3O|Y¢0%Ë0%|>O 3OR{6». 3e ³@? >l|NM%ÅWWlY >OJO ¦e¦¬¦e¦¬¦¬¦e¦¬¦FAPE
è>¦%$5¦%$ µ«le%|È}3ÅO¬ ³ Á}3WIOOW >R 3.SW%%|A ¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦FA'Q
è>¦%$5¦
#
à|kS´³We 3eÅO|A¢0%Ë0%|>O; ³ Á}3WIOOW >RË0£%|>£%SlW£¬¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦
*'>
è>¦%$5¦è ÓA 3RleW>CÌÈ 3 H ¦e¦¬¦¬¦e¦¬¦e¦¦e¦¬¦¬¦e¦¬¦e¦¬¦e¦¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦ *'*
è>¦
# e
> 3¬ ³´I|klY > a¡ 3|È}3WAOO >R 3e ³@? >l|ÈSS|>£SW榬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦
* E
è>¦# ¦%$ à}3}3Sll|Æ ³ÌÒS©Ë0O4%|Á|3S¢0 ³ÌÁ 3¬Ë5lf¦e¦¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦ * E
è>¦# ¦# à}3}3Sll|Æ ³ÌÒS©Ë0O4%|ÈO 3l% 3 ¦e¦¬¦e¦¬¦e¦¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦fE =
g ÷"_ùõóAúÿóÈöEþaöÈóYùÔô½þNõh0;¨þ2dþ8N÷dóÈô6³ùiIôj³ù÷IkY¨ó l K
A³¦%$ ÙSSWe 3¬W>I¬%R}£%W% 3W a¡F 3¢0% 3W%R 3.¯°%% 3W ¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦FQPE
A³¦# Õ£O 3SW ¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦e¦¬¦e¦¦e¦¬¦¬¦e¦¬¦e¦¬¦e¦¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦FQ'Q
A³¦# ¦%$ E%¯-©|>OO4 3¬W%k >WW%%|Y ¦¬¦¬¦e¦¬¦e¦¬¦e¦¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦FQ =
A³¦
# ¦#
ÓI%|>S3SSSW£ È3 3S¸¦¬¦¬¦e¦¬¦e¦¦e¦¬¦¬¦e¦¬¦e¦¬¦e¦¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦
= $
A³¦# ¦( ÓA3SSSW£ ³ Á}3WIOOW >î¦e¦¬¦e¦¦e¦¬¦¬¦e¦¬¦e¦¬¦e¦¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦ = è
A³¦
(
Í!3S|klW|ÆO¢0Oe 3|«W%¬ 3eSlWË0 ¦¬¦¬¦e¦¬¦e¦¬¦e¦¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦
= è
A³¦è Í!|>%S >l|Á¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦e¦¬¦e¦¦e¦¬¦¬¦e¦¬¦e¦¬¦e¦¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦ ='*
m n
÷_úú8kó<03õÒö0þoEõpEõóÈôþrqNóAøøEó«ÿ74S÷°ô68kóYúts*óYö5ùþNõ÷dórIdóAú K
* ¦%$ ».£ª>|3Sl|> 3eO 33 3WO4}* 3R 3O)S©Ë0O¢0O%Wl%SlO ¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦ = E
*
¦%$5¦%$ »K£ª>|3Sl|~ 3eÅ}3W%l%We¯-.¯-|> >%|Yl ¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦
= E
* ¦%$5¦# »K£ª>|3Sl|~ 3eÅWOO|> 3.¯-.¯-|> >%|Yl%R 3ORO 33 3WO ¦¬¦e¦¬¦¬¦ = Q
* ¦%$5¦( Í8>CÌÁ a¡ 3|Á¢0O%W% 34|>©EÅ 3¯OȦe¦¬¦e¦¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦ ='=
* ¦#
§alWË0e a¡S©Ë0O¢0O%Wl%SlO}k 3|>e{6». 3eO 33 3W´0%|3|>¦¬¦¦e¦¬¦e¦¬¦¬¦-$
> $
* ¦# ¦%$ S|>%S}* ¦e¦¬¦¦e¦¬¦e¦¬¦¬¦e¦¬¦e¦¦e¦¬¦¬¦e¦¬¦e¦¬¦e¦¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦-$ > $
* ¦# ¦# à}3}3Sll|Æ ÁSlWË0e a¡S©Ë0O%|~O 3l% 3Ʀe¦¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦-$ >'#
* ¦(
».£%WO%l|« 3O)SSË5|>OO%|AlO4 >|>R 3|>eS©Ë0e¢0O%Wl%Sl ¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦-$
>'#
* ¦( ¦%$ à}3}3Sll|Î.Åe 3£%WO%l|Ô 3O[SSË5|>O[O%|AlO! >|>[ 3|>)S©Ë0%|ÔO 3l% 3P$ > A
vu¥¤¡ ¥Z¨è¤f¤¡ ¥N{@¥ tIV@ I¨¤¡¨¤¡:V&&¤L7w!:!¤f
¤x:zy|{} ~
K
þNõþ*ø¨þo8kõ0÷dó/03õÔõhqNþNøEú
,
üküNü
EI¦%$ Í!|YW̳We£O ³l«¦¬¦¦e¦¬¦e¦¬¦¬¦e¦¬¦e¦¦e¦¬¦¬¦e¦¬¦e¦¬¦e¦¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦-$'$'$
EI¦%$5¦%$
R
>%lY >O|>l|>R a¡|kWl ¦e¦¬¦¬¦e¦¬¦e¦¬¦e¦¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦-$'$'$
EI¦%$5¦# >lË5l 3OW%WOOW|kSWOC³¡>£%W5W%l£%W5W ¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦-$'$%è
EI¦%$5¦
( )
SW%%|YW. 3O)}k>lË5lO ¦¦e¦¬¦¬¦e¦¬¦e¦¬¦e¦¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦-$'$
*
EI¦%$5¦è Í8>CÌÁ 3.ÅA >SSW£¬ a¡S©Ë0%l; 3O)¢5lWW ³Ì ¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦-$'$ *
EI¦# Í!W|>Ë5}33l¬}kR´0|>Rä # » ¦¬¦e¦¦e¦¬¦¬¦e¦¬¦e¦¬¦e¦¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦-$'$E
EI¦
#
¦%$ »KO%S}3l|« 3e¡|3Ë5lË5}3>
#
»p 3SSl£~¦e¦¬¦e¦¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦-$'$E
EI¦# ¦# »K£%W 3l%%|A4 3e¡FÌ>%|«OW|>Ë5}33lA >~¦e¦¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦-$'$Q
EI¦# ¦( Í!|YS|YWO.%)SSSl|>K ³ È´³W%e a¡S©Ë0%l ¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦-$'$ =
l ,/YùóYö5ù÷dþNø ÿóYú °÷I8NøEóYúö0óIø*ùõhdóAú©ó0ùÔÿEóAúö0þNø*ùþ2¨õúÿóYúts>÷dúúói ú>ø8o÷°ø¨ú ü û
Q³¦%$ Í%W£%ll|~ 3OR¢lW ³ÌÎ|3Ë5 3S|> ¦¬¦¬¦e¦¬¦e¦¬¦e¦¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦-$ # è
Q³¦%$5¦%$ »4S¢0%WOR 3£ª>|3Sl|>4 3e%W¤%WO4%)¢Sl£OO¸¦e¦¬¦e¦¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦-$ #'*
Q³¦# à}3}3WIW>O 3SSl|YÅ}3>lË5l¬©>£%©lA >Ô¦e¦¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦-$ # Q
Q³¦( µ~£%>I 3OR 3e 3S¢I ¦¦e¦¬¦e¦¬¦¬¦e¦¬¦e¦¦e¦¬¦¬¦e¦¬¦e¦¬¦e¦¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦-$ # Q
Q³¦è µ~£%>I 3O) 3SSl|ARlORI 3%lOR 3£¯-©3lO ¦¬¦e¦¬¦e¦¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦-$ ('>
Q³¦* à4|kS´IW.; 3SCÑV£OW>%SlOKSS|>£SW¦e¦¦e¦¬¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦-$ ( $
Q³¦
*
¦%$ ÓA3SSSW£ ³ È 3£%WO%W% 3 ¦e¦¦e¦¬¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦-$
('#
Q³¦* ¦# ».£%W%S|kl|~ 3e¡F£O>%Sl}3S©lȦe¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦-$ ('#
Q³¦* ¦( ».£%W%S|kl|~ 3e¡S|AW%¢Sl; a¡F£OW>%SlO¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦-$ ('(
Q³¦* ¦è e Wk|ASSl|3|kË0 3e¡FO}kOÑV£OW>%SlO¦e¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦-$ ( è
Q³¦* ¦BA Ù3 >l|« 3ORS|³¯°©l|>K 3.¡FO}kOÑV£OW>%SlO ¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦-$ ( è
,/YùóYö5ù÷dþ*ø ô_ù÷AöEó!"dóYúÿóYúd÷I8*ø¨óAúö0óAø*ùõdóYú©ÿóYú 3õùAõóAú©ö0þNõþ*øi>÷dõóYú ü!G¨ü
= ¦%$ Õ£%}|>W¬ 3|>e¢5Sl£O%W¤%W¦e¦¬¦e¦¦e¦¬¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦-$%è$
= ¦%$5¦%$ ».£ª>|3Sl|~£%W%|> ³ >¬ 3e¢5Sl£Oe%%W¤%W ¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦-$%è #
= ¦%$5¦# ».£%W%S|kl|~ a¡ 3|>¬W£%}|>W¬ ³ÌÎ}3Sl ¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦-$%è #
= ¦# e
¢5S kl|~ 3e ³S¢0%WWO£%>A 3O a¡FÌI%l|f 3O)SSË5|>OO%|AlOy¦¬¦e¦¬¦¬¦e¦¬¦-$%è
*
= ¦( |SW%%|Y; 3SCÑV£OW>%SlO 3Ò 3£%WO%l|Ø 3OSSË5|>OO%|AlO 3O¢5lWW ³Ì
|3Ë5 3S|>¸¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦e¦¦e¦¬¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦-$A
>
= ¦( ¦%$ ».£%W%S|kl|~ 3OR}k%WO4 3e¡FO}kOÑV£O>%SlO¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦-$Aè
= ¦( ¦# e Wk|ASSl|3|kË0 ³ È}k%W£O>%Sl;¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦-$APE
= ¦( ¦(
ÓA3SSSW£ ³ È 3£%WO%W% 3K 3eSSË5|>¬ 3K¯-|> ¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦-$APE
= ¦( ¦è 4©Sl$l|~ 3O)W£%}|>WOצ¬¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦-$A =
= ¦(
¦BA ».£%WO%l|« 3SCÑV£O>%SlO. 3O)SSË5|>OO%|AlO ¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦-$A
=
= ¦è Õ£OW 3SW ¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦e¦¦e¦¬¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦-$ *'#
= ¦BA à4 3WO}3}3Sll|>Ʀ¬¦e¦¬¦¬¦e¦¬¦e¦¦e¦¬¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦-$ * Q
=
¦BA³¦%$ ».£%WO%l|~ 3O)¢5lWW ³ÌÁ|3Ë5 3S|>R 3eÅW£%S|> ¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦-$
* Q
= ¦BA³¦# à|kS´³We 3eË5¢A 3WO4 3)WIW>Ʀ¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦-$ * Q
ü<
þaÿ!°÷dú³ù÷dþNø ÿEó54%3õpEõó3õùYõ÷dó!!ÿYùóYö5ù
üK*ü
$ > ¦%$æW}5Sl|« a¡ 3|ÈI 3%l ¦¬¦e¦¬¦e¦¦e¦¬¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦-$E #
$ > ¦#
».£%WO%l|~ 3W©lA >O4 3.}S|YW}kl% 3Sl%W ¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦-$E
#
$ > ¦# ¦%$p§&OR}S|YWÌIW¤%O ¦¬¦e¦¦e¦¬¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦-$E (
$ > ¦# ¦# §&OR}S|YW 3e3C¯d 3Wl|½¦¦e¦¬¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦-$Eè
$ > ¦# ¦(
§&OR}S|YW a¡S|YW%WWO%l|즦e¦¬¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦-$E A
$ > ¦( {6S©l|f ³ È ³Å%W 3OW%WO ¦¬¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦-$E *
$ > ¦( ¦%$pµ«le%|z. 3¢AW ¦¬¦¬¦e¦¬¦e¦¦e¦¬¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦-$E *
$ > ¦( ¦#
Õ£O 3SW ¦e¦¬¦e¦¬¦¬¦e¦¬¦e¦¦e¦¬¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦-$E
*
$ > ¦è à4}3}kl%%|Y4 3O 3% ³ÌÎ}3WO%l|> ¦¬¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦-$E =
üNü<
þ*ø¨ö!IEú÷dþNø ó0ù 06óAõú06óYö5ù÷s*óYú
ü
lNû
g
þNøEö5ù÷dþNøEúÿEó~ÿ÷7Eú÷dþNøEúó0ù LþNøEö5ù÷dþNøEú06þ>ùóIø*ù÷_ór"_óAú
ü l K
Eó!IkY¨óAú©øEþ>ù÷dþNøEúÿEóz8Yþ*ôjYùõ÷dófÿ÷AõóIø*ù÷_ór"_ó~ó0ùõ÷dóAôj>øø÷_óIøEøEó
ü
lo
Ç.¦%$Kl|> ¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦e¦¦e¦¬¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦-$Q =
Ç.¦# µfA 3£%Sll|~ a¡ 3|>eS©Ë0e}kR 3|È%}3Sl%%|AK a¡F%|>W%;3lO4 3.|3S¢0 ¦¬¦¬¦e¦¬¦-$ ='>
Ç.¦# ¦%$ ».£%S¢0£OOR}3W%l%WO >|>ÅkW I2 ¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦-$ = $
Ç.¦# ¦# ».£%S¢0£OOWOO|> 3O4 >|>)ÅkW I2 ¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦-$ ='#
Ç.¦( µfA 3£%Sll|~ a¡ 3|>eS©Ë0e}kR 3|>e 3¯Oî¦e¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦-$ ='(
Ç.¦( ¦%$ W%l%We¯-.¯-|> >%|Yl ¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦e¦¬¦¬¦e¦¦e¦¬¦e¦¬¦¬¦e¦¬¦-$ = è
Ç.¦è Õ%Ål|È%|AW¬lORO 33 3WO4 3ORlW}3>WOR%lORO 33 3WO ( » ¦e¦¬¦¦e¦¬¦e¦¬¦¬¦-$ ='=
þaÿrdóYúÿóz0õþ;dúÿó<°÷I8NøEó
&ü
ÍK¦%$ 4l| ¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦e¦¬¦e¦¦e¦¬¦¬¦e¦¬¦e¦¬¦e¦¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦ #'> $
ÍK¦# µ~I 3%l.kW ¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦e¦¬¦e¦¦e¦¬¦¬¦e¦¬¦e¦¬¦e¦¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦ #'> $
ÍK¦
(
µ~I 3%l.ËY >Wl%|Á¦e¦¬¦¦e¦¬¦e¦¬¦¬¦e¦¬¦e¦¦e¦¬¦¬¦e¦¬¦e¦¬¦e¦¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦
#'>'#
ÍK¦èðµ~I 3%l.}kSlY >¦¦e¦¬¦e¦¬¦¬¦e¦¬¦e¦¦e¦¬¦¬¦e¦¬¦e¦¬¦e¦¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦ #'>'#
ÍK¦BA µ~I 3%l.Å|3Ë5 3ÅSW«¦¦e¦¬¦e¦¬¦¬¦e¦¬¦e¦¦e¦¬¦¬¦e¦¬¦e¦¬¦e¦¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦ #'>'#
ÍK¦
*
µ~I 3%l.lW È ³ ÁI 3%l¬ ³ È¢5lWW ¦¦e¦¬¦¬¦e¦¬¦e¦¬¦e¦¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦
#'>'(
, ,È÷sNóAõú8Nõh3ÿ"÷dóAø*ùúóIø ö0þ2dór¨õ 2
»¦%$ âK ³l%|Y©Ë5S|k ¦¦e¦¬¦e¦¬¦¬¦e¦¬¦e¦¦e¦¬¦¬¦e¦¬¦e¦¬¦e¦¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦ #'> A
»¦# âK ³l%|YW¢0O%Wl%l 3¡¾lÜ£¢À>&Ä0t%KÏ6ÀkÀIܼ.Eà ¦¬¦e¦¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦ #'> A
»¦( âK ³l%|Y4 3t¤*E&Àk½%¦¥ §¨N¦¬¦¬¦e¦¬¦e¦¦e¦¬¦¬¦e¦¬¦e¦¬¦e¦¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦ #'>'*
+
r©Vø¨ó~ÿ4%3öPkY÷dú÷_ù÷_þ*øª03õÔõPq*þNøEú
{R¦%$ðâ.£%|>£%W% 3 3e´0|>Rä ¦e¦¬¦¬¦e¦¬¦e¦¦e¦¬¦¬¦e¦¬¦e¦¬¦e¦¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦ #'>'=
{R¦# V|AW%%l|~ 3O)´0|>Rä O¢0OeÅ©l%W ¦¬¦e¦¬¦e¦¬¦e¦¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦ #'>'=
{R¦
(
ÓA´IWW%OR a¡S©Ë0%l ¦e¦¬¦e¦¬¦¬¦e¦¬¦e¦¦e¦¬¦¬¦e¦¬¦e¦¬¦e¦¦¬¦e¦¬¦e¦¬¦e¦¬¦¦e¦¬¦e¦¬¦¬¦
#
$'$
Áw xq6® ï°¯ s xtu;® w
±³²µ´J¶o·¸¶o·
§¨O.O¢5 ³Ì~ 3O%W>OW¡S|>%S¢0%|Ye >|>KlO|AWÌIW ³ fSW%%|Y a¡S©Ë0O¦aÍ! 3Ñ
©S|>¬ 3O4W%l%|>OO}3}3SlA >£OO4O|3|A « 3|È 3£%¢0%l}3}%%|Y.O|>l 3£%3lOOR 3%|3l%WOK|3|>£OO
O. 3£%¢0%l}3}%%|Y£%|A)|>%|YRSl£.;¡F£%¢0S 3l|Á}3l 3e 3O8}%¯-©|>OO) 3Kl% 3a%) 3
WIWã5Ë0© 3O;W ³S|kW% 3W¦§&SW%%|Y a¡S©Ë0©¢AlWÔÈ 3W©lW%; 3O;SW%%|YWA 3[W
¯ll%|YK 3}kO¢5|YK¢Al >%Sl%%|A4 Á©|A >%Sl%%|Ye%RO 3¢AW;% >%Sl%%|YK 3|Á|>3W¬¢5l£
%¬Ë5|> ³l|Y a¡}3}3Sll|>W%SlO;Y >¡S©Ë0%lÔW%SSSSW5&¡S©Ë0%l©£O ³ll5&Å΢Il 3£O
3¢0%SSÅ|>O5!l~%S|>£%©³8l~O|YWålf|>| 3O >%C¯8¡S©Ë0%l~ 3SÑVW|>WÆ%ÒO >lA >5¦S¦S¦
»e|>Ô 3|>~}3}3Sll| a¡|kS´IW~ a¡S©Ë0OÔ| ³lS|3Ë5 >«O 3%|AÁ 3% ³Ì V´I}*OÔ 3ÁSWÑ
%|AW! ³SW[SW%%|YW) 3)k8|3S¢0 Ô%8SW%%|YW 3Rk 38|3S¢0 ¹FµÆQ
#hº
¦Y§¨O[SW%%|AW
3)k6|3S¢0 ÔO|>O%|>%|Y!lOSW%%|AW8 3)|k 3WR|Y 3£%lA >£?aO% >£O[|>W%|3S!O}3WR ³
O|AW%|Y t 3¡S©Ë05¦&Ll.O|>lW%|A¬Ë0£%|>£%l%%|Y%|f 3|>£%} 3}3W£%SW%%|YE5¡FOÑLÑV ³SW
%|ΡF£%SSS|kl|« ³ Î3 3SR%) ³ 3»k &A}3 3l)%|Î 3|>.£%}K 3.W%Ë5%|Al|&3}kSl|È 3K¡S©Ë0
%| >ÑW£%Ë5l|>e>Ë0%|>O¦E§&OeSW%%|YW 3k 3¬|3S¢0 O|>O%|>%|A 3O¬SW%%|YW;¢ACÑ
|AS|YW%}3W£%W%)lKO|YW%|A Á 3¡S©Ë05¦³%0|> >!|> >!S|YW£%WOWW|>!}3S >!}kl% 3Sl%W%%|Y ³Ì
}3W3l£%©lA >O 3}3W£%SW%%|A 3©k;|3S¢0 æ% a¡FÌI%l|Ø 3Ò%W£%llA >O >|>;l
³W¬ a¡ 3|>;}3}3Sll|f a¡S©Ë0%l£O ³ll5¦
¼ ²W¶2½¾7¿W¶2½À²µ´vÁ
§¨O;¢ ³Ìæ}3W£OW%|YW£O >|>OÒ 3A% 3%|A|Y£%W£©S¢0£O}k 3|>Ò}3}3Sll|Ø}3lA >
¢Il|YÁ¥ 3£%¢0%l}3}%Ô 3| 3SS|³¯-©lA >~ a¡l 3Æ ³ÅË5|>5lA >« 3OÔ}k>lË5lOÎW ³lÑ
¢5W% 3ÅSWO¦8§&O©Å ³lOÒW ³lÑ¢% 3ÅSWOÔWOWW%|Y©ÅWOO|> 3È >W~ 3ÁSSW£f >|>l
|> 35I}3WO6lO6©Å ³lO[S|³¯°O%l% >O0%6Å.}3W%l%W4 >WR 3)SSW£4 >|>6lO}k´I[S|> ³ >Ñ
ÅSlW£O-¹F§&O >'#º CYA 3S|3ç)SSSl|>8 3}*%W|3|>O[%|©% 3W%|A!kY >K|3|>£O5¦Y"!O|>£OY >%|AY 3
|>;3W% ³Ì~O¢5 ³Ì« 3¬WO>%WW>|Y.£%W£%|AW%}3leª>|f 3l% ³Ì«O}3W%|> ³W;%.}3}3W£%>%|> 3%
lO)}k>lË5lO4W ³ÅY >O¦>§¨}k>lË5l¬Å}3S >O 3|YWOW!¡¥PÂIÃÄ£ÅÆÇÉÈɧģÅÆÇËÊON%SlW%S|ARÅ
W%WO%|3Ë0%|> ³W%|Y8l[}3S > 3¢0%|Y 3|>)IO%S >l|}kl%Sl) Wl) ³ SS3WRW£%l%>}3}%l£O
Ç£Â5ÄÉÏoÆÇËÊO¦0§6¡F£OO 3l%%|Y ³ ©|3ËSS%|A|Y!lRË. 3[%|ÌI´IË0%|>R%|©O}% 3£R%}*% 38 >|>l
}3SWK 3O!I 3SÅ 3O!O%SS 3lO) ³ ÎË. 3A5¡FOÑLÑV ³SWe 3|ÔS|³¯W% > ³ δ0IW 35¦
§&O¢5S!OO}3S[ >|>;O%W>OW¡S|>%S¬ >|>¬l ³W a¡ 3|}3W% ³ ¥Ë5W 3}%%|Y
W%l%|ACªkY >©W£%Ë5l|k[ÙS 3l 3V©Ë0%lÒÓASË5|kÍW ³lÑ¢5W% 3ÅSW~Ú×áWâͤa¼.ÛKA 36O}3W%|> ½l§EÑ
WSW;ÓASË5|k&V©Ë0e%4Í!; 3|3ll|>Ú¤2â$¼.Û8 3.¡ |3S¢0%WWSW£¬ 3.ESl%Wkle§¨WSW
a¡F{ > 3O)à)£%WI ³´A|klA >OeÚÏdãR±Û 3KSl%WIl4§¨WSW. 3Õ4OW>%WW>eL©Ë0%leÍW ³lÑ
¢5W% 3ÅSWR%[»K´I|klY >4Í8SW% 3ÅWSWK ³ ©».£%}kW%%|Y!µ~£O ³lOÑÍ83S 3Ë5la 3ÍW ³llË5lK ³
¼ävåæ 3ESl%W;%.l§E*WSW a¡FL|³¯-©lY >%e a¡FL©Ë0%lV|> ³ >l%SlÈÚÏçâWÛ4 3§¨
ÕIW>%Sl5¦Í!¬Ë5W 3}%%|Y.W%l%|YCªkA >}* 34³O%C¯6l¬ 3£%¢0%l}3}%%|Y%|~}kW%|kÅ.¢0O
3O.S|> ³ >l%la 3ÅÔWO>%WW>©%|ÆS©Ë0%l5&WSË5|ka%K£O|3lA > 3O-»> 3l 3O}3}3SlA >£OÔÅ
}k>lË5lW ³lÑ¢W% 3ÅSW5¦*§&}3W%4|> >O|>O%|k|YeW¬}3ÅO >|>Rl; ³W 3¡S©Ë0%l
3OE¢lW ³Ì 3¥ Ïrè Ð"Æè ÅÎ¥£éÃÐ×Ê%¦5VI¡Ë5SE a¡F£% > ³l%%" 3[ 3£%¢0%l}3}%" 3|>[£%>I 3[Ë0£%|>£%l!} 3
3£%WO%W%*WOO|> 3SW5&|kS´³W%K%K¢Il kSlW%KlO¢5lWW ³Ì~$|3Ë5 3S|>K%K}3S >K}kl% 3Sl%W%%|Y
lO©W%WOÔOW|kSWO¦6§6¡F£%Ål| a¡ 3|>ÈS©Ë0È 3Á´I|Y>OWÁl ³S%|>Wl|3|>%SlÈ}%%
a¡F£?aO% >%K 3OKS 3Ål|>. a¡F£OO 3l%%|AWe|3Ë5 3S|>. 34 3O4W%Ë5%|YWeW£%l%lK}k>lË5lY >O
%S|>& a¡}3}W%R 3|>.S|> ³ll|«´I}3W©lA >¬%) 3|>.%SSl% 3W¬£%¢5S kl|« ³ ÁW%W%|YlWÑ
%|Y>£%A ³´I|klY >© 3OeW£%|>5WO¬ 3eÅÔ}%¯d >Wl|¥´0IW ³lY >5¦E§&£O 3O%S|½} 3ÁlW
3£O%l 3% a¡ 3|ÈSW%%|AK}3}3W}3l£Å}k>lË5l5¦kà)% >%Sl%%|YNÅA >SSW£¬ a¡S©Ë0%l 3O
¢5lWW ³ÌÎÅl% ³ÌÁ >}3W£O¡F£% > 3¬ 3OW%WOROW|kSWO4%RÅ}3S >) 3SSlW£O¬OW!¡|3Ë5lË5Ñ
}33le}k)´0|>Rä # »¦ê¦3{Sl¬}*%% 3K¯SW¬}3}khëlWW 3R 3OS©Ë0OR3l ³S%|>l|3|>%SlOkÅ
}3WO%l|Ò 3OW%WO 3S¢|A[}3S >l% 3W8S|>%l 3%|>OO¦³Lk¡Ë5S8 3|>5³e}kS 3OO! 3|3|>£OO)|³Ñ
Ë5lË5}33lA >O6 3!}3W}*5W%6 £O 3O%S| 3|>!WOO|> >%l| ( » 3O"W%WO[OW|kSWO¦5§&WWA >5
O >|>4l;}3W£O%|Y*l¬|>;3W a¡S|>%l 3%|>OOeOWR¯S3l5>¡ 3SSll|¥ a¡ 3|fA 3%l;Ë0£OÑ
£%lA >.l ³S%|>l|3|>%¨ 3O)¢5lWW ³ÌÔOW!|>£OOOSW.}* 3}kSSl%RlK©|>A >e a¡S|³¯°©l|>
¯- 3|3lO[}k!lO6S©Ë0O 3R}3WO%l|&¦I».|>!OO|AWÌIW5AlO8¢lW ³Ì©W|Y!W 3¢0%|Y!A 3£%Sl£O
}k 3O4%´ASS|> ³WO)Ë0£%|>£%Sl£O4%RW|A}kRO|>W£OA >%|YK%W£%lW£O4}kR 3|È%|>W%3l; 3¬O 3}O
O%|YW£OO! 3 3|>O%WSWR¢IS >%Sl)}kW|A}k6lO6O%|AWO[ 3RO%SlÑV%¦0§Ee 3£%©WW>Ë0£%|>£%l
a¡ 3|>eWOO|> >%l|
( » O}3W%|> ~lW)lO£%}*ORW 3S¢|AWO¦¹'Í)â¬Í!Õ
= è º
Ú°¯¦Iª>Ë5 3W $5¦%$ÛC
$5¦}3W£%SW%%|A4 3OS©Ë0O|3Ë5lË5}33lA >OìCISa¡Ë5SR 34¯-SWKWOWS!lO¢5lWW ³ÌÒ}k
}3}4 Á¯-|> Á 3¬kY >eS©Ë0îí
# ¦)̳%l|¸ 3OSSË5|>OO%|YlO%;O|AW 3W 3O¢5lWW ³ÌïC¨O%WÔ£%}*ÔO|>lWÔ a¡ 3|>
}kÎ 3£%WO%W%elO.}S|YW;}3}kW%|k|YÔÅÒSSË5|>¢IS >%Sl}kW|A ½O%|YW 3O.¢5lÑ
³Ì«|3Ë5 3S|>%K a¡ 3W¬}kK© 3£%WO%W%4O% ³Ì~}3}kW%|k|Aeů°W|Yl%WW£%}k|Y4lO
¢5lWW ³ÌÁ ³ Á¯-|> Á 3e¡S©Ë0îí
(
¦!¯-©l|¥ a¡F%|YSW£O¬W >% 3W%SlOCklOK}S|YW. 3£%WO%W£Oe >|>K¡F£%}*}3W£OO£O 3%|YW|YeÑ
ËY|3l£OR%|YW¬% ³ÌÎ 3.©|3l%W¯°%lO) 3% ³ÌÎ%|ASW£OR >% 3W%SlOA >.W|Y)lORSSË5|>O
O%|AlOÈ%©lOÎO|AW 3WÁ 3OÎW%WO¦Í!%Åt}%%Ò a¡F3W%|3SÎ 3|>~S|³¯°©l| 3ÒÅ
lISll|f%)Å}3>lË5l; 3O)¢5lWW ³ÌÁ 3£%WO%W£OYí
è>¦R}3}kl%%|AÔ 3OW >% 3WO
# » 3£%WO%W£OO<CSR¡Ë5S 3Î%WÈ%|ØOWO}*|> >|>OÈlO
%Ë5%|YW.W£%l%l 3£%WO%W£OOWOW}*|> >|AK ³ÌΤ%O >% 3WOK|kWlY >OYí
A³¦WOO|>W >%l| ( »1CkÅ 3£%WO%l|Æ 3ORSSË5|>OKO%|YlO. 3kY >;S|>%l 3%|>O;}*%%K a¡FOÑ
S%;ÅÒlASl$l|l ³S%|>l|3|>%SlÔ 3ÅÎSSË5|>O%|All ³S%|>l|3|>%SlÒ 3Oe¢5lÑ
ð
GY$,×ñOEE)òO R0/+'Rc+,N+',-,-$2R ¨,NW-+'+Bó) O,-×ó,*$$ $+F,a$ 4
$,-,-+³"$$ $c$V$ +
W ³Ìa6Åæ 3£%WO%l| 3OÒO|AW 3WÎ}*%%|AÈ%|> 3SWf a¡FOS%ÎlOÔ}k%WOÁ 3~Å
O 3}*e ³ ~%´ASS|> ³WeË0£%|>£%Sl£5>%4S|>& a¡Mk3SSl%OÒÅSSË5|>¬O%|Yl; 3O)¢5lWW ³Ìa¦
%E|> >;|> >S|AW£%WOWW|>}3S >}kl% 3Sl%W%%|YÔ ³ÌtA kWÔ}3W%l%WO£%}O 3©Å~ 3£Ñ
©W>5¦EÍ!O¬£%}OeW|Y¬ a¡ 3|>S}|>OW 3W}kl% 3Sl%W}3 3lWA &¡F%SlO¬O|> ³Sl|3|>%|A; ³CÑ
WO%W%%|A4ÅA kSSW£¬ 3eÅWOO|> >%l| ( »pY 3¨W 3S¢A³¦
§¨OS©Ë0OOW|>Ë5}33lY >O|Y 3OS©Ë0O}kl% 3Sl%W%%|Y© ³@ô©%SlO©«SW%}3 3lÑ
A &¡F%SlO4|YR3 3SW£OO»k >O3}3W£O%|YW%|Ye 3.¯-WOR¢5Ål|>K 3¬O|YW%O}W%|Y. 3O
>% 3WO 3 ³@?£%W%|AWO¬SSlO;ÐרÊlO.¢lW ³Ì¦LK >eW 3kSW|>¬ 3|>3W%|3S¬ 3|>|3|>
I 3£%Sll|¥ 3O¢5lWW ³ÌakO;Y 3E}kWW}k4 3|>%W£%ll|¥ 3¬l% 3WKSSË5|>O.O%|YlO.%
3«l% 3W© ³Å%WO¦8V¡Ë5SÔlW© 3~ 3£%WO%W%Ò 3W©lA >%%|YÎlOSSË5|>OÔO%|YlOÒ%©lO
O|AW 3WR 3K¢lW ³ÌÔ|3Ë5 3S|>) 3. ³@?£%W%|AW) ³Å%WO}kSR a¡S©Ë0O3 3SW£OO}3W£OW%|Y|A
3¯-WO¬¢5Ål|> 3©O|YW5¦E§¨ÁWS 3l|%ÅlY >%%|A 3}3W£O©}* 3¬W£O > ³WO}3WÑ
3l%!O|>lW8%|ÅlW8%|. 3¢IW[ a¡ 3|>[¯°|>%l| 36W£%}|>W8 W%S| a¡ 3|}3WAOO >¨ a¡|kS´³W
; 3SCÑV£OW>%SlO¬SS|>£SW õfů-|>%l|~W£%}|>W%K%|Æ£%¢Al 3%|>O;lO%|YW 3O¢5lWW ³Ì~© 3|>
£O>%Sl) 3|3|>£O¬Ú° SSl 3|3|>£OÛ5% õ¡|kS´I8; 3SCÑV£OW>%SlO6¯° 3|3S 3O"S©Ë0O64 ³@?£%W%|AW
|3S¢0 ³ÌÔ 34 3£%SlA}*%%|A)S|>WN 3RSW% 3O8¢lW ³Ì© 3 ³Å%WO ³S¢0%W¦I§¨eW£%}|>W
%R¡|kS´³We; 3SCÑV£OW>%SlO.W|ARË0£%|>£%l%%|YKlWOR%|z. 3¢IW¬%|Á 3SSl|AWO}O%S¢0%%|YKlO
3Sl)©>£%©lA >ORA >.W|YÅË0£O£%le ³@?a£%W%|Yl%Sl¬%lO e A kl|> ³ÌÒ».£%S¢0£OO)"Ñ
l%SlOÚ×ã_¡töÛ¦kÍ!OR 3% ³Ìί-©SlO¯- 3|3lWW%|ARÅkW.©>£%©lA >; ³ÌÎO¢5 ³ÌÁW£SlW£O
>|>4O%We>OW5¦
±³²µ´J¶÷L½øtùì¶2½À²µ´vÁ
§¨OO|AS3 3l|>6 3!O%W[>OW!O|>O%|>%|YOW%|Yl%Sl%%|YlO" 3©S|>O" 38¡£%Sll|
a¡S©Ë0O}k-ã_¡tö %R 3¬¡FÌI%l|« 3OSSË5|>ORO%|YlO¦
ôjrd÷dþNõh³ù÷dþNøæÿ74l÷dô68kó03õv+J,/. 4 >!}3}*W|>8Wl8O|AS3 3l|>}3S|>%S}klO >|>6l
3©S|>R 3¡£%Sll|Ò a¡S©Ë0O6}k7ãJ¡vö¬¦§¨K}3W%l%WRO|>O%|>)lOSW%%|AW[W%ÅC¯-6
ÅKW£OWS 3l||A 3£%lY > 3Oã_¡töúM4%ÅWlA >OO 3!SlW$Ë05¦5§6¡FSË5S|kSSW£R 3O%WR}3}3WA>RO
3RO|>Wl 3£%W%[lOWO3|3lY >O! 3)W£OWS 3l|© 3OWã_¡töØ >¡|3Ë5lR 3O6£%>I 3O6SW£%S¢0O8 ³SWO
3KWOW>%W>e 3}S|Y!ª3Ì35¦!K >3W%|>|>RlW! 3|>4£%>I 34ËY|YlW|A)ÅO|Y¢0%Ë0%|>Oe ³
}3WIOOW > 3ÔW£OWS 3l|Ø%¯- 3|3lW|AS|>W! 3OO}kOO 3SCÑV£O>%SlO©O}k%W%;ªN3lO¦
{|æ 3SSl|AOO;W£O 3SW;>£OlY >OE|> >;}3W£OW%|YW|> 3|>£%>I 3ÒSË5S|klÔ 3©W£OWS 3l|
3ΡF£OA kl| 3Á ³@? >l|ØSS|>£SWÈA 3!}%%6%| O|AWåÅ|Y©Åf¢ISWOWWÎ 3ÁO|A¢0%Ë0%|>O« ³
}3WIOOW >K 3; ³@? >l|&* 3}3W}5W%K 3|>|kS´³W; 3SCÑV£O>%SlOeSS|>£SWY 3"Å}kl% 3ÅSW£
3©}3W£OW%¢0%lO¬O|AW 3W¦4 >;3W%|>|>;S|>8 3|½|> 3¢0 ½ª>SWÔ 3 ³@?* >Wl|lWW}}3W£Ñ
W%|A|Y 3%SSl% 3WO}%¯-©|>OO; 3Ò 3£%3 3SË0ÔA &¡ 3|tª>SWÔ 3Ô ³@?* >l|¸|3lWW}5¦E"
SSl% 3W|> >. 3SSl|>eO}3WIOOW >e >|>KÅÔ}3kW 3}3W£%SW%%|Y a¡ 3|SË0S3 3 3£Ñ
WO%l|Î 3O8O|AW 3W¦I§&O8O|AW 3W3W%|Y >W|Y83l%|Ô 3£%WO%W£O%63l%|ÒlASl£O[A >OS[ 3
3O.S©Ë0O¬%|Æ|3S¢0 ³Ì¥ 3Ë5le ¥ 3O.S©Ë0O¬%|¥O 3l% 3¦&§¨ÎWOO|> 3O|YS3 3l|æO|>O%|>
l«W%k >WW%%|YÒ a¡S©Ë05¦7K >S|AWA ³ 3lW|>Ô 3|>È|> 3¢0%Slã_¡töì 3Ϊ>SW« 3È>A«S|>}3SW£O
3ÎÅ~}3>lË5lÁ©>£%©lA >ÈA 3!}%% 3ÒW%k >WW%lOO|YW 3W© 3©¯áO| 3lÎ%
prétraitement
détection des points de lignes centrales et contours
formation d’entités structurelles
prétraitement
détection des points de lignes centrales et contours
formation d’entités structurelles
angiographie 2
appariement des structures
reconstruction 3D
arbre vasculaire reconstruit angiographie 1
û]üIýWþYÿ%ÿ
! "$#$$% #$&' !)(*
