On the Choice of Similarity Measures for Image Retrieval by Example

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!72€fB(&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$,"ƒ
B(&C'?9V&C"!?="!$\?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$:"!d!"-..1(Fa-5^1
9
>0X‡'ˆ‰2TŠT-0
++?R
!"-01(Fa-(5!!J1.9!>0!6Q7"!'&C"N;1"!$R‹=Œ\7E;fI[5
$:"
+";I[.'I6"*&.!!'Eo
1P+nR?SP-.
V7E"??926€Q75^7ES7"?9.L‹<Q
;0"
5/"
9
JP-.X>C<"!$S!X
5/1.
9
>0!8*‹=Œ‹
 2)b0"!
¼
»C¼0½ ¾ ±›Ž(¿9À²f§kà ÁO ±›Ž 8Æ
,Ä`Å
?*l?-.XŽL"?"K<$:"5.J1
9
>0!NI6S;7ED5.J‹<`7E"N;
;2fj585;7"!+"WJ&C$:7E;5=7E"NL!!;
+`$,"5.7E["%IJ575H5.=l?-Ž%>C"!.N2
¼ ¾
À  ²
±y²
IJ5.SŽ§Ç±›Ž  ²`V5.Jl?-.X;7E"D
01*ÀL§Ç±YÀ  ²Oc5.6$:
-.
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 ±›Ž(¿À
²f§ÉNÊRË!ÌPÍ Î(ÏÑÐ
2VºT"
,7E650
VIJ5*Ó@§ÔyJ
01ÕAÖ}y!
5.S*+!+''-.
» Å ½ ¾ ±›Ž(¿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’,“C”O•;–]—0˜%‘O–P™k’›š@œ.“0–('ž•;ŸRš ŸR”`•8¡Oœ¢œ0£`œ0–‡'ˆ‰
¤¥9¢’:
žYŸC•
š–(¡e£3¦{‹=Œ8§dr
‚g¨©,œ0;–(™*’,¢ª«‹
0.36
§­¬G’:šœ.“0–(®f–(•

0.34
¨©,œ0;¤
0.32
0
0.1
0.2
0.3
¯LnR?\!"-..1(Fa-5*1.
9
>0!;Q5.S>C'-0;1%$,"Q"-.QBPF
&C'P9"0o
0.4
0.5
α
0.6
0.7
0.8
0.9
1
‘J’,“R”O•;–#Ø3˜)ÓOÙ¡c’,œ.“0•œ0šA™*’,¢ª{¨N©,œ.;;’:¨œ0©×\Å
Ú=×QÛZœ0ÜO¡{×QÝ
¡c’:¢œCÜO¨–(¤ÞÓOÙ¡c’,œ“C•;œCšß®c©,Ÿ0¢;¢ª`–àœPáC–(•;œ.“0–«®c•;–(¨N’:;’,ŸCÜ
|7E.S1.9!>.L‡'ˆ
°
áC–(•”O%Ó\ÚD”`;’›Ü`“M;’›š’:©,œ0•’,¢9¦âš–Pœ.”O•;–
‰ Œ
oV\7".9Q"!$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"
$× Û
× Å
7"
"!VBP-.\¯
9!>.2Q¶\"
"f
!>+++<%7E
|(5.!&C=¯=9!>.‡'ˆ
°
'&"
;%5.
585.!â× Û
'&."N5;-(+98>?
}EB(Gw!å/2
1.9!>.;2
‰ oQJ[$:"'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‡'ˆT·o=7E"?9
0x/7E;[y¸¸8!!;
&CS7E<±Yx!¸!¸X!!;²E2Q465L1
9
>0[-018"(+8$,"
°
5./× Ý
|P*+![;-(+9[I\"!>0N18"HN3"!5.["-01PFY-(5
‰ Œ2
¬X!!;[&CS7E<±Ywx
r%
;²E2
°
Õ}7!M'&."N
;-(9'>?G‚?åæ;N
Z&;7E"`2iW"!"NJ5.W-.Z"!$
7EL"!$D¬
;J;!79532QYJ,[BP!7E;18$,"µv6"P1.h
6J'&C"9
?[50!/Z‡'ˆ
‰ ¤
!!8!
S„;-(92b0"!X09
07\X5.";IJG"
4OBP-¯
9!>.%‡'ˆT´9oJY!"-.&.x
¬N~*
;JP"/s!s
°
»R¼0½ ¾ ÚVŸCÜg‡'ˆ
"@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$,"[Õ@§Ôy(Õ@§â~%!.1/Õ@§âé=ê#2D4O;9[50;NT>C
¶\"EC¯=
9
>0!T‡'ˆSŒ
oVYQ7"?9
.6xPyS79,!;¸T!!;
7"
"!X5("
W2/465.'"!>9
;1A7-N;&;?H
BP%-
&C$,"';1W"!^‡'ˆ
‰ 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‡'ˆ
1.9!>.2
‰ Œ
0‡'ˆ
´
!.1W‡'ˆLŒC
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&.72Zbc2VZ5";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$,;
-;JëSzTv7"
"!
€\1(mT?9
"âUS,"!
ð±›"!5C²^q 
t$,"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
Š-.
++??-0P
\($:""Xc&;?;1<>?S$:
-.
N;79""!13"[.7;!6&C;1<
01T"S;NQ''"?2OzLN
Z$:;-.H;7E"*lP-)ŽPDI6W1(…0'5./"NS"!$=@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
TŽ
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+$JÀ*
01
0.34
0
0.1
0.2
0.3
0.4
0.5
α
0.6
0.7
0.8
0.9
‘J’,“C”O•;–'ñ3˜[Ó`Ù¡c’,œ“C•;œCšASžŸC•S¡c’òQ–(•;–.ÜC¢[žY–(œ¢”O•;–X;®Oœ0¨–([œCÜ`¡
Õ]§y¤)óH–(¡Ô•;–(®c•;–(–.ÜC¢œ¢;’,ŸRÜOWœ.•;–R˜WôT¡O“.–]õ'•’,–ÜC¢œ.¢’,ŸRÜ
1
Ž!<Z5.!'X7ET"!T"!;2L$f5.P-.%>C["!$\!'&;J
!!H"-.!5`V5(,l?-.;"!]7!M>C/!.I6;1M>?M9,7
;.(2fŠT($:"-0+??'5T7"!?BP6"!$3!!L!
aPI6
"(+H5.TI\"'!'&(oQÀ
018ŽP2
öH’:¢Ÿ0“C•;œ0šø÷–PŸRªVùHžYŸC•)ª`œ.®V–RڑOŸR”O•’,–(•¡O–(;¨N•’:®O¢ŸC•AžYŸC•
¢–(ú3¢”O•;–CÚ/ûü8ýþ¨!ŸC©,ŸC•gœ0ÜO¡µÿQœ.®c©,œ0¨’,œCܵ™X–(’,“RªC¢–(¡ûü8ý
1000
d
11
d
¨!ŸC©,ŸC•HªO’:¢Ÿ0“0•œ0šA¤
12
900
800
9
07!2=v\Z-.(.'5.&0
!'LÓ\RI6X!%!>"/'&."N
5[;N
J&.;79,"!*-.&"=Nå$,"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
`˜GôLú3œCšA®c©–gŸ0ž'’:ÜR¢;•;œ(Ù¡c’:¢œ0ÜO¨– ÅÅ œCÜO¡e’›ÜC¢–(•;Ù
ÅÛ ¡c’:¢•
’,£V”`¢;’,ŸCÜOžYŸC•âûü8ý ž–Pœ.¢;”O•;–eáC–(¨¢ŸC•
ž•ŸCšþ¢;ª`–¢9™Ÿ ¨N©,œ0;–(¡c’:;®O©,œP¦C–¡’:Üâ‘J’,“`¤g
÷¨!œ0¢;©,–œCÜO¡
”cÜO–P¢*ž•;ŸRš
¢;ª`–
ŸC•;–(©6¡Oœ.¢œ0£Oœ.–0ù;¤
‘J’,“R”O•;–
¡c’:¢œCÜO¨–
b0"!'!KN8"!$'&(+,79?fI6W-&.&C"H50*"(+MI6"1(+nRP
JÅ8
01[ÛH!Z;!
+!>(WG5.Z1
9!>.Z
01 50
Å 2ã465.1.
9
>0!W
"g-.'1#"-01PF
-532Hj5 À/
"^>C"." Å O5./*
)';!-.
§C ±›Ž(¿À
²50!ZG&">0
>+++}1(>.-("â$:-..7E"e±›&R1($9²
ÅÅ ± ²E2j5}À>C"N8" Û T 1(+nR?8&R1($ ÅÛ ± ²'
">(9
.1}$:"! Z5";IJÔbc2L‚g"!ÔG;
I\"#7E!;
1.9!>.2H465.1P,9
07 §C
±›Ž(¿9À²T>CI6)ŽW
01)À*<
+F
I[*&C"N+N^
01M5(-.%&R1($:
ÅÅH!.1 ÅÛW
Z1…..;1 "(+
7E
ŽM>C"N8"
"q ¸(¿Eé=ê)ta2VŠ-.
++?(!
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$J5*
/!
JƒX&C$,;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.!
"ZŽPc%‹<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.! ´
"^Ž(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"!$=!!?'!!;%
I[+5W;&C;79S"*¸(2D.1;1RPI6=50;N!o
±aN²
6O±)(R²f§ ~y 9: É?± ( é<~ ; ²É?± Æ (~ é=; ²>;
% 2f465P-0A@O§Ž Æ À;`5.Q=7?;1'
01
Æ À; Æ W
465Z
BP*h;
"]"!$<;N!Z&;7E"g'-01]]5.8$:"!+F
";I[./"87E"'&0
=I6"/1PnR?=*+,
+Z';!-.;J"Z5
'$:;-.<&.72
?;N`§Ž
7"!P
?>@  §Ž 
"H
% 2
I[+5
(''7=&R1($DIJ5.ÀXLZ5.*
'%79,!T50
@ŽP2XmTZ5.
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§**±)(,+ %±›Ž²²`>C\5.Q&R1($."!$.$,;
-
;7E"-(âK(";I[M5.7EH"
$5Al?-#ŽP
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"
$65.
?
F1(9!.7
ÅÅ
2cŠJ5\7E?
?+*`5."!e±a!015P-0
5 !07EL$:"! 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"!/$,"+?VI\H!-.''Ž; Æ Ž!.1MÀ; Æ À;T!'+1)I[5
!.1)À  !*5*7"!'&C".P9L"!$[Ž
87?;1@&R1($6É?RIJ5'Ž 
01À%;&C;7ENE?2
4(O2
!!
>
(A1"!;L5%B(&C;799
"@"!$68!.1"!
LK3˜NMZ”cš^£V–•ÇŸ.ž]’:šœ.“0–(Ç•;–P¢;•’,–PáC–(¡„ž•;ŸRš ¢ª3–
”O–(¡eœ.Aœ
‘J’,“R”O•;–
¡Oœ¢œ0£Oœ.–œ0@œž”cÜO¨¢’,ŸRÜ«Ÿ0ž¢ª3–¡c’:¢œ0ÜO¨–
¢ªO•;–(ª`ŸC©,¡Q¤
O
465.<I\"&R1($›
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*+!+@';!-.;"
$65.*7"'&C"!.?92'465P-.`5
0C±›Ž(¿9À²67
W>CIJ+Z!o
1P9!07E
C±›Ž(¿À
²f§
6 )(
%
Ä
Ã
5
Á
,Ä`Å
±›Ž  Æ
À  ²
7(
%
ç` O± 0²C>Cf5.f&R1($("!$P5D
01("}
,
>; CO§Ž; Æ À Æ W
 § Ž  Æ À  2Q|?.7SŽ  Æ Ž  !.18À  Æ À  50;NL!'S&R1($`ÉN
I[+5
81
6O±)(CY²c\=(''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%Wo
±)!
@ 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';!%"!$RPF
Ä
Û CC
Å
C ± Æ @(²J§ Æ % C ű)Û @(§²E2= j#ÅÛ +±)@(5^² T5.X‹h· 5 ±)"/@(²;"é 1ÛEU B(Ä`&0ÁÅ 0 % " 35 `±)5@(X²O!!.7+ F
5
07\"!$(5.Q5 ?F1(9
07D,F@?ÅÛVT‹X·.± 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" ƒ
{±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."ƒ±Y~²E(I65W1(;1-.7o
bT_%± % Å~dÛ c Æ @ Å% Å ÅÅ ²
±›‚N²
b."㱛‚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($:oOëLPE!5`;jA>.-+a!z!'P
z!-.F
,
`.ŠT+$,"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˜¥šœ“0–
‘J’,“R”O•;–
–Pú`œ0šA®c©,–(Wž•ŸCš
¢ªO•;–P–]¨©,œ0;–(˜¨œ0Ù
MHŸ0¢;’,¨–)¢ª`œ¢¢ª`–@áœ.•
’œ0£c’:©,’,¢E¦}’›Ü
¢ª`–(–¢ª`•–P–}¨N©,œ.;–()ŸáC–(•g—mnÔ
m ’›šœ.“.–M’,
¢;©,–CÚ\”cÜO–P¢'œCÜ`¡â“0•œ.;¤
¨ŸC©ŸC•Gž•;ŸRš
•;œ.¢ª3–•/¡c’òQ–(•;–.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(,"!
ƒ&.;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
ŠT.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*$›!7EX5.
X7"
"!
15
60
castle class
60
25
10
40
40
5
20
20
20
0
0.2
0.4
0
0.6
60
0
0.05
0.1
0.15
0
100
100
50
50
0
0.1
0.2
0.3
# of components
0
40
20
0
0
0.02
0.04
0
0.06
100
0
0.1
0.2
0.3
0
60
60
40
40
20
20
0
0.05
0.1
1−Poisson
2−exponential
3−uniform
4−Rayleigh
5−Gauss
6−lognormal
7−gamma
8−Weibull
15
10
0.15
5
50
0
0
0.05
0.1
0
0.15
0
0.1
0.2
0.3
0
0
0.01
0.02
0
pR˜AôLú3œCšA®O©,–(^Ÿ.ž%–šA®c’:•’:¨!œ0©®D¡`ž^Ÿ0ž'ûü/ý힖Pœ(Ù
‘J’,“C”O•;–
¢;”O•;–WáC–(¨¢ŸC•%ž•;ŸRš
¢ª`–Z¨!œ0¢;©,–W¨N©,œ0;¤ôLœ.¨ª
2
3
4
5
6
7
8
6
7
8
grass class
”O£`Ù®O©,Ÿ0¢*¡O’:Ù
®O©,œP¦O=¢ª`–WÜ`”Oš@£V–(•Ÿ.ž6®c’,ú3–(©:<™'’,¢ª)¢ª`–8œCš@–H¨Ÿ0©,ŸC•NÚcœ.<œ
rq
30
®V–(•¨–ÜR¢œ.“0–^Ÿ0žS¢ª`–^’›š@œ.“0–@;’ N–CÚVáC–(•”O%¢;ª`–^¨ŸC©,Ÿ0•?¤
25
1−Poisson
2−exponential
3−uniform
4−Rayleigh
5−Gauss
6−lognormal
7−gamma
8−Weibull
±›"â;N!@'"W5.!âx
¸Nåï"!$=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.Y2OŠ-.
++?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
?‚R˜Tû'–(”O©,¢SŸ0žV¢ª3–ƒHŸC©:šŸ0“0ŸC•;Ÿ(á3م„OšA’:•
Ü`Ÿ(ᢖ¢JŸRÜ
4%† ª3–^Ü`”Oš@£V–(•%Ÿ0žS¨ŸRš®fŸÙ
Ü`–ÜC¢;'Ü`Ÿ0¢*•–ˆ
‡ –(¨¢–(¡#’:'ª`Ÿ(™Ü áC–•”OX¢ª`–^®f¡OžTÜ`œCš–C¤
‘J’,“R”O•;–
¢ª`–^¨!œ0¢;©,–Zœ0ÜO¡]“0•œ.;*¨N©,œ.;–(¤
bc(2\s^&.?9
57
01!7E;28UL"!!<5"Ie5.%(-%>C
"
$L$,;
-W7"!'&C"?950*A…%75]&R1P$L'"P1(a2AY%
79!O5.
c€fB(&C"?,?&R1($(&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
( 2ƒ´ 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
+!+
$:"X5.H>C*"D"A× ¾
¾
± (²D§
2
';!-.;DIJ5.8I6H;!75
1(9
07;a2 =Ó§Ôy2Q465P-0(I6=5.;N
5
)@ €+ @‰+
j#+5)B
'&;OI\*+-.
5.";I5.'>C;*+!+';F
-.'I[+5
× ¾
7
)>C/1N1)1&C01(W"!$[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$ Š
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;1Œ 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
Œ 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.
0Œ ¾ ±)(
@ ²LTP
!?
-01(<7
!!
"."
$O0
@ 2/465
+"IS-0T"Z'&(+$5
$,"!+";I[^1!
".>?^-*/5.
5%!!!.7*"
$H
@ 0.54
precision
Œ ¾ )± @(²f§
465@&C;1
5.!&C@"!$=5@&R1P$
y!2
465
;!75Ç$:"!Z5.M>C;@*+!+';-)I[+5{× ¾
0.535
0.53
0
<Œ 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
—3˜4
ŸRšA®`œ0•’:ŸRÜG£f–P¢9™X–P–Ü)¢ª`–PŸC•;–P¢;’:¨œ.©6œCÜO¡G;’›š@Ù
‘J’,“R”O•;–
”O©,œ¢–(¡#œPáC–•;œ“0–^®c•;–(¨N’:;’,ŸRÜ⒛Üg¢ª3–)üœC”O;;’,œ0ܨœ0–^™ª`–Ü
6.1
Gaussian
465/'&(;<'"P1D"^-.'X50
<5‹
Õ]áœ.•
’–¤
·
7"!'&C"?9
±›Ž  ²T"
$65.%$,;
-'N;7E"!<ŽH
/z!-0
)!.1"ƒ!!
>;
$,"!+";I[o
YR±›Ž+ ŽO²V§ c ~^7Ž É Ê $ ‘ $ $
±y¸N²
I[+5<';
=h"S!.1=9!01!1<1P"!4D
Ž 23j#+5=5.f&.?"-.
"!9"!0I6=50;NÉP±›Ž²f§R
Y ±›ŽN²E2
Û
465J7"'&C"!.?9c>C<z!-.,
*I[+5*
!07EŽ
N=7"'&C"
F
?9[1(+nR.70*
@ L"z!-.,
WI[+5W
!07E~^Ž 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
Œ 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
<Ž{§k‚2gbc2\¬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
–Ž
9L';!Z
˜ ±›ŽW+ ŽO²f§ Ž y
É Ê
‘ ~ Ð  RŽf2=T,T'&("
!.1W9=9
01!1^1?
"!
&."N50*5.81(+nR078"!$TI6"@B(&C"?,J!.1"æ
+F
&Ž],XZçc!&(7@±›"%1"->/B(&C".P:²
!>(;X"
$T&.!!'E
!.1"!
,
>I[+5W&R1($o
™ ±)@‰+ ŽO²f§ ~^y Ž É Ê–š ‘›jš
Û
9Q';!'6h"%!01'+96
!07E=~^Ž
2D465.L'"'?Q"!$O"1
’H"
$ *@ $:"!+";I[.8%çc
&7=&R1P$co
Û
+ @‰+ “ §{± @ ~ ²•”$ \w ±2’ égy²
465.$:"!0+9J&C;1/S
$S'&(+…07
"!0o
Û
Œ ¾ ±a× •t ’ ™ tœÉ
²V§ w\±Y~Õ8égw y;²±:Õ8Æ égw yÛ ² ±:Õ/é#y²
IJ575HJ1…..;1$:"[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
,@
ž„y!
Œ ¾ ±a× •t ’ ™ tœÉ
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 –
ŸRšA®Oœ.•’:ŸRÜW£V–P¢E™–P–.Ü¢ª`–PŸC•;–P¢;’:¨œ.©CœCÜO¡W;’:š@Ù
1
1.5
2
2.5
‘J’,“C”O•;–/— 3˜
‘J’,“R”O•;–)—0—.˜=ýX–(¢<Õ
”`©,œ.¢–(¡
žYœCšA’:©¦
™'ª`–Ü
œPáC–(•;œ.“0–µ®c•;–(¨N’:;’ŸRÜÜí¢ª`–­ôLú`®VŸRÜ`–ÜC¢;’,œ0©M¨!œ0–
3.5
1/b
4
4.5
Å
œ0œZž”cÜ`¨¢;’,ŸRÜGŸ0ž
QB±)@‰+ À¿uv;²E¤
Õ]áœ.•
’–¤
3
x
5
5.5
6
žYŸC•%œ@®f¡OžS’›ÜG¢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.
Œ ¾ ± h BJt£¤Y ™ É
²V§
>CEI6*5.J&C";I6f01J5.[EB&C"!.?
*5.J&R1($3
01X5
"!&
`!
-."
$VÕVp
n6
B±)@‰+ À¿uv;²f§ ^~ vDw\±)v;²Àjx É Ê–š ›j} š
y
’
'"!'?["!$c"1 /,o
+ @‰+ “
§âÀ
@ Û ² ”$
2’
±ar
Ÿ
±: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
Œ 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;
"<"
$
Œ¾
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+
Ÿ
,"!=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"
$`bc(2(~P2
6.4
Uniform Å
Abc2Dyy!OIJ5
x
B±)@‰+ À¿kv²L>CF
!"?;=."!=(…0+?CY2 OIJ5.
0.5
1
1.5
2
β
2.5
3.5
4
<ŸRšA®Oœ.•
’,ŸRÜÇ£V–(¢9™–(–Üâ®c•;–(¡c’:¨¢–(¡Çœ0ÜO¡ÔŸC£`Ù
‘J’,“R”O•;–—(Ø3˜
–(•;áC–¡œ(áC–(•;œ.“.–®c•;–¨’:;’,ŸRÜM’›ÜA¢ª3–W”cÜ`’,žŸ0•!šï¨œ.–™ª`–Ü@Õ
á(œ0•’,–(¤
_L"!5T'3=5";IJbc(2Dy;~P`5.%&;1(7E1@
01@*F
-;1#;N
^&.;79,"!0/!ZN]7E"^"A;75#"!5'$:"!
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"!$SH-+$:"!ƒ!01("ƒ!!+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"*'&(+$85<!.
+,I6<!-.'50
Û
ÕZQ…B(;1X"X~P?a2 ± (²f§
2f01(;1RN5.J€D-07E+1;
/1(9!.7
5
)@ *@
'&(;?A'&(+…07
".%"!$S5.H&C;1R2Mbc;Q5
&C;1H>C;7"!';o
ŒÛ±)@(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
Œ 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"#"
$<"!$$,;
-
predicted
simulated
7E"'&C"?96Ž*
01WÀo
Œ Û ±)@(²D§
¦
$$
precision
y
‰ Ò
ÏÑÐÊ
‰Ò
ÏÑÐÊ
y
Æ
|?07Ž !
01}À5.;N@5A
'A&R1P$%ÉNLI6A5.;N ±›Ž
Û
Û
Û Û
~ Ž
0
01/5P-.o
Æ ~ Ž ±›Ž Æ À² J§â~ Ž
Æ s Ž ŽJé r Ž
\¨ •¨
¡
y
Œ Û ±›Ž²D§ ¦
"
$
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("!]"
$=|P;7E"]ZIJ5.
§
¼
¼
±›Ž
01^ÀX
%!-.';1
Æ ÀN."57<IJ5. /§Ž
Æ À
&C"+²E.I\<1;1(-07T5T$:"
+";I[.;79….;1H&;7E"`o
@
Ž
h Û ±›Ž²f§ f
‹·
~ Ž
Û
%
Û
 Ó6±±Y~Ó
y² Ž
Æ
c ~g ލ
~
¼
Û ¼
Û
Ê
é)Ó Ž
¡
‚ Ž
Æ
¼
¼
Ž
¼
Ê
Å Û
±›Ó
Æ
Û
Û ¼
éG Ž
y;² Ž
Æ
Û
Ê
Û ¼
~P± Ž
Æ
¼
0.2
0.4
0.6
0.8
1
α
1.2
1.4
1.6
1.8
2
<ŸRšA®Oœ.•
’,ŸRÜÇ£V–(¢9™–(–Üâ®c•;–(¡c’:¨¢–(¡Çœ0ÜO¡ÔŸC£`Ù
‘J’,“R”O•;–—(ñ3˜
–(•;áC–¡
™ª`–Ü
Ž
Ž
Æ
0
±y;~²
¼
¼ Û
²² Ž
²
Û
œPáC–(•;œ.“0–d®c•;–(¨N’:;’,ŸCÜÜ`–d–(ú`®VŸRÜ`–ÜC¢;’,œ0©G¨œ.–
Ó#áœ.•’,–('’›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
Œ¼
Û
Ó
±›Ž²D§
±±Y~Ó
Æ
s± Ž
Œ ¼
465A&C;1
¨¼
y² Ž
Æ
Û ¼
‚ Ž
Ê
Û
¡¼
Ž
éMÓ Ž
¼
¼
éM Ž
Ê
Å Û
Û ¼ Û
±›Ó
Æ
~(± Ž
Æ
¼
y² Ž
Æ
Û ¼
Ê
Ž
Æ
Û
¼
Ž
¼ Û
²
Û
²
Û
Ž
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$D7"-5=
²
."
'Z"?"P1
±yN²
….X>CI\G%-(,"G!.1M5"$:"!'
+JK?01
"!$c(P57T1
9!>.;2Q465=(P57T1
9!>.X-0\>C1EF
;1HZ-075ZXI6;850S5=';-="!$V5=%-;1W;?F
/P
,
?/I[+5â;&C;798")57
A"
$XŽP2
465^;!75g$,"5.W>C;/*+!+]';!-.HI[+5
3Œ ¼
lP-(PD"
BP*hE5.S&C;1
» ¼0½ Û
±›ŽN²VI[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$:;-.Q7"'&C"!.?9R5."!-1
°
jA>.-(O1(>.-("`o
ª ±›Ž+ À¿ut²f§ t À ^Ž y Ê
 }/{ ~ Ð  "!>9;1^>PW!&&+P'5.<&C";I6T$,-..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"!$V"!1'8
’ { o y
’
Ž “ §âÀ¤” Q
{ w ± t égy²
Å
&C;1W±y;²E?I6L1;1(-0765L&C;1%$:"!6Tj)E>-+0&R1P$3QT$:-..7EF
Œ 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"O‹X·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\PF€Q 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$,"„v6";IJ
ŠLN+?<Š=|_<[$:"!!
-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•·P½‹µD´)´!µD¶…¾`~~(±Yw!²Eo w!rj¿(w
sN~P
a2
~!¸¸Py2
!795(;\$:"!J5"!!*FY>0!;18!!<7E+…C7"`2
ÀuÁ'ÁÁÂW¶u³•·W¾D³A¹|´)¼°º•·W¾º•·PõDĶu³•ʼnÃ4µD´)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´rÎVˆÍµ º•¶D¼°µGÊ>µD¾Ïn¶\ºAÐk³AÐ|¼)Å ¼#´µDÍ ¾
µD´Ê>µ4¾k´J³•´)¼#¾k´)¼°Ñ|čµÌ³•´rÎVµDÍ Ì³•´)¼°Ñ|čEµ 2C€Q1(+"0JiHCiW"7"-3
y¬sP2
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•·ˆÓjµD¶kµD·n¹…µ&º•· Ò º•ÌXÏnÄ´!µD¶Ô7¼#¾k¼°º•·Õ°À ÒÒ ÔXÖ ×AØ|Ù;&0
;
x
sr®P
¿ x!¬!(3¶6
%>.1(Š=|(_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¿0ys¸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…µuʕ¼r·»•¾&º\Ó
ÀuÁ'ÁÁ Ò º•·jÓjµD¶uµD·¤¹…µGº•· Ò º^̖ÏnÄ´!µD¶«ÔF¼r¾…¼)º•·³•·¤ÊG²³•´)´!µD¶D·
¸Oµu¹…ºk»•·W¼#´)¼°º•·R|(!?9Xv[
>0
(0Š|_<3y¬¬!s(2
$,"S!?77"!??S795.!79h;
"32C
q s
t<º2³Q7E"07E"NS!018_2ç`&.&!32(_Ô-.($P%?I}"!$
«²E¶uºj¹…µkµuʕ¼#·>»•¾GºÓ–ÀuÁ'Á'ÁÀ…·´!µD¶…·¤³•´)¼)º•·¤³dÅ
Ò º•·ˆÓjµD¶kµD·n¹…µ&º•·P²³•´)´!µD¶D·«¸Vµu¹kºk»•·¼r´)¼°º•·SÕ°À Ò ²¸Ö ÜA܅Ù
!!=*+,
+?2
v[
7".(C|(&0`0~!¸¸!¸(2
q ¬
tX¶L2³Q9!W
01/ºX2v6"-!†!(2ŠT&.!1P'7"
"!
1P,>-".[$,"[!!=ao6¶6
HI6<1("*>C9pH
ÉOʕÝ^³•·¤¹…µD¾0¼#·*Ô7¼#¾kÄW³dÅnÀ…·jӈº•¶…Ì3³^´)¼°º•·«ÞÚ^¾k´!µDÌG¾|ߋ²E¶uºj¹®ß àEÖ ´rÎ
À…·W´®Ö Å Ò º•·jÓjß2á0ԉÀ…Þâ‰ÉVV½ 0~!¸!¸¸(2