An automatic building extraction method : Application to 3D-city modeling
Texte intégral
(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. An automatic building extraction method : Application to 3D-city modeling Florent Lafarge. — Pierre Trontin — Xavier Descombes — Josiane Zerubia — Marc Pierrot-Deseilligny. N° 5925 May 2006 Thème COG. N 0249-6399. apport de recherche.
(3)
(4)
(5) !
(6) " # $ !% &(')+**#,-! /.0123546 &7 8:9<;5=?>A@CBDFEHGIE5=KJL>. MONP >Q=?=K>SRTE5=?=K;5[ @UB P @ >A=?=KM!;5V BKdeEXYW >AP >QZK=> 9<Y9 >AJLZK@C[Af ;L\^]_>AZ M_` ;LZ P E5@!>Sa>A=?b!] P E M_c NP P P gih2j#kl
(7) m7n-o)prqtsXuIvwjKklKuFx#y{z{|~}v}u _wy{ lvu7Tw}|H F{2HyQIvFtllKx3h~l#3x3h2l|5O{Q{prSsQ{-p{Hz{l?u ∗ †. ‡. ∗. ∗. †. !K# 2¡{{¢£ |vwh~}¤u:l#5y{wvK¥L¦,l2lKuwl#|Av:{|§¨2vwy{k&vw}x©2¨2}¤ªt}«|~zl#¬AvQxev}«yQ|klvwh~yXwyQk¯®T}¤z° «} v{ª,±_ª«lK²vw}¤y{|³yX2l#ªu´®µ±_u3¶e·¸gih2l®T±_Su¹{wlz{l#|~l#3 vwl?^¨~uw}«|2z§|³{ª«zQy{}vh2kº©~QuIl?¸y{|» vk&Qxe¬Xv}¤lKk
(8) ¸¨~ky{°<¼~kÀy ¦)vwh2lÁyQw®µk±_¨2ª¤vwu}¤y{v|§h2w¨~yQuI¨2}¤z{|2hÂzvwh~|ÃwlKl¨t°½²Avy{}¤l#k&¦¾ v}«k&}¤xkzQlKluKv·h2yt¿!Ä}¤uI©HvK{¥CuwvlKh2»l&yQ©2|Ĩ2}¤k&ªt{}«|~wÅQzlK¸yXy{5vwy{2}¤|A}«vÆ|Av32u:wyt{wx#l¹lKuluI¬Xl?u° vwh2lKs»ll#2lKuwl#|Avwl?¸©Xs¸|ÄQuwuwytx} v}«yQ|¸yTlKxv|~z{ª¤lKuK·Ègih2lK|U¥Ovh2lKuwllKxv{|2z{¨2ª©2¨2}¤ª¤2}«|2z Ç yXy{vw2}«|Av3ull#zQ¨2ª¤{w}¤É#l?Á©Xs}¤k¹~wy ²X}¤|2z©5yvhÈvwh2l&xyQ|2|2l?xevw}¤y{|Èy,vwh2l&|~l#}¤z{hX©HyQw}¤|2zwl?xev{|2z{ª¤lKu {|~Ávh2l{x#Qtlt}¤uxyQ|Avw}¤|A¨~}vsÁtl#vwlKxvw}¤y{|U·
(9) ʧly{©2v}¤|§uIvw¨~xvw¨2lKyXy{vw2}«|Av3u#·
(10) gih~lKuwlyXyv2w}¤|Avu {wl7¨HuIl?¹y{"vh2lµËQ®F°Ìx}«vs¹k¹yttlKª«}¤|2z©XsxyQ|~uI}tlKw}¤|2z~{{klvw}x722yQQx3h©H{uwlKy{|Æ
(11) uIÅQl#ª¤lvwyQ| ~wytxl?uwu¦7h2}x3hÁª¤ª«y ¦Fu,vy¹kyttlKªCvwh2lyXyÍvy{~uK· ÎÁÏAÐLÑÒ
(12) Ó Ô!{¢ u vwlKª«ª¤}«vwl,~ v~¥ Ë{®T°<lKx#y{|~uIvw¨~xev}«yQ|U¥®T}¤z{}«v{ªA±_ª«lK²vw}¤y{|
(13) yX2l#ª<¥tl#|~uwl¨2w©H|
(14) {wl?{uK¥ ©~¨2}«ªt}¤|2z&l¬XvQxevw}¤y{| ¥Ak&{wÅQlKÆ5y{}¤|AvF2yXx#lKuuIl?u. ÍâÕHàÖìÚ×3ûHÛÚØÚÝ üÙÌÛ<×eÛ ôKëêÛOÙÜ!õ!ÖÝßöÞ3×eà ã!÷eÞ,ÞÖÚÞ3ÛÚáHÝêè×eâéà ã!ÝêÞ3ø#äUëêôÙ âÍÙiÜOã åâç#ÞæÛ<ôçTÝêè×eáLöIà ÖçKÞ3ÝêëQ×eÙôèáCÖé?ç?Ù ÝßÞ3ÞÝêáÍàÜ!ÛúàáùÙÛ<ÝêèÞ3×eàëêúëÝêý ìUöïÜUá5áHöÖÙÙ×eíFíFà Þ3Þ3Þ3Ýêô?ÝêëëÛÚîïîïÝêøKã ã!ôÞ3Þ3Ù í7í7ÙÙeð ð ñXñtÙÛÞ3Þ3ìÚìÚÛÚÛÚà à Þ3úÞ3í7Ùí7ÙwÙwò!ò!ëÝêÝêàý ÷eû~ÖÚàAì<ÝßðÞ?è ó«Öð Þ3ó«ÖüÙ á þt×eôëê×eôìÚÙ á ÙIíFÞ3Ýêëîïã Þ3í7Ùeð ñtÞ3ìÚÛÚà Þ3í7Ùwò!ì<ôèÞ3ÙIÖ×ð ×eÖ÷ ∗. † ‡. Unité de recherche INRIA Sophia Antipolis.
(15) % &º
(16) -! ï"! # 7 º' +**#,-!
(17) ï7, C !"! $!
(18) 7$.0 ¢ ®:|Hu¹x#l3~HyQIv?¥"|2y{¨Hu~ ?uIlK|Qvy{|~u¨2|2lk vh2yttlÁ¨tvy{k& v}A¨2l l#¬Xvw3{xev}«yQ|Ätl © vw}¤kl#|Avu ~wvw}¤
(19) tlyX2j#ª¤lKu T¨2k #} A¨2l?u ±"!ª K² vw}¤y{| ´Ú" F±¶e·"m,lKutlKw|~}«lKuuwy{|Av#z K$| #% Ku H¨~| ª¤z{yQw}«vwh~k¹ly{|~& ÈuI¨~¨2|~lSyQwk¨2ª¤vw}¤y{| ~{¼Hyvk&¬X}¤k&ª:¨tvw}¤ª¤}¤u|Av2lKu}«k&zQlKuÆvw}° uIv K KyQuxyQ2} A¨2l?u#·µ®µ{|~uT¨~|S2l#k}¤l#µvwl#k~uK¥Lª«l?u:l#k2}¤uwlKuµtl© vw}¤kl#|Avu:uwy{|Avµl#¬Av{}vlK'u Æ~{Iv}« 2l" F±¾~¨~|2lk vh2yttl{¨tvwyQkvw(} A¨2l&y{|H& #luw¨2ª¤lKu
(20) 2yXx#lKuuI¨HuHyQ|~xev¨2l#ªuk&{% A$¨ ?u x#lKu lK~kw}uI2l?wuF}uwlKlKu&xvuwy{|~|Az{vƨ2ªK2}¤w%l?Ku7uwl#uI|AyQv|AKvTlKu KuIz{yQ¨2¨~ªu})uyQKwlKkuilÁl#|§ ¨2k |2lS#ª¤}«QyQuwuw{yt|AxvF} ª¤vw}¤y{x|Ây{|~t|2ll¬t}¤lKy{x|vt|~l?z{uFª¤lKuKlK· xev3±"|2|~zQuwª«¨2l?}uFvl{²Q¥7y{}xuIl?}¤u&|~Ç uKl#¥~k¹lv° lKuIvw|Á¨~& xvwv¨2lK%xe#v3l?u#|A·&vTm,ª¤lKlKuFu:2l#}¤kux2yQ|Q}¤vuw}«lK|Xu-¨2}«uwv y{K|AlKvuF¨t2vwl}¤ª¤}¤# u#*Kl?{u-tl?Hu#yQ+· ¨2F-y{ª¤¨Hu7lKy{x©tyQv|~l#|2uIvwyQ|~¨~uFxev{}«}«yQ|~|uw} ¨2tl?©~uF}¤lK|2k¹l¹~l#w|^}uIl?Ë{u7® t~l{,© :¨~vw}¤|2klÆl#|Atvu° ~wytx3h2lµ~3k vw(} A¨2l7yQ|~& #l-uw¨2,¨~|2ytxlKuuw¨~u,2l:%u A¨2l#ª¤lvwvw}uwvw}¤y{|tl?ul#k2}¤uwlKu,HlKwkl#vIv{|Avitl kyt& Kª«}uIlK7ª«l?u7% -vlKu,/ .vw}¤j#lKuK· ? #¡ 1 µ¢ ¨~0¾w©~Ó {}«|~Ñ lKui tl#|HuIl?2u#y{¥2|2l#$|¬XKvw3lK{uUxeuv }«vyQl#|ª¤ª«t}«vl{}«©lK uKvw¥?}¤kwl?l#x|Ay{v|HuKu¥tv2w¨~ytxvwx}¤lKy{u|uw¨~Ë{u7®t¥l-ÁHytyQt}«|Aj#v3ª¤2l u7Fk&¨~3k 4QK¨,w(}KAu ¨2l_ ±"ª #² v}«yQ|U¥ É#yQ|2lKu.
(21)
(22)
(23) ! "#$%. Ë.
(24)
(25) !7
(26) Ô !¡,+ Ó * ')(* K Ó. .0/21 0435Ï * Ï t%+ Ó * 5 > Ë~@· ?( Ï ¡{K * 3 1ÚtÆ 7+ 1Ô8+ * 39½ÓUÓ ":!+ * ? Ð »t<; Ï Ô=: Ó + * :! Ó ¡ Ï K Ï 6 _Ë~·@w?Q}¤·@|~? x}¤2ª¤l·Å{·:l?·Æ·-5·y{}¤·|QvF·-~·wyt·-x·l?uw·-u ····:·:···-·-···-·-·····-·-···-·-···:·:···-·-·····-·-···-·-···-·-·····:·:···· Ë~@· ?Q· ®TlK|~uI}«vs&yQwk¨2ª¤vw}¤y{| ···:··-··-···-··-··:··-···-··-··-···:·· Ë~· Ë~F@· lK?Quw· ˨2ªv3uinµ·-t·vw}¤·:k·}«É?·- vw·}¤y{·| ·-··£ ·-·-···-·-·····:·:···-·-···-·-·····-·-···-·-···:·:···-·-·····-·-···-·-···-·-·····:·:···B · ??A Ë~· 2@· ? 7lKuw¨2ª«vuiy{|D C ± T®µ±,quw}«k¨2ª vw}¤y{|Hu»··-··-··:··-···-··-··-···:·B · ?? Ë~· 2· m,y{kkl#|Avui··-··-··-···:··-··-···-··-··:··-···-··-··-···:·B · ?? Ï 3 m,1tyQ|2+|2EQl?txe% vw+ }¤Óy{|* ©5¢-lv¦ÓXÒ l#l#t| Ô |2ÆlK}«zQKhX#©H!yQw¡}¤ |2 z¹ wÏ l?Ô xev9½{ÓU|2Ó z{% ª¤lK: u + * ·-K· ·-··:··-···-··-··-···:·B· 'F??6 Ë G @· ? ¿2¨~uw}«yQ|x#y{| HHz{¨23 v}«yQ|~u···:··-··-···-··-··:··-···-··-··-···:·B · ??Ë G @· ?Q@· ? m,yQuIv¨~|~xev}«yQ| ··-··-···:··-··-···-··-··:··-···-··-··-···:·B · ?G G @· ?Q· ª¤z{y{}«vwh2k ··-··-··-···:··-··-···-··-··:··-···-··-··-···:·B · ?I G @· ?Q· Ë ¿H{xK{tlt}uwx#y{|Avw}¤|X¨2}«vstlvlKxvw}¤y{|··:··-··-···-··-··:··-···-··-··-···:·B · ?,A G · FlKuw¨2ªv3ui·-··:··-···-··-··-···:··-··-···-··-··:··-···-··-··-···:·B · ?? G ·Ë :7: 1+Ú¡{t, + Ó * Ó 6$/ Ñ ¡ + Ð Ó Ô Ï 1
(27) + * 3 J 5 2·@? qtÅ{l#ª¤lvy{|2yXx#lKuuiy vwh2l-yXyv2}«|Avu^··-··-···-··-··:··-···-··-··-···:··'FQK 2· qtlvIv}«|~z&y!vwh2l©2¨~}«ªt}¤|2zh2l#}¤z{hAvuF··:··-··-···-··-··:··-···-··-··-···:··Q 2· Ë FlKuw¨2ªv3ui·-··:··-···-··-··-···:··-··-···-··-··:··-···-··-··-···:·· G >ML Ó * ¡ 1 !% + Ó * .ON P + 1+ O Ó 3 :RQ Ð .ON &. ä ä+àS$TVUVWVT.
(28) G.
(29) . O
(30)
(31) 8"V$ V " . ï &_ ¿H{x#lKƦ7}«vwhvwh2l-zQwy ¦ivh&yUvh2l-¨2w©H|2}¤ÉKvw}¤y{|U¥Qvwh2l{¨tvwyQkvw}xTËQ®F°½wl?xyQ|~uvw¨Hxevw}¤y{|&y{ ¨2©~|lKQu hH{ui©5lKxyQkl¹vwy{~}¤x-y{!}¤|Avwl#lKuIv7}«|vh2lª{uIv7l#¦ s{lK{uK· "}«yQ¨~u7~2ª«}x#vw}¤y{|~uK¥2uw¨~x3hÁ{uvwh~l
(32) xyQk° ~¨tvw}¤|2zy_lKª«l?xevwy{k&{z{|2l#vw}x¦i²{l2y{HzQvw}¤y{|U¥Hvwh~l¹¨~w©~{|2ª|2|~}«|2zy{µvwh~lx#wl? v}«yQ|Áy,²X}¤Iv¨~ª lK{ª«}«vw}¤lKuK¥2l A¨2}¤wl-vyÆ©5l
(33) ©2ª¤l-vwy¨tvy{k& v}¤xKª¤ª«s©2¨2}¤ª¤ÁËQ®F°½kyX2l#ªu7¦7}vhSxyQ|2|2l?xevwl?2ª¤{|~F{xl#vu y{ vy ¦7|~u#· . . . qtl#²{lK{ªC¨tvy{k& v}¤x-klvh2yt2u7zQ}«²X}¤|2z&uwvw}uQxevwyQws&lKuw¨2ª«vuih~²Ql-©HlKl#|Átl#²Ql#ª¤y{5lK¨~uw}«|~z{l#}¤{ªC}«k¹° { z{l?uUy{!ª{uwl#ïuwxK|2|2}¤|2zH· il#}ªA}«k&zQlKu!lOvwh~lkyAuv!HyQ2¨2ªïÅX}«|~
(34) yH~ vFvwy-tlK{ªQ¦7}«vwhvwh~}¤u vsXHl y{!~wyQ©2ª«lKk&u#·_®µ} 5lKwlK|Qv7vlKx3h2|~}A¨2l?u7h~²{l-©5l#lK|Á2wyQHyAuIl?uw¨~x3h{u75l#3xlKtvw¨HªUyQwzA|2}¤ÉKvw}¤y{| ? ? <¥ 5y{ª¤sXh2lK2{ª 2~wyA{x3h ? ½¥~H3klvw}x-kyX2l#ªu ? yQTuIvw¨~xev¨2{ª ~2wyA{x3h Ë <· C QuIlKTux#|~|2}«|~z }u_{ª¤uwy²Ql#s
(35) 5y{2¨2ªuI}¤|~x#l7vwh2l:tlKx#wl?{uwl7yCvh2lµQx A¨2}uI}«vw}¤y{|Æx#yQuIvK·ïFª«vwh2yQ¨2z{hƪ{uwl#_k¹l?{uw¨2l#kl#|Avu {xKwlµ| ²{AlK¨2wysÆvlµQx#vxh2¨~l~vw{l{¥A{ªk¹{uwl#l#vwi}¤uwx:xK|2~|22}¤w|2yAz¹{x3}¤huÅXy|2 y ¦7?K |<· vwyh~²{l:
(36) ª¤y ¦ tlK|~uw}vs&y{ 5y{}¤|Qv3u#·O¿~y{i}«|Huv3|~x#l{¥X¦,l }¤Tk&y ¦zQQlK2uK·Fstgiu#¥5h2lvh2}¤¨tu-v~¨2wyQl©2D ª«lKC kº± £ x#T{®µ|§±,©5q§lvuwQvwx3lKÅXª«ª«ª¤l?}vlKuµ©XsSl|~lKyuwvwHh~l?l#x-}vª¤sXª«sHl¦y{l#ª¤ª!2Q2v tvÇ lKvwh2vl&yuw¨2t©tl?°½kª ¦7lvw}«vw}h§x¹©2u¨2 v}¤ª¤l#2ª¤ª«}«}«|2vwzl ËQ®F°½lKxyQ|~uIvw¨~xev}«yQ|Svh2wyQ¨2z{hÈvh2lÆh2}¤z{h¸lKuwy{ª¤¨tvw}¤y{|^y{i}¤k&zQlKu&´~· Ik¹l#vwlK3¶{|~Èvwh~luvl#l#yAuwx#y{2}x x3{hHl#}¤3{{ªtxe}«vk&l#{}¤z{uIvwlK}u_x#u7´lFvwh2l#h2lµ}¤z{²XhÆ}«lKuw¦F¦uO°vwh¦7}¤t:vwh2·ê{{|~¶·!giz{h~y{lF¨2k&|H¹}¤x#|y ²{{lKt² {{z{|Ql{v3· zQTlKy uO¦,y{lKC²{ulK Kv¥{l#uwª¤¨~ª«}«x3vwhÆl:22 v3v-xh~yQk²QlF~IlKwlKª¤vwy ° v}«²Ql#ª¤sµª¤y ¦ "wl?uIyQª«¨2vw}¤y{||~
(37) ª¤y ¦ _qX}«zQ|~ª{vw'y Fy{}uwl_F v}«y´Ú&q µT¶CvyTtl?ªA¦7}vh
(38) Ë{®T°<lKx#y{|~uIvw¨~xvw}¤y{| £ v~w{yQw©2s
(39) ª«lKvwk&y
(40) u#uI·ïv{¿2|~yQ2"{l¬2klK2w}ª¤l{ª~¥Q}«D k&CU± zQlKTuO®µ¦7±,h~}¤qÆx3h&uw}«h~k¨2²QªlF vw}¤©5y{£ y{|H¨tuOv7h~{:²{lT2}«¬t2l#ª}u"¬tlK5ª¤l#u_Hu lKA_¨~u {Aw¨~l7{kwl7lvkl#?l#vw· l#£ |tvwl#h2|H}uIu_}«vs¹l#5x#y{y{w|tvK° ¥ vh2lklvh2yt~wyQHyAuIl?Ʀ7}¤ª«ªU©5l~2ª«}¤lKvwy& CU± µ®T±,quI}¤k
(41) ¨2ª v}«yQ|~uy{|ÁtlK|~uIl-¨2©~{|{wl?{uK· . . . . !. . " #. $ %. '&)(#*,+. -*. 10. 2.. /.. 10. T{|~¨tvwyQvwk&h2l vwËQ}®Fxµ°½k¹wl?l#xvwyQh2|~ytu2vu7w¨H{xewvwlµ}¤y{k| yQ·!uIgivwª¤h2s&}u kH~Q3tuIl:v7¨2uIvwlKy{U}¤u7v¦,|~yyv7uIvw|2l#lKHx#u lKuÇ uwv{h2wsl-lvyƬXvwuI3yQ{kxvwl:}¤y{k|Æl#y{vw h2©2yt¨22}¤u7ª¤2¦7}«|2h~z}¤x3hyXytv}¤2wl?wxe}¤|Avwª¤vs u ¨HuIlÆxK{2Quv{ªOk{~uuw¨~x3h¸{u ê ,y{ ½·S|XsSklvh2yt2u|2lKlK^©2¨~}«ªt}¤|2zª¤yXxKª¤}«É? v}«yQ|§k&{uwÅtu}¤| yQ2l#Uvyµ}¤|2}«vw}ª¤}«ÉKl_vh2l,yAy{vw2}¤|Qvïl¬XvQxevw}¤y{|ª¤z{y{}«vwh2k¥?y{ïl¬2{k¹~ª«l Ë <¥ ?? ½¥ ê tyQ ê ? ½· £ |vwh~}¤u x#y{|Avwl#¬XvK¥Xl#¦ x}«vsË{®T°½k¹yttlKª«}¤|2zAu{wl-lK{ª«ª¤s¨2ª¤ª«sA°Ì¨tvy{k& v}¤x{¥A}<· l{·O¦7}«vwh2yQ¨tvF©2¨2}¤ª¤2}«|2zª¤ytx#ª¤}¤ÉK v}«yQ| k&QuIÅtuK· 3. 4 %. 5 # 6 7 8 3. $. !. £ |Ævwh2}u_l#5y{wvK¥X¨~ª«ª¤sA°½{¨tvwyQkvw}x7yXyv2}«|Av_l#¬AvQxev}«yQ|Æklvwh~yX&wyQk ®µ}¤z{}«vª5±"ª¤l#² v}«yQ|ÁyttlKª¤u ´Ú®T±,u¶T}uµ~wl?uIlK|QvlKC·:gih2l®µ±_u-{wlz{l#|~l#3 vwl?¨~uw}«|2z|S{ª«zQy{}vh2k+©~{uwlKÁyQ|SÆk&¬X}¤k
(42) ¨~k° ¼Hy ¦ y{k
(43) ¨~ª¤vw}¤y{|¨HuI}¤|2z¹vwh2l#l#°<²X}¤l#¦ }«k&zQlKuK· ¿!x#lK}¤uuIuIl?vKu¥2vwh2lvh2zQl¹ª«yQ©2©~¨2}¤ªUª¤tuw}¤h~|2{zHlyXyy{vw!~©~w¨2}¤|A}«ªvtu:}¤|2zQl
(44) uTkytltll#¬Xª¤vwlK3Á{x©XvwslKlK©Xxesv3|2zQkª«llvª¤h2sQyty{¨t©~v3u#{·:uwlKgih2yQl#|| ¥Hk&vh2{wlKÅQuwl¹lKwl?HxeyQv}«{|A|2vFz{2¨~ª¤{y° ©~¨2}«ªt}¤|2Ç z-yXyv2w}¤|Avu"{wlil#zQ¨2ª¤{w}¤É#l?©Xs}¤k2wy ²X}¤|2z:vwh2l7ª¤}¤|2ÅX}«|2z¨~&y5vwh2l7|2lK}«zQhX©HyQw}¤|2z:wl?xev{|2z{ª¤lKu âã!äUâÍÜ.
(45) .
(46)
(47) ! "#$%. {|~¸tl#vwlKxvw}¤|2zÁvh2lÆQx#{2lt}uwx#y{|Avw}¤|X¨2}v}«l?u#·Ágih2ly{©tv3}¤|2lK^©~¨2}«ªt}¤|2zÁyXyv2}«|AvulÆuvw¨Hxevw¨~wl? yXy{vw2}«|Av3u Ç lK{x3hl#ª¤l#klK|Qv7l#2lKuwl#|Av3uuwHl?x}@HHx-~{Iv7yO|¨2©~|uIvw¨~xev¨2wlQ· ~FwlKytuwx¨2l?ªuwv3u_u
(48) }¤{uw¨~lÆuw{lKÆ22vwª¤y}«l?k¹ÈytvwtyÁlKvª5h2vwlh2l:Ë{®TwyX°Ìy{xÍ}«vwvy{s§Hku_y{ytUt©2l#ª¤¨2}¤|2}¤ª¤zt}¤©X|2sSzAu#¨~·"uwgi}¤|2h2zSl:Át} 5~lK{wlK{|Qkvilh2vwlK}}«x¹zQhQ{v32u_2y{ yQ©2Q¨2x3hU}¤ª·t}«|~zQuiuIÅQxl#yQª¤|~lvwuyQv}| ° v¨tvwl-~{{klvwlKu_¦7h2}x3hl:lKuIvw}¤kvwl?|H&vwh~l#|wlKz{¨2ª}«ÉKlK}¤|yQ2l#"vy¹²{y{_vwh2l-yXyÍvwyQ|H zQlvwvwl#7y{ yXy!x#y{|Avw}¤|X¨2}«vw}¤lKuK· 0 7i! gi:h~kDl ¨2H~ªv3}uI°½vOlKuIuwvwy{lKª¤¹¨tvwx#}¤y{y{|~|¹uw}}«ukv3u 2}¤ª¤|
(49) l#kzQlKl#|Q|2v3lK v}«vwyQ}¤|¹|2z-y{L®T
(50) ±_m,Syu!¬¹wyQ|~k 7Ë °½y ²As}¤l#yQ¦³tvw}«k&}¤k&zQªtlK¼HuK· y ¦³g y:k&2 y:v3x3uwh2y~}«¥{|~µzk}«k&lvh2zQytl7
(51) ©~ª¤z{Qy{uIl?}«vwh2yQk | ?%A }¤ui¨HuIl?C· gih2}u"kl#vwh2ytC¥Atlv3}¤ª«l?}«| ?<I ½¥A{}«k&u"v_uIyQª«²X}¤|2z:vwh2lµuI¨2w{x#liwl?xy{|Huvw¨~xvw}¤y{|¹2y{©2ª¤l#k¾y{k{ª° }¤É#l?SQuµk¹}¤|2}¤k}«É? vw}¤y{|§y_{|Sl#|~l#z{s{·-gih2lª¤Quv-y{|2l}¤u-x#y{kHyAuIl?Áy_2vvIv3{x3h2kl#|Avµvwl#k {|~l#z{¨~ª¤{w}¤É#}¤|2zµvwl#k ¦7h2}¤x3hÆ2l#5l#|~2u_y{|¹vwh~lTuIkyXyvh2|2l?uwuOy{Lvwh2lTuw¨2w{x#l{·ï k
(52) ¨2ª«vw}«°½wl?uIyQª«¨tv}«yQ| {22yQQx3h
(53) }uO|2lKx#lKuuw{wsvwy{x3h~}«lK²{liwl?{uwy{|~{©2ª¤l~wytxl?uwuw}¤|2zTv}«kl?u"y{|l#¬Avl#|~2lK&lKQuï|~¹}¤k¹~wy ²Ql ¿!y{}¤©~z{¨2¨~ulv|2?FlKu2ulK©XuwsÆl#|Awv3l?u_uv{}«lK|~uw}«¨2|2ª«z¹v_y{k&©t v3v3x3}¤h2|2}«lK|~¹z{y{k
(54) k ©2}¤Ë z{°½¨~²X}}«vlK}«¦Äl?u#· CU± £ µ®T±,quw}«k¨2ª¤vw}¤y{|~u"y{|Æuw}«|~z{ª¤lF©2¨2}¤ª¤2}«|2z ´ÚFk}¤l#|~uFx#}vsh~ª¤ªC°_¿23|Hxl?¶· . %. . . £ v¿!h2}¤z{l¨2{ul uwyX? x#Ç }¤Ë vw°½l?²A}¤l#®µ¦ ±_D C ± ´ T®µ£ o ±,µqÁ¶ uw}«k¨2ª vw}¤y{|Hu7yïvwh~l
(55) Fk}¤l#|~uµx}«vsh~{ª«ªC°i¿23|~x#l-°µ´ m+F±q2¶7|H ä ä+àS$TVUVWVT.
(56) .
(57) . O
(58)
(59) 8"V$ V " . 7_ ¯## & - *ï +¹4$ 7 *È *ï :1 , l#T¬X}«vwzQ3h {xetv}«lKyQ|~|§uI}«vtsÂ}Æyx¨2¨2ª«v©~vwy| {x3h~}«lKlK{²{ul{·|~ʧ lÆx#{y{}«kk2 ª¤lv¬t}tvl#sòQl#y{ª¤y{2hA}¤¨~|2kz{| |^k&¨t{vty{l§k&y{ v©t}¤ xl?xekvulvwk&h~yXÈÅ{l¦7vwh2h2}x3lÈh^©2t¨2yX}¤ª¤lK2uw}«| |2 z v |~{ª«l#zQlKy{Ä}©2vh2¨2k }¤ªt©~}«|~QzÈuIl?ª¤ytx#yQ{|ª«}¤k&ÉKvw}¤y{Å{|»l?k&5y{H}¤|Auv7y{2wyt}«|~x#}lKvu}¤uI{l?ª«}¤u,ÉK}u7vw}¤¨~y{uw|ÄlK uIv??vw l?½u#· ·Âg y¸ty^uIyH¥,SyXyvw~w}¤|Avl#¬Xvw3{xev}«yQ| .. *. 3.
(60) . gih~}¤uklvh2yt}u©~{uwlKy{|{|yQ©t lKxvi{22yQ{x3h }«vi2wy ²X}tlKu,lKxev3|2zQª«lµª¤sQy{¨tv3u_¦7h~}¤x3hwlK2wl?uIlK|Av vuwh2¨~lx3h©2¨2{|}¤ªt}«2|~2z&yQyXQyx3vwh~w}¤}¤uT|A¦,vuKlK·,ª«ª!¿~{Q2xl?{tvw¦7l?}«vwhuI}¤|~vh2x#ll}xv:yQk22y Ç ª«²Al#}¬tt}l?vuFs&|~kytvwth~l#l
(61) ª¤}«|~tzÆ}¤²{©Xl#3suw}uwv}¤sÆk¹y{~ ª«lvh2zQll#yQ©2k¹¨~}«l#ªvwt}¤}¤|2x-z&yQ©ty{ lKk&xvu#u ¥ ´}Ú· l:wl?xev{|2z{ª¤lKu3¶"{|~{ª«ª¤y ¦Fu_vwh2l-}¤|Qvwytt¨Hxevw}¤y{|y 2}«yQw}5ÅX|2y ¦7ª¤lKtzQlµxyQ|~xlKw|~}«|2z
(62) vwh2l:y{©2 lKxeviªsQ° yQgi¨th~vl{z{|~ª¤»y{©HtyXª_lKkuw| }¤|2 v
(63) }¤k
(64) |2¨2lKlKk ¸y{}¤|2F}«vwvw}h2}ª¤u¹}«É?l# |2vwlK}¤y{w|»zQs§uIv}u
(65) vwvwl?h2u#lK·|»T|»y{¨~l#|~|2»lKw©XzQs¸sS}u2~Qª«uwsXuw}¤yt|2xz§} §vlK§7l#vw²Qyl#3l?uI{}¤x3©2h»ª¤l x#{y{¨~| k¹H~zQĨ23Á vwy{}¤|Ay{vw| l · m{wª¤yÅ{y ²m,h~{}«|Áuk2ª¤l#il#k©Hl?2tlK}¤|AvwyÆuI}¤k
(66) ¨~ª¤vwlK|~|2lK{ª«}¤|2zuwx3h2lKkl ½· 7. 0 t Ï Ô Ó ! Ó ¡ Ï K <;. 6 ' '. :. + * :. lvOxyQ|~uI}tlK!µHyQ}«|Avï2yXx#lKuu X ª«}¤²X}«|2z:}¤| K = [0, X ]×[0, Y ] ¦7h2}x3h
(67) l#2lKuwl#|Avu!|}«k&{z{l{· X Ç}¤uikl?{uw¨2{©2ª¤lTk&2~}«|2z
(68) wyQk 2y{©H©2}¤ª«}«vs&uIH{xl (Ω, A, P) vy¹x#y{|H~zQ¨23 vw}¤y{|HuOy 5y{}¤|Avu´ ??y¶ ¦7}«vwk&h¸{wÅQk&lK§HÅyQ}«¦7|Ah2v}2x3h¸ytxª¤lKª«uy u-¦F}¤uµ| v∀ωSyt=∈lH~KΩ,|~l×x|ÈM∈y{K,©t}¤u
(69) l?X(ω) xev?H· yQ}«|A=v{x2ytx, lK...,uu-x¦7h2}lKwl&l?{x3hÈHyQ}«|Av}u{uuIytx#}¤vwlK }u-vh2l&k&ÅSuIH{xl&¦7h~}¤x3h^ª¤ª«y ¦FuK¥U}¤|¸y{¨2 xK{uwl{¥Xvy2lKux}«©5l-{|~ty{k xy{| H~z{¨23 v}«yQ|lKxv|~z{ª¤lKMu Ç ´Ú{¶ π π M = [− , ] × [L ,L ] × [l ,l ] ÊÈl|2y{vwl C vh2l
(70) uwlvTy{ï{ª«ª H~|2}«vwl
(71) x#y{2| H~zQ2¨23 vw}¤y{|HuiyOy{©t l?xev3u7y S ·i¿!}«zQ¨2wlË&uIh2y ¦FuT|l#ª¤l#kl#|AvTy{ S 5y{·:}¤|A¿!vT}¤z{2¨2ytl¹xlKÆuu7wlK}¤2| wSl?uI·FlK|AÁvuTyQwlwtl?lv3ª¤}«É?}¤ ª¤uTv}«y{yQ|Á|Á5yy{,}¤|QvµH2yQw}«|Aytvµx#lK~uwuIytl?uFxl?uw|~uµ}¤| vh2Kl#}¤-{|~S22ª¤}x#w l?v}«ª¤yQ}«É?|~ uFvw}¤xKy{|Á|Áy{©5_lÆy{k&¨~|~ÁÅ{l?}¤| ?K <· C. max. max. 1. i. min. max. n. min. max. %. . Ï * %+ Ð 9½Ó 1Út% + Ó * ÊÈlµx#y{|~uw}tl#_k{wÅQlK¹5y{}¤|Qv2yXx#lKuu X tl"H~|2lK©Xs|&¨2|~|2y{k&ª¤}«ÉKlK&tlK|~uI}«vs h(.) y{k C vwy R {|~¹-wl#l#l#|~x#l,}¤|Avwl#|HuI}«vs
(72) klKQuI¨~wl ν ´tl"H~|2}¤|2z:wl#l#l#|~x#li!yQ}¤uuwy{|
(73) 5y{}¤|Av"2yXx#lKuuOt}uvw}¤©2¨tv}«yQ|H¶e· 6 ' .. /. âã!äUâÍÜ.
(74) I.
(75)
(76) ! "#$%. ´ A¶ ¿!}¤z{¨2l
(77) ¢ wl?ª¤}«É? v}«yQ|y{O5y{}¤|AvT2ytxlKuui}¤| ~wytxl?uwu}¤Ç| S. K. ´ ©H¶ ¢ lKª¤}¤ÉK v}«yQ|y{"k{wÅQlK5y{}¤|Qv. Xc. X. l. Yc. O. L. Y. ¿!}¤z{¨2lË T|^l#ª¤l#kl#|Av-y ° ¥Cvh2l&xlK|Qvl#-y_vwh2llKxev3|2zQª«l° (θ, L, l) ∈ M ¥Cvh2l yQw}¤l#|Av3 vw}¤y{Ç |y vwh2llKxv|~z{Sª¤l{¥t}«v(Xuiª¤l#,|2Yz{vw)hÁ∈|~K}«vui¦7}Xvwh c. ä ä+àS$TVUVWVT. c.
(78) A.
(79) . O
(80)
(81) 8"V$ V " . gih~l¹¨~|2|2y{k&ª¤}«ÉKlKÈtl#|HuI}«vs h(.) tl#}«²QlKuµy{kvh2l#ll#|2lKwzQ}«l?u-tl#²Ql#ª¤y{5lKÈ}«|Èvh2ly{ª¤ª«y ¦7}¤|2z|~ 2lv{}«ª¤lK}¤| ? G <·"¿~y{FxyQ| H~z{¨~vw}¤y{| x ∈ C ¥2}«vF}uiz{}¤²{l#|©Xs Ç ´ÚËQ¶ h(x) = exp − [U (x) + U (x) + U (x)] Ï $ 1 Ï Ï 3HÐ gih2}uvwl#k klKQuI¨~wl?u"vh2l Q¨Hª¤}vsÆy{!¹xyQ| H~z{¨~vw}¤y{|ÆzQ}«²Ql#|Ævh2l2 v32¥ }P<1· l{·!vwh2lµ* ®T±_»* · £ vix#{|&U ©Hl:tlKx#y{kHyAuIl?{u_
(82) uI¨2k y{LlK|2l#z{}¤lKu U (.) 5l#,y{©t l?xev,uw¨~x3hÆ{u U (x) = ¿~y{lK{Ux3h¸(u)yQ©t · lKxv u ∈ x ¥"Sª«ytxKªi2 v3Ál#|2lKwzQs U (u) }¤u¹xyQk¹~¨tvwl?»©Xs§¨HuI}¤|2z§Sklvwh~yX»¦7h2}¤x3h x#¿!y{}¤z{k¨2~{l wl?u_°e´vAh2¶luw®µh2y ±_¦F u&t^}¤u~x{yQI|Av&vw}¤y{|A-¨~}¸v}«l?®µu±_vwy vwh~¥_l^©HyQlKxtvlK|~uz{y{ª¤lÈ v´h2}«| ly{¦7©th2 l?}«vwxelv ¶&u· |HÄuwª«}xl?u&l#²Ql#|2ª¤s³t}uwHyAuIl? ´}«|¸©~ª«¨2lG ¶e·ÁÊÈl}¤k v
(83) l#¬AvQxev}«|2zuwy{kl&5y{}¤|Avuy{7}«|AvwlKwl?uv
(84) wyQkºlKQx3h¸uIª¤}¤x#l|H¸x3h2lKx3ÅX}¤|2zvwh2l x#y{h2lKwlK|~xl©5lv¦l#lK|vwh2l?uIlHyQ}«|Av3uT|Hvwh2l
(85) wl?xev{|2z{¨~ª¤{TuIhH5lyOvh2ly{©2 lKxev?·Fïy{}¤|AvuFy{O}«|AvwlKwl?uv {wl¹tlvlKxvwlKS¨~uw}«|2z~wy H~ª«l¹uI}¤k2ª¤} HHxK v}«yQ|Sª¤z{yQw}«vwh2k¯tl#v{}«ª¤lKS}«| @? G ï°,vh2l#sÁl#2lKuwl#|Av-®T±_ 2}¤uxyQ|Qv}«|X¨2}«vw}¤lKu
(86) y{|^vh2luwª¤}¤x#lKu´ÚuIlKl H~zQ¨2l G °e´©H¶w¶e·§gih~l#|U¥ïvh2wlKlx}«vwl#}ÁyTx#y{h2lKwlK|~xlÆ{wlƨHuIl? vyl#~x#wy{l?kuIlK2|Q¨tv¹vuIl lKz{Uk(u) l#|Av·u
(87) gi¨~uwh2lKl ^H~v3y§uv-xxyQk}v2l#¨t}«vwyQl|Ávwkh2llK{²{uwyQ¨2ª«¨~lKk¹uµlƲ{yQvwª«l?¨~¶k¹·Èlgih~lvwluwlK´xuwl#yQl |~^HHz{y{¨2|~ll xG yQ°3w´ÚxKlK¶7uw°i5y{zQ|~wlK2suª¤vw}¤y§|2lK u k3 yQvl?k¹¶lK· |A±"vF²Ql#|Avwvwl&¨~{´uwª«ª¤l#s{l ¥?vH~h2zQl"¨2vh2l }«G3
(88) °3´Ú~x#w¶}«vw°_lKzQw}¤wy{lK|sÆkª¤}«|2l?{l?u7uw¨2wl#l?2u 7lKuwª¤l#yt|Ax#vF{ª«uI}¤lKÉKz{kvw}¤y{l#||Av33ui vw¨~lµuIl?´uwl#lvwyÆHHz{xyQ¨2kl 2¨t°evw´l-l¶Cv°Ch2l7zQky{Qkt}«lKlK|Q|Avv G }ui©5y¬Xl?}«ï}vF}uFxª¤yQuwl-l#|2yQ¨2z{hvwy¹vh2lxyQwlKuwHyQ|~t}¤|2z
(89) lKxv{|2z{ª¤luI}tl?¶· Ï $ 1 Ï Ï 3HÐ gih2l7}¤|Qvl#|~ªtlK|2l#z{s ª«ª¤y ¦Fu vwyzQ}«²Qli-uw~ v}¤{ª~uIvw¨~xev¨2wlvy-vwh2l x©5#("y{* l|v¦HHz{l#*lK¨2|»3 y{v}«©2yQ* | lKxexv3·u£ ¦7vUh2x#}x3|&h¸©5lT²Quwy{l#3lKu|Æ{ª¤u"}«zQ|2kl#l#zQ|A¨2vª©5}«lÉKv}«¦U|2z:l#lKv|¸l#(x)wk l?xexvyQ{|2kz{Hª¤lKyAuKuI¥Ol?xyQyk¹L~vwh2ª«l#vwl#}¤l7y{|»ÅX}¤|~2|Hu_»yuICyQ}«k|AvlÆl#3~{xe²Xv}«}«yQ|~|z ©5l#hH²A}¤y{?·ï¿ }¤z{¨~wlwlK2lKuwl#|Avu,vwh~lKuwl-vwh2l#l-}¤|Qvl#3{xvw}¤y{|~uK· #¡ 1 , + y{1t~3ª¤ª«lKÓ ª* lKÏ xe* v3Ï |2zQ3~ª«Ð l?u#U·!qX¨~x3hgi|h~l#}¤uL¬2vxl#ª¤¨~k uI}¤y{|²Qy{lK|2}2l#uLz{lKsµt}¤¨2u |H|22lKx#lK|AuvUuwy{{©2ws: lKuIxe}¤v3|~uCx#©XlOsTvwh25l_l#|~wl?{tª«}¤¨2É#|~}¤|22z7{v|Ah2v l"l¬t}¤|A2vwªl#3|~uwlKxevwv}¤y{}«yQ|~| u y{ vh2l2 v3¹k
(90) ¨~uIvF©Hl²Qy{}tlK|~vwh~l vIvQxev}«²Ql:}¤|AvwlKQxevw}¤y{|Hu,k¨~uIvF|2yv7©5l-vwyXy&uvwyQ|2z~· 6'6 :!% + +E{2% + Ó * ÊÈS l¬t¦}«k{|A¨2vk v)!y H~ï|HyQ»uIvwlKvh2w}¤lÁy{x}Oy{´| H~Tz{¨2,3¶i vl?}«uyQv|»}«k&¦7 h2vy{}x3 hÄk&¬X}¤k}«ÉKlKuvwh~l2l#|~uw}vs h(.) ·ÄʧlÁuwlK3x3h»yQ¹vwh2l Ç θ ´G ¶ θ = arg max h(θ) gih~}¤u
(91) }¤uÁ|2y{|»x#y{|X²{l#¬§yQtvw}¤k}«É? vw}¤y{|¸~wyQ©2ª«lKk}¤|»Áh2}¤z{h»{|~¸² }©2ª¤lÆt}¤k¹lK|~uw}«yQ|»uI~Qxl C ·S Fl#²{lKuw}¤©2ª«l {¨2kÈÁy{|AvwlÆmª¤yÅ{y ²m,h~{}«|Èuw{k¹~ª«lK G ?K Ol#k
(92) ©5lK~tlKS}«|Èuw}«k¨2ª¤vwl? {|2|2l?ª¤}«|2zux3h2l#kl-}¤uF~wvw}x¨2ªª¤s&¦,lKª«ªUQ2tvlKvwyvh2}¤uF2wyQ©2ª¤l#k· ". . ext. int. excl. ext. d. u∈x. ext. d. d. . . d. int. int. excl. M AP. M AP. θ.
(93) %1 #. âã!äUâÍÜ.
(94)
(95)
(96) ! "#$%. . !¿uwª¤}¤}¤z{x#lK¨2uTl ´}«G|Ç ©2±Oª«¨~¬Xl?v¶ l#|~ ªï¢ l#|~l#tl#z{vwslKx°vwl? SHyQ¢ }«|Avu,~y{CI}¤v-|Avwyl#,lKuIv®µ±_¡ ¹¢ ¥U²{y{ª¤2¨2ky{5lFyQ3uw lKvÁl lKÔ xv¢ |~z{kª¤ly{k´}¤lK|È|Qv,¦7h2}vvwl?l ¶:Ï|H ¢ ª¤ytx#{ª«}¤ÉKvw}¤y{|3 vl. ¿!}¤z{¨2lS Ç £ |Qvl#|~ªTl#|2lKwzQs¸° â ª¤}«zQ|2kl#|AvÆ}¤|Qvl#3{xvw}¤y{| ¢ ~²X}«|~z¸}«|AvwlKQxev}«yQ| ¡ â x#y{k2ª¤lv}«yQ|}¤|Avwl#3{xvw}¤y{| ä ä+àS$TVUVWVT.
(97) ? ?.
(98) . O
(99)
(100) 8"V$ V " . £ vxyQ|~uw}¤uIvuµ}«|ÈuI}¤k
(101) ¨~ª¤vw}¤|2zt}uwx#wl#vwl¹Å{y ²m,h~}¤| yQ| y{_}¤|A² {w}|Avµkl?{uw¨2wl Ú´ uI5lKx#} HHlKÈ©Xsvwh~ltl#|HuI}«vs h(.)¶-¦7h2}x3h^HlKIyQwk&uuwk&ª¤ªC (X¨2k~) u©5lv¦l#ClK|¸uI~Qxl?uyi² }¤{©2ª«l&tπ}«° kx#y{lK|X|~²{uIlK}¤wy{zQ|HlKu#uF·vwnµy ¦i|2l¹3y2_u vwh2l¹y{k&{}¤|A|§sÁ{}¤2|2²}«vw{}|Avª"x#zQy{lK|uµH~yzQ,¨2uw3¨~ x3vwhÈ}¤y{| uk· 2£ ª¤vl#:k}¤lKu:{v|~h~uµ v:vwh~vwh2vl}«x3|~h~}v{}¤}«{|Ȫ«}¤ÉK{uwvwsA}¤ky{|§tvuIyvwvlK}¤~xKu-ª¤y{ª«s ©~¨2}«ªt}¤|2z&ª¤yXxKª¤}«É? v}«yQπ|k&{uwÅtu7lµ|2y{vF|2l#l?tlKU· X £ |Æ~Qxevw}xlQ¥{vh2lµ Q§mÈm³uk2ª¤l#,}¤u_l#k©Hl?2tlKÆ}«|Avwy¹uw}«k¨2ª¤vwl?&|2|2l?ª¤}«|~z
(102) uwx3h~l#kl Ç vwh2l ÉK2l#l#|~y&uw}{vsu th(.)vwlK|~2u7}vuiy&uI¨~}«| ©~H~u|2v}}«vv¨ts{vw·,l?ÆvTvyvwh2h(.) l©5l#¦7zQ}«h2|2l#|~}«l|2zDy!}u7vwh2¹l
(103) uI{l ª«QzQ¨~y{l#|~}vx#h2lTkºy ´vw}Ú·lKl{k¹·,5¦7l#h23l# |v¨2vh2lKl-u,vw¦7lKh2k¹}¤x35hl#3vw lKv|~¨22ulvw}¤y u h~}«zQhH¶e¥Xvh2l2yXx#lKuu_}ui|2y{vilK{ª«ª¤sÆuwl#ª¤lKxev}«²Ql }«vTª¤ª¤y ¦Fu"vy¹l#¬t2ª«yQwlµvwh~ltl#|~uw}«vsÆkyX2lKuK·!Ê h~l#|vwh2l v}u"l#k|~lK5xl#l?3uw uvw¨~wslivtylK}¤x#k¹wl?5{yQuwuwlKlTuK¥x#xy{yQ|~| tH~}«vwz{}¤¨~y{|Hu_vw}¤xy{yQ|~|~u xlK¦7wh2|~Ç }}«x3|2hz-h~vh2²QlFlv:l#kh25}¤z{l#h¹3 tvwl#¨~|HwuIlT}«v2slK¦7x#}¤s
(104) ª«ª2vw©5yll#|~²{uw¨2yQwlil?Cvw·h2l:Fy ª¤¦z{l#y{²Ql#}«vw?h2¥ k }v x#y{|X²{lKwzQl#|~x#l{·)¯ª¤y{zQ{w}«vwh~k¹}xtl?xlKQuIl ¥F¦7h2l#l }u³xy{|Huv3|AvÆh2}¤z{h lK|2y{¨2zQh vx#yÁy{|X²{ª¤lKª«y w¦¾zQlKuKvw·h2l&l#¬X~ª«yQvw}¤y{|Sy{ª¤ytx#{ªOk¹}¤|2}¤k&Dy=il#|2lKwzQs{¥U5l#k}v3u-vwyÁc ©5lÆuI¨~wl¹vwhH vvwh~lƪ¤z{y{}«vwh2k t t∈N. 0. 1 Dt. t. *. t. . . c log(1+t). . . . . ig h~}¤u©~¨2}«ªt}¤|2zÁl¬XvQxevw}¤y{|Èklvh2yt^z{}¤²{lKuu v}¤uI{xvw£yQwsÁlKuw¨2ª«vu:y{ª¤{wzQl3|2zQly7®T±_Su´uwl#l ?KË y{Twl?uI¨2ª«vuFy{|y{tv}¤xKª {|~ C :qX±_ ®µ±_u3¶e· |vh2ly{ª¤ª¤y ¦7}«|2zH¥2¦ly{|2ª¤s2lKuwl#|AvFlKuw¨2ª«vu7yQ| yQtvw}x#{ªUuwvwlKª«ª¤}vl®T±_Su#· Ï 1? Ó * D1 ( / 1 , + 1Út% + Ó * 6 . ' ¿!}¤z{¨2l IÆ~wl?uIlK|Qv3u:wl?uI¨2ª«vu:y{k¯ CU± £ µ®T±,q^uw}¤k
(105) ¨2ª v}«yQ|~u-y{|ÈFk}«lK|~ux#}vs³´Ú¿23|~x#l?¶·¹¿!}¤z{¨2l¹ uwh2y ¦Fu"v¦,ylKuw¨2ª«vu,y{|2l#|~uwlT¨2©~{|lKQu#·!7lKuw¨2ª«vulµu vw}uI{xevy{s Ç ªz{l7k& y{}vs¹y ¨~w©~{| uIvw¨~xvw¨2lKuilxyQwlKxvwª¤sÆtlvlKxevlKC· Ty ¦,lK²{l#?¥~¦lxK|Suwl#lv¦,yt¦7©H{x3Åtu#·F¿!}¤uIvK¥Cuwy{kl©2¨~}«ªt}¤|2zyXy{vw2}«|Av3uTh~²Ql|2yv-©5l#l#|§tl° vlKxvwlKU·ïgih~l#s&xyQwlKuwHyQ|~vwyª«y ¦Â¼Hv,©2¨2}¤ªt}«|~zQu,yU}¤|2|2l#ixyQ¨2wvsQ32u!vh~ v,vwh2l:2y{5yQuwlK¹klvwh~yX l#xK¬X|2vw3|~{yxevÆv}«yQt|lvklKxlv&vh2uw}¤yt|~xltlvvh2lKlKxeuwv3luF©2uwy{¨2k}¤ª¤tl:}¤|2vwzAl#ulKuh~´ H~²{z{l¨~ª¤wy l¦ °e®T´x?±,¶I¶6· Fty }¤u¦xl#yQ²{|AlKvwK}¤|A¥Q¨~vwh~}v}¤}«uFl?u#2· lqX¨~lKx#ªvTy{|~xKU|¥_v©Hh2llÁx#y{©2¨2w}¤l?ª¤2xevw}«|2l?z ©XsÆ}¤|Avwytt¨~x}¤|2z&¹²{lKz{lv3 v}«yQ|k&{uwÅÆ}¤|vh2l2ytxlKuuK· %.
(106). . *. *. . Ó Ï * ? gih~Ë{lF®Tw°<l?uIlK¨~x#y{ªv3|~u_uIvw¨~lFxuvw }¤y{vw}|uI{2xevyXy{x#lKsuu7}¤|y{k+u vwvwlKh~ª«lKª¤}«uwvwl
(107) lT{lK|~xe&v3|2¨tzQv¨2y{ªk&F v©2}¤¨~x7}«ªx#ty{}¤|A|2vwzl#¬XyXvK·y{vwF2y ¦}«|Al#v3²QuTl#lK?|2¥{z{lK2|~~tª«sXl#}¤3|2uTz{tIv}¤wll?Qxevwxeª¤vs u }¤| vh2l§ËQ®F°½wl?uI¨~ªv3uÆ{u}v}¤uuIh~y ¦7| }«| ½·¾gih2l?uIlÈwvwlQxev3uÆlk&}¤|2ª¤sÂt¨~lvwyÄ|2y{| yQtvw}¤k&ª ªx#y{s{|2yQ|~¨tlKvxeuv}«|2yQlK|~lKu¸©5vly^v¦©Hl#ll#|ÂwlK|2z{lK¨2}«ªzQhA©5}¤É#y{lKU}¤|2¥Oz§lKuwHlKl?xxv}{|2ª¤ª«z{s^ª¤lKvuh2l´uwl#ª«}¤l|2ÅX¿!}«}¤|~z{z§¨2¨2l ÂA{©5¶e· lv¦gil#hHl# |ÄvÆ|2}ul#}¤z{¦7hXhA©5s³y{vw}«h2|~l?zSuIllKxelKv3xv|2zQ|~ª«z{l?ª¤u#l · ÊÈl{~twl?uwu,vh2}¤uF2wyQ©2ª¤l#k }¤|vwh2l-yQª«ª¤y ¦7}«|~z¹uwlKxvw}¤y{|U· 6 . .. L. *. 3. âã!äUâÍÜ.
(108) ??.
(109)
(110) ! "#$%. ´A¶. ´©H¶. ´ xK¶ ´~¶ ¿!x#}¤}¤z{vw¨2l?l®µ ±_Ç uµ |~wl?¢ uI¨~Dªv3CUui± y£ T®µlKx±,v{qÁ|2uwz{}«¨2kª¨2iª¤©2vw}¤¨~y{}«|~ªtui}¤|2yQz&|ÁlF¬Xkvw3}«{lKx|~vwuF}¤y{{|~wu-l?{´ u-´£ µm+£Fµ±,¶ q~¶ ¡ Ô ¢ {uuIy{° . ä ä+àS$TVUVWVT. .
(111) ?.
(112) . O
(113)
(114) 8"V$ V " . ¿!}¤z{¨2l I Ç O± ¬2k2ª¤lKu7y{ ©2¨~}«ªt}¤|2z&l¬Xvw3{xvw}¤y{|wl?uI¨2ª«vu´ £ µ £ µ¶. ¿!}¤z{¨2l A Ç O± ¬2k2ª¤lKuiy{ |2yQ|yQtvw}¤k&ªUxyQ|2|2l?xevw}¤y{|Hu,©5lv¦l#lK||~l#}¤z{hX©HyQw}¤|2z¹wl?xev3|2zQª«l?u:´ £ µ £ µ¶. âã!äUâÍÜ.
(115) ?Ë ?.
(116)
(117) ! "#$%. 7
(118) ! - # ' ! ¾ï C ï" ï7 & - *ï. gih~l¹lKxv{|2z{ª¤l
(119) ªs{yQ¨tvu-l
(120) l#zQ¨2ª}«ÉKlKÁ©Xs}¤k2wy ²X}¤|2z~¥ HHuIvwª¤s{¥Lvh2l&xy{|~|2lKxvw}¤y{|È©Hl#v¦,lKl#|È|2l#}¤z{ht° ©5´vwy{h2}¤y{|2¨~z-z{whl?xe
(121) v{|2Qz{x#Qª¤lKtuil´vwth2}¤uxy{yQ¨2|AzQvwh¹}¤|A-¨~}ª¤vytsx#{2ªXlvw¨~l?uIxe}¤vy{}«|yQ|Hy{¶eH·"lKxev7v3vh2|2l-zQª«l#l?|~u¶!C{¥~|~¦,Cl-¥{y{uwlK©2x#vy{|~}¤|Átª¤us{v¥wvw¨Hh2xelFvw¨~5wyQl?uw}«vw©2}¤y{¨~|¹}«ªty5}¤|2z¹{x#QyAty{lKvIu° ~w}¤|Avu¦7h~yQuwlÆl#ª¤l#kl#|Av3u
(122) lx#y{wl?xevwª¤s§x#y{|2|~lKxevlK Ç lKQx3h¸y{|2lwlK2wl?uIlK|Avuuw5lKx@} HHx~wv
(123) yF{| ¨~w©~{|uIvw¨~xvw¨2l{· . . . . . . .
(124). . . . . . ÊÈli}¤k v }¤k2y ²A}¤|2zTvwh2lixyQ|2|2lKxvw}¤y{|©5lv¦l#lK|
(125) |2lK}«zQhX©HyQw}¤|2zFlKxv|~z{ª¤lKuK· ¿!}«zQ¨2wl °e´A¶Cl#2lKuwl#|Avu vsX2}x#{ªUxy{| H~z{¨23 v}«yQ|y{ v¦y¹|~l#}¤z{hX©HyQw}¤|2z¹wl?xev3|2zQª«l?u_vh~ vF¦l-¦{|AvvyÆxyQ|2|2lKxvK· o:lK|2l#3ª¤}«ÉK}«|~zÆË{® ²Qy{ª¤¨2klKuK¥~uw¨~x3h{u7}¤| I ½¥5x#y{¨2ªª¤ª«y ¦ vwyÆ}¤k2y ²{l-vwh~lª«}¤|2ÅX}¤|2zƨ2Á©5lv¦l#lK| |~5l#l#}¤wz{vwhX¨~©Hw©~yQw}¤vw|2}¤y{z|~uTlKy{x|v{v|2h2z{lª¤lKuKlK¥ x|~v{l#²{|2lKz{Iª¤vlh2~l#ª¤lK3uu
(126) kuwl#y{vwkl#3luF©2x#y{¨2¨2}¤ª¤ªtÁ}¤|2}¤zÈk¹~twly v3²Ql-}¤ª¤uvwh2¦,l¹yQx¨2y{ª¸|~|2©HlKlxvw}¤ª¤y{yQ|UuIvK· ·§TTy 2¦,2lKª¤²{sXlK}«K|2¥5zÈuI¨~uIk&x3h{ª« ª kl#vwh2ytÆxK|2|2y{v,©5lT¨~uwlKuI}¤|~xlTvwh2lµ}«|2y{kvw}¤y{|&l#ª vlKvyvwh~lTz{lK|2l#3ªHª¤sQy{¨tv"y{Uwl?xev3|2zQª«l?u"¦7}¤ª«ª v©5¦l
(127) yª¤yQwuIl?vKxe·:v3gi|2h2zQlª«l?x3u,h~}¤yQ|Auwvwl#y|5uwy{y{ª¤sAª¤¨tzQvwy{}¤y{|~|u¦7x#y{h2|~}x3uwhÁ}¤uIvuTlµ}«|S5k¹l#wlKlKwzQxvw}«|~ª¤sz&x#vwy{h2|2l|2|2l?l#xev}¤z{lKhX©5{y{ui}«¦|~zÆl-xKwl?xe|Áv3uwl#|2l-zQª«y{l?| u#¥HH~}Úz{· l{¨~·µwlk¹yQ°ew´~©Hh2¶}«· |~z . /*. Ú´ Q¶ ´©H¶ ¿!}«zQ¨2wl Ç ¢ v¦,y|2lK}«zQhX©HyQw}¤|2z¹wl?xev{|2z{ª¤lKu Æ¢ l¬2k2ª¤l-y!¨~uw}¤y{|. ! Ó ¡ Ó t Ó - ' '. . %+ *. ,+ *. * 3. ÊÈl}¤k vFkl#z{}¤|2z¹v¦,y&|2lK}«zQhX©HyQw}¤|2z¹wl?xev{|2z{ª¤lKu (R , R ) ¥2}«vTklK|Hu7¦,luwlK{x3hy{Tx#y{|2|~lKxev}«|~z ©5yvh5y{}¤|Qv-¾{|~Á5y{}¤|Qv ´y{¨2vuw}¤tl¹uIl?xevy{e¶e¥L|~5y{}¤|Avm |HÁHyQ}«|Av-® ´}«|~uw}tl¹uwlKxvwyQ3¶iy{ H~z° &. ä ä+àS$TVUVWVT. 1. 2.
(128) ? G.
(129) . O
(130)
(131) 8"V$ V " . ¨~wl_°3´ÚQ¶U}«|yQ2l#CvyµxlKvwl"5y{ª¤sXz{yQ|~u (P ) ¦7h2}x3h
(132) l"5l#wlKxvwª¤s-x#y{|2|~lKxevlKÆ´ÚuIlKl H~zQ¨2l_°e´©H¶w¶e· y{ïvw£h2vïll¬tlK}xuv3vu {|2k&z{{ª¤lK|AuKs-¥tvwl#h~ªl# }¤vT}«²Qy{l"}¤Hl#yA|AuIv}«vwvw}¤y{}¤y{|H|u y{|~2v¦,vyµh2|2l#}¤l#µ}¤z{thX}©5uIvy{|H}«|~xl{zF·7wl?¿Hxe{v3xl?|2zQª«¦7l?uU}v¦7hÁh2vw}h2x3l
(133) hh2t}«lKzQHhÁlK|~|X¨2k
(134) yQ|©5vwl#h~µl,y¦7OH}XyAvwuh ° uw}¤©2}«ª¤}«vw}¤lKuK¥U|l#¬XhH¨~uIvw}¤²{l¹tlKux}«2vw}¤y{|y{,ª¤ª!vwh2l¨~uw}«yQ|§xyQ| H~zQ¨2vw}¤y{|~uT¦7}«ª¤ªï©Hl¹²{lKwsh2l?²Xs{·-ʧl hH²{l-x3h2yQuwl#|vwylKuIvw}¤xvvh2l|X¨2k
(135) ©5l#7y{!5yQuuw}«©2}¤ª¤}v}«l?uvwy 16 ¨~uw}«yQ|x#y{| HHz{¨23 v}«yQ|~u#· |~lKxev¿!}«yQ}¤z{|§¨2©5Jl lv??¦Æl#2lK|^lKuwHl#yQ|A}«v|Au v4 x#y{|2|~|~§lK5xevy{}«}¤yQ|Q|Sv x7yQ¶| · H~gizQ¨2h2lKuwl&vw}¤y{x|~yQuT|H~yz{O¨~vh2lvw}¤yQy{¨t|~vu:uw}tl¹luw©~lK{xuwvwlKyQ§y{´}«|Èvk}«|AlKvl#3|HuIuFl?xevvwh2}¤l¹y{|Hx#uµy{|ty{° uIvw3}¤z{hAv-ª«}¤|2l?utl H~|~lKÈ©XsÁvwh2l&¦7}XvhÈ{|~Ȫ«lK|2zvh§y{,lKxev3|2zQª«l?u#·Æm,y{|Hxl#|2}¤|2zvwh2l&}¤|~uw}¤tl&uwlKxvwy{ ´}Ú· livwh~lFxy{|~|2lKxvw}¤y{|¹©Hl#v¦,lKl#|HyQ}«|Avm³|~¹5y{}¤|Av_®:¶¥ vwh2l G ukl7xyQ| H~zQ¨2vw}¤y{|~uï{wl7ª¤ª¤y ¦,l?´uwl#l HHz{¨2l ? ?K¶·ï±"²{lK|Qv¨~ª¤ª¤s{¥ ¨~uw}«yQ|Æxy{| H~z{¨23 v}«yQ|~uOl72y{5yQuwlKC·!gih2l#sª¤ª¤y ¦³vy
(136) tlKux}¤©HlT-ªz{l 3lKx|~vz{{l|2z{y{ª¤"lµvwh2l#lª kv}«yQ²QuIlµv-5wyQl?uw}«ª¤vw}¤}¤16uIy{vw|~}x
(137) uK· xK{uwlKuK·-¿!}¤z{¨2Jl ?Æuwh2y ¦Fu:ƨ~uw}¤y{|§x#y{| HHz{¨23 v}«yQ|Á}«|Svwh2l#lt} 5lKwlK|Qv L Ó K 9 * ¡{% + Ó * -' . £ |¸yQ2l#-vwy§uIlKª«l?xevvwh~lÆkyQuIv{2{tvwl?§¨~uI}¤y{|»x#y{| HHz{¨23 v}«yQ|U¥ ¦lÆtl HH|2lx#yQuIv¨2|~xev}«yQ|¸¦7h2}x3h k©5yl?v{huw¨2vwwh2l?lu®µvh2±_l x#y{h2|~lKwlKv|~h2xl-lv¦,©Hl#y¹v¦,}¤|2lK}l#v}¤|»{ªUvh2lKlxev32w|2yQzQHª«yAl?uIu#l?·O¸gixh2yQ}u7| H~xyAz{u¨~v7}uFvw}¤xy{yQ|»kH|HyA^uIl?vwh2ly{ 2vwh~vwlKlµl#v~l#wk&l?uIulK|QvlK^©Xs Ç ´Ú{¶ C=C +ω C +ω C ¦7h~l#l ω |~ ω l#2lKuwl#|Av7¦l#}¤z{hAvu¦7h2}x3hÁlTv¨2|2lK©XsÆvw}ªU{|~l#wyQK· 0 ¡ Ó K gih2lÁ®T±_ vwlKwk ª¤ª«y ¦Fu
(138) vwy^tl HH|2lvwh2l A¨~ª¤}«vs¸yFvh2l2wyQHyAuIl?³x#y{| H~zQ¨23 vw}¤y{| ¥ zQ/2}«²Q1 l#|vwh2l®µ±_¸·Hg yty&uIyH¥t¦,l:lKuIvw}¤k& vwl:vh2lvwl:y!h2}«zQh}¤|AvwlK|~uI}«vsÆ2}«¬tl#ªu¦7h2}¤x3hl:}«|~uw}tl-vwh2l ~wyQHyAuIl?¹yAy{vw2}¤|Qv´}<· l{·O2}«¬tl#ªu_¦7h2}x3hx#y{wl?uI5y{|H¹vwy¹2}«l?xl?u_y{ ©2¨2}¤ª¤2}«|2zX¶e·"gih2lµh2}¤z{h2lK_vh2l-vwl{¥ vh2lª«y ¦l#µvwh~lx#yQuIvK·¹gih2lh2}«zQh§}¤|AvwlK|~uI}«vsÁ2}«¬tl#ªul¹tl#vwl?xevwl?S©Xsvh2wl?uIh~y{ªt}«|~z Ç vwh2lvh2lKuwh2y{ª v² h2{l-ª«¨2|Xlµ¨2xk
(139) y{©5l#lKiuwHyyQ |~vw2h2u!l?uIvwl-yh2hH}¤z{ª«h :}«|A¼~vwlKyX|~y{uw"}vh2s&lK}«2zQ}«hA¬tv_l#ª¦7u}}«v|~h&uw}wtl?l:uI5vwlKh2xl-v"2vwyy{vw5h2yQlFuwlKzQwyQ¨2yX|~y{vw2ª«}«vw|A}«v?vw¨H¥2t|~l{· CUNl#v,¥XxvwyQh2|~l-uw}¤²Qty{lKª¤¨2kNl ¥ y{yQ_ª«ª¤vy h2¦Flu yXÇ yvw~w}¤|Av´}<· lQ·vwh2lvyv{ª"|X¨2k
(140) ©5l#y{~}¬tl#ªu3¶e·Ægih2lK|U¥Uvh2lÆ®T±, x#yQuIv
(141) x#{|§©5l&¦7w}«vIvl#|¸{u ´Q¶ N C =1− i i∈N?.
(142) &. . DEM. 1. 1. recovering. 2. contour. 2. t. DEM. Nt. 3 Ïvl
Documents relatifs
cosinus (en bleu à gauche) et d’une droite (en noir à droite) sur les données simulées pour 4 années à une température de 45°C, avec un bruit de fond interne réduit de 100,
Florence CARRÉ ~ Réoccupations funéraires de sépultures collectives néolithiques dans la boucle du
2 Vue plus en détails dans le chapitre 1... 2 phénomène d’agrégation des protéines amyloïdes en fibres et d’autres facteurs impor- tants doivent être pris en compte comme
In this chapter, we prove an a posteriori error estimates for the generalized overlapping domain decomposition method with Dirichlet boundary conditions on the boundaries for
Revue française d’héraldique et de sigillographie – Études en ligne – 2020-10 © Société française d’héraldique et de sigillographie, Paris,
Dans ce cas, comme les coulées du Bras de Sainte-Suzanne appartiennent au massif de La Montagne daté à plus de 2 Ma (McDougall, 1971), l’ensemble des coulées pahoehoe
In infantile Pompe disease patients, the glycogen storage diffusely affects brainstem motor and sensory neurons, and the whole spinal cord sensory neurons, interneurons, and
De ce point de vue, il est possible d’affirmer que la mission est accomplie : les projets de renouvellement urbain (GPV et ORU) élaborés depuis 1998 dans une centaine de villes