Quadtree-Based Distances between Images
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Texte intégral
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(11) ùúûoöKüÚøMõ ý þ1ÿgÿ
(12) ="!Pª38Z$# %S³'&µ(&2)&µ ³ 0m2Ü0uµ m´Eµ ³'*.o³èµ(+4. *o , )0 %-+ .o³ (µ + . *oâ).12 . .M/. &Ü1 0,µ@)2 23%SY2!.o5³ 476o9. 8)0u(µ %o0u(µ 6;:$³3%<0>=@3*o/. .?%SY2!µ@2 @BA ÕuÇkÇU˪ÅkÌoÕ}ÍWÐKÄsÍWÓ ÆußKÈUÃWÕuÇ É DFGF H ¥KqWrx]_j@jÑ`kej{Jv I&l q K`cb)¦|Xf}em`cxP] |) qKªl ]_dw¨W`cbXdª
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(14) npo qsrGt]uivvxw(y3qsz]vr"{p|}z]tiqs~ vzvxt3vv~ qsbvz. . =.o³)Y0\ m2 ./=x /3 Z<5>&u)./=(=4/µ"!Pr3&b4\&Ü2Ü+& =!6./#2 m2 ./=x // "2 . :0u . .M.102µ m2./=x //\ = µ#):$³Ym0<m2©./= // 980uµ .èm2./=x /3 Z"2)2Y % , 2)2YP.12. ../&Ü6.o³)2)2)0&u'=@2% , . Ym0)4<µ(&.o³%o0aYm0 Ym)0 4i(µ &.o³©µ +4 . *o &Üm 2 % , &(µ + (µ = .10 (µ +4 . *o & 0a.1)2 2Ym0 )2 2).o³. &m2 % , (µ + . *o & )2 2).12 Y./#g2)=4+4.12)#2 2)2Y %/8 ³)µ '³ * Ym)0 4(µ +4 . *o/ 5 l2Y (µ +4 . *o 0um2Ü0uµ@m´1/. =)(µ &¡% , 2Ü ³ ./. &Ü %S³4)2 2Y &µ +4(µ = .1b0 ¢ µ@m2 4£% , ./. &(µ #$8 m0 #g 8)2)/. = , .12Y0 &% , ´$(µ &)/. =(µ +4 . *o¤ # %S³C2ܳ2 &' #2/. &# %-=%o06= m2/. =x /
(15) ¥3p¦ + µ@)2 2§ /-¦ 2Ü 2'= µ '³ *m2 /. =x /- Z )2Ü $2Y0 =k-/.o
(16) ³ ¨)³).1)2 2!m2 /. =x /--© 3 ªµ #2).m2/. =x //5¦ +4µ@)2 2m2/. = /
(17) ¥ « Z %o¡0 &)2) . 8 8= 2) . :0a . ..102µ m2è/. =x //\ 7<(µ +4µ{\. /- 3µ m2 /. =x /-¬ Z l 2Y &(µ +4µ = .10uµ@m2 4®+/. &uY0 Y 8 ³) &l%S³ )2 2Y' &m0 ¯°&£#g0uµ@2Üm0uµ{. .o³) %S³ )2 2)0u 8)0 &ܳ2.12µ %S³ % , )2 2)4(µ +4 . *o , .12Y0 &= µm2,/. =x /- Z ª± ³ !ª² 3 &b4&2Ü +& )2 2) +4.oµ ³³ +m)2 23%$1 # %S'³ &u(µ &Ü)2 & µ ³è0u 8)0 &ܳ2µ 3³ */. #2â(µ +4 . *o´ % , )2 2Y©).12 . ./. &Ü .4è. µ?¢X)(µ +³ &µ %S³)/. = , .12Y0 ´o #gb2 %o0 = 6./&Ü2Ü == xµ /- Z 2E' & ¦)2 2) (µ +4 . *o!).12 . ./. &Üè3 %E &3³ %oB2 &Üb2 %o0 0/. = (µ + . *o &.Y26)2 2Y , .12Y0i´o #gb2 %o0 &0 80 &ܳ2µ 3³ *)2 2Y<(µ +4 . *o & 2Y &µ +4(µ = .10uµ 2 4 . m2 0Pm³ (µ +4 . *o &(µ &´# %-+8MY2Ü , )0 %-+ )2 2Y (µ &Ü2.o'³ #ga .mm2 0m³ )2 2Yµ@0 , .12Y0 ´o #gb2 %o0 & = ./&Ü2Ü =(= xµ /- 7< . : m2/. =x // Z ¶&u' #2 )2 2).12 8))0 %<$(µ + µ@2 4 µ ³ )2 2Y +' =@2·µ ¢X(µ +'³ &(µ %S³)/. =<&b8M/. #g 0 ¸) #g)2 &)2 2Y$ &(µ + (µ = .10uµ@m2 4% , )2 2Y (µ +4 . *o &P= µ ³ // Z , .12)0i´o #gb2 %o>0 % , )2 2Y Ym)0 4!(µ +4 . *o(µ &# %-+8Y2Ü .o³) /. == )2 2Y<(µ +4 . *o &% , 2)2Yi).12 . .M/. &Ü/ 30l23%-&Ü , .12Y0i´o #gb2 %o0 &>&.12(µ & , 44)2 2Y &u(µ +4(µ = .10aµ@2 4#g0uµ@2Üm0aµ %S§³ Y.10 8)0u &ܳC2Ü /. &)2 2) Ym)0 4 0 &' = 2 =w> =.M3 ª4m2©/. = // Z ¹8 8³)µ 3³ *º%S³ )2 2Y &Ü2Ü0a' #g2Y0âµ ³)Y Yµ 3³ * )2 2Y (µ +4 . *o &è.o³)» %S³ )2 2Y± +4m2Ü0u(µ #¸(µ &Ü2.o'³ #g ' &ܧ )2 2Y 6 µ{³)è(µ +4 . *o , .12Y0u8´o #gb2 %o0 & Ym)0 4. # %-+ &6. s oÿ ¼ ½ G¾ , %o06 Y/. +8=@. 0l2'%-&Ü )(µ &Ü2.o'³ #g , )0 %-+ )2 2Y Ym0 4 ´o #gb2 %o0/.10u¿ &)+4/. =(= m0!)2 2.oÀ³ %o0 )/. =:b2 % . &b8 #mµ Á) )(µ &Ü2.o³ #g 0u.o'³ *o 6\%o04. pÿ b Gÿp Â\Ãu þ ļ ½ G¾ , %o0 $/. +8=@ ± 6 µ ³) )2 2YÆ Å¢X³Y.10 &2 (µ +4 . *o , .12)0 ´o #gb2 %o0 &Ä0µ )2 2 0 &)8 #g2èb2 % Ç. #23%-&³ )µ &Ü2.o'³ #g +/. &)0 6\Mµ ³¸. +© =@2µ )(µ +4'³ &µ %S³)/. =M´o #gb2 %o£0 &b8/. #gè= "2Y)3³ *m28/. =x +' =@2µ (µ +'³ &(µ %S³)/. =
(18) ´o #gb2 %o0 &)8/. #g #m.o³ //È 7.12. 4S/. +4.¸m2</. =x /-¬ Z « 2Y /. =(&)%.< . +4m2Ü0u(µ #£&b8/. #g!= 6µ /. # #mµ .m2,/. =x /-¬ 0u.oµ ³.m2/. =x /- Z /. #2â(µ +4 . *o , .12Y0B +4. 4Ä2.´o &m´om0u/. =0u 8)0 &ܳ2.12µ %S'³ &= µm2,/. =x /- Z . M NGM MOPGQ)R<ST UN UV)WUGXV)WU Y Z\[]T UG^3_a`bZ cGd e c fGd d g_`G`-hiY j\_lk[f.
(19) npo qsrGt]uivvxw(y3qsz]vr"{p|}z]tiqs~ vzvxt3vv~ qsbvz. É. µxØ/&m´om0u./=³E'+m0uµ#m./=60 8)0&ܳ2.12µ%S³'&% , 2)2)µ@04Y&)#g0uµ(8)2b%o0& ./=(&b%9#m./=(=@ &(µ *S³).12Y0 & "-¸.o³ 4Ç!ªÊ 3 &b4\&Ü2Ü +& /. &ËÌ!P) = = µ#):$³Ym0m2./= // Z , %o0 µ ³ &Ü2.o'³ #g/ «#2).10u/. #g2Üm0u(µ ªm!(µ + . *o &.4;*-=%/./. =&µ *S³).12)0 &!=Ú/ }*3")2 2YÍ # %-=%o0 2)(µ &s¢ 2b%/*o0u/. +Î% , )2 2Y³2µ@0(µ +4 . *oKZ , %o0i)2 2Y 8Y)0 8?%-&Ü % , (µ +4 . *o0m2Ü0aµ@m´W/. = , )0 %-+ . ).12 . .M/. &Ü<=w3)µm2 /. =x // Z -Ï>%<0Pm´om0 , %o0 +4.o³ 4 . 8'8= µ #m.12µ %S³©.10u/. & *-=%/./. = #2).10u/. #g2Üm0uµ ª.12(µ %S³ /. =%S³Yº #m.o³)'³ %o24'³ &Y0uÐ &u.12(µ & , /. #gb2 %o)0 4 0um2Ü0uµ@m´1/. =60 &' =@)2 &ª³ 2)2Y +)µ #m/. =,3 %-+ .oµ ³ , %o0! $/. +8=@/ ¤=(%#m/. = , .12)0 & .10 ³YmY§ ¤. #m.o' &Ü 2)2Y©³' +. m0 % , 8.1)2 23%-=%/*/4Ð. .10uµ 3³ *8µ E =(&µ{³ .o³¸(µ + . *o(µ &60 = .12µ ´o =4º&)+4/. =(= # %-+8M.10 b2 %¸)2 2)4³C2µ 04(µ +4 . *o .o³ .o5³ 4*-=%/.M/. =&µ *S³).12)0 0%S = 3³ %o2 . &' ÑÒ#mµ@³)2 =4 (µ +8M/. #g2Üèb2 %&Üm0´o</. & .o³ .12Ü2Ü0u(µ .Y2Üi' &Ü , ' = , %o0 µ +4 . *oi0m2Ü0uµ@m´1/. = = ¦ 24$ m24/. =x //È Z ² =%/./. =&µ *S³.12Y0 &µ *S3³ %o0uÄ &b8.12µ /. =60 ={.12µ %S'³ &)2)(µ 89. ¢ 2m0m±³ 8·µ $ =(&l%o0,0 *S(µ %S'³ &i= *o0 %S3 8% , 8·µ $ =(&aZ «%Í%z´om0 # %-+)2 2(µ &l= µ +4µ@2.12µ %S§³ &Üm´om0a/. = . 8'8))0 %S/. #2Y & =w. 2'+4.o m2</. =x /-¬ =.' ªm2©/. =x //\ ² ' 8)2.èm2 /. =x /-¬ 7<(µ + m2/. =x //\ m2/. =x /
(20) ¥3 µ ³ m2©/. = /3 -//. =:$µ m2 /. =x // Z<' &Ü. ).12º . &Ü2Ü0u #g2Y0/ §#m/. =(=@ ¼½3 5/b = ¦ /. +m 2 /È
(21) ¥ Z ¦ #2 . 2Ü0mÄ &2Ü0u' #g2Y0/ 0>23%-&Ü 3³ %$Y &&Üb2 %o0 )2 2) , .12Y0u &% , /. #27# %o00u &b8?%S³))µ 3³ * (µ + . *o ).o)0u.o³C 2 )µ &' &Ü /. &. ½\ ·]Ó /Ô Õ Úÿ &Ü2Ü0u' #g2)0Ì %o0³. Ö <þ Uþ ÕÔ pÿ 0 80 &ܳ2.12µ %S§³ ¶/. #2 (µ +4 . *oè(µ &# %-+8.10® 0µ@)2 2 )2 2Y Ym0 4 (µ +4 . *o ' &uµ 3³ * )2 2Yµ@º 0 *-=%/./. =£&uµ *S³).12Y0 .o³) µ , )2 2Yµ@Ä0 &µ +4(µ = .10uµ 2 4>(µ &Ð. =%×0*Ç. *Sµ@´o³ 2)2Y0u &)23%-= § M)2 2Y³ )2 2Y # %o00 &)8p%S³)µ 3³ * ).o)0u.o³C)2 & % , (µ +4 . *o &i.10 # %-+8M.10§ .o³) &b%º%S³ =@m´o =¡.4=@m´o =x§ 2(µ &Ì+©' = 2·µ ¢8)0 #m(µ &uµ %S1³ &u(µ +4(µ = .10aµ@2 4 Ym)0 4$µ 3³ *Ð#m.o³ . :' &Ü!b2 %# %-+8.10:)2 2Y:³2µ@0i(µ +4 . *o &<= m2 /. = /
(22) ¥ ¤ Z %o0b2 %4/. ==%<0 ½Ã i ¼½' G = µ :o 6 µ{³) (µ +4 . *o &>0l23%-&)(µ &Ü2.o³ #g . m2 0Pm³¸)2 2Yµ 0b2 %/83¢=@ , 2 0 *S(µ %S³ .o³)!)2 2Y8b2 %/83¢=@ , 260 *Sµ %Sͳ % , . #2'%-&ܳ Ym0 4 (µ +4 . *oi(µ &P)³)Ym0PB. *Sµ@´o³ 2)2Y0u &)23%-= ' 6 = µ ³èm2/. =x /3 -¸/. =(:Eµ
(23) m2,/. =x // Z ª³>)2 2)µ &4.102(µ # =@/ 01 8))0 %/8?%-&Ü1 Ø¢X)(µ &Ü2.o'³ #g/ PÆ. *o³Ym0a/. = µ ª.12µ %S»³ % , .oY2Ü0m ¢ ./. &<)(µ &Ü2.o³ #g &?.mm2 0m³©(µ +4 . *o & }0>2)(µ #2(µ &
(24) Y Á³Y/. &¦ . = µ ³).10 # %-+´.µ{³).12µ %S³ % , )(µ &Ü2.o³ #g &. m2 0Pm³ ).oY2Ü0m©3³ %E) & )> # # %o0a)µ 3³ *4b2 % )2 2Y 0Pµ *-2C)2 &,/. &)&b%\#m·µ ¢ .12Ü® 0µ@)2 2 ).oY2Ü0mè3³ %$Y &©.o³ )2 2)!Y ÁM³)µ@2µ %S;³ % , )2 2Yè)(µ &Ü2.o'³ #ga . m2 0Pm³. M NGM MOPGQ)R<ST UN UV)WUGXV)WU Y Z\[]T UG^3_a`bZ cGd e c fGd d g_`G`-hiY j\_lk[iY.
(25) npo qsrGt]uivvxw(y3qsz]vr"{p|}z]tiqs~ vzvxt3vv~ qsbvz. ¥. 2m0% ³'%EY&))µ·Ù m0³C2 , ./+4µ(={µ@&"% , µ(&Ü2.o³'#g&. m2m0m³/µ(+4. *o& )# %-+8?%-&Ü ' &uµ ³3* ).o)2Ü0m& -#m.o³. )µ(&Ü2µ{³3*S)µ(&)2)§z&./#2 , ./+4µ(=4´2./&8.102µ(#m= .10¡8)0)%/83¢ m02µ & .o³)(µ &"' &Ü , ' =$µ ³ &b8 #mµ Á#¤# %S³))µ@2(µ %S'³ & oÄ- %o080#mµ(&Ü=4/12m0% , ./+4µ(={µ@&J% , )µ &Ü2.o'³ #g &. m2 0Pm³ ).oY2Ü0um &Ü2Ü0u #g2Y0 & '#m/. =(= Ä Ú Û´ 1ÿ Ö = Ú , %oº0 Ü ) Z .o³)± Ý Û´ 1ÿ Ö = Ý , %o0 Þ ½' - b 1ÿ Z $.o³). , /. +4(µ =4% , 8m0 #g 8)2)/. =Y)(µ &2.o'³ #g & . m2 0Pm³ µ +4 . *o & «#m/. ==@; ß xÛ´] G 1ÿ Ö i= ß , %o®0 à G½' Z . 8'8 .10 2Ya = .12Ü2Üm0 ´$(µ &)/. ==4a# %-+8M.10 &m2 0% (µ + . *o &,' &uµ 3³ *)2 2Yµ@0 .oY2Ü0m0 8)0 &ܳ2.12µ %S³â.o³) 2)2YÍ %o)2 2Ym0m2 0%;# %-+8.10u ).oY2Ü0umÐ &2Ü0u' #g2Y0 &©0 8)0u &ܳC2µ{3³ *âµ +4 . *o & 2Y µ ³2Üm0 &ÜÌ2 % , )2 2YÒ ØB¢¹:(µ &Ü2.o³ #g4(µ &8)2 2).12µ@)2 &:Y Á³µ@2µ %S³ (µ & *o³Ym0u/. =&)% )2 2).1 2 ¶&= Z $(µ &2µ 3³ * ).oY2Ü0um ¢./. &Ü )(µ &2.o'³ #g &B8))0 %/8?%-&Ü® .4 > 2+4.o m24/. =x6= /-¬ Z ² ' 8)2. m2 /. =xi= /-¬ Z 7<µ + m2 /. =xi= // Z l m2 /. =xi= /
(26) ¥ Z lµ ³ m2 /. =x = /3 Z
(27) .o³) -¸/. =(:Eµm28/. =x"= // Z ¦ . 8'8 .10,/. & 8.102µ #m' = .1l0 #m/. &Ü & % , )µ &Ü2.o'³ #g Ø = Zc2 /. ==%<0l& b2 % Y Á³Y<³) 0)(µ &Ü2.o'³ #g &.mm2 0m³/(µ +4 . *o & 2(µ & .10u2(µ # =@ (µ &Í%o)0 *S.o³)(µ ªmµ ³%)2 2Y , %-=(=%<0,µ 3³ *®0P<. 4/ ¦ #g2µ %S³ 0 #m/. ==(&è)2 2Y 8)0aµ '³ #mµ 8= &% , ).oY2Ü0um/0 80 &ܳ2.12µ %S§ ³ ¦ #g2µ %S³ É 8)0 &³C)2 & )2 2Y³ *o³)m0u/. = Y ÁM³)µ@2µ %S;³ % , ØB¢¹:(µ &Ü2.o'³ #g/ ¦ #g2µ %S³ ¥ Y Á³Y &&Üm´om0u/. =¤8.102(µ #m = .10 #m/. &Ü &% , ØB¢¹:(µ &2.o'³ #g/ ¦ #g2µ %S³ # %-+8.10 & )2 2YÌ 8))0 %/8?%-&Üè)(µ &Ü2.o³ #g &0,µ@)2 2Í%o)2 2Ym0 . 83¢ 8)0 %S/. #2Y & ¦ #g2µ %S³ &)23%×0l&$&Üm´om0a/. =) \8m0a(µ +³2/. =Y0 &' = )2 & µ ³)/. =(=4/ ¦ #g2µ %S³ # %S'³ # = &µ %S'³ & ¬ Y0a. 0l&&)%-+´. ó. züÚû ©øõû5æçö<ä. á ²âã'ä ;å. . µ è.o³ )³../= .o³'#g ).12.è&2Ü0u'#g2Y0.µ(=@2Ò.4 0u#mY0&µ@´o )µ ´Eµ·¢ &µ(%S³'&% , 2)2)&)8/. #gµ{³ , %SY08 )./=¢&µªm)µ(&i¨b%Sµ ³2 .oY0u.o³2)&= ¦ ./+m2 /È
(28) ¥ Z 2µ(&l&Ü2Ü0a'#g2Y0(µ &>0µ Y=4 '&/2b%è0 80&ܳ28µ(+ . *o&
(29) µxØ/M2b%º&Ü2b%o0uµ+4. *o& =k-/.o³3%SY´E0uµ@m0m2/. = /- Z %o0b2 %;&Üb2 %o0è.o³) µ{³)Y µ(+4. *o , .12)0& =w7<µ(+ m2/. = //\ m28/. =x /
(30) ¥3 µ ³ m28/. =x /3 -¸/. =(:Eµm2,/. =x // Z
(31) ³- %o0 8)0u #m(µ &Ü =4/)2 2Y ).o)2Ü0m£ #m.oг .:' &Ü b2 %2).o³) =@l 8?%-&µ@2(µ %S³)/. =µ ³ , %o0 + .12µ %SÒ³ % , ¼ ½' -/) (&. M NGM MOPGQ)R<ST UN UV)WUGXV)WU Y Z\[]T UG^3_a`bZ cGd e c fGd d g_`G`-hiY j\_lk[]é.
(32) npo qsrGt]uivvxw(y3qsz]vr"{p|}z]tiqs~ vzvxt3vv~ qsbvz ë êë ë êê ë êë ë êê ë êë ë êê ë êë ë êê ëêëëêê ëê ëëêê ë êë ë êê ë êë ë êê ë êë ë êê ëêëëêê ëê ëê ë êë ê ë êë ê ë êë ê ëêëê. 01. 00. 030. í ìí ìí ì íìíìíì. 031. 02. 0330. 032. 0331 0332. ó òó ó òò ó òó ó òò ó òó ó òò óòóóòò óò óóòò ó òó ó òò ó òó ó òò óòóóòò óò óò ó òó ò ó òó ò óòóò. Image 1. 0333. ñðññ ï ðð ïïîîî. ô ô ô õ ôõ õ ôô õ ôõ õ ôô õ ôõ õ ôô õôõõôô ô ôô õ ôõ õ ôô õ ôõ õ ôô õ ôõ õ ôô õôõõôô ôô õ ôôõ õ ôôõ õ ôôõ õôôõ. Image 2. . ù øù ù øø ù øù ù øø ù øù ù øø ù øù ù øø ùøùùøø ùø ùùøø ù øù ù øø ù øù ù øø ù øù ù øø ùøùùøø ùøø ù ù øøù ù øøù ù øøù û û úú ùøøù û û úú ûûúú û úû ú û úû ú ûúý üûú ý ü ýü ÷ö ö÷ ö÷ ÷ö÷ö÷ö ý üý ý üü ý üý ý üü ýüýýüü ÷ö ö÷. Image 3. Image 4. Image 7. Image 8. 01. 00. 0310 0311 030. 0313. 02 032 033. 0312. ±M]¬aqbU`g áÍ8ËréKÆu×ÌWÊsË"ÕaÖ$ÅwÙKÍmÈUÃKËrÈUÄsÉ"Äs× ÆaÓ}Ë ÐKÆuÈXÆuä1ÆaÅkËaà Image 6. Image 5. Legend. . 0. ÿ3þÿ3þÿ3þ ÿ3þÿ3þÿ3þ ÿþÿþÿþ. 0. 00. 0. 03 01. . Level 0. . . 02. . 00. 03 01. . Level 1. . 02. 033. 033. 03 00. 01. 030. 02. 031 032. 033 030. . 030. . 031 032. Quadtree of image 1. Level 3. 0330 0331 0332 0333. 0330 0331 0332 0333. 031 032. Level 2. . Quadtree of image 2. 0330 0331 0332 0333. Node identifiers in a quadtree 0. Underlined values of nodes 0, 03 or 033 represent the proportion of black nodes in sub−trees rooted by nodes 0, 03 or 033. . . 00. 0. 03. 01.
(33)
(34)
(35)
(36). 02. 030. %&% &%. 031 032. 033. 00. Level 0. '' ' ##$##$ $##$ !!"!"! "!"! 03. 01. Level 1. 02. 030. 031 032. Level 2. 033. ±M]¬aqbU`)(z  ÃKË Þmß1Æ}ÐÈkÇU˪ËÇU˪ÌzÇU˪Åk˪ÍmÈXÆuÈUÄsÕaÍWŦÕaÖYÈUÃKËÖ_ÕaßKǦÛWÇUÅwÈÄs× ÆaÓa˪ŦÕaÖ+*$ÄsÓ}ßzÇUË-,}à Quadtree of image 3. Quadtree of image 4. µ(+ . *o , .12)0& «={µ:oÒ# %-=%o0è=w>=.M3ª4m2©./= // Z&)2). 8 /="2). :E0u. ..10u2µ m2 ./=x // Z %o0 )2 2Y =(%#m/. = (µ ª.12µ %Sº³ % , %/.\¨ª #g2 , .12)0 &=w 2'+4.o m2/. = /-¬ Z «%Ä. 0 8)0 &ܳ2ÜÆ .4 . ¼ ½' -/) .o³ (µ +4 . *o4(µ &i0u #mY0 &µ@´o =(4/)µ@´$µ Y µ ³b2 % , %SY0 )/. =¢&µ ªm ).o)0u.o³C)2 &")³2(µ =EÌ . &Üb2 %/8'8µ '³ *># %S³))µ 2µ %S³©µ &«+m 2 /&b%:)2 2).12"/. #2 3³ %$Y£ % , )2 2Y ).oY2Ü0um<0 8)0 &³C)2 &,. .oY0u.o³2 % , )2 2Y(µ +4 . *o/ M Y/. +8=@ &% , &b8= µ@ 2 #g0aµ@2Üm0uµ . .10Ä # %-=%o0 %o02Ü $2Y0Ä 2'%-+%/*o³Yµ@m2 4®% , .o³>(µ +4 . *o ).oY0u.o³2 = ¦ + µ@)2 2 m2 /. =x /
(37) ¥ Z %o0!Æ. +4
(38) . Y(µ +4/. = ³E' +. m0 % ,Ì, .12Y0u³ 8?%Sµ ³)2 &4µ ³ /. #2 (µ + . *o ).o)0u.o³C2=w. 2'+4.o m2/. =x /-¬ Z 2)/)0 %%o2 3³ %$Y 0 8)0 &³C)2 &è)2 2Y µ{³)µ@2µ /. = ).o)0u.o³Cº 2 # %S³2.oµ ³)µ '³ * )2 2); 0l23%-=@ (µ + . *o/ , .o³ (µ +4 . *o:3 %E &3³ %o" 2 # %S³ , %o0 +b2 %)2 2) #23%-&ܺ³ &b8={µ@2 #g0uµ 2Üm0uµ %S§³ )2 2Y³ 2)2Y .oY2Ü0m8)0 %%o¤2 2)/. & , %SY06Y &)#g³).o³C263³ %$Y & 0u 8)0 &ܳ2µ 3³ *©)2 2Y , %SY¤0 Á)0 &Ü2. M NGM MOPGQ)R<ST UN UV)WUGXV)WU Y Z\[]T UG^3_a`bZ cGd e c fGd d g_`G`-hiY j\_lk[g.
(39) npo qsrGt]uivvxw(y3qsz]vr"{p|}z]tiqs~ vzvxt3vv~ qsbvz. . @m´o="µ(+ . *o ).oY0u.o³2)&
(40) ³3%$Yµ(&:.Ð=@. , 0l2Y³âµ@2)&Ì# %o00&)8p%S³)µ ³3*!µ(+4. *o ).oY0u.o³2# %S³ , %o0+Ò&2b%2)2YÌ&b8={µ@2$#g0uµ@2Üm0aµ%S³ %o2)2)m0)0µ(&Ü,2)2Y:³3%E),µ(&Pµ ³2Üm0u³)./= %o03³ %S\³ ¢U2Üm0 +4µ ³)/. =x (µ *SY0 8)0u &ܳC)2 &6.o³! Y./+8=@ % ,, %SY0 ).oY2Ü0um&0u 8)0 ¢ &ܳ2µ 3³ *è)2 2Y , %SY£ 0 Á)0 &28(µ + . *o &Ì% , µ *SY0u «%º+4 . :o4 \8= .o³).12(µ %S'³ &Ì# =@.10 0P8 &Ü8B . &b8 #mµ /. =(=(4&u(µ +8=@> #m/. &ÜÌ 0l2Ym08)2 2YÌ &b8= µ@2 #g0uµ@2Üm0uµ %Sa³ 0l2)µ #2Í&Üb2 %/8&P)2 2Y &' . µ@´Eµ &µ %S£ ³ % , .o³(µ +4 . *o ).oY0u.o³2 (µ &23%-+%/*o³Yµ@2 4/. # # %o0u)µ{3³ *ib2 %<)2 2Y 8µ E = # %-=%o<0 3.= /. #):Ð%o 0 0>2)µ@2Ü/ ÿ Ö þ 5 %o0 ¼ ½' - Ö þ 5 Z 0µ@)2 2 «%/. &)&b%\#mµ .12Üi.o³!µ{Y³C2(µ Á)m0:=w/. =&b%#m/. =(=@ _þ Ö /kþ1 . ).oY2Ü0m©3³ %E)/ ))·µ Ù m0³C2 , )'³ #g2µ %S³ &#m.oij . <' &Ü = ¦ /. +4m 2 /È
(41) ¥ Z l2Y &Ü , )'³ #g2µ %S³ & /. =(=%×0¶= Z b2 % /. &u(µ =4 0m2Ü0uµ m´o©.o³â(µ +4 . *o ).o)0u.o³C2 , 0 %-+ )2 2Y(µ +¢ . *o µ Y³2µ Á)m0©.o³) )2 2Y!µ{Y³C2(µ Á)m´ 0 % , . ).oY2Ü0m!3³ %E)a %o0 = Zb2 %â0um2Ü0uµ@m´o 2)2Y ).oY2Ü0m3³ %$Y©/. &&b%#mµ{.12Ü 0µ@)2 2â.o³âµ +4 . *o ).o)0u.o³C 2 ª³/)2 2(µ &,.10u2(µ # =@/ 0P©' &.è ; ¢%o0uYm0 , '³ #g2µ %S§³ , %-=(=(%<0µ '³ *)2 2Y/ .²8 ¦ .² ¦ %)µ@0u #g2µ %S'³ & 0l23%-=@ µ@0 & 2 ³E' +m0u/. = µ Y³2µ Á) &,)2 2Yµ ³)µ@2µ /. = .oY0u.o³2,0 80 &ܳ2µ 3³ *!)2 2Y (µ + . *o,.o³) )2 2Y0 %%o¤ 2 % , )2 2Y ).o)2Ü0m= &Üm %S³ )2 2Y = , 2 % , (µ *SY0 & .o³) Z 8' +m0u/. =& %o0 É , %-==%<0µ{3³ *)2 2Yµ@0 8.10u³C2'³ %EY<µ{Y³C2(µ Á)m0 Mµ Y³2µ , 4 2)2Y , %SY0 Á)0 &Ü2 =@m´o =µ +4 . *o ).o)0u.o³C)2 &.o³ )2 2Y , %SY0 Á0 &Ü2 =@m´o = .oY2Ü0m 3³ %$Y & S3 #mY0 &µ ´o =4/-&3 .3¢ ).oY0a.o³C)2 &% , .o³ (µ +4 . *o ).oY0u.o³ 2 Å.o³ #2)µ = Y0³ % , . ).oY2Ü0m 3³ %$Yº Å .10 µ Y³2µ Á)9 .49Å1070l2Ym02 04365 879717É;: "¦m2 < . )2 2)Ð &m2 % , ).oY2Ü0m 3³ %$Yèµ Y³2µ Á)m0 & ¡ 0¤% 3³ %E) &0,µ@)2 2 )2 2)Ä &/. + µ )³C2µ Ám0 Å x= Å=3 < Zµ ³ m2 0% )·µ Ù m0³2 ).oY2Ü0m &.10Ð #m/. =(=@ Â$ þ 4 þ _þ C þ ½ ÿMþ<5G ¹8 8 ³))µ '³ *>%S³)2 2)0 8)0 &ܳ2.12µ %S ³ % , (µ +4 . *o &Cµ ³2Üm0u³)/. =Y3³ %$Y &¡% , ).o)2Ü0m & #m.o ³ &Üb2 %o0·µ Ùm0u³C2 :$µ ³) &§% , µ ³ , %o0 +4.12µ %S§³ , %o0 Y/. +8= )2 2Y # %-=(%o«0 2)(µ &b2 %/*o0u/. + % , )2 2Y£ # %o00 &b8?%S³))µ{3³ *©(µ + . *o ).oY0a.o³C)2 & $)2 2Yi³E' +.m"0 % ,«, .12Y0u 8?%Sµ ³)2 &6µ ³ /. #2 ).oY0u.o³"2 %o0µ ³ , %o0 +4.12µ %S³è . .?%SY2)2 2Yµ 0 Y &)#g³)).o³2 3³ %$Y & $ª³ µ *SY0 8))0 %/8?%o02µ %S̳ % , .={/. #):i3³ %$Y &µ ³<)2 2Yµ@0¦)0 %%o2ÜB &3 .3¢ Wµ ³C2Üm0a³)/. =S3³ %$Y &&Üb2 %o0u&)2 2Y 2'+4.o¸m2,/. =x /-¬ Z ).oY2Ü0m!= &Üm©)³Ym0 = µ ³) ´1/. = Y &,µ ³ µ *SY0u Z ª³ =w. (µ + . *o &2).z´o8B . &b4\+´.?%-= µ #0 8)0 &³C2.12µ %S³!.o³)!.100u #mY0 &µ@´o =(4) # %-+8?%-&Ü =. M NGM MOPGQ)R<ST UN UV)WUGXV)WU Y Z\[]T UG^3_a`bZ cGd e c fGd d g_`G`-hiY j\_lk[ie.
(42) npo qsrGt]uivvxw(y3qsz]vr"{p|}z]tiqs~ vzvxt3vv~ qsbvz. ¬. µ ³2b%©.B&b8.12µ{./=.100u.o³'*o+³C2¤% ,, .12Y0>8p%Sµ{³C2)&Pµ ³ . .oY2Ü0m/Er³ 2)2)µ(&¤#m./&Ü/ ./#2 =@. , ³'%EY!0 8)0u&ܳC2)&.o³ µ+4. *o .oY0u.o³2# %S³2.oµ ³)µ{³3*â.12= ./&Ü2%S³Y , .12Y0Ð 8?%Sµ ³2.o³) /. #2>µ ³2Üm0u³)/. =63³ %$YÍ # %S³2.oµ '³ &4)2 2Y ³' +. m0 % , , .12Y0 8?%Sµ ³)2 &"% , )2 2)µ@0 )0 %%o2ÜÄ &3 .'¢U2Ü0m/ ¦ m´om0a/. = . 8'8)0 %S/. #2Y & = ² 3 8)2. m2 /. =x /-¬ 7(µ + m2 /. = //\ >m2!/. =x /
(43) ¥3 µ ³ m28/. =x /3 -//. =:$µ¦m2:/. =x // . .o3³ *!m2,/. =x /-É Z0 8)0 &ܳ2 /. #2 (µ +4 . *o; .4 . .oY2Ü0mÆ 2).z´Eµ '³ * . Á3E ³E' +. mº0 % , =@m´o =& =w' &)/. ==4 . , ' =(= É ¢=@m´o = ).oY2Ü0mKZ &r³ )2 2)µ &#m/. &Ü/ /. #2 (µ +4 . *o (µ &0 80 &ܳ2Üè .4 . , ' =(="./. ={.o'³ #g ).oY2Ü0um/ &/. #2 ).o)2Ü0m/3³ %$Y =wµ{³C2Üm0u³/. =%oÐ 0 =@. , Z &b2 %o0 & 2)2Y , .12Y0u &% , )2 2Y # %o0u0 &b8?%S³))µ '³ *µ +4 . *o ).oY0u.o³ 2 , %o0 Y/. +8=@<a. # %-=%o0 2)µ &Üb2 %/*o0u/. + = ² 3 8)2./m2©/. =x /-¬ m2/. =x /
(44) ¥3 µ ³ m2/. =x /3 Z %o0. # %-+.µ ³).12(µ %S£ ³ % , # %-=%o0
(45) &)2) . 8 &.o³)2Ü E2Y0u #m . 8)2Y0u<´$µ . 2)(µ &b2 %/*o0u/. +&=k-//. =:$µ m2&/. = // Z ¦ ' #24´. &Ü2Ü0u' #g2Y0u/ 5#m/. =(=@4. B½\ ·]Ó ( 3Â5] GUþ)-s / Y/. =(=%<0>& b2 % Á= 2Üm08(µ + . *o &8.1£ 2 &Üm´om0a/. == m´o =(& % , 8)0 #m(µ &uµ %S³ =U980aµ . m2:/. =x /3 Z µ *SY0 É *Sµ@´o &.o³ Y/. +8= % , +© =@2·µ ¢=@m´o =-2(µ &Üb2 %/*o0u/. +&¶/. #2 ).oY2Ü0mP3³ %E)$ # %S³C2.oµ{'³ & 2)2Y # %-=(%o$0 2)(µ &Üb2 %/*o0a/. + % , )2 2) # %o00 &b8?%S³))µ{3³ *8µ +4 . *o .oY0u.o³ 2 %o0µ ³ &Ü2.o'³ #g/ 2)2Y> 2)(µ &Üb2 %/*o0u/. + = . . =@ / # %o0u0 &b8?%S³)' & b2 % / ).oY0u.o³ 2 -*Sµ@´oÒ³ .4)2 2Y> Á)0 &Ü2 &' . µ@´Eµ &µ %S£ ³ % , )2 2Y(µ + . *o/ 5Ï,µ &Üb2 %/*o0u/. +&&b2 %o04µ ³/. #2Ò#2(µ = 3³ %$Y<= = . . =@ Z % , ).oY2Ü0m©3³ %E) / # %o00 &)8p%S³ b2 % )2 2Y , %SY>0 &3 .3¢ ).oY0u.o³)2 & // b2 % /-É % , .oY0u.o³2 / =w.12)2 2Yib2 %/81% , )2 2Yi0uµ *-2 2 &µ Yiµ ³ (µ *SY0 É Z . ±M]¬aqbU`?> áÍ8ËréKÆu×ÌWÊsË"ÕaÖ$×PßWÊØÈUÄØÏ{Ês˪ãg˪ÊSÃWÄsÅwÈUÕaÓaÇXÆa×Ūà. M NGM MOPGQ)R<ST UN UV)WUGXV)WU Y Z\[]T UG^3_a`bZ cGd e c fGd d g_`G`-hiY j\_lk[iZ.
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(47) npo qsrGt]uivvxw(y3qsz]vr"{p|}z]tiqs~ vzvxt3vv~ qsbvz. . w= 3,)µ"m2./=x // 3)µ"m2©./=x /-¬ Z".104µ ³´W.10uµ{.o³C2i2b% 2Ü0a.o³'&)= .12µ%S³
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(54) U ø ö¾ Ø (µ & ¿. +m2Ü0uµ # )(µ &Ü2.o'³ #g³ . #m.o &ܸµ@2 µ &4Æ. = µ ³).1Ò0 # %-+´.Mµ ³).12µ %Sè³ % , +m2Ü0a(µ #,(µ &Ü2.o'³ #g &. m2 0Pmº ³ 23%-+%-=%/*/%S' & ).oY2Ü0um83³ %$Y &:= fihSZ \ l2' &Ä¿Yj 7 j Å .o³) l )2 2Y0um<)·µ Ù m0³C2 µ +4 . *o &0 8)0u &ܳC2ܳ .4 ).oY2Ü0m & ¶ = Z ظk= j 7 jrnZ . #m.o &Ü ¿?ů3 < TfihEk= j 7 jªnZ = Z ظk= j 7ml }Z ÀØ = lÄ7 jª"Z . #m.o' &Ü ¿?ů3 < YfihYk= j 7ml }Z fihE= lD7 jrZ = É ÒZ Ø k= j 7 j Å ÇZ Æ Ø k= j 7ml Z È Ø = lÄ7 j Å BZ . #m.o' &ÜÉ fih (µ & ¿. +m2Ü0uµ # )(µ &Ü2.o'³ #g¸)2 2Y³ ¿?Åc3 < QfihEk= j 7 jmÅÑ Z Æ4fih$k= j 7ml )Z ÈFfihE= lD7 j ÅÑZ,.o³)â)2 2 &°ih9fihEk= j 7 j ÅÑZ Æ4°ih9fihEk= j 7ml Z È °ih9fihE= lD7 j Å Z . #m.o' &Ü ¿?ů3 < T°ih³² ØB¢ (&. M NGM MOPGQ)R<ST UN UV)WUGXV)WU Y Z\[]T UG^3_Ð`sZ cGd e cGfGd d g_` `/hiY j\_>k'[m` `.
(55) npo qsrGt]uivvxw(y3qsz]vr"{p|}z]tiqs~ vzvxt3vv~ qsbvz ~Ë¶Ì É É HGWS+¨1IkPbI©MTIkdePQKyde¨É_^IkKM®OePQRTSUKBØ2Ê Ø¥Í³OQP^_qØ Î. . # # %o0u)µ ³'*2b% 2)2Y#2'%Sµ(#g% , °ih¢# %E ÑÒ#mµ@³2)&.o³)TÏ×%o0¦2)2Y#2'%Sµ(#g$% , fih¢Xµ(&Ü2.o³'#g/ ØB¢¹:(µ &2.o'³ #g #m.o³ . # %-+£. Ø Ê ~Ë ¢X)(µ &2.o'³ #g/ 12 . :Eµ '³ *8µ ³b2 %:/. # # %S)³C2 %S³ =43³ %$Y & . 8'8 .10uµ{3³ * , 0 %-+ )2 2Y/)0 %%oa2 =@m´o =,b2 % 9. *Sµ@´o³ =@m´o =)Ð = &Üm ¦ #g2µ %S³ É É Z %o= 0 Ò}Ñ Ó xÔ ¢X)(µ &Ü2.o'³ #g/ :E. =%<0Pm0 .?%S)³) % , )(µ &Ü2.o³ #g & = &m ¦ #g2µ %S³ É É Z %o0 ØWÍ¢X)(µ &Ü2.o³ #g/ .0 *Sµ %S³¸)(µ &Ü2.o'³ #g = &m ¦ #g2µ %S³ É É É Z 1ÿ. Ø2Ê ~Ë Û´ Ö É É ¿ .E2 /=(=°ih¢# % ÑÒ# )&. Y³ . E mµ@³2 4.10 )./=x ./=(= ).oY2Ü0m ³3%$Y&2).´o 2)2)Ä&./+ 0Pµ *-22âµ ³ 2)2YèØB¢¹:µ(&Ü2.o³'#gÇ# %-+8Y2.12µ(%S³§>Ï>%<0Pm´om0<µ@2âµ(&³8?%-&)&uµ.=@/ , %o0 µ ³ &Ü2.o'³ #g/ )2b%è./&)&µ*S³³0µ(*-2C2,2b%!³3%$Y& ./# # %o0a)µ ³3* 2b% 2)2Yµ 0l=@m´o=µ ³ 2)2Y©2Ü0m &b%©)2 2).126)·µ Ù m0'³ #g &P . 8'8 .10uµ 3³ *µ{³4)2 2Y:3 8'8 m$ 0 =@m´o =&8=w³Y.106)2 2Y8)0 %%o2aZ &23%S' = 2).z´o Ç . 2)µ *-2Ym0è(µ +8/. #gÍ2 %S³ )2 2Y )(µ &2.o'³ #g/)2 2.o³ )·µ Ù m0'³ #g &è . 8'8 .10uµ 3³ * µ ³ =%×0m> 0 =@m´o =(& )³Y.10,)2 2Y =@.z´o &l% , &3 .)2Ü0um & m³ 2 Ø2Ê ~Ë k= j 7ml ºZ . )2 2Y¿ ØB¢¹:(µ &Ü2.o'³ #g¿ .mm2 0m³ (µ +4 . *o ).oY2Ü0um &§j .o³) l 0l2)m0 , %o0/. =(='³ %EY &Å%x= ÅÕ3 < Z© . 8'8 .10uµ '³ * , )0 %-+ )0 %%o 2 =@m´o =i= =@m´o = Zb2 % =@m´o =YÐJa°ih¯Á
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