On the Choice of Similarity Measures for Image Retrieval by Example Jean-Philippe Tarel and Sabri Boughorbel INRIA, Rocquencourt Domaine de Voluceau, BP-105 F-78153 Le Chesnay Cedex, France [email protected] [email protected] ABSTRACT &0!7;* 8lP-(P+$J5.8"P7E 1g*+, +M';!-.; !!#"!$%'&()*+, + !*7";7975."`2%_T87".;l?-..7R5.%7"'&.!""!$ '-.%!/-0132465.8795"!7$:"!*"8*+!+)';- $: -.8&0!7;*7E"?9 @?,+M5H ''($:"! " "!<!"!5.,=!.+1(>?@ AB(&C'?9 D7E"'&0 F ;1<"W5l?-.;"3o<IJ50 <5'>C;X* )';!-. "!G"! 50f%-.V>C6-01"7E"'&0 \I\"L$,; -[N;7E"!VI[+5(5. H!>C;1 1.9!>.2@46581(IJ>07KA" $L-075M! &F &"N!795)=50 ;OIJ5+8H P-.%>C="!$J&C"N>(8*+, + !'$,; -<&0!7p '-.Q7 *>C6;;1RNI6S1("." QKP"IG5"IG"=BP.1$:"! 5T"!>9 ;1/-+92DUT";I6?5.T795"!7" $V<"?"P1W*+!F /5.T7"?BPJ"!$O T.1BP.(. P'*+!+H';!-.; +'-.X1.T"H."!7!>'>C=;-+92'Y=,KP"IJ I6=&."&C";13q rP0st3$,"S%-'!?2c4\I6"'1PnR?J*F 5. X5*75."!7/% ;1M"Z5./ !>+++ " $L5/!!; +!+8';-;[-0;18"85<!'T$,; -&07E<!=-0-. ++ I[+5(G5.H!'W79,!2465$:"!6I\W&."!&C"NZ@'"P1J" $ 7"!'&0!1HZJ"!$Q&.7E"!FY;7+\1P! u"! W! HES.%!.1]1(;1-.78@75.'/$,"1?. 1.9!>.2Dv6-(6!\." ,7E;1*@q wP.x?Cyta?5.L795"!7L"!$`* 5%>C;* ^';-8E"!$6* ^';-; ';!-.'X (A ;1)"Z5.!!!>(++M"!$S5.'$: -. !-.*.A&.!!'E,78'"P1J" $5.8 , >+++]"!$T$,; - N;79"2\465(-.I\<>01H"-L &.&"N75W"!Z*9 7f!. +F ;7E"OI[+5(5.\!'679,!2D_LB(&C'?9 P! +1."!%" $ 2QzL'=Q"!$R&C">(T*+!+%';-;NI6J&"&C"N 5T'"P1(`!01'5.T1N18*+!+/';!-.;Q6&C$,"';1 =75.'6$,"Q1?.T5S>C\*+!+%';-6%5D; "!@?57<!"-01(Fa-(5^1. 9 >0!;2bc0+?C$,"d"-.LBPF $:"!{L&.! '7Q'"P1EP"!$.5\!!!>(++X" $.$,; -6N;7E"!2 &C'P93I6' N'N Q-;"8$,"!+"Ie$:"!5*1(;)" $ !"-01(Fa-(5H1 9!>.;J";I[.'+!>(<7".7E-0".J"!85 }|P;7E"~?LI\B(&C'?9+g5.";Ik'&."N'?9%50 7 W>C=B(&C;7E;1/>?/I\+f1!&(%5.*+!+W';!-.T" !75W"!$f>CJ*+!+H';!-.;2 5.<$: -.%&0!72fB(&C'?9L %(+W&C$,"';1Z"@ $: -.&.7"!$D7" "T5(" 0>-S"!5LK?018"!$V$: -. 1. INTRODUCTION ]!!Z! T.*>PGB '&[!*g!? "!5 7E"'&.-(DP"/N5[($:"! ""!$R?;Q;!795 H'-.' h;1)G5W"!F7+1#0-.2g465.W " $\?"P1-.7E.8-075A8-.'!8L"81-07EX5.%!'"!-.?" $ ($:""H"*>C=&"P7;;1R2 5(51('."0C&.72DiZ ?%$: -.S&.7;fI6J&"&C"N1 B(&C'?9 ++ 7"!'&0!132 ='"P1."!$R!!L! 02V/|P;7E"P?I6S&.;P "-J'"P1`"!$V!!=! O.2\465(S'"P1(3!N;[5. 7+"H%*+!+';!-.L%-0\ BP*h2f465/H|(;79F "]\I\W&."!&C"N^795'/"A1N/5.W>C* ';!-.<50 T%-.>C-0;1WA"!$[*+!+W';-; _SH!!<J5(-.[&.;P1H>?W%$,; -XN7E"J+(*W 01 &0!7; *,"8-0;1R2<465.%!. +,L"!$\5;;-+9T;l?-( j)/>C+NH5. g 0 +PF H" $%5";Ik5."@$,; -)&0!7;W A7E"'&0 ;1#8;l?-;1 "Z&"!;M>.-(+,1P.Z>C=!![2@mL$ 7E"-.!N5V!. +fV." f;"T&C$,"WN!01<5.E$:"6I\ $,"P7-0*"!g7E"'&0 .Z$:;-.Z&.7%&.?@G;.7 5!'*$,""!M!>C"!-<!!;V>.-(=M1(+nR?=I6;2 Z-075^*7!C+$Dl?-0!?h.%"L!=."!;13.I6"*$,; - !N85.T9 7 O'"P1R" $c5.L-0;1$:;-.;2D/5T.EB( ;7E"!`.I\=PN <&C"N>(<&.!!'E,7'"P1(6$:"L7" "! 5"!!d$:;-.;T$," B(&C'?9V&C"!?="!$\?EI=2< |(7E"@r8 01@xPCI\*1(N=5.>C;=*+!+^';!-.;J$:"! I6E+FYKP.";IJM&R1($:D-075M%z!-., `D-.(+$:" 01)B(&C"F af$:"!%1PnR?*9<"!$L*+!+A';-;2Wj)*9 KN/1PF !!?9!!="!$c5;=1! "!06"'7"!'&0!L5.'"P1(R"'%-F ".S"!Z(?5.7TB(&C'?92D465`(I6= <"'<7E-. "MIJ5(,75]&C;7E+ C7"0%@!"-..1(Fa-5 1 9 >08%-.X$,"!+F ";I#"<">9/E >7"!07E-."!0Q5. \7!>CS-0;1%$,"6" 5. 1.9!>.;2 2. SIMILARITY MEASURE OPTIMIZATION I\+[KP.";IJ)50% W$:;-.8&07ED;-+9X" $J*F !!^G>CZ'&"N;1-0/>?#>C8795"!7^"!$ 5.**+!+A';!-.2"!1="W-),7XB(&C+F '?9?I6T-0T!"-01(Fa-(5 =1 9!>.;[ 01/ +35.TEF -+96 =;N ;1"N[3l?-*!!;2Dbc(2Cy=5"IS\$:EI !!%7E!;T$:"!d!"-..1(Fa-5^1 9 >0X'2TT-0 ++?R !"-01(Fa-(5!!J1.9!>0!6Q7"!'&C"N;1"!$R=\7E;fI[5 $:" +";I[.'I6"*&.!!'Eo 1P+nR?SP-. V7E"??926Q75^7ES7"?9.L<Q ;0" 5/" 9 JP-.X>C<"!$S!X 5/1. 9 >0!8*= 2)b0"! ¼ »C¼0½ ¾ ±(¿9À²f§kà ÁO ± 8Æ ,Ä`Å ?*l?-.XL"?"K<$:"5.J1 9 >0!NI6S;7ED5.J<`7E"N; ;2fj585;7"!+"WJ&C$:7E;5=7E"NL!!; +`$,"5.7E["%IJ575H5.=l?-%>C"!.N2 ¼ ¾ À ² ±y² IJ5.S§Ç± ²`V5.Jl?-.X;7E"D 01*ÀL§Ç±YÀ ²Oc5.6$: -. N;79"6"*>C=7E"'&0 ;1'I[585.l?-?2f · ,\5=1('." "!$R$,; -S;7E"2D465(QK?01%" $3*+!+*';!-.;VI[!Q&.EF ?"-0+-01<I[+5*!1!!?9!!;c>?/q ~t"'¶\"!( [1 9 >0 I[+5/7"!"\5"!!2D.1;15.S-0;1'KN.\" $R5.J$:" ½ Ò È ¼0½ ¾ ±(¿À ²f§ÉNÊRË!ÌPÍ Î(ÏÑÐ 2VºT" ,7E650 VIJ5*Ó@§ÔyJ 01ÕAÖ}y! 5.S*+!+''-. » Å ½ ¾ ±(¿9À²V;1-.7;f"5.L× ¾ 1P9!07E2 0.48 L1 L 2 L∞ 0.46 0.44 precision for recall=1 8% 0.42 4.7% 0.4 0.38 4.2% J,CO;]0%OPk@.0(';R R`8¡O¢0£`0' ¤¥9¢: YC (¡e£3¦{=8§dr g¨©,0;(*,¢ª« 0.36 §¬G:.0(®f( 0.34 ¨©,0;¤ 0.32 0 0.1 0.2 0.3 ¯LnR?\!"-..1(Fa-5*1. 9 >0!;Q5.S>C'-0;1%$,"Q"-.QBPF &C'P9"0o 0.4 0.5 α 0.6 0.7 0.8 0.9 1 J,RO;#Ø3)ÓOÙ¡c,.00A*,¢ª{¨N©,.;;:¨0©×\Å Ú=×QÛZ0ÜO¡{×QÝ ¡c:¢CÜO¨(¤ÞÓOÙ¡c,C;Cß®c©,0¢;¢ª`àPáC(;.0«®c;(¨N:;,CÜ |7E.S1.9!>.L' ° áC(O%Ó\ÚD`;Ü`M;:©,0,¢9¦âP.O; oV\7".9Q"!$Os(yL7E!;\"!$`¬*F !!;=;75G±Yx~!¬!²Ec 01@7"?9 .=46³«>"N179 !'&( ;[" $V?,1("N&0PN2+2+2 XI6EJKP"IJ)5. X5./795"!78"!$T^!"?"P1 bc2[~@$:"!8Óã§äy[5Z-0W" $× Û × Å 7" "!VBP-.\¯ 9!>.2Q¶\" "f !>+++<%7E |(5.!&C=¯=9!>.' ° '&" ;%5. 585.!â× Û '&."N5;-(+98>? }EB(Gw!å/2 1.9!>.;2 oQJ[$:"'1H>?Hr 7E;SI[5 çOK(";IJT5.'&C"!9!.7%" $J8!"?"P1)795"!7*" $6&.!!'EF <Ó\2'jA'1 ..*Ó`F1P! è5.*7-.N%"!$J;N &.7E+F bc+¯= 9 >0'T·o=7E"?9 0x/7E;[y¸¸8!!; &CS7E<±Yx!¸!¸X!!;²E2Q465L1 9 >0[-018"(+8$," ° 5./× Ý |P*+![;-(+9[I\"!>0N18"HN3"!5.["-01PFY-(5 2 ¬X!!;[&CS7E<±Ywx r% ;²E2 ° Õ}7!M'&."N ;-(9'>?G?åæ;N Z&;7E"`2iW"!"NJ5.W-.Z"!$ 7EL"!$D¬ ;J;!79532QYJ,[BP!7E;18$,"µv6"P1.h 6J'&C"9 ?[50!/Z' ¤ !!8! S;-(92b0"!X09 07\X5.";IJG" 4OBP-¯ 9!>.%'T´9oJY!"-.&.x ¬N~* ;JP"/s!s ° »R¼0½ ¾ ÚVCÜg' "@IJ5.ZI6% Z&0 !'LÓg@*+!+'-. »C¼0½ ¾ Ô±y;²E6$:"!8@!NGÕQ2gbc26~!N;'7"'&.!"g>CI\ &R1($O ..%J1;7E>C18^|(;79"!^wP2 ÓOF1( !6$,"[Õ@§Ôy(Õ@§â~%!.1/Õ@§âé=ê#2D4O;9[50;NT>C ¶\"EC¯= 9 >0!T'S oVYQ7"?9 .6xPyS79,!;¸T!!; 7" "!X5(" W2/465.'"!>9 ;1A7-N;&;?H BP%- &C$,"';1W"!^' 2J465%!0 -<-0;1HT'&(/5.<ëSzTv !"!-..1@¸Pì (2jA&C$:"'1Z9L"Z5X" 5.L"-01PFY-(5 &C\7ET±Y~?y;¸<!²E2fD,DBP7E1'$,"e5.L¶\" 1.9!>.;S' 1.9!>.2 0' ´ !.1W'LC 01/I\<">9.;185<!' K?01^"!$J5.!&C;TI[+5)ëSzTv{7E"!"<5"!!2'iW""N`5. &C"N+"" $=5.ZB(X-.í!!;/++1(&C.1(.)" $=5. ¹D;7E"(FY;7 +c1(!!!J!TI[1(+8-.;1'"%! -0T!! 1.9!>.2Ç465.$,"^5.ZÓOF1P, î/+G ;1 Ef2SºTN5.;CI\%1(;7E1;1H"-.X"!+H5 "(+Z"/5%-01Z$,; -'&0!72ºT" 7X5. < A!1;l?-0XÓ ;N!'&;7E"A"H7"'&.!%1(+nR?<*+!+';-;2 ±Óà§æ¸(ì AI[+5gÕ«§ïy²X'&."N;%5^;N!!Z&.;79,"!>P jA/1 ..;1A58;N!/&.7E"!M"@>C'58;N!/"!$J5 '"L50!HsNåã7"!'&0 ;18"X5=Q-.7E+1; Z1(9!.7 P-%>C=" $LE P!!H '".85./ » Å ½Û 2 N;1A ; 465.`\I\^795;7KN;1)50'5.W*+!+G';!-.H7!]>CW"&(F "NL+`5<lP-'!!;["!$V5.1. 9 >0!2 *h;1$,""!5.$,; -8&.72Zbc2VZ5";ISÓOF1P, jg5"-(!?@"!5.=K(";I[1!O5.%>C;* @';- $:"!o 5.c">C[!75.;1XI[+5'S>.-(\$:"!7S!&.&"N!79532f465.[7E"'&.-(F -.[b0"-/1;7&("*$:"!EB(-8$,; -;JëSzTv7" "! \1(mT?9 "âUS,"! ð±"!5C²^q t$,"Z5.!&CZ$:;F 9"067E"N<"!$Q5 &.&."75@'&(;T5. I\%X-01-07E 5"!!µ 01çc &7E 8I6E!5?;18ëSzTvg7"!"J5(,"! èq ¬t 5/;!75)"@Z +[X"!$L*+!+A';-;2Zj)'5. $:"!67" "\$,; -;2f*5(,DB(&C'?fÕ^§Ôy( 01%5P-0NIJ5 1-07E*"-N;T"85'<" $[*+, +@';-;TI[+55 Ó §«y!C5.<-0;1^*+!+Z'-.1H,J5.X7E7\×\Å1PF N1g ;$:"! 0.48 0.46 I6" l?-.;8!@ ++â1PnR?; N^+$D5.;Xl?-.;T!XZ5.X!'X7E2v6-(;C5L&"&(F rgb−hist laplrgb−hist four eoh Z,"!=+ 0;1ZIJ5.^5.!X! D>?ZB!'&( $:"!%-(,;1)!H7E+ C7" &."!>k>C;7!-0'5'7E<"!$ 5.<l?-8J." TKP.";IJ32\j)<&$:5.E$:"!0"'>CL!(F +(h%IJ5. -.-0 ++^&C$,"';1W@ *! D 0.44 precision for recall=1 >?/B!'&2 0.42 -. ++??-0P \($:""Xc&;?;1<>?S$: -. N;79""!13"[.7;!6&C;1< 01T"S;NQ''"?2OzLN Z$:;-.H;7E"*lP-)PDI6W1( 0'5./"NS"!$=@7"!PPF 0.4 >0!;1M! Sè"@EN/5/$,; -HN7E"<50 ![5S'"fKNEX"=>C[*5J!'S7EQV5.Sl?-.?2O465. 0.38 M1P+nR07Ef7"!'&0!1@I[+5 7E+ C7 "G!&&."75`V 50LI\%1("."!LKP.";I}5.XlP-H7E2Sj)J-.KP.";I}50 T 0.36 [X 01"!ã;h;"W" $O+9[7E2\465.3(!N8!?'$: -. N;79"<ÀX5%1 9 >0!O5.X&."!>dT"H1;7E1(X+$JÀ* 01 0.34 0 0.1 0.2 0.3 0.4 0.5 α 0.6 0.7 0.8 0.9 J,CO;'ñ3[Ó`Ù¡c,C;CASCS¡còQ(;.ÜC¢[Y(¢O;X;®O0¨([CÜ`¡ Õ]§y¤)óH(¡Ô;(®c;(.ÜC¢¢;,RÜOW.;RWôT¡O.]õ',ÜC¢.¢,RÜ 1 !<Z5.!'X7ET"!T"!;2L$f5.P-.%>C["!$\!'&;J !!H"-.!5`V5(,l?-.;"!]7!M>C/!.I6;1M>?M9,7 ;.(2fT($:"-0+??'5T7"!?BP6"!$3!!L! aPI6 "(+H5.TI\"'!'&(oQÀ 018P2 öH:¢0C;0ø÷PRªVùHYC)ª`.®VRÚORO,(¡O(;¨N:®O¢CAYC ¢(ú3¢O;CÚ/ûü8ýþ¨!C©,Cg0ÜO¡µÿQ.®c©,0¨,CܵX(,RªC¢(¡ûü8ý 1000 d 11 d ¨!C©,CHªO:¢000A¤ 12 900 800 9 07!2=v\Z-.(.'5.&0 !'LÓ\RI6X!%!>"/'&."N 5[;N J&.;79,"!*-.&"=Nå$,"fëSzTv 700 7"!"!D5(" e!01 '"!50 yå«$,"Jb0"!-.S1;7E&("$:"[09 07!2 b."ï"-*$:I-.B(&C'?9[!G07;!^"!$~!åæ"!$<;?F !&;7E")"!7; >2HA&.!7-(, 5*"1(.Z" $ 5'N;1@ ;'&."N132H465<.1(7 V5.";I '&C"!9!?[[5<;!75W" $V>CS*+, +8';-;2 number 600 500 400 300 200 465) I6"G â&.">(/I[+5â5.@B(&C'?9 < &F &"N!795Z1(;7>C;1/>C$:"!2Dbc;(+J,6"!J&C">(<"X&C$:"! EB&C'P9f"+C5.J&C"N>T*+!+'';-;V50 \" 7!W! 05<;!75^&0!7=,J"?"*!!2L|(;7"!0185<>C; *+!+';!-.*=">9.;1A"!+@$:"Q"!-..1(Fa-5 1 9 >0V!.1^I\*50;N."H7E-.X5.";I{5T;-(+< +h; "X, L1.9!>.;2 465W0 N/"Z5./B(&C'?9 [ &.&"N75 ,"@'"P1( =! OQ"%"%&"!;J/5.=" -("W" $ 5;<I6"/&."!>2Sb0"!u''"P1EV"!$D5.<">.N;1Z&C-F >. ".D" $R5.6$: -.S&.7I6S5.";I#BPf5.";IG"<1N65 >CS"P7E 1Z*+!+8'-.LI[5(W*J" $f*+, + '-.2 3. STATISTICAL MODEL ¶\"!?!H"Wq x;ta.I6<>C+N5. J!!=c>?/B!'&( 5"-(,1Z"!>C<'"P1(;1^T7E! 07 "!A&."!>W2S.113 79,!+$,[email protected]!>./ +";IS!!'aV>.-(1"?;=." 100 m11 0 0 0.5 1 m12 1.5 2 `GôLú3CA®c©g0':ÜR¢;;(Ù¡c:¢0ÜO¨ ÅÅ CÜO¡eÜC¢(;Ù ÅÛ ¡c:¢ ,£V`¢;,CÜOYCâûü8ý P.¢;O;eáC(¨¢C Cþ¢;ª`¢9 ¨N©,0;(¡c:;®O©,P¦C¡:ÜâJ,`¤g ÷¨!0¢;©,CÜO¡ cÜOP¢*;R ¢;ª` C;(©6¡O.¢0£O.0ù;¤ J,RO; ¡c:¢CÜO¨ b0"!'!KN8"!$'&(+,79?fI6W-&.&C"H50*"(+MI6"1(+nRP JÅ8 01[ÛH!Z;! +!>(WG5.Z1 9!>.Z 01 50 Å 2ã465.1. 9 >0!W "g-.'1#"-01PF -532Hj5 À/ "^>C"." Å O5./* )';!-. §C ±(¿À ²50!ZG&">0 >+++}1(>.-("â$:-..7E"e±&R1($9² ÅÅ ± ²E2j5}À>C"N8" Û T 1(+nR?8&R1($ ÅÛ ± ²' ">(9 .1}$:"! Z5";IJÔbc2Lg"!ÔG; I\"#7E!; 1.9!>.2H465.1P,9 07 §C ±(¿9À²T>CI6)W 01)À*< +F I[*&C"N+N^ 01M5(-.%&R1($: ÅÅH!.1 ÅÛW Z1 ..;1 "(+ 7E M>C"N8" "q ¸(¿Eé=ê)ta2V-. ++?(! L3e\lP-(P &C$:"!OI6+.f7E7.!!6! (;75.l?-.2cb0"! "@^"'"! 7E+ 07 "H&C"!?6"!$`?I=P LC6/D 001PF !!'"!$Q5.*1 9 >0!2465.E$:"!c!N)/1(9!.7*5.;5"!1 *!&.&(.%$,"5.1.9!>.=!J"*5<T" $D7E >C2)465$:"!D$J5* /! JX&C$,;7E; X65HN1 N# G Z1(;IJG$:"!ï7E X2 +`I[+5( !!; _ÇKZ!1!!?9!!" $f ! V>?WEB. '&C50L5 2.5 distance 5/*" $1P,9 07%"!$J5.8l?-."^;75M*F 5.=P-.X>C6" $D ;LÀ<" ´ $ Å I[5^%";I6T1P,9 07=5.! "ZPc%<a'Åű ²<§< ÅÅ!± ² 2Z'ÅÅ*>?A1 .+" 5.7-.X- NL1(>.-("!8$,-.079"!A±a71P$9²\"!$ ÅÅ 2Q|P*+, +? 5.P-.X>CJ"!$D ;ÀX"!$[Û<I[+5@";I6=1(9!.7X5.! ´ "^(VX ÅÛ ± ²X§µ ÅÛ ± ² 2@465P-0f5.'"!9[P-.*F >C*" $=N1 !!;%%5P-0*<±a'Åű ²Dé*ÅÛ± ²²E2]465. æ§ Ï ´Ò#!" Ï ´Ò !$ Ï ´:Ò 2 d 5;N &;7E"/I6L?"P1-.7;1'/5T&.P"!-06;79"!`2 &C7?9!!Z"!$=!!?'!!;% I[+5W;&C;79S"*¸(2D.1;1RPI6=50;N!o ±aN² 6O±)(R²f§ ~y 9: É?± ( é<~ ; ²É?± Æ (~ é=; ²>; % 2f465P-0A@O§ Æ À;`5.Q=7?;1' 01 Æ À; Æ W 465Z BP*h; "]"!$<;N!Z&;7E"g'-01]]5.8$:"!+F ";I[./"87E"'&0 =I6"/1PnR?=*+, +Z';!-.;J"Z5 '$:;-.<&.72 ?;N`§ 7"!P ?>@ § "H % 2 I[+5 (''7=&R1($DIJ5.ÀXLZ5.* '%79,!T50 @P2XmTZ5. v\-65.f50 5.;5"!1*"'5.S1P,9 07!? J! >CE<-0'85;5." 1A"@5.*P-.X>C" $[N;1 ;2V="-3I6"S7E;c&">(W;I6D.;1T"J-w!¸åâ" $ 5"!9OP-.X>C6" $c!J85<1.9!>0!2D$c5! JÅ2}4`" '&C$,;7E;S +L5.W;1G!!;!W ENZ 1-07E;6"o }§'ÅÅ!±±a*ÅÅQéM'ÅÛ² Ê IJ5 X-0%>CZ795"NG#-075] ²;é*'ÅÛ± ²f§Çy!N 01<5(-.`5.\;N!![&.;79,"! ;65;5." 1 I65. D*ÅÅ!± Å ±y²² ±Y~!² 1"?;/."!H!&&C;!H!?('"2{465//++-0;1# % &% bc(2PwLI[+5%I\"T$ \ &0 6z -0!'&R1P$NIJ5 ÅÅ 01 ÅÛ =5.'; H" $c5.T?FQ!.18? F1(9!.7;;&C;7ENE?2 jA'.";I«.;1@"WKA71P$'ÅÅ'!.1)'ÅÛ*"H5.'&R1P$<"!$[5 ' Ð )± (R²V§**±)(,+ %±²²`>C\5.Q&R1($."!$.$,; - ;7E"-(âK(";I[M5.7EH" $5Al?-#P 01*V ±)R( ²^§ *±)(+ %±YÀ²²`>CQ5.6&R1P$0"!$5.[79,!D" $RÀ\X5[1.9!>0!2f465; &R1P$J!<1( 0;1"85T$: -.<&.7// . (Y2 0W ( >CE"!.J"8 . 2 21 3.æ-.-0+g@$,; F $,-++gKP"IJ32â_ ./1( 7-(+ %50 À 50!Q"(+X(''76&R1P$3I[+5;&C;79 B DC C 5 5 E6 5.X?F1P9!5 07E ÅÅ 5 5.*-k"A +\7"'&C"!.?9T" $65. ? F1(9!.7 ÅÅ 2cJ5\7E? ?+*`5."!e±a!015P-0 5 !07EL$:"! q t:²EP5L&R1P$F ÅÅ 7"PN!;Q" F -*.< 0+S 465.@&R1($" $5@? F1P,9 07 L$:"!H"A7E"'&C"? S Å Å O± Ê ± ²² Ê ± ²E2S465&R1P$f"!$f5.? F1P,9 07<J57"(F Å Å N" -("^"!$ O± Ê ± ²² Ê ± ²[I[5W+9+$O·''2J01(;1R 6 I[ 1.S'z!-.!^1(>.-("`(IJ5.Z·'!"?;["% 0(+?2D_ *+, =;-+7 A>C%1N;1Z$:"!5.?F1P,9 07Wq tao5. &R1($ ÅÛ 7"PN;"I6!1HGz!-., Ô1P>-"3LIJ5 ·G!"?;8"M 0(+?2«_T/!++-. "3I[+5}X·}§ G ? F1(9!.7 ÅÅ !.1^?F1(9!.7 z!-.!^1(>.-("02 $,; -[N;7E"!2cç` &7E7+=,L."!; +7%"H!-.'X5. 5;%&R1P$ Æ H y;s!¸( "!$Qbc23/"?"!KWKN ÅÛ "!$cN;18 ; *ÅÛ± ~ < ²3éM'Åű ² -Z&0!7W" $5!5#1('."0+?2#_L*A7E"0lP-07E\5 1P;7EJ '&+."!$35.;L&R1($Q;l?-;6=!T(-%>Cf" $O*F %!'&;3"!&C">X"875N<^&.79,7E2<465P-0C5 7E"'&C"?9S" $Q5=$:;-.%;7E"T!X-';1H01&C01(? *±)(R²X/ $," ;75"!52{465(8!-.'&"!#';!.*50 ÅÅ ± ² &"P1-.7ES"!$Jy¯{&R1P$C 018[5P-0[;S"!'&(!2[_Ç;7E"01 21 1P 7-+%D5. D5Q'"P1(.D+C"?"7"!'&+7 ;1%$,"[T$,"F R!. +2\_LQ7"!0;l?-.07'5L&"&C"N1&.! '7 1P9!07E '"P1(aO5'7"'&C"!.?9T" $65.X$:;-.'N;79"<!'!-.';1 % .1&C.1?6!0150;?.<5.T!'TK?01'" $c&R1($3I[+5H1P+nR? &.! '2Vb0"!\'&(J1("0I6S "-'650 f5 I J$ Ê Û I ÅÅ % threshold ÅÛ "!+H1(+nR?J&0 !'6,[5.T';!8"H75Z7"'&C"!.?;2 iW"!/$,"+?VI\H!-.''; Æ !.1MÀ; Æ À;T!'+1)I[5 !.1)À !*5*7"!'&C".P9L"!$[ 87?;1@&R1($6É?RIJ5' 01À%;&C;7ENE?2 4(O2 !! > (A1"!;L5%B(&C;799 "@"!$68!.1"! LK3NMZc^£VÇ.]:.0(Ç;P¢;,PáC(¡;R ¢ª3 O(¡e.A J,RO; ¡O¢0£O.0@cÜO¨¢,RÜ«0¢ª3¡c:¢0ÜO¨ ¢ªO;(ª`C©,¡Q¤ O 465.<I\"&R1($ 4. OPTIMIZATION CRITERION 5(,^;79"!`I6 &.&.";BP A5M;N &.;79,"! ]±Y~²L"H>CE<!. +(h%+9KWI[55.*7E?;1&R1P$6É'" $ $,; -<N;7E"!J7"'&C"!.?92 zT.+?P*+!+X';!-.;V&."!&C"N;1%%5\++ -L -"!$J*+!+@';!-.;" $65.*7"'&C"!.?92'465P-.`5 0C±(¿9À²67 W>CIJ+Z!o 1P9!07E C±(¿À ²f§ 6 )( % Ä Ã 5 Á ,Ä`Å ± Æ À ² 7( % ç` O± 0²C>Cf5.f&R1($("!$P5D 01("} , >; CO§; Æ À Æ W § Æ À 2Q|?.7S Æ !.18À Æ À 50;NL!'S&R1($`ÉN I[+5 81 6O±)(CY²c\=(''7\$:-07E" +Q,f." [1P '7-+D"=&."N[50 ÅÅ P 01 ÅÛ >C./!&&.";BP N+Wz!-0 ` 5.E!J-.' h;1=>?=5.V'; % 01< , 07!2f465.6'! Q%^ÅÅ)Û § ÅÅ!±)@(²Z§ ±)@(² ²E2 5 "!$<5^? F1P,9 07ZH'&(]!N>P Û · ± (²E2fY9[ , 07 ± (² Æ ÅÅ §·.± 5 )@ @ 5 )@ 465.Q7!Q" $?F1(9!.7VO6+D'"D7"!'&+7 ;1R2Oj5 E% !T TI[+5H&C;7E6" @!`5%I\"H&R1($:0ÅÅX!.1RÅÛ*! $ <!&.!;`!.1Z5%! Dd!N;L&C$:;79<;-+92_ '"= +,7X+-0 "!^[IJ5.H % DS +OI[+5Z;&C;79L" 5.*9!01!1)1(? ")" $O@ 28465=">.! "A;!1.<-0T" &C$,"«7".1"!1\4cP"!\B(&.!0"!'" ±)@ é% ²VI[+5 5 ;&C;79S"G%Wo ±)! @ CéSW % Y²T ±)@ Y²3é<H % C ±)@ Y²3é ~y % Û C C ±)@ ² 5 5 5 5 5.T1(+nR?J7E"'&C"?6'; 0 5.*9!01!11? ""!$ j#+5*5D!&&.";BP"`I6L1;1(-0765. D5.J';!%"!$RPF Ä Û CC Å C ± Æ @(²J§ Æ % C ű)Û @(§²E2= j#ÅÛ +±)@(5^² T5.Xh· 5 ±)"/@(²;"é 1ÛEU B(Ä`&0ÁÅ 0 % " 35 `±)5@(X²O!!.7+ F 5 07\"!$(5.Q5 ?F1(9 07D,F@?ÅÛVTX·.± Û ±)@(² Æ ±)@(² Û ²E2`j)fI[+ T (506+6[-W 1 7E?["-0"!15 \h"X5 $,"J7"!0? EB&.!."!W"!$ % 2 465I6"&R1($:X ÅÅ=!.1P ÅÛ<>C8 &.&"BP NEWz!-.!` +6 "%+";IS6-.D"1NS<'&D;l?-0"!'$:"Q5.S;N!! &;7E" {±Y~!²E2Çj)@1(." !?RY ±)C( ²W§ Z Å Û\[ ÉNÊ $^ ] $ 5 1-07E;1Wz -0!W&R1P$!.1P% _ ±)R( ²V§ Ê ] Ý RY ± ² +9[71($2%_ ±)R( ² =,"HK(";IJ!T5.X"$,-.079"!`2v\@(''8"!$% _ ±)R( ² 01].7@ ÅÅ §`@ ÅÛ J!5.";IJ]gbc(2JwP\I6Z1(;1-.7H50 § I " Û I J$ S5. IJ5&_ ÅÅ ± ´ Z Ê Ia ! ²3é_ ÅÛ ± ´ ZÊ aI !J$ $ ²\§{y2 b."±Y~²E(I65W1(;1-.7o bT_%± % Å~dÛ c Æ @ Å% Å ÅÅ ² ±N² b."ã±N²E!IJ5X5\c."L1(+nR.7\%'!0Q±)% ÅÛ §% ÅÅ ²E 5I6"87E;5.;N<B7E+W5% 'X&R1P$\ 01W5P-0[5.F ! .{!NDT7"'&(E+% 01"!Ç;-(;Y2 } §¸(ì wP2 ºL";I=?I6S-.>.-([5.[">(9 .1*';!.Q 01*!!!.7;f"!$7 ÅÅ 01 ÅÛ H5=;N =&.7E"!M±?²Eo Û C C ±)(@ ² bTe_%±f ~ · % ² ±Yw!² 5Û ~Wg ±)( @ ² Æ ±)(@ ² Û 5 5 465([!T;l?-. "/,6'&C"9 ?J07+L +";ISS-.\"*&.;1P7E 1P9!07E6, ° mT.&.!!'E[&R1($:oQ¹V" "`.DB(&C"!.? a2 ° 4\I6"J&0 !'R&R1($:oOëLPE!5`;jA>.-+a!z!'P z!-.F , `.T+$,"µ!.18ç`""Y2 q yEtY5f!-5"`9!;1T"[PN;NQ9,7 (!&&."75.; $:"!L'"P1(+.*7E"??FY>018! O!015.8," PN;N;1MH&0 !'7% W"!$S7E"'&C"?<&R1($:2WºTPF 5;0"!-.S!&&."N!7958-.06"!-J"*>C=5.S1(+nRPS1(-. "85%$!7E<50=I61"8." -.'X50 +Q5*&0 !' ![$,-++%KP.";IJ%IJ5X5[! C{&"P7;;D=l?-.?2 465O;!1.V-0`"T;!75X$,"c5\>C;D*+!+<';!-.Q 5. "% 0$:"!ã5.&R1P$["!$O5.=7"!'&C"?9\?"X-.+$,"&R1($:2 5J;N!![&.;79,"!'">9.;1%>?X!X [! .W 3@^"!$[$,; -/;7E"7"!*F 2@465 5 "!$5 lP-. "]"&C.%5.W&C">++g" $<!. +P7 T-01P* KP"I[W5.*&R1P$["!$[5'1(+nR.7 &C"!.?9D!%H$:-07E"!M"!$J5./7"!'&C".PX1P,9 07 "!& V*+!+Z';-X>.;1W"!Z5.<$:;-.N;7E"!T&R1($ ÉN($:"!S-.-0`!!=! O.2 '_ jA[1."!6 _X2f465.` Å Ê 5\PN6" $05.6"V$:-07E" I\P"P1(-075T$:" +";I[.;79 .;1W;N =&;7E"`o hji ±)@(²D§_ Ê Å k+ 3+ ²f§ f ± 465W;7E+ .;1]&;7E" 5(5. hji · % Û ~ lg 5 Û C C ±)@(² ±ar² ±)( @ ² Æ ±)(@ ² 5 5 ±)@(²' +I['&C"N+N2_S01RQ5 ~ Û hji ±)@(²[,R5>CELL5!!XEfW2_ 7E+ 0;1A&;7E"M" $Jh"Z'; 0505'è&C$:"! #&C"?"!+KNG 01("î!'&2ã_L# .+@;7E+ 0;1 &;7E"Z'; 0\5. [5.<à&C$:"!J&C$:;7E+?2 3¥0 J,RO; Pú`0A®c©,(WC ¢ªO;P]¨©,0;(¨0Ù MH0¢;,¨)¢ª`¢¢ª`@á. 0£c:©,,¢E¦}Ü ¢ª`(¢ª`P}¨N©,.;()áC(gmnÔ m ..M, ¢;©,CÚ\cÜOP¢'CÜ`¡â0.;¤ ¨C©CG;R ;.¢ª3/¡còQ(;.ÜC¢¤ 4O"<B(&C'?9 ++;\5L1P+nR?\'"P1(NI6S&C$,"';1' o="!'"!""?F|(*."/;="Ax!¸!¸/!!;T" $["-01PFY-(5 1.9!>.2^j)/75."?"/5/ëSzTve7" "*5(,"! í!$: -. N;79"c>C;7!-0!I[+5%7E"!"!Vc;!c"T>-+1X7E!;2QzLN <7"!"!J&07ETl?-0 ?h "3?5.L7"!"\5"!!«6=';!-. 5. FEATURE PDF FITTING ]&7E7!65.8&R1($L"!$58$: -.HN;7E"!7"'&C"!.?9% "!$.5.[7" "Q1(>.-"!%X5.Q !a2 !?;75*7E"'&C"?f"!$ 5.XëSzTvÔ5(,"! &.;P9T5X&">.!>+++^50<8&(+BE -.-0+g."!/KP.";IJ32Ç_kl?-;" ,o)IJ508K?01]"!$<&R1($ "!$V5!<5.[5.<7"!;&C".1(.7" "2J_LSB(&(,.;1H>CEF /-0$,-T"M'"P1(S Z$: -.8-01g] ^! $:"!fI6/7"!0150*7"!'&C"?9 '.1&C01P" $J". p¯-.D"L56;1-.7;1<P-.%>CO"!$. ;c&Cf7EI\ !"!5Q!01A5P-.=I\/$,"P7-0X")5./7" "*&R1P$J"!$S;75G7"*F 5.;NS"!-.'L&.!!'E,7J'"P1E0I[+5/"!+=$:I#(-%>C &C"?'&.!+MI[5(g G!!W7E!2g_J+[ ;G " $f-.K(";IJ8&.!!'E2 7ET7"?9 @ '"L5X 'X?-0c$," "!`R 01W;!795 T.X%1.9!>.T>-++6$:"!ã"!-..1(Fa-57E!;["!$O ; bc2r(2VjAL-.;18x7E!;6"!$Qy;¸¸=!!;6;75`ofw7E!;6$:" 5\5.!&Cf"!$(5.D&R1P$R$:"`;757"'&C"!.?O7!=>CD; 132 5.T¶\"EO1 9 >0%±a-.0E;P'"-.?93NI[$+Y.7!!0 01 7Ef50!f=1(+nR?VN"!$37E"!"D !>+++?Nc+-. ;1% UL";I6NC5.(-%>CJ" $\'P9S&C79,!5."!-1Z>CX!! !&("9²E!JOEB(-D7EO50OI\67" ;79;1"!-.NN 01 ."-5H"* +"I+!>(7"!07E-."!02 0. ++!"!-91"?"!67E!\50;?.'y;¸!¸ 01"!e ;f$:"e5. ¶\"EV1.9!>.<"!$V81(+nR?J"-(91"?"!L7E.;2 jA/;1A"@75."?"HWI[18&0!6" $T&R1P$="^>C/ ;132ZjA 7E"01(S5T$:" +";I[.&R1P$o ¯-H5.*9VI6'"?"K@?"Z!77"!-.?X5*$!7EX5. X7" "! 15 60 castle class 60 25 10 40 40 5 20 20 20 0 0.2 0.4 0 0.6 60 0 0.05 0.1 0.15 0 100 100 50 50 0 0.1 0.2 0.3 # of components 0 40 20 0 0 0.02 0.04 0 0.06 100 0 0.1 0.2 0.3 0 60 60 40 40 20 20 0 0.05 0.1 1−Poisson 2−exponential 3−uniform 4−Rayleigh 5−Gauss 6−lognormal 7−gamma 8−Weibull 15 10 0.15 5 50 0 0 0.05 0.1 0 0.15 0 0.1 0.2 0.3 0 0 0.01 0.02 0 pRAôLú3CA®O©,(^.%A®c::¨!0©®D¡`^0'ûü/ýíP(Ù J,CO; ¢;O;WáC(¨¢C%;R ¢ª`Z¨!0¢;©,W¨N©,0;¤ôL.¨ª 2 3 4 5 6 7 8 6 7 8 grass class O£`Ù®O©,0¢*¡O:Ù ®O©,P¦O=¢ª`WÜ`O@£V(.6®c,ú3(©:<',¢ª)¢ª`8C@H¨0©,CNÚc.< rq 30 ®V(¨ÜR¢.0^0S¢ª`^@.0@; NCÚVáC(O%¢;ª`^¨C©,0?¤ 25 1−Poisson 2−exponential 3−uniform 4−Rayleigh 5−Gauss 6−lognormal 7−gamma 8−Weibull ±"â;N!@'"W5.!âx ¸Nåï"!$=5 7E"'&C"?9c!QP-+,²ENc;f$:"!c5.Q7"!"!Ql?-.!?h; "<50 I\'75."?"N8±ar/>(0T&C7"!"<B(;!.1^5P-.~PyrH7"!'&C"?9 $,"*5H7" "*5(,"! /²E2)j)/." ,7E850'7"!'&C"?*&R1($: [+5.V'"!." F`"!V>+FY'"P1.Y2O-. ++?5.\V!%'&C"9 ? # of components 5(" H &.! 1 35 20 15 '"P1(%A¸P2'bc2cx85"IS&(7 DB!'&(;T"!$\5.%'&7 &R1P$2 jg5 10 y;¸!¸H! -.;3+&C"N>*"/&C$:"!k BP%-KNE+F Ro="!'"!""?F 5"?"P1=; "=" $(5f&0! 'R"!$(;!795=&R1P$2V_ 5 |P*."=q !tCD5*-.;1*"=-0 J5.J!"?"P1.F" $,Fa .;2 ëS;7+[50 ;V5(;*7".,9 7E"'&0 .fI[+5G× Ý 1(F 9 07!\5.8B(&C'?9 S 01M5."!7 T7-.X- N81(+F >-"Z$,-.079"!02<465*× Ý 1(9 07,T1 ..;1Z!L5. BP+F X-.{>(1P+nR07E2f465f;6&" ?1Q<7+"'$,"\'"P1( ;7E"!`2 &o="!'"!""?F|(*.";-+9*&C$,"';1M" 0 1 2 3 4 5 ?RTû'(O©,¢S0V¢ª3HC©:00C;(á3Ù OA: Ü`(ᢢJRÜ 4% ª3^Ü`O@£V(%0S¨R®fÙ Ü`ÜC¢;'Ü`0¢* (¨¢(¡#:'ª`(Ü áCOX¢ª`^®f¡OTÜ`CC¤ J,RO; ¢ª`^¨!0¢;©,Z0ÜO¡]0.;*¨N©,.;(¤ bc(2\s^&.?9 57 01!7E;28UL"!!<5"Ie5.%(-%>C " $L$,; -W7"!'&C"?950*A %75]&R1P$L'"P1(a2AY% 79!O5. cfB(&C"?,?&R1($(&C$,"3>C`5.!=¹V" ,"!%&R1P$ $,"<"%&.!!'E=&R1($:2XjA>.-+D 01!''&R1($:&C$:"! >CE\7E"'&0 ;1X"5["!5.fI[+5*I\"=&0 !'2f|P*+, -+9S5.;N>C8">.N;1$:"J5.T"!5.L79,!;2 21 ¯T-.%"H5'7"!'&BP+^N-.T .1P'P`+=<1( 7-(+" 5.;N*/1 .+N*7E"079-."A"!@IJ5(795@&R1($D5.$:;-.'7"!*F &C"!.?9=<$,"!+"I[2ºTN5.;V5$,"!+";I[@$:!*++)" $ &R1P$JJ-(9 >o s )± (+ À¿utC¿uv²f§ wQ±)v;t ²Àjx (ny x Ê Å É Êz|4} { ~ d] ±Yx!² "!>9;1Ç>?!&.&(+(g5.M&C";I6^$,-..7E"( "{!' 01("þ!!!>(O ( 2´ v\1E 0+"3=5.)D-{ Z$,-.079"! ´:ÄF3 " Ý Å wQ±)v;²f§ ´:Ä x Ê ÉNÊ 2OU +$Fz -0(z '(j)E>-+a DBPF &C"!.? a(ëL;P5&R1P$6 +R&.!7- [76"!$35D$:!*F ++?2Zb0"!=.9!.7V5.UT +$,Fz!-.!M"!>9 ;1A$:"!&A t §µ~ 01[ v §Çyj ~?2 Õ 6. OPTIMIZATION OVER ¶\"'&.!;1/"W±y²E85J;7E"30I6=;7ES5.<EL" $D*F +!+ $:"X5.H>C*"D"A× ¾ ¾ ± (²D§ 2 ';!-.;DIJ5.8I6H;!75 1(9 07;a2 =Ó§Ôy2Q465P-0(I6=5.;N 5 )@ + @+ j#+5)B '&;OI\*+-. 5.";I5.'>C;*+!+';F -.'I[+5 × ¾ 7 )>C/1N1)1&C01(W"!$[5'&R1($J'"P1(F +.^5.!!!>(++)"!$J5.$:;-.87"'&C"!.?92465.`VI6 9!KL!1!!?9!!J"!$R5.;L1! "!0V"! +1.[5.J&."!&C"N;1 '"P1EY2 j5@5'*+, +@';-%=× ¾ O+=T?;.H"8." F 7=50[5.=;7E+ .;1H&.7E"!W)±arN²J7!H>CIJZ[5. &."P1(-07EJ" $VI\"%o · % h ¾ )± @(²f§`f ~ @ Û ºT" 750 h¾ Û Õ ±:Õ Q Æ y² Wg + @+ Û ¾ ~ + @+ ¾ Æ S1 ..;1"(/$:"![Õ)Öây2 Ê Û + @+ ¾ @ Û Û ±asN² c g±as²Ec5.% .< I $ a$ PN"!N"+@5.'1P'0" ÁÛ Â O ·T" $.5.f$: -.6&07E[!.1<56;N [l?-0 ;11(+nR.7\" $ Û 7E"'&C"?['; 0 "!$ 02D465 (T"X5T!!!.7 E% @ @ e\"!Q ;1'"=ÕQ( 01%5P-0V"=5.L*+!+'';-2 jA=0 ';1/5<;7".18µl?-0 ;13(5.<&C;1 ¾ ±)@(²\"!$V5 predicted simulated 0.545 &;7E"3o Õ Û + @+ ¾ Ê Û Û Û @ ¾ Û ¾ .± + @+ ² Æ + @+ ±:Õ y² Æ Û Û Û ±a¬² ¾ )± @(²%' ;1g"A5^795"!7Z" $=Õ{!.1]"A5 &â 6 " $<5.@7"'&C"!.?91(+nR07;?} @ ±a!01 5P-.L"85'50 &C*"!$6É!²E2%v6-."!7*5. 0 ¾ ±)( @ ²LTP !? -01(<7 !! "." $O0 @ 2/465 +"IS-0T"Z'&(+$5 $,"!+";I[^1! ".>?^-*/5. 5%!!!.7*" $H @ 0.54 precision ¾ )± @(²f§ 465@&C;1 5.!&C@"!$=5@&R1P$ y!2 465 ;!75Ç$:"!Z5.M>C;@*+!+';-)I[+5{× ¾ 0.535 0.53 0 < ¾ )± @(²<I[5];&C;7E'" lP-(P%"A BP*h.Z5.W&C;1 ÕD2 0.5 1 1.5 2 β 2.5 3 3.5 4 34 RA®`0:RÜG£fP¢9XPÜ)¢ª`PC;P¢;:¨.©6CÜO¡G;@Ù J,RO; O©,¢(¡#PáC;0^®c;(¨N:;,RÜâÜg¢ª3)üCO;;,0ܨ0^ª`Ü 6.1 Gaussian 465/'&(;<'"P1D"^-.'X50 <5 Õ]á. ¤ · 7"!'&C"?9 ± ²T" $65.%$,; -'N;7E"!<H /z!-0 )!.1"!! >; $,"!+";I[o YR±+ O²V§ c ~^7 É Ê $ $ $ ±y¸N² I[+5<'; =h"S!.1=9!01!1<1P"!4D 23j#+5=5.f&.?"-. "!9"!0I6=50;NÉP±²f§R Y ±N²E2 Û 465J7"'&C"!.?9c>C<z!-., *I[+5* !07E N=7"'&C" F ?9[1(+nR.70* @ L"z!-., WI[+5W !07E~^ Û 2Q465(-. &R1P$X6O±)( @ ²= "z!-., `2^v6E$:""^7"!'&.-*5;N!! &;7E"M±Yw!²EI\=.;15.='"!'?6"!$f"!1 W " $,0@ o "Å O + @+ <§{±Y~ @ Û ²$ \w \w ± ± ÛÅ ² ² Û IJ5(795=`1( 0;1"(+TIJ5.OH Ö Æ y!2V_J$,`-.>.-("'±a¬N²E I\<1;1(-07L5.$:" +";I[./&C13. $,T'&++ C7 ".o "Å Û ¾ ` Û ¾ ±J_t À À²V§ Õ \w ± Å ²\w ± Û w ¾ O" ± Å ² Û Æ ² w Û ± ¾ O" Å ² ±y!y² Û Û Û $:"!CIJ5.H5.=$: -.&R1($O,Tz!-., `R×QÛ,J5.=>C;T*+F !+8';!-.TI[+5H5<S× ¾ 2 y ºL"!7'50X$,"è"-%1("`V5&C;1A1 ..;1A"!+ $,"JÕAÖây2 4`"/! +1.5=&."!&C"N;1Z'"P1Ec"!$f!!<f I\Z7"!'&0!1M5W;N 8&.;7E"]">(9 .;1MG5Zz -0F A7!H±y!y²S"5.X;N!!%&;7E"@">9.;1Z>?Z%-( F "!8"!8=I\"7E;[(?5.7S1.9!>0!T" $V~ ¸¸ ;D;75`2 465=P-.%>C\"!$V7"'&C"!.?96·XJ["Hy;¸!¸(2Q465.?57 1 9 >0%'&+&."P1(-07;1)>?A!'&(^z -0! 1(" % !! >HI[+5 F <{§k2gbc2\¬A5.";IS%5 6.2 Exponential 4D(&(,7 ++?C5.=$:;-.X7"'&C"!.?9S!X5"!!T 01H5P-0 5.E<! -. ."+h;1A>CI6)¸Z!01 y2W465(-.O"Z>C B79;.&?"!-0[&R1($c!=(&(,7 ++8,79;18"Zq ¸(¿;yEta2 j)Z";Iu!-.'W5. $:;-.@7"!'&C".P9' ZB(&C"?, !.1"! , >;6I[+5W&R1($o 9L';!Z ±W+ O²f§ y É Ê ~ Ð Rf2=T,T'&(" !.1W9=9 01!1^1? "! &."N50*5.81(+nR078"!$TI6"@B(&C"?,J!.1"æ +F &],XZçc!&(7@±"%1"->/B(&C".P:² !>(;X" $T&.!!'E !.1"! , >I[+5W&R1($o ±)@+ O²f§ ~^y É Ê j Û 9Q';!'6h"%!01'+96 !07E=~^ 2D465.L'"'?Q"!$O"1 H" $ *@ $:"!+";I[.8%çc &7=&R1P$co Û + @+ §{± @ ~ ²$ \w ±2 égy² 465.$:"!0+9J&C;1/S $S'&(+ 07 "!0o Û ¾ ±a× t tÉ ²V§ w\±Y~Õ8égw y;²±:Õ8Æ égw yÛ ² ±:Õ/é#y² IJ575HJ1 ..;1$:"[Õ)Öây="!+?2 §íyZ 01 ;N!H&.;7E"]">(9 .;1M$:"!1(+nR?%-;%" $TÕâG5 bc2fy;¸/1(&(,T5.<5."7\ 01^%-(,;1@!!%&.EF .!%q ¸(¿ taP7"'&.!;1%"5"E,7 C! -.2f465.[ .Q>CI6 7E".L'$,-..7E"^"!$fÕD2465%%-( "W1(".=I[+5Z5. &;1(7E1X 01%X- ;1;N 6&;7E"0cc NE!"?"P1 !'%&0! 'T5.!@5.%&?"-0<;79"!`2465* .=>CEF H-075HX7=.7T5.T9!.1.!181? "!8" $ %6 N+ I\G5.8I6"A7-.NX*."!*>01M$:"!'ÕàÖèy\'%>C 7"'&.!;1"%5.T-="!$ 5./I\")!&&.";BP ".%I6Z1P,1M#|P;7E"]2gb0"*Õ ,% 2 ,@ y! ¾ ±a× t tÉ ²T1"? "-(<"!$65*1(" "!$J1( 0("!" $J&C;1R b."µbc2C¬P0I67 Z=50J5.<;N &.;7E"WJ BP+F ." T(7+ZBP.13.+KN<^5Xz!-0 72T465.&."!&C"N;1 X-.â$:"!fÕZ§â~P2f465(,f7 X>C6 "&."N1 0P7+?2D465F '"P1E3[+*+;18*; 795HI[+5(W× ¾ I[+5HÕ)Öây2 14 0.7 asymptote optimal β predicted simulated 12 8 0.6 β precision 10 6 4 2 0.5 0 0.5 1 1.5 2 β 2.5 3 3.5 0 4 m RA®O.:RÜW£VP¢EP.Ü¢ª`PC;P¢;:¨.©CCÜO¡W;:@Ù 1 1.5 2 2.5 J,CO;/ 3 J,RO;)0.=ýX(¢<Õ `©,.¢(¡ YCA:©¦ 'ª`Ü PáC(;.0µ®c;(¨N:;RÜïÜí¢ª`ôLú`®VRÜ`ÜC¢;,0©M¨!0 3.5 1/b 4 4.5 Å 0ZcÜ`¨¢;,RÜG0 QB±)@+ À¿uv;²E¤ Õ]á. ¤ 3 x 5 5.5 6 YC%@®f¡OSÜG¢ª3 &.-(85W&C;1M]5W7!HIJ5.85.8$,; -Z7"!'&C".P9 _Lg-.'!?TI[5Ç5M&."!&C"N;1Ç'"P1(aI\ 50;N !L-.($,"e!.1"e!!!>(2Q-075/7P5.L1(+nR07 5. J$:"!T WB(&C"? `&R1($(5.="!& O*+, +8';- "!$`I\"*7"!'&C".P9f6%7P;1 .-(![!.1"!à!!!>( I[+5(W× ¾ ±"L|?'&."Aq t,²6I[+5W'"!'?9\"!$c"1 3o ,J×\Å 2 + @+ 6.3 Exponential of a Power jA=50;N=&?"!-0+H5.";IJH50J5.=>C;L*+, +8';- I[+5()× ¾ =6<Zz!-.!)&R1P$[!.1A× <× Û IJ5 X^çO!&(,!7/&R1($2@_l?-;" Å =6 IJ5. ¾ ± h BJt£¤Y É ²V§ >CEI6*5.J&C";I6f01J5.[EB&C"!.? *5.J&R1($3 01X5 "!& `! -." $VÕVp n6 B±)@+ À¿uv;²f§ ^~ vDw\±)v;²Àjx É Ê j} y '"!'?["!$c"1 /,o + @+ §âÀ @ Û ² $ 2 ±ar ±:Õ/é#y² Û Û ±:Õ/éG~² ±Y~;Õ/éy;² Û rÕ ±:Õé]w!² 0.6 @ predicted simulated Û §ÇÀ Û xl Ï¢¡ x x Ò Ò 2[Y9 Ï x Qw ±)vQw±2<±)v;é#² y²² 0.58 precision @ 465X'!W" $ /Lh"/!01/9S !07E< 2 ± <éy;²± éG~!² 465.="!>9;1W&C1/L1( 0;1'$:"JÕAÖây<!o !;o'<5./^1(;7E+.K iW"!=$:"+? HS!-.';1"*>Co §â~ 0185P-.\5.=&C18o 0.56 Û Û Û Õ Æ y;²`é#y²Õ ¾ )± B²f§ dw w Û ±a±)^vv;²v ² Û wQ±)v;²wQ±)vw ±Y~±)Õv±:é Û y;²² Æ w ±)v!±:Õ/égy²² ¶\"!'&0 ;1<"J5.D&.P"!-0OB '&;$:"! ( BP*h; "<" $ ¾ I[+5@;&C;7ET"8Õ 0.54 5.=7"'&(+,7 ;1R2%465P-.3I\%5. P-'7 ++Z; 795Z$,"L57-.N<" $D5<>C;LÕD0$,"1P+nR? ,v 0 ! -;["!$ 2 465*">(9 .1@;-(+9=!*5";IJbc(2Dy!y2*|(-&..!+?R+ &.&C; 50 × Å -2[b0"!T+ ,"!=A!. D5.*>C;*+!+@';F x q y¿;y!ì x!r !ta`× Å J5=>C;T1(9!.7I[+5( × ¾ .I[+5WÕ)ÖÔy!2[465(,J/B(& HIJ5?H× Å 5.";ISS>CJF -(+9\7"!'&0!1%"<×\ÛJ!.1'×E3 " Ý{*5SEB&C'P9V" $`bc(2(~P2 6.4 Uniform Å Abc2Dyy!OIJ5 x B±)@+ À¿kv²L>CF !"?;=."!=( 0+?CY2 OIJ5. 0.5 1 1.5 2 β 2.5 3.5 4 <RA®O. ,RÜÇ£V(¢9(Üâ®c;(¡c:¨¢(¡Ç0ÜO¡ÔC£`Ù J,RO;(Ø3 (;áC¡(áC(;..®c;¨:;,RÜMÜA¢ª3WcÜ`,0!ï¨.ª`Ü@Õ á(0,(¤ _L"!5T'3=5";IJbc(2Dy;~P`5.%&;1(7E1@ 01@*F -;1#;N ^&.;79,"!0/!ZN]7E"^"A;75#"!5'$:"! ÕMÖÔy!2S465.<7-N=J07E;.'$,"µÕ§yC!01/5(-.J× Ý 5.T>C;S* H'-.SI[+5Z× ¾ PÕ)Öây($:"!SX-.(+$:" &R1($2 7E"';5.*1(>.-"!A$:-07E"A"!$SH-+$:"!!01("!!+F >PÕQ""<";I[ 1.\ .+?2c4O"%75.79K%5((I\7"!*F 3 7. OPTIMIZATION OVER Ó I[+5 "NLÕD2=v6-L5.";IJ@|(7E"~P`!^"!&*h; "@"NLÓ S "'"!$V?;;2Q4O"*'&(+$85<!. +,I6<!-.'50 Û ÕZQ B(;1X"X~P?a2 ± (²f§ 2f01(;1RN5.JD-07E+1; /1(9!.7 5 )@ *@ '&(;?A'&(+ 07 ".%"!$S5.H&C;1R2Mbc;Q5 &C;1H>C;7"!';o Û±)@(²f§ ¥ )± @(² y ¼ ¼ Û §î±Y~ Ó ¼ Æ w y² Q± Û ¼ 0.7 y Æ Û ¼ Û Å éey;²6éÓw ± Ê éey;² Æ ±Ó Æ Ê ¼ ¼ ¼ y y y²wQ± Ê éHy²w\± éHy²c 01¯ ¼ §w\± ¨ éHy² Æ dwQ±®¡ éHy²wQ± Û ¼ Û y Û Û ¼ Û ¼ y y y y é y²Vé]w ± éây² Æ ~P±)w\± é}y;² Æ w ± é}y²² 2X465.*&C;1 ¼ ±J¬É®B°v #y ²C,O1 ..;1"!+y IJ5.&tÖ]¸( y ÓMÖ Æ?y¨ Ó Ö Æ tRéX~ !.18ÓMÖây Æ yÛ 2 %5.[&?"-0f;79"!`NI\J"&*h;15.J*+, +X';- Ò§¦ Ïa Ê a IJ5 ¥ ±)@(²=§ Ò $ <5*¹V; "MKP-.",2W|(7".13OI\ Ïa Ê a $ 7!#IJ+Z5.W&C;1#1P7E+#!/@$:-..7E"#" $<"!$$,; - predicted simulated 7E"'&C"?96* 01WÀo Û ±)@(²D§ ¦ $$ precision y Ò ÏÑÐÊ Ò ÏÑÐÊ y Æ |?07 ! 01}À5.;N@5A 'A&R1P$%ÉNLI6A5.;N ± Û Û Û Û ~ 0 01/5P-.o Æ ~ ± Æ À² J§â~ Æ s Jé r \¨ ¨ ¡ y Û ±²D§ ¦ " $ Ð Ê ¨ Ðk© Ð ¡ Ð $ Ò Û ÏÐ $ Ê Ð $ $ Û À² Æ 0.6 § y Æ 0.5 jA.";I«?"P1-.7'5.Óâ&0 !'"!$L*+!+A';-; » ¼0½ Û!2MvQ -@ 1!&@5H1("!]" $=|P;7E"]ZIJ5. § ¼ ¼ ± 01^ÀX %!-.';1 Æ ÀN."57<IJ5. /§ Æ À &C"+²E.I\<1;1(-07T5T$:" +";I[.;79 .;1H&;7E"`o @ h Û ±²f§ f · ~ Û % Û Ó6±±Y~Ó y² Æ c ~g ¨ ~ ¼ Û ¼ Û Ê é)Ó ¡ Æ ¼ ¼ ¼ Ê Å Û ±Ó Æ Û Û ¼ éG y;² Æ Û Ê Û ¼ ~P± Æ ¼ 0.2 0.4 0.6 0.8 1 α 1.2 1.4 1.6 1.8 2 <RA®O. ,RÜÇ£V(¢9(Üâ®c;(¡c:¨¢(¡Ç0ÜO¡ÔC£`Ù J,RO;(ñ3 (;áC¡ ª`Ü Æ 0 ±y;~² ¼ ¼ Û ²² ² Û PáC(;.0d®c;(¨N:;,CÜîÜ`d(ú`®VRÜ`ÜC¢;,0©G¨. Ó#á.,('Ü » ¼0½ Û ¤ Û t _TV5";IJX%ÓOF1P, c"!$Cbc2(y;PIJ5 %§Çy!56&C;1< 1E 0.1<"!+=$:"!cÓMÖây2VºLN5;cO5.";IJX>?<X- "3 Å +fBP9VL! -.Q"!$CÓZ79"\" Û IJ5\56%-(,;1X&;7E" V BP%-.W2`465(,f7 %B(&(,X5.[-+9V1;79>C1X'|(7!2?~?2 465';7E+ 01&.7E"!Ag±y;~²TTIJM5.X&."P1(-07E<" $ I6"TN!V8±asN²E2D|?*+!+? 5.6I]&C;1X7!*>C61 ..;1 !o ¼ Û Ó ±²D§ ±±Y~Ó Æ s± ¼ 465A&C;1 ¨¼ y² Æ Û ¼ Ê Û ¡¼ éMÓ ¼ ¼ éM Ê Å Û Û ¼ Û ±Ó Æ ~(± Æ ¼ y² Æ Û ¼ Ê Æ Û ¼ ¼ Û ² Û ² Û Û Û 7.2 Design of Ground-truth Databases 5.[&?"!-0f;7E"!0P(?5.761 9 >0D5.6>C*-.;1 "Z! +1. '5''"P1Q>?)5"I[W5.* .>CI6)5.'&.EF 1(7E1Z!01ZX- ;1Z;N!&.7E"!02mL$D7"-5= ² ." 'Z"?"P1 ±yN² .X>CI\G%-(,"G!.1M5"$:"!' +JK?01 "!$c(P57T1 9!>.;2Q465=(P57T1 9!>.X-0\>C1EF ;1HZ-075ZXI6;850S5=';-="!$V5=%-;1W;?F /P , ?/I[+5â;&C;798")57 A" $XP2 465^;!75g$,"5.W>C;/*+!+]';!-.HI[+5 3 ¼ lP-(PD" BP*hE5.S&C;1 » ¼0½ Û ±N²VI[5;&C7E\"<Ó\2 <&.;79,"!HS+!>(2 b0"!ï"-.'EB&C'P9QI6Z5.H$:;1#N T&C;7E+ C7F ".[5<(P571.9!>.=%-.6$:" +";I=o 7.1 Weibull b."|P;7E"HwP<'"L; +7&R1($R50 8B(&C"!.? CQ5 465.D9!.1.!1=1(? "<"!$P5c$:;-.Q7"'&C"!.?9R5."!-1 ° jA>.-(O1(>.-("`o ª ±+ À¿ut²f§ t À ^ y Ê }/{ ~ Ð "!>9;1^>PW!&&+P'5.<&C";I6T$,-..7E"«( IJ5G(Z! { Å EB&C"!.? .!.1"{!! >2fb0"!dq tY9f'; %\À w\± é { y Û Å Û $ y;²EN 01=+9O !07E[À ±)w\± éy² Æ w ± é'y²²E2ViW"!6.+? y +9['"'P6"!$V"!1'8 { o y §âÀ¤ Q { w ± t égy² Å &C;1W±y;²E?I6L1;1(-0765L&C;1%$:"!6Tj)E>-+0&R1P$3QT$:-..7EF ¼ J± ¬ÔÉjBJv # ²f§ )w yÛ ± \± é#y² Æ I6"X$:;-.<7"!'&C".P92 É Ê _J$,<->0+-"!A"!$Q5.*&?"-0L'"'?lP-. "@@5 "!W"!$fÓ\o >CJwJ';O5(5.f5.!<5.[1P+nR07E6"!$.';!.c>CI\ w Û ± yÅ s é#y²² Û Ó ¯ ® Û Û ¼ ¼ 465.'P-.X>CT" $6! ° &C7E5."!-1>C*5(5. 50!W~!¸!¸(2 ° 465.6hQ"!$5.f$:;-.6N7E"OX·L5."-(1>CD55O5.! y;¸¸P2\Y$c"!J5.=;N!<&;7E"W>C;7E"';6"?"*"!?2 465.X,!=I\"H-;= *NZ'&C"!9!?T"85.&^A1;!. ;6"!-..1(Fa-5A1. 9 >0!;X!-.;1 |P;7E"G~?2HY$65.; &C;7E+ 07 ".!<$:" +";I\;133+TS5Z&C"N>"/!. +h "W" 5.<!1 9 >0X*+!<)7"??<"H5.'!"-01 -5(F1. 9 >0!?5.J>C;6*+!+';-L"!>9 ;1'"'5. "!-..1(Fa-581.9!>0!2 8. CONCLUSIONS jAJ50;NS5.";IJ5.";Ig"<1(NJ5.J>C;\*+!+'';-[ H"!$J*+!+';-;>0!;1A"!)H&"&C"N1A'"P1D" $ *! Q2465'9 7 Q'"P1ED-.'LF 1(&C.1?f$:;-.T7"'&C"!.?9cI[+58 'L&.! '7J'"P1( $,"=5.%&R1($>-<1P+nR?='; 02'4`"Z'&++$,^5.XB(&!. F "!0[I6H50;NZ!-.';1M50'5.H!!Z1.9!>.Z50!%I\" 79,!;[>-%58&"&C";1G'"P1(S7 ]>C/BP01(;1)I[+5."-( 21 1P 7-+;6"X!!J(-%>CQ"!$c7E;2\465['"P1C6&.!F +);1)"M;J1.9W>? W"!$J$,; -H7"!'&C"?9 "NVL1(;1(7;1<1.9!>0!2Vb0"!O .T7" "c5(,"! !$:!*F ++]±Yx²IJ5795A +h;%z!-0Oj)>.-(+6 01Mz '8&R1($: J7"PN(?;2 -*.Az!-0 `JB(&C"? a[-.(+$:"W\!.1GjA>.-+S&R1($: $,"'5./$:;-.W!! >++?2]4651! " *-0$,-JIJ5. 7 G>C/'"P1E1)>PA^K(";IJ)$!*++ " $6&.!!'E,7<&R1($:24O""-KP.";I[;1!3NW++%50!T>C 1("*"'"P1+./5.%!! >++@"!$6$,; -;-0;1^!! Ef2SºTN5.;05(SL&">0 >+Z'NH*F &C"!9!?[->;7E6"-.1(%+$3I6SI[!?Q"%1(N"&>CQ!! EV2 Y$P5.f`."[I6;T"J1NQ['"P1!$:"`5.V$:;-.Q , >+++? ; 795/"!$35.S>C;[*+!+*';-T7 8>CS&C$,"';1'" /"!-.01PFa-51. 9 >0!2'465(,=!"&(*h;"A&">( "N*5.W&.!!'E*"!$/"!$<*+!+G';!-.;2}465 &.! 'h;1}Z" $**+!+â';!-.;±y²Hâ7"!F ?$:"*-075]Z&-.&C"N!2)M&.!7-(, \I\85.H5"IJ I[+5H5;=*+!+8';-;\?;.%.7;S" $f;NF X&.;7E"32=j)<." 7;1Z50 L5.<>C;<*+!+W';- ' +] ;1g"A5W$:;-.@&0!7^ 5/5.!g" 5A75." 7" $X5@1. 9 >0!2ãb0"!î"!-./;98"!â?57 1 9 >0VI6*$,;1) \-;50 A%-.=>C*$:" +";I\;1 81;!.X"-01PFY-(5/1. 9 >0!;\$:"![+, ><7"!07E-0"!0 "!Z5.X795"!7"!$D5.>C;=*+!+Z'-.!2TY$D5;X&C;7EF + 07 ".*!$:" +";I\;13QX5.M&C"N>"@!. +h\" " 5.f!!L1 9 >0\*+, D7"!??;5.J>C;\*+, + '-.">(9 .1W"Z5.<"!-..1(Fa-5Z1 9 >0!2=4O"'97K? 5J" Fa ..L&.">(WN5.f50 %"=-0[5.J7E? .+*+ 5"í!I6H1(13D M?^&C"N>+++)X"Z-./5 l± v\PFQ W5"èq tO"'"!>9 HHIJ5(795Z .=5=;NF <&.7E"!H2 465X .+*+=" $Q5* &.&."75@L5. I\*!-.'X.1&C(F 1(?O$,; -\N;79"c7E"'&C"?92c4656;7E"01+*+O`50O5 !! 07;6" $`5S$,; -7"!'&C"?9\!T-';1';l?-0 a2VjA T&(, .="< B%5.;L-'&".f'$:-(-.[I6"!K2Q465 )&C&C;7EN" $[5<I\"K@,="Z1(N"& "+5<$," !1. &.H5'*+, +@';-*&0 !'>P@&C$,"*. ; .(2 Acknowledgments 465/!-5"!/$:-(6"Z¯=;?,1vT2f¶\"?"!&CX$,"v6";IJ LN+?<=|_<[$:"!! -0 >M1P,7E-0". 01}?; 7E"''?92 9. REFERENCES q yEtX|R2_LK(";8!01/ë2.iA2U!+,7KC20b0 -.T."+h " !01+K+5"?"P1(FY>0!;1Z*+, +8';-;\$:"!S!! ²³´)´!µD¶ ·¸Oµk¹kºk»·W¼#´)¼°º·P½µD´)´!µD¶ ¾`~~(±Yw!²Eo w!rj¿(w sN~P a2 ~!¸¸Py2 !795(;\$:"!J5"!!*FY>0!;18!!<7E+ C7"`2 ÀuÁ'ÁÁÂW¶u³·W¾D³A¹|´)¼°º·W¾º·PõDĶu³ÅÃ4µD´)ÆEº^¶kÇ^¾cy¸±Yw²E`y;¬!¬¬(2 q t_<2n! È Z!.1W_2(³Q +P(2.!!! `-0.*7"!"L!.1 5.!&C2¤²O³^´)´!µD¶D·¸Vµu¹kºk»·¼r´)¼°º. · C~!¬(±asN²Eo+y~ ®.¿ y~Dy;¬!¬rP2 q !t<³2W= o "!"!+"-KR.ºX2(¹V".KN"(0_<2C|PKN""!K(5"P13!.1 _<2.4`"-.>(.2¤ÉV¼°Ê>µ|˰ÌD͵ ̺¼#¶kµÊ>µ4´rÎV͵ º¶D¼°µGÊ>µD¾Ïn¶\ºAÐk³AÐ|¼)Å ¼#´µDÍ ¾ µD´Ê>µ4¾k´J³´)¼#¾k´)¼°Ñ|ĵ̳´rÎVµDÍ Ì³´)¼°Ñ|ÄEµ 2CQ1(+"0JiHCiW"7"-3 y¬sP2 q wt<vT2.iW"!50!1.1. µ!.1W_2(¹V?!.132¹Q"!>0!>(+7<P-. «ÀuÁ'Á'ÁÀ ·´!µD¶ ·¤³´)¼)º·¤³dÅ Ò º·ÓjµD¶kµD·n¹ µ&º· Ò ºÌXÏnÄ´!µD¶Ô7¼#¾k¼°º·Õ°À ÒÒ ÔXÖ ×AØ|Ù;&0 ; x sr®P ¿ x!¬!(3¶6 %>.1(=|(_È!-.%y;¬!¬Nw?2 ; .%$,"S">(;79T1(;7E"!`2 jAX5.;N++-0;1^5(T1! "!"!N fEB. '&;LF 5/$,; -8!! >++ q ~tXmX2.¶\50 &C+0¹V2U nR.!01/³X2³\ &.(KC2|P-.&.&C"!JN;7E"! q r t_<2(jÔ2C|P'-1.iA2(j)"!.0|R20| ?(a0_<20zT-&9P È ²O³´)´!µD¶ ·ÉV·¤³dÅ Ú^¾k¼#¾4³·nÊÛR³d¹ μ#·µ À ·W´!µ|Å#Å ¼8»>µD·¤¹ µE0~~P±y~²Eo+y!N¬j¿0ys¸PV~ ¸¸!¸(2 018ë<2 32R¶\"??FY>0!;1/ =! O J5.T01 " $c5.!+8N;!2 q xt<º2³Q7E"07E"NS!018_2ç`&.&!32(_Ô>0?; 8$: 'I6"!K ²¶\ºj¹ µ µuʼr·»¾&º\Ó ÀuÁ'ÁÁ Ò º·jÓjµD¶uµD·¤¹ µGº· Ò º^ÌÏnÄ´!µD¶«ÔF¼r¾ ¼)º·³·¤ÊG²³´)´!µD¶D· ¸Oµu¹ ºk»·W¼#´)¼°º·R|(!?9Xv[ >0 (0|_<3y¬¬!s(2 $,"S!?77"!??S795.!79h; "32C q s t<º2³Q7E"07E"NS!018_2ç`&.&!32(_Ô-.($P%?I}"!$ «²E¶uºj¹ µkµuʼ#·>»¾GºÓÀuÁ'Á'ÁÀ ·´!µD¶ ·¤³´)¼)º·¤³dÅ Ò º·ÓjµD¶kµD·n¹ µ&º·P²³´)´!µD¶D·«¸Vµu¹kºk»·¼r´)¼°º·SÕ°À Ò ²¸Ö ÜAÜ Ù !!=*+, +?2 v[ 7".(C|(&0`0~!¸¸!¸(2 q ¬ tX¶L2³Q9!W 01/ºX2v6"-!!(2T&.!1P'7" "! 1P,>-".[$,"[!!=ao6¶6 HI6<1("*>C9pH ÉOÊÝ^³·¤¹ µD¾0¼#·*Ô7¼#¾kÄW³dÅnÀ ·jÓº¶ Ì3³^´)¼°º·«ÞÚ^¾k´!µDÌG¾|ß²E¶uºj¹®ß àEÖ ´rÎ À ·W´®Ö Å Ò º·jÓjß2á0ÔÀ ÞâÉVV½ 0~!¸!¸¸(2
© Copyright 2026 Paperzz