3-D geometry reconstruction using a color image stereo pair and partial differential equations

   BiL4i|h) hiUL?t|hU|L? t?} @ UL*Lh 4@}i t|ihiL T@h @?_ T@h|@* _gihi?|@* i^@|L?t wt *@hi3 @?_ a@ih 5@?Ui3 #iT@h|@4i?|L _i W?uLh4@|U@ ) 5t|i4@t N?iht_@_ _i w@t @*4@t _i B @4Tt N?iht|@hL _i A@h@ Df.c w@t @*4@t ,4@*G i *@*@hi3 % t@?Ui3 j 9_t*T}Uit `iM@}iG ||TG % % tih_t_t*T}Uit % *@*@hi3 % ,ALMK@BM Lq wklv zrun/ zh suhvhqw d qhz prgho iru d ghqvh glvsdulw| hvwlpdwlrq dqg wkh 6  G jhrphwu| uhfrqvwuxfwlrq xvlqj d froru lpdjh vwhuhr sdlu1 Iluvw/ zh suhvhqw d eulhi lqwurgxfwlrq wr wkh 6  G Jhrphwu| ri d fdphud v|vwhp1 Qh{w/ zh sursrvh d qhz prgho iru wkh glvsdulw| hvwlpdwlrq edvhg rq dq hqhuj| ixqfwlrqdo1 Zh orrn iru wkh orfdo plqlpd ri wkh hqhuj| xvlqj wkh dvvrfldwhg Hxohu0Odjudqjh sduwldo glhuhqwldo htxdwlrq1 Wklv prgho lv d jhqhudol}dwlrq wr froru lpdjh ri wkh prgho ghyhorshg lq ^5` > zlwk vrph fkdqjhv lq wkh vwudwhj| wr dyrlg wkh luuhohydqw orfdo plqlpd1 Zh suhvhqw vrph qxphulfdo h{shulhqfhv ri 6  G uhfrqvwuxfwlrq/ xvlqj wklv phwkrg iru vrph uhdo vwhuhr sdluv1  Ai    }iL4i|h) Lu @ U@4ih@ t)t|i4 @?_ |i U@*Mh@|L? ThLM*i4 At tiU|L? t @? ?|hL_U|L? |L |i   ( }iL4i|h) Lu @ U@4ih@ t)t|i4 @?_ |i U@* Mh@|L? ThLM*i4 Lt| Lu |i hit*|t Thiti?|i_ ? |t tiU|L? U@? Mi uL?_ E | 4U 4Lhi _i|@*t ? d . o  AL t|_) |i ThLM*i4 Lu U@4ih@ U@*Mh@|L?c i ** ti |i U*@tt U@* T?L*i 4L_i* U @tt4it |i t4T*it| ThLiU|i 4L_i* uLh |i U@4ih@ 4@}i @U^t|L? Ai U@4ih@ t hiThiti?|i_ M) @ ThLiU|L? T*@?i 7 ?   ( @?_@uLUt  ' E  % c + c 5  Ai ThLiU|L? Lu |i TL?|  ' E %c+c5 Lu|i  ( tUi?i ?|L |i U@4ih@ t }i? M) |i ?|ihUiT|L? Lu |i *?i  | |i T*@?i 7 c E tii }hi   6}hi G hLiU|L? Lu @ # TL?| ? |i U@4ih@ T*@?i AL U@*Mh@|i |i U@4ih@ 4i@?t |L ?_ L| |i T@h@4i|iht U _i|ih4?i |i @) |@| |i ThLiU|L? Lh!t Aihi @hi 2 |)Tit Lu T@h@4i|ihtG |i ?|h?tU T@h@4i|iht @?_ |i i |h?tU T@h@4i|iht  _}|@* UL*Lh 4@}i U E %c+ ' E U  E %c+  cU 2 E %c+  cU  E %c+  t }i? M)  4@|hUit ihi |i @*it U & E %c+  & ' c 2 c  hiThiti?| |i  UL*Lh U@??i*t E hi_c }hii? @?_ M*i ? i@U T i* E %c+   Ai T i*t hiThiti?| t4@** Ui**t ihi |i *}| @hhi ?|L |i U@4ih@ Ai ?|h?tU T@h@4i|iht @hi |i uLU@* *i?}| sc |i T i* t3i E R % cR +  @?_ |i TLt|L? E S % cS +  ?|L |i U@4ih@ Lu |i ?|ihUiT|L? TL?| Mi|ii? |i T*@?i 7 @?_ |i TihTi?_U*@h *?i |L 7 T@tt?} |hL} |i uLUt  6Lh ?t|@?Uic u |i uLUt t Ui?|ihi_ | hitTiU| |L |i T*@?i 4@}i _4i?tL? |i?G S % ' 6Keo Js Jo5J?|@, R%e,r 2 S + ' 6Keo Js eo|S@, R%e,r 2 uhL4 @ ThLiU|i TL?| Lu i s @?_ E R % cR +  @hi ?L| ?_iTi?_i?| ? |i ti?ti |@| u i |@!i @ UL?t|@?| & |i ThLiU|L? }i?ih@|i_ M) |i ?|h?tU T@h@4i|iht s @?_ E R % cR + t |i t@4i |@| |i L?i }i?ih@|i_ M) |i T@h@4i|iht &s @?_ E &R % c&R +   Ai?c ?t|i@_ Lu t?} |i T@h@4i|iht s @?_ E R % cR + c i ti |i ?Lh4@*3i_ T@h@4i|iht k % ' R % * s @?_ k + ' R + * s 5L |L UL?U*_ic i @i e ?|h?tU T@h@4i|ihtG k % ck + cS % cS +  Ai ?|h?tU T@h@4i|iht _L ?L| _iTi?_ L? |i U@4ih@ *LU@|L? ? |i   ( tUi?i W? }hi 2 i **t|h@|i |i ?|h?tU T@h@4i|iht Ai i |h?tU T@h@4i|iht Lu |i U@4ih@ _i|ih4?i |i   ( *LU@|L? Lu |i U@4ih@ ? |i tUi?i | hitTiU| |L tL4i @ ThLh  i_ hiuihi?Ui t)t|i4 Ai i |h?tU T@h@4i|iht @hi }i? M) @ |h@?t*@|L? iU|Lh | ' E | % c| + c| 5  @?_ @ hL|@|L? 4@|h - ' E o   | hitTiU| |L |i  i_ hiuihi?Ui t)t|i4 5?Ui @ hL|@|L? t }i? M)  T@h@4i|iht E |i hL|@|L? @ i 2 6}hi 2G W?|h?tU T@h@4i|iht **t|h@|L? @?_ |i hL|@|L? @?}*ic |ihiuLhic |i) @hi S i |h?tU T@h@4i|iht W? }hi  i **t|h@|i |i i |h?tU T@h@4i|iht Ai ?i | hit*| it|@M*t L |i ?|h?tU @?_ i |h?tU T@h@4i|iht _i|ih4?i |i @) |i ThLiU|L? Lh!t AiLhi4  E6@}ih@t d.o wi| Mi E  'E   c 2 c  c e  5S  c |i? |i ThLiU|L? TL?| D 6 ' E 6  c6 2 c6   5S 2 Lu @   ( TL?| E  ? |i U@4ih@ t }i? M) ! + 6  6 2 6  " , ' ! + k % h  n S % h  k % | % n S % | 5 k + h 2 n S + h  k + | + n S + | 5 h  | 5 " , ! - - +    2    e " . . , E  ihi h  hiThiti?|t |i hLt Lu |i hL|@|L? 4@|h - W? @| uL**Ltc i ?L|i M)  |i e %  4@|h U _i|ih4?it |i ThLiU|L?c |@| t D 6 '  E  `i ?L|i |@| |i 4@|h  t @ *?i@h ThLiU|i @TT*U@|L? U t _i?i_ T |L @ tU@*i u@U|Lh AL U@*Mh@|i |i U@4ih@ i ** @tt4i |@| i !?L @ ti| Lu   ( TL?|t E   @?_ |ih hitTiU|i ThLiU|L?t D 6  ? |i U@4ih@ 5L i uLh4*@|i |i U@*Mh@|L? ThLM*i4 @t |L ?_ L| @  4@|h tU |@|G D 6  '  E   ;  ' cc E 2  6}hi G , |h?tU T@h@4i|iht **t|h@|L? ihi  t |i ?4Mih Lu TL?|t |@| i ti W? Th@U|Uic i ** ti @ tTiU@* LMiU| tL? ? }hi e uLh U i !?L |i   ( TLt|L? Lu |i M*@U! t^@hit W? u@U| i ** ti @t TL?|t i   |i ULh?iht Lu |i M*@U! t^@hitc @?_ @t TL?|t h 6  |i ThLiU|L? Lu i   ?|L |i U@4ih@ `i ?L|i |@| 4@|h  @t 2 i*i4i?|tc @?_ |@| uLh i@U E i   c h 6   i^@|L? E 2 ThL_it E L?Ui |i ThLiU|i T@h@4i|ih t hi4Li_c 2 *?i@h i^@|L?t | hitTiU| |L  i*i4i?|t }i? M)G  [  ' R     n R e  6  #  [  ' R     n R e $ ' f E  [  ' R 2    n R e  6 2 #  [  ' R     n R e $ 'f `i?  E |i ?4Mih Lu T@ht E i   c h 6   t M}}ih |@? Dc @?_ |i TL?|t @hi ? }i?ih@* TLt|L? E |@| tc |i) @hi ?L| ? tL4i tTiU@* _i}i?ih@|i_ UL?}h@|L? |i?c i U@? hiULih 4@|h  uL**L?} |i hi*@|L? E 2 Ai |iU?^i |L it|4@|i  t ih) t4T*i `i ?L|i M) R ' E R  cR 2 ? cR e  |i 2 i*i4i?|t iU|Lh }i? M) |i *?it Lu 4@|h  Ai?c |i hi*@|L?t E  U@? Mi h||i? @t R 'f c ihi  t@2 % 2  4@|h  5?Ui R t _i?i_ T |L @ tU@*i u@U|Lhc i U@? @tt4i |@| n R n '  Ai?c i *LL! uLh @ iU|Lh R U 4?43i |i i?ih}) . E R  }i? M)G . E R ' n R n 2 ' R )  ) R | |i UL?t|h@?| n R n '   t|h@}|uLh@h_ UL4T|@|L? )i*_t |L R i^@* |L |i i}i?iU|Lh @ttLU@|i_ |L |i t4@**it| i}i?@*i Lu  )  ? |i L|ih @?_c t?} t|@? e 6}hi eG   ( LMiU| ti_ uLh U@4ih@ U@*Mh@|L? _@h_ |iU?^itc L?Ui |i 4@|h  t !?L?c i U@? _i_Ui |i ?|h?tU @?_ i |h?tU T@h@4i|iht ,i? u 4@|h  t @ ThLiU|i @TT*U@|L? @?_ | t _i?i_ T |L @ tU@*i u@U|Lhc i U@? hiULih tL4i ih) tiu* iU*_i@? ?uLh4@|L? uhL4  6ht|c i U@? hiULih |i uLUt TLt|L?  Lu |i U@4ih@G  '  A  !  ! + R e R 2e R e " , @?_ }i? @ TL?| 6 ' E 6  c6 2  ? |i U@4ih@c |i _hiU|Lh iU|Lh  6 Lu |i *?i 6 t }i? M)G  6 ' A  !  ! + 6  6 2  " , ihi A  ' ! + R  R 2 R  R 2 R 22 R 2 R  R 2 R  " , Ai?c t?} c i U@? @ttLU@|i |i *?i 6 |L @?) TL?| 6 ? |i U@4ih@ ihi |i   ( TL?|  @t|LMi*LU@|i_ Ai ,TTL*@h BiL4i|h) D N?|* ?Lc i @i uLUti_ Lh @||i?|L? ? |i U@ti Lu  U@4ih@ W? |i U@ti Lu 2 U@4ih@tc i @i |L it Lu |i t@4i tUi?i ,@U U@4ih@ @t |t L? 4@|h  |@| i ** ?L|i M)  @?_   @?_ uLh @?)   ( TL?|  c |ihi i t| |L ThLiU|L?t 6 @?_ 6   `i ?L|i |@| u i !?L  @?_   @?_ |L ULhhitTL?_?} TL?|t 6 @?_ 6  c |i?c i U@? hiULih |i   ( TLt|L? Lu  @t |i ?|ihUiT|L? Lu *?it 6 @?_ 6     At t **t|h@|i_ ? }hi D 6}hi DG   ( BiL4i|h) Lu @ t|ihiL T@h Ai TL?| 6  |@| ULhhitTL?_t |L 6 ? |i L|ih U@4ih@ @t |L *i ? |i ThLiU|L? Lu |i *?i 6 ? |i L|ih U@4ih@ At ThLiU|L? t ?@4i_ iTTL*@h *?i @ttLU@|i_ |L 6   t|h@}|uLh@h_ U@*U*t )i*_t |L |i uL**L?} i ThittL? uLh |i iTTL*@h *?itG E 6  Q c6  c  k   h  l %   e  3 Q 3 C 6 Q 6  4 D 'f ihi |i t)4ML* d | o % @ttLU@|i_ |L @ iU|Lh | t |i @?|t)44i|hU 4@|h G d | o % ' 3 C f  | 5 | + | 5 f  | %  | + | % f 4 D |i  %  4@|h 8 ' k   h  l %   e  3 Q t ?@4i_ u?_@4i?|@* 4@|h c @?_ | _i|ih4?it |i iTTL*@h }iL4i|h)c |@| tc | _i|ih4?it |i iTTL*@h *?i @ttLU@|i_ |L i@U TL?| 6 W? S 6}hi SG ,TTL*@h BiL4i|h) }hi S i **t|h@|i |i iTTL*@h }iL4i|h) Ai iTTL*it @hi |i ?|ihUiT|L? Lu |i *?i   | |i T*@?it ? ML| U@4ih@t 2 #i?ti _tT@h|) 4@T it|4@|L? @?_ T@h|@* _gih i?|@* i^@|L?t `i ?@4i _tT@h|) |L |i _tT*@Ui4i?| Mi|ii? |i TL?| 6 L? |i 4@}i U @?_ |t ULhhitTL?_?} TL?| 6  L? U   Ai @UUh@U) Lu |i _tT@h|) it|4@|L? t ih) 4TLh|@?| MiU@ti | _i|ih4?it |i ^@*|) Lu |i   ( hiUL?t|hU|L? ih |i )i@htc ?4ihLt @*}Lh|4t uLh t|ihiL tL? @i Mii? ThLTLti_c U ti _gihi?| t|h@|i}it  6i@|hi M@ti_G ALti @*}Lh|4t it|@M*t ULhhitTL?_i?Uit Mi|ii? tL4i ti*iU|i_ ui@|hit i |h@U|i_ uhL4 |i 4@}it d 2 o c tU @t i_}i T i*t d ec e o c *?i ti}4i?|t d Sc c 2 o Lh Uhit d 2c bc e. o  Aih 4@? @_@?|@}i t |L )i*_ @UUh@|i ?uLh4@|L? @?_ |L 4@?T*@|i hi@tL?@M*) t4@** @4L?|t Lu _@|@c |t }@??} ? |4i @?_ tT@Ui UL4T*i |) Aih 4@? _h@M@U! t |i tT@hti?itt Lu |i hiULihi_ _iT| ?uLh4@|L? At U*@tt Lu 4i|L_t @t Mii? _i*) ti_ tL4i )i@ht @}Lc i? | @t ?L| TLttM*i |L hi|hii @ _i?ti @?_ @UUh@|i hiUL?t|hU|L? |? @ hi@tL?@M*i @4L?| Lu |4i .  hi@ M@ti_G W? |iti @TThL@Uitc _i?ti _iT| 4@Tt @hi ThL_i_ M) ULhhi*@|?} |i }hi) *ii*t Lu 4@}i T@|Uit ? |i it Mi?} UL?t_ihi_c @tt4?} |@| |i) Thiti?| tL4i t4*@h|) dDc Hc 22c efo Aiti 4i|L_t @hi i** @_@T|i_ uLh hi*@|i*) |i |hi_ @hi@t( Liihc |i) }i?ih@**) @tt4i |@| |i LMtihi_ tUi?i t *LU@**) uhL?|T@h@**i*c U U@tit ThLM*i4t uLh t*@?|i_ thu@Uit @?_ ? T@h|U*@h ?i@h |i LUU*_?} UL?|Lht Lu |i LMiU|t w@t|*)c |i 4@|U?} ThLUitt _Lit ?L| |@!i ?|L @UUL?| |i i_}i ?uLh4@|L? U t @U|@**) @ ih) 4TLh|@?| ?uLh4@|L? |@| tL*_ Mi ti_ ? Lh_ih |L }i| hi*@M*i @?_ @UUh@|i _i?ti 4@Tt  ,?ih}) M@ti_G  *@t| !?_ Lu @TThL@U U _Lit ?L| tgih @?) Lu |i tLh| UL4?}t Thiti?|i_ @MLic UL?tt|t Lu tL*?} |i ULhhitTL?_i?Ui ThLM*i4 ? @ 4? 43@|L? @?_ hi}*@h3@|L? uLh4*@|L? d 2c .c bc 2Dc eDc eSc ebc DS o  Ai 4i|L_ |@| i ThLTLti ? |t T@Tih Mi*L?} |L |i i?ih}) M@ti_ 4i|L_t AL it|@M*t |i 4L_i* i ** ?|hL_Ui tL4i ?L|@|L?tG i ?L|i M) 8 ' E s   |i u?_@4i? |@* 4@|h @ttLU@|i_ |L |i t|ihiL T@h `i _i?i |i @ *@h) u?U|L?tG @ E %c+  cK E %c+  @?_ S E %c+  ? |i uL**L?} @)G @ E %c+ ' s  % n s 2 + n s  c K E %c+ ' s 2 % n s 22 + n s 2 c S E %c+ ' s  % n s 2 + n s   | |t ?L|@|L?c |i iTTL*@h *?i @ttLU@|i_ |L @ TL?| 6 ' E %c+  t }i? M)G @ E %c+  %  n K E %c+  +  n S E %c+ 'f  E e i ** ti |t i^@|L? ? Lh_ih |L T@h@4i|h3i |i _tT*@Ui4i?| Mi|ii? @ TL?| 6 ' E %c+ L? U @?_ |t ULhhitTL?_?} TL?| 6  'E %  c+  L? U   2 @h@4i|h3@|L? Lu |i _tT@h|) N?_ih |i @tt4T|L? |@| ULhhitTL?_?} TL?|t ? ML| 4@}it @i i^@* UL*Lh *i i*tc |L it|4@|i |i _tT@h|) t i^@*i?| |L *LL! uLh @ iU|Lh u?U|L? $  E %c+ G' E  E %c+  c E %c+  | tU |@|G U  E %c+ ' U   E % n  E %c+  c+ n  E %c+  ; E %c+  5 7 2  ' c 2 c  E D ihi U  E hitTiU| U    hiThiti?| |i  UL*Lh U@??i*t Lu 4@}i U E hitTiU| U   `i ?L|i |@| |i ULhhitTL?_?} TL?| E %  c+  ' E % n  E %c+  c+ n  E %c+  Mi*L?}t |L |i iTTL*@h *?i @ttLU@|i_ |L E %c+  @?_ |i? | t@|titG - e E %  c+  ' @ E %c+  E % n  E %c+  n K E %c+  E + n  E %c+  n S E %c+ 'f H Wu i T@h@4i|h3i |i iTTL*@h *?i t?} @ u?U|L? b E %c+  |i? i LM|@?G  E %c+ '  b E %c+  K E %c+  s @ 2 E %c+ n K 2 E %c+   @ E %c+  % n K E %c+  + n S E %c+  @ 2 E %c+ n K 2 E %c+  @ E %c+  c  E %c+ ' b E %c+  @ E %c+  s @ 2 E %c+ n K 2 E %c+   @ E %c+  % n K E %c+  + n S E %c+  @ 2 E %c+ n K 2 E %c+  K E %c+  c ihi b E %c+  hiThiti?|t |i T@h@4i|ih Lu |i iTTL*@h *?i `i ** ?L|i    E b E %c+  ' E  E b E %c+  c E b E %c+  |L ?_U@|i |@| |i _tT@h|) |ih4 _iTi?_t t| L? |i T@h@4i|ih b E %c+  `i TL?| L| |@| |i U@ti b E %c+  ' f _i|ih4?it |i TL?| ? |i iTTL*@h *?i U 4?43i |i _t|@?Ui Mi|ii? |i iTTL*@h *?i @?_ 6 'E %c+   W? }hi . i **t|h@|i |i _tT@h|) T@h@4i|h3@|L? t?} b E %c+   6}hi .G @h@4i|h3@|L? Lu |i _tT@h|) i |c i Thiti?| |i 4L_i* |@| i ThLTLti |L it|4@|i b E %c+  22 Ai ThLTLti_ i?ih}) 4L_i* AL it|4@|i b E %c+ c i ** UL?t_ih |i ?i | i?ih}) u?U|L?@*G . E b '  [  ' ] l E U  E %c+   U   E % n  E b E %c+  c+ n  E b E %c+  2 _%_+ n  ] l E K b  ) ( E K U 4@  K b_%_+ E S b Thiti?| ? |t tUi?i `i ?L|Ui |@| |i @*}Lh|4 t ih) hLMt| | hitTiU| |L |i ULUi Lu |i T@h@4i|iht @?_ |@| | i^@* Lh t4*@h @*itc i LM|@? }LL_ hit*|t ? ih) _gihi?| t|@|L?t 6Lh 4Lhi _i|@*t @ML| |i ?4ihU@* i Tihi?Uit )L U@? t| |i iM t|iG ||TG%%tih_t_t*T}Uit%*@*@hi3%hiti@hU%_i4Lt%L*Lh5|ihiL6*L U!?L*i_}i4i?| At Lh! @t Mii? tTTLh|i_ M) |i ,hLTi@? A+ ?i|Lh! VtULt|) 5L*|L?t @?_ |ih TT*U@|L?t  +iuihi?Uit d  o w *@hi3c w wL?tc a Lhi*c W4@}i ti*iU|i t4LL|?} @?_ i_}i _i|iU|L? M) ?L?*?i@h _gtL? WW c 5W a 4ih ?@*c VL* 2bc HeDHSSc bb2 d 2 o w *@hi3c +#ihUic a5@?Ui3 @?_ a`iU!ih|c #i?ti _tT@h|) 4@T it|4@|L? hitTiU|?} 4@}i _tUL?|?|itG  #, @?_ 5U@*i5T@Ui @ti_ TThL@U c W+W +@TTLh| _i +iUihUi  J H.ec 2fff d  o w *@hi3c a `iU!ih|c a 5@?Ui3c  tU@*itT@Ui @TThL@U |L ?L?*LU@* LT|U@* L U@*U*@|L?t c  i*ti?c  aL@?ti?c 6 *ti?c a `iU!ih| E ,_tc 5U@*itT@Ui |iLhit ? UL4T|ih tL?c wiU|hi L|it ? L4T|ih 5Ui?Uic 5Th?}ihc ih*?c VL* SH2c 2D2eSc bbb d e o w *@hi3c a `iU!ih|c a 5@?Ui3c +i*@M*i ,t|4@|L? Lu T|U@* 6*L uLh w@h}i #tT*@Ui4i?|t c AiU?U@* +iTLh| L 2c @_ih?Lt _i* W?t|||L N?iht|@hL _i i?U@t ) AiU?L*L} @t Mih?i|U@tc N?iht_@_ _i w@t @*4@t _i Bh@? @?@h@c 5T@?c bbb d D o  )@Ui @?_  O@?ti? +iU|U@|L? Lu 4@}it uLh M?LU*@h @?_ |h?LU*@h t|ihiLtL? W? ?| W?|ih?@|L?@* L?uihi?Ui L? @||ih? +iUL}?|L? c T@}it Sc U|LMih bHHc i?}c ?@ d S o  )@Ui @?_ 6 wt|4@? 6@t| @?_ hi*@M*i T@tti |h?LU*@h t|ihiLtL? W? hLUii_?}t Lu |i t| W?|ih?@|L?@* L?uihi?Ui L? L4T|ih VtL? c T@}it e22e2.c wL?_L?c ,?}*@?_c a?i bH. W,,, L4T|ih 5LUi|) hitt d . o 5A @h?@h_ 5|LU@t|U 5|ihiL @|U?} ih 5U@*i W?|ih?@|L?@* aLh?@* Lu L4T|ih VtL? cVL*c.2cbHb S dHo aw @hhL?c #a 6*ii|c @?_ 55 i@Ui4? ihuLh4@?Ui Lu LT|U@* L |iU?^it W?|ih?@|L?@* aLh?@* Lu L4T|ih VtL? c 2EGe..c bbe dbo  @tU*i @?_ + #ihUi ,?ih}) M@ti_ 4i|L_t uLh 2# Uhi |h@U!?}c hiUL?t|hU |L?c @?_ hi?i4i?| Lu # Uhit @?_ @TT*U@|L?t W? 5W, hLUii_?}tc VL* 2fc  Vi4h E,_c BiL4i|hU i|L_t ? L4T|ih VtL? WW c 5@?#i}Lc @*uLh ?@cN5c a*) 2c bbc T@}it 2H22b dfo 6 ih}L*4c ,_}i uLUt?} c W,,, Ah@?t @||ih? ?@* @U W?|i**c VL* bc .2S .ec bH. do O hi3tc Tih@|iht 4@ 4@ 4L?L|L?it i| ti4}hLTit _i UL?|h@U|L?t _@?t *it itT@Uit _i O*Mih| c Lh| OL**@?_c 4t|ih_@4c b. d 2 o A h?| @?_  h@_) 5|ihiL @|U?} Lu hit W4@}i @?_ VtL? L4T|?} c VL* Hc L c TT DfDSc bbf d  o  @hML??ihc w *@?U6ih@_c B Mih|c  @h*@_c AL _i|ih4?t|U @*u^@_h@|U hi}*@h3@|L? @*}Lh|4t uLh UL4T|i_ 4@}?} c hLU W,,, W?| L?u W4@}i hLUitt?} E WWbec t|?c L Sc bbec VL* 2c W,,, L4T|ih 5LUi|) hittc wLt *@4|Ltc SH.2c bbe d e o + #ihUi @?_  6@}ih@t wit ,# i? |h@|i4i?| _it 4@}it i| tL? T@h Lh_ ?@|ih Ah@|i4i?| _ 5}?@* VL* c L Sc bbS E @*tL @t W+W +iti@hU +iTLh| 2Sb.c L bbD d D o 6hi_ihU #iih?@) @?_ *ih # 6@}ih@t L4T|?} _gihi?|@* ThLTih|it Lu # t@Tit uhL4 t|ihiLtULTU 4@}it |L| # 4L_i*t hLU W,,, L?uihi?Ui L? L4T|ih VtL? @?_ @||ih? +iUL}?|L?c 5i@||*ic `c a?i 22c bbec T@}it 2fH2 d S o ` ,?!i*4@??c W?it|}@|L? Lu 4*|}h_ @*}Lh|4t uLh |i it|4@|L? Lu LT|U@* L i*_t ? 4@}i ti^i?Uit c L4T|ih VtL?c Bh@TUt @?_ W4@}i hLUitt?}c VL* ec Df..c bHH d . o  6@}ih@t Ahii#4i?tL?@* L4T|ih VtL?G @ BiL4i|hU ViTL?|  WA hittc @4Mh_}ic c bb d H o *ih 6@}ih@tc ih?@h_ OL|3c Oihi @|ic Aihh) Vi**ic ~i?})L ~@?}c @tU@* 6@c ,hU AihL?c w@hi?| L**c Bih@h_ ihh)c ai@? V**i4?c @|hUi ih|?c @?_ @|ih?i hL) +i@* |4i ULhhi*@|L? M@ti_ t|ihiLG @*}Lh|4 4T*i4i?|@|L?t @?_ @TT*U@|L?t W?|ih?@|L?@* aLh?@* Lu L4T|ih VtL?  AL @TTi@h d b o #a 6*ii| @?_ # aiTtL? L4T|@|L? Lu UL4TL?i?| 4@}i i*LU|) uhL4 *LU@* T@ti ?uLh4@|L? W?|ih?@|L?@* aLh?@* Lu L4T|ih VtL? c DG..fec bbf . d2fo #a 6*ii| @?_ # aiTtL? 5|@M*|) Lu T@ti ?uLh4@|L? W,,, Ah@?t @|| ?@* @U W?|i* c DG2D2SHc bb d2o w 6*Lh@U!c W4@}i 5|hU|hi c k*ihc #Lh_hiU|c bb. d22o @tU@* 6@  T@h@**i* t|ihiL @*}Lh|4 |@| ThL_Uit _i?ti _iT| 4@Tt @?_ Thi tihit 4@}i ui@|hit @U?i VtL? @?_ TT*U@|L?t c SEG Debc `?|ih bb @*@M*i @t W+W hiti@hU hiTLh| Sb d2o `,w Bh4tL? L4T|@|L?@* , Tih4i?|t | @ 6i@|hi @ti_ 5|ihiL *}Lh|4 c W,,, Ah@?t @||ih? ?@* @U W?|i**c VL* .c L c a@?@h) bHD .ec bHD E5ii @*tL WA i4L .S2c a@?@h) bHe d 2e o # Bi4@?c B +i)?L*_tc L?t|h@?i_ hit|Lh@|L? @?_ |i hiULih) Lu _tUL?|?|it c W,,, Ah@?t @||ih? ?@* @U W?|i**c ec S.Hc bb2 d 2D o 6 Oi|3c  ihi3c @?_  L|i4) *|tU@*i 4?43@|L? Lu }*LM@* i?ih}) u?U |L?t ? tL4i t@* hiULih) ThLM*i4t VBW G W4@}i N?_iht|@?_?} cDb E G2D ec a@?@h) bbe d 2S o A W4@c @tU |iLh) L? ?Lh4@*3@|L? Lu T@||ih? E ? U@ti Lu |)TU@* L?i_4i?tL?@* T@||ih?  c **i|? Lu |i ,*iU|hL|iU?U@* w@MLh@|Lh)c VL* 2Sc SHHHc bS2 E ? a@T@?iti d 2. o + ai?!? @?_ # aiTtL? +iULih?} *LU@* thu@Ui t|hU|hi |hL} *LU@* T@ti _gihi?Ui 4i|L_t VBWG W4@}i N?_iht|@?_?} c DbG.2bc bbe d 2H o #B aL?itc a @*!c  UL4T|@|L?@* uh@4iLh! uLh _i|ih4??} t|ihiL ULhhitTL? _i?Ui uhL4 @ ti| Lu *?i@h tT@|@* *|iht c B 5@?_? E,_c L4T|ih tL?  ,V <b2c wiU|hi L|it ? L4T|ih 5Ui?Uic VL* DHHc 5Th?}ihc ih*?c bDefc bb2 d 2b o aa kLi?_ih?!c Ai t|hU|hi Lu 4@}it c L*L}U@* )Mih?i|Utc VL* Dfc S.fc bHe d f o A w?_iMih}c  tU@*i ti*iU|L? Th?UT*i uLh it|4@|?} 4@}i _iuLh4@|L?t cW4@}i @?_ VtL? L4T|?}c VL* Sc L ec bSb..c bbH d  o aO UW?|Lt @?_ k|U @|U?} 5|h@}| w?it c L4T|ih VtL?c Bh@TUt @?_ W4@}i hLUitt?}c e E GHS2bc bbH d 2 o Bi_L? @?_ +i@|@ 5i}4i?| @ti_ 5|ihiL @|U?} c L4T|ih VtL?c Bh@T Ut @?_ W4@}i hLUitt?}c  E G2Hc bHD d  o k` Lh|L?c w @)ihtc 4ihU@* 5L*|L? Lu @h|@* #gihi?|@* ,^@|L?t c @4Mh_}i N?iht|) hittc @4Mh_}ic bbe H deo OO @}i*c L?t|h@?|t uLh |i it|4@|L? Lu _tT*@Ui4i?| iU|Lh i*_t uhL4 4 @}i ti^i?Uit c hLU ,}| W?| aL?| L?u L? h|U@* W?|i**}i?Ui EWaW <Hc k@h*thic }t| H2c bHc beDbDc bH dDo OO @}i*c ? |i it|4@|L? Lu LT|U@* LG hi*@|L?t Mi|ii? _gihi?| @TThL@Uit @?_ tL4i ?i hit*|t c h|U@* W?|i**}i?Uic VL* c 2bb2ec bH. dSo OO @}i*c ` ,?!i*4@??c ? ?it|}@|L? Lu t4LL|?itt UL?t|h@?|t uLh |i it |4@|L? Lu _tT*@Ui4i?| iU|Lh i*_t uhL4 4@}it ti^i?Uit c W,,, Ah@?t @||ih? ?@* @U W?|i**c VL* Hc DSDDbc bHS d.o  i*ti?c + #ihUic ?LU*@h _i?ti _iT| hiUL?t|hU|L? t?} tL|hLT) UL? t|h@?|c B Lh}iuLht E ,_c AiLh) @?_ @TT*U@|L?t Lu 4@}i ThLUitt?} WW  ti*iU|i_ @h|U*it uhL4 |i b| 5U@?_?@@? L?uihi?Ui L? W4@}i ?@*)ttc `Lh*_ 5Ui?|U M*t?}c 5?}@TLhic 2.efc bbD d H o  i*ti?c + @@tc `a itti?c wa 6*Lh@U!c  |ih O@@h +L4i?)c ?LU*@h t|ihiL uhL4 }hi)tU@*i 4@}it c a @| W4@} VtL?c VL* fc f22c bbb d b o @th@M@_  5|ihiL VtL? AiU?^i Nt?} hi5i}4i?|t @?_ +i*@ @|L? @|U?}c W,,, Ah@?t @||ih? ?@* @U W?|i** ce E Dc DSSD.2c @)c bb2 d ef o ki| t@h@ h@U|U@* hi@*|4i 4@}?} t|ihiL 4@|Uih T|U@* ,?}?iih?} c 2 E Dc DSDeDc bHe 5ii @*tL WA W ,..2c }t| bHe d e o v |@ @?_ A k@?@_i 5|ihiL M) ?|h@ @?_ ?|ihtU@?*?i ti@hU W,,, Ah@?t@U |L?t L? @||ih? ?@*)tt @?_ @U?i W?|i**}i?Ui c .GbDec bHD de2o  ihL?@c a @*!c 5U@*i tT@Ui @?_ i_}i _i|iU|L? t?} @?tL|hLTU _gtL? c W,,, Ah@?t @||ih? ?@* @U W?|i**c VL* 2c S2bSbc bbf d e o 5 L**@h_c a,` @)ic @?_ a 6htM) 6 G @ t|ihiL ULhhitTL?_i?Ui @*}L h|4 t?} @ _tT@h|) }h@_i?| UL?t|h@?| ihUiT|L? c eGeebe.fc bHD d ee o  L**iui)tc + kLUc @?_ w V@? BLL*  t4T*i @?_ iUi?| hiU|U@|L? 4i|L_ uLh }i?ih@* 4L|L? W? hLUii_?}t Lu |i .| W?|ih?@|L?@* L?uihi?Ui L? L4T|ih VtL? c T@}it ebSDfc Lhuc BhiiUic 5iT| 22ec bbb W,,, L4T|ih 5LUi|) hitt d eD o  hLit4@?tc , @i*tc w V@? BLL*c LT*i_ }iL4i|h)_hi? _gtL? i^@ |L?t uLh *L*ii* tL? c  |ih O@@h +L4i?) E ,_c BiL4i|h)_hi? _gtL? ? UL4T|ih tL?c k*ihc #Lh_hiU|c b22Hc bbe d eS o w +LMih|c + #ihUic #i?ti _iT| 4@T hiUL?t|hU|L?G  4?43@|L? @?_ hi} *@h3@|L? @TThL@U U Thitihit _tUL?|?|it c   |L?c + TL**@ E ,_tc L4T|ih tL?  ,V <bSc VL*4i Wc wiU|hi L|it ? L4T|ih 5Ui?Uic VL* fSec 5Th?}ihc ih*?c ebeDc bbS b de.o wU +LMih| @?_ *ih 6@}ih@t hiM@ti_ t|ihiLG 6}h@* UL?|?|) @?_ Uh@ |hi W? hLUii_?}t Lu |i W?|ih?@|L?@* L?uihi?Ui L? L4T|ih VtL? @?_ @||ih? +iUL}?|L? c T@}it D.S2c w@@?@c O@@c a?i Sc bb W,,, L4T|ih 5LUi|) hitt deHo wW +_?c 5 tihc , 6@|i4c L?*?i@h |L|@* @h@|L? M@ti_ ?Lti hi4L@* @*}L h|4t c )tU@ #c VL* Sfc 2Db2SHc bb2 debo a 5@c  ?L?*?i@h _gtL? 4L_i* uLh _tUL?|?Lt _tT@h|) @?_ @*uLUU*tL?t ? t|ihiL c hLU W,,, L4T 5LU L?u L4T|ih VtL? @?_ @||ih? +iUL}? |L? EV+ <bc i vLh!c a?i D.c bbc W,,, L4T|ih 5LUi|) hittc wLt *@4|Ltc eefc bb d Df o  5?)_ihc ? |i 4@|i4@|U@* uL?_@|L?t Lu t4LL|?itt UL?t|h@?|t uLh |i _i|ih4?@|L? Lu LT|U@* L @?_ uLh thu@Ui hiUL?t|hU|L? c W,,, Ah@?t @||ih? ?@* @U W?|i**c VL* c fDec bb d D o a 5TLhh?}c  i*ti?c w 6*Lh@U!c  aL@?ti? E ,_tc B@tt@? 5U@*i5T@Ui AiLh) c k*ihc #Lh_hiU|c bb. d D2 o  A!L?Lc Vv hti??c 5L*|L?t Lu W**Lti_ hLM*i4t c aL? `*i) : 5L?tc `@t?}|L?c #c b.. d D o a `iU!ih|c AiLhi|U@* uL?_@|L?t Lu @?tL|hLTU _gtL? ? 4@}i ThLUitt?} c L4T|?}c 5TT* c 222Sc bbS d De o a `iU!ih|c ?tL|hLTU #gtL? ? W4@}i hLUitt?} c AiM?ihc 5|||}@h|c bbH d DD o a `iU!ih|c 5 Wt!@@c  W4)@c w?i@h tU@*itT@Ui @t ht| Mii? ThLTLti_ ? a@T@? c a @| W4@} VtL?c VL* fc 2.2D2c bbb dDSo  vL!L)@ 5|ihiL 5hu@Ui +iUL?t|hU|L? M) *|tU@*i*|t|@}i +i}*@h3@ |L? AiU?U@* +iTLh| A+bfeDc ,Aw ,*iU|hL|iU?U@* w@MLh@|Lh)c At!M@c a@T@?c Li4Mih bbf d D. o )h* ~i**ih @?_ *ih 6@}ih@t TT*U@|L?t Lu ?L?4i|hU tL? |L tL4i t@**) }_i_ |@t!t W? hLUii_?}t Lu |i W?|ih?@|L?@* L?uihi?Ui L? @||ih? +iUL}?|L? c T@}it 2Sc aiht@*i4c Wth@i*c U|LMih bbe L4T|ih 5LUi|) hitt wL?}ih ihtL? @@*@M*i @t W+W +iti@hU +iTLh| ++2fH S TTi?_  , t|i?Ui @?_ N?^i?itt Lu |i @h@ML*U ,^@|L? `i tL |i i t|i?Ui @?_ ?^i?itt Lu tL*|L? Lu |i T@h@ML*U i^@|L? E H Ai T@h@4i|iht  @?_ D U@? Mi @hM|h@h) TLt|i hi@* ?4Miht 6ht| i ?|hL_Ui @? @Mt|h@U| 2f uh@4iLh! ihi i t|_) |i @MLi t)t|i4 At uh@4iLh! t ti_ |L tL |i i t|i?Ui @?_ ?^i?itt Lu |i tL*|L?t @u|ih@h_t Mt|h@U| 6h@4iLh! 6Lh t4T*U|)c i ** @tt4i |@| |i 4@}it @hi _i?i_ ? 7 2  `i _i?i M G' u 2 E 7 2 c 7  c @?_ |i _gihi?|@* LTih@|Lh  G ( E    M $ M }i? M)G  E b '   _E ( E u U 4@  u b   i _i?i l ' 7 2  7 2  7 2  `i ** @tt4i |@| UcU  5 `  c " E 7 2 c l AihiuLhi u U 4@ t ML?_i_ @?_ |i i}i?@*it Lu 4@|h ( E u U 4@  @hi t|hU|*) TLt|i AihiuLhic @t : fc |i LTih@|Lh  E b  t @ 4@ 4@* 4L?L|L?i LTih@|Lh 6Lh 4Lhi _i|@*t @ML| 4@ 4@* 4L?L|L?i LTih@|Lht i hiuih |L hi3t d  o  i |c *i| t ?|hL_Ui |i u?U|L? 8 G M $ M _i?i_ M) 8 E b '  [  '  U   U   E U_ n $  E b    @ YU   Y+ E U_ n $  E b  n K YU   Y% E U_ n $  E b  s @ 2 n K 2 Ai? |i @Mt|h@U| iL*|L? ThLM*i4 U@? Mi h||i? @t  Yb Y| n  E b ' 8 E b  5 M ; | 5 d f cA o b E f ' b f 5 M E f ?) U*@ttU@* tL*|L? b 5   E d f cA o ( M  _  E d f cA o ( ( E   Lu E f t }i? M)G b E | ' 7 E |  b f n ] | f 7 E |  r  8 E b E r  _rc E ihi i 7 E |  j |: f t |i UL?|h@U|L? ti4}hLT |@| t @ttLU@|i_ |L |i L4L}i?iLt ThLM*i4 #i?|L? `i t@) |@|  5  E d f cA o ( M  t @ }i?ih@*3i_ tL*|L? Lu E f  u | t@|tit E    , t|i?Ui @?_ N?^i?itt +it*| AL t4T*u) |i _tUttL?c i ** @tt4i |@| |i iTTL*@h *?i t@|tit |@| @ 2 n K 2 t t|hU|*) TLt|i W? u@U|c |i U@ti @ ' K ' f ULhhitTL?_t |L iTTL*@h *?it *LU@|i_ @| |i ??|) T*@?i E 6  ' fc U t Lu ULhti ?L| ih) ?|ihit|?} uhL4 @ Th@U|U@* TL?| Lu i W? Lh_ih |L ThLi i t|i?Ui @?_ ?^i?ittc i @i |L it|@M*t @ *i44@ ht| wi44@  wi| t @tt4i |@| Uc U  5 `  c " E 7 2 c l c |i? 8 t @ wTtU|3 u?U|L? 2 hLLuG Bi? b  cb 2 5 M c i @i |i uL**L?} TL?|ti it|4@|i m 8 E b    8  E b 2  m '       [  ' E U   U   E U_ n $  E b   #  K YU   Y% E U_ n $  E b   s @ 2 n K 2 n @ YU   Y+ E U_ n $  E b   s @ 2 n K 2 $  E U   U   E U_ n $  E b 2  #  K YU   Y% E U_ n $  E b 2  s @ 2 n K 2 n @ YU   Y+ E U_ n $  E b 2  s @ 2 n K 2 $     c   [  ' m U  E U_ n $  E b   Y  U   E U_ n $  E b    U  E U_ n $  E b 2  Y  U   E U_ n $  E b 2  m n m U  m  m Y  U 3  E U_ n $  E b    Y  U 3  E U_ n $  E b 2  m c   [  '  2       K Y E  U     Y% E U_ n $  E b   s @ 2 n K 2  K Y E  U     Y% E U_ n $  E b 2  s @ 2 n K 2      n 2       @ Y E  U    Y+ E U_ n $  E b   s @ 2 n K 2  @ Y E  U     Y+ E U_ n $  E b 2  s @ 2 n K 2       n n U n "        K YU   Y% E U_ n $  E b   s @ 2 n K 2  K YU   Y% E U_ n $  E b 2  s @ 2 n K 2      n n U n "       @ YU   Y+ E U_ n $  E b   s @ 2 n K 2  @ YU   Y+ E U_ n $  E b 2  s @ 2 n K 2      c   [  '   m U   m 2   ` Q ?   m$  E b   $  E b 2  m n2 n U n "  n U   n ` Q ?   m$  E b   $  E b 2  m   [  '   m U   m 2   ` Q ?  n2 n U n "  n U   n ` Q ?   m b   b 2 m c `i UL?U*_i |i ThLLu Lu |i *i44@ M) ti||?} u '  [  '   m U   m 2   ` Q ?  n2 n U n "  n U   n ` Q ?    At tLt |i @ttih|L? Lu |i *i44@ L i U@? ThLi |i i t|i?Ui @?_ ?^i?itt |iLhi4 AO,+,G Wu UcU  5 `  c " E 7 2 c l |i? uLh @?) ?|@* _@|4 b f 5 u 2 E 7 2  c |ihi i t|t @ ?^i tL*|L? Lu E H   22 hLLuG Nt?} |i ThiLt *i44@ i _i_Ui |@| 8 t *TtU|3 tt4i |@| b Q E | @?_ b E |  @hi tL*|L?t Lu E uLh ?|@* UL?_|L?t b Q Ef @?_ b Efc |i? i @ic t?} |i u@U| |@|   t _ttT@|i EU )i*_t n 7 E |  s n M n s n M c @?_ |i wTtU|3 UL?|?|) Lu 8 |i uL**L?} it|4@|i n b Q E |   b E |  n M n b Q Ef  b Ef n M n u ] | B n b Q E r   b E r  n M _r TT*)?} |i BhL?@**i**4@? *i44@ do }it n b Q E |   b E |  n M  e u|  n b Q Ef  b Ef n M c U )i*_t ?^i?itt Lu |i tL*|L? u | i t|t L UL?t_ih |i @?@U tT@Ui _i?i_ M) . ' i b 5  E d f c 4 ( M  rS |@| tT | , B n b E |  n M e ! g|  4j i?_Li_ | |i ?Lh4 n b n . ' tT | , B n b E |  n M e ! g| wi|  G . $  E d f c 4 ( M Mi _i?i_ M)  E b  E | ' 7 E |  _ B n ] | B 7 E |  r  8 E b E r  _r Wu g:u c |i?  E .   . c @?_  t u g wTtU|3 t?Ui n  E b Q    E b  n . 'tT | , B n  E b Q  E |    E b  E |  n M e ! g| c  tT | , B ] | B u n b Q E r   b E r  n M _re ! g|  tT | , B u n b Q  b n . e ! g| ] | B e gr _r  tT | , B u g n b Q  b n . e ! g| E e g|    u g n b Q  b n .  `i _i_Ui |@|  t @ UL?|h@U|L?c @?_ M) @?@U<t  i_ TL?| |iLhi4 |ihi i t|t @ ?^i b tU |@|  E b ' b  At t |i }i?ih@*3i_ tL*|L? Lu E fc @?_ |i ThLLu t UL?U*_i_ 2 6}hi bG 2e 6}hi fG 2D