A Markov Random Field Model and Method to Image Matching
7KH,QWHUQDWLRQDO$UDE-RXUQDORI,QIRUPDWLRQ7HFKQRORJ\9RO 1R1RYHPEHU
$0DUNRY5DQGRP)LHOG0RGHODQG0HWKRG WR,PDJH0DWFKLQJ 0RKDPPHG2XDOL+ROJHU/DQJHDQG.KHLUHGGLQH%RXD]]D /,7,2/DE8QLYHUVLW\RI2UDQ$OJHULD 5 '*URXS*HQHUDO'\QDPLFV&DQDGD&DQDGD 'HSDUWPHQWRI&RPSXWHU6FLHQFH7DLI8QLYHUVLW\.6$ 'HSDUWPHQWRI&RPSXWHU6FLHQFH8PP$O4XUD8QLYHUVLW\.6$ $EVWUDFW ,Q WKLV SDSHU WKH FRUUHVSRQGHQFH SUREOHP LV VROYHG E\ PLQLPL]LQJ DQ HQHUJ\ IXQFWLRQDO XVLQJ D VWRFKDVWLF DSSURDFK 2XU SURFHGXUH JHQHUDOO\ IROORZV *HPDQ DQG *HPDQ¶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
,QWURGXFWLRQ 'HQVH VWHUHR PDWFKLQJ DOORZV H[WUDFWLRQ RI GHSWK SK\VLFDOSURSHUWLHVIURPWZRLPDJHVRIWKHVDPHVFHQH 'HSWK SK\VLFDO SURSHUWLHV PD\ EH XVHG LQ DSSOLFDWLRQV VXFK DV URERW QDYLJDWLRQ REVWDFOH DYRLGDQFH SKRWRJUDPPHWU\ WHOHRSHUDWLRQ DQG PHDVXUHPHQW LQ VFDQQLQJHOHFWURQPLFURVFRS\WRQDPHDIHZ'HSWKLV LQIHUUHGIURPWZRRUPRUHYLHZVRIWKHVDPHVFHQH,I WKH SURMHFWLRQV RI WKH VDPH VFHQH SRLQW DUH NQRZQ WR FRUUHVSRQG WR HDFK RWKHU WKH KRUL]RQWDO GLVSDULW\ UHVSHFWLYHO\ YHUWLFDO GLVSDULW\ FDQ EH FRPSXWHG DV WKH GLIIHUHQFHRIDEVFLVVDVUHVSHFWLYHO\RUGLQDWHV2QFHWKH GLVSDULW\ PDS LV HVWDEOLVKHG E\ PDWFKLQJ WKH OHIW DQG ULJKWLPDJHRIWKHVFHQHGHSWKPD\EHFRPSXWHGXVLQJ WKH GLVSDULW\ PDSV WKH LQWULQVLF FDPHUDV¶ SDUDPHWHUV IRFDO GLVWDQFH SL[HO VL]H &&' JULG VL]H LPDJH FRRUGLQDWHV RI WKH FHQWHU RI SURMHFWLRQ DQG WKH H[WULQVLFFDPHUDV¶SDUDPHWHUV PDLQO\WKHFRPSXWDWLRQ RI WKH URWDWLRQ DQG WUDQVODWLRQ PDWULFHV EHWZHHQ WKH FDPHUDV &DPHUDV¶SDUDPHWHUVDUHGHWHUPLQHGWKURXJK DFDOLEUDWLRQSURFHGXUH>@ ,PDJH PDWFKLQJ UHOLHV RQ WKH FKRLFH RI PDWFKLQJ SULPLWLYHVDQGDPDWFKLQJDOJRULWKP3ULPLWLYHVPD\EH SRLQWV UHJLRQV RU FRQWRXUV 3ULPLWLYHV VKRXOG SRVVHVV IHDWXUHVWKDWPD\EHXVHGIRUPDWFKLQJ3RLQWVSRVVHVV WKHLQKHUHQWJUD\OHYHORUEULJKWQHVVDWWULEXWH%XWWKH\ PD\ DOVR EH FKDUDFWHUL]HG E\ IHDWXUHV OLNH /DSODFLDQ ]HUR FURVVLQJV JUDGLHQW ORFDO H[WUHPD RU HYHQ IDQF\ SKRWRPHWULF DWWULEXWHV VXFK DV WKH VSHFXODU UHIOHFWLRQ FRHIILFLHQW GLIIXVH UHIOHFWLRQ FRHIILFLHQW DQG WKH QRUPDO YHFWRU FRHIILFLHQW > @ 7KH PDLQ IHDWXUHV WKDWPD\EHXVHGZLWKUHJLRQVDUHWKHFHQWHURIPDVVRI
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
$0DUNRY5DQGRP)LHOG0RGHODQG0HWKRGWR,PDJH0DWFKLQJ
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¶V S\UDPLGV WR FUHDWH VPDOOHU YHUVLRQV RI WKH RULJLQDO LPDJHV 0DWFKLQJ LV XVXDOO\ HDVLHU DW ORZ UHVROXWLRQ DQG WKH FRPSXWHG GLVSDULW\ PDSV DUH SURSDJDWHG WR KLJKHU UHVROXWLRQV 3UHYLRXV ZRUNV DGGUHVVHG HQHUJ\ PLQLPL]DWLRQEDVHG GHQVH VWHUHR PDWFKLQJ DQG VHYHUDO PHWKRGV ZHUH SURSRVHG $PRQJ WKHVH ZH FLWH OHYHO VHW PHWKRGV >@ DQG PHDQ ILHOG
DQQHDOLQJ>@6WHUHRPDWFKLQJFDQ DOZD\VEHFDVWDVDSUREOHPRIDVVLJQLQJHDFKSL[HOD ODEHO 6XFK SL[HO ODEHOLQJ SUREOHPV DUH QDWXUDOO\ UHSUHVHQWHG LQ WHUPV RI HQHUJ\ PLQLPL]DWLRQ 7KLV IUDPHZRUN FDQ EH MXVWLILHG LQ WHUPV RI PD[LPXP D SULRUL RI D 0DUNRY UDQGRP ILHOG $ *DXVV0DUNRY UDQGRP ILHOG PRGHO FDQ EH XVHG WR FRPSXWH WKH RSWLPDO %D\HVLDQ HVWLPDWRU *OREDO RSWLPL]DWLRQ PHWKRGV GHILQH WKH PDWFKLQJ DV DQ HQHUJ\ RU D FRVW IXQFWLRQRIWKHGLVSDULW\ILHOG7KLVIXQFWLRQDOXVXDOO\ XVHVDFRUUHVSRQGHQFHWHUPDQGDUHJXODUL]DWLRQWHUP WRHQIRUFHWKHVSDWLDOFRKHUHQFHRIWKHGLVSDULW\ILHOG 7KH IRUP RI WKHVH WHUPV YDU\ IURP RQH DSSURDFK WR DQRWKHU DQG PDQ\ VROYHUV EDVHG RQ %D\HVLDQ LQWHUSUHWDWLRQ DQG 0DUNRY UDQGRP ILHOG KDYH EHHQ SURSRVHG > @ 7HFKQLTXHV IRU FRPSXWLQJ WKH RSWLPDO HVWLPDWRUUDQJHIURPJOREDOHQHUJ\PLQLPL]DWLRQ>@ WRPHDQILHOG>@ 6WHUHRPDWFKLQJLVDQLOOSRVHGSUREOHP>@ LWGRHV QRWFRQIRUPWRWKH+DGDPDUGPDWKHPDWLFDOSDUDGLJP IRUZHOOSRVHGQHVV ZKLFKVROXWLRQLVKLGGHQE\ORFDO PLQLPD DQG ZKHUH WKH QRWLRQ RI JUDGLHQW GRHV QRW H[LVW7KLVZRUNDLPVDWLPSURYLQJUHVXOWVE\DGGLQJD JOREDO DVSHFW WR WKH VWHUHR YLVLRQ SUREOHP WKH FRUUHODWLRQ KDYLQJ LQKHUHQWO\ D ORFDO DVSHFW DQG PDNLQJWKLVPRGXOHFRRSHUDWHZLWKRWKHUHDUO\YLVLRQ PRGXOHV SRVVLEOH )RU LQVWDQFH VKDSH IURP VKDGLQJ DQG SKRWRPHWULF VWHUHR ,Q RUGHU WR DWWDLQ RXU REMHFWLYH ZH IRUPXODWH WKH SUREOHP DV D 0DUNRY UDQGRPILHOGDQGZHVROYHWKHIXQFWLRQDOPLQLPL]DWLRQ ZLWKLQ D VWRFKDVWLF IUDPHZRUN :H DOVR SURSRVH D UDQGRPWUDQVLWLRQJHQHUDWRUWKDWLVFRPSDWLEOHZLWKDOO WKH VWHUHR FRQVWUDLQWV DV ZHOO DV D GLVSDULW\ YDOLGLW\ FULWHULRQ WKDW YHULILHV WKH V\PPHWULF SURSHUW\ RI GLVSDULW\ PDSVOHIW DQG ULJKW GLVSDULWLHV VKRXOG EH HTXDO ZLWK RSSRVLWH VLJQV 7KH SDSHU LV RUJDQL]HG DV IROORZV VHFWLRQ GHDOV ZLWK WKH LQWHUSUHWDWLRQ RI VWHUHR FRQVWUDLQWV LQ WKH FRQWH[W RI HQHUJ\ PLQLPL]DWLRQ DQG 0DUNRY UDQGRP ILHOGV ZKHUH ZH OD\ GRZQ WKH VWDWHV UDQGRP JHQHUDWRU WKH HQHUJ\ PLQLPL]DWLRQVROYHULVSUHVHQWHGLQVHFWLRQ ILQDOO\ VHFWLRQ GLVFXVVHV WKH H[SHULPHQWDO SURWRFRO DQG UHVXOWVLQERWKV\QWKHWLFDQGUHDOLPDJHU\
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
7KH,QWHUQDWLRQDO$UDE-RXUQDORI,QIRUPDWLRQ7HFKQRORJ\9RO 1R1RYHPEHU
[ \ ^ Q` GHQRWH FROXPQV DQG OLQHV UHVSHFWLYHO\ DQG , O DQG , U EHLQJWKHOHIWKDQGDQGULJKWKDQGVLGH LPDJHV7ZRFDPHUDVDQGREVHUYHWKHVDPHVFHQHKDYH D FRPPRQ ILHOG RI YLVLRQ $ SRLQW LQ WKH VFHQH LV SURMHFWHGRQWKHWZRLPDJHVLQWZRSRLQWVZKLFKKDYH GLIIHUHQWFRRUGLQDWHVGXHWRWKHGLIIHUHQWSRLQWVRIYLHZ RI WKH FDPHUDV :H H[SUHVV WKLV VKLIWLQJ E\ KRUL]RQWDO DQG YHUWLFDO GLVSDULWLHV LQ WKH WZR GLUHFWLRQV OHIW ZLWK UHVSHFW WR ULJKW DQG ULJKW ZLWK UHVSHFW WR OHIW G[ D [ \ [E [ D DQG G\ D [ \ \ E \ D ZKHUH
D E ^ O U U O ` 7KH WZR FDPHUDV GR QRW REVHUYH H[DFWO\ WKH VDPH SK\VLFDO SRLQWV LQ WKH VFHQH EHFDXVHVRPHSRLQWVFDQEHRXWRIWKHFRPPRQILHOGRI YLVLRQ RU KLGGHQ E\ REMHFWV $ SRLQW REVHUYHG E\ D VLQJOHFDPHUDLVGHFODUHGDVDQRFFOXVLRQLQWKHLPDJH ZKHUH LW DSSHDUV 2FFOXVLRQV DUH QRWHG 2O [\ DQG 2U [ \ ^` ZKHUH VWDQGV IRU DQ RFFOXVLRQ 3RLQWV WKDW DUH VHHQ E\ ERWK FDPHUDV FDQ EH PDWFKHG 'LVSDULWLHV FDQ EH FDOFXODWHG E\ WKLV SRLQW PDWFKLQJ 7KH GLVSDULWLHV D GHSWK FDQ HDVLO\ EH FRPSXWHG E\ WULDQJXODWLRQ XVLQJ WKH FDPHUDV DQG WKH VWHUHR ULJ SDUDPHWHUV
5HVHPEODQFH&RQVWUDLQW 7KLVFRQVWUDLQWDOORZVWKHPDWFKLQJRIWZRSRLQWVRQO\ LI WKH\ KDYH WKH VDPH JUD\ OHYHO ,Q WKH FDVH RI ODPEHUWLDQ VXUIDFHV D SRLQW LQ WKH VFHQH KDV WKH VDPH JUD\OHYHOLQERWKLPDJHV$SRLQWLVDFRUQHURIDSL[HO IRUZKLFKZHDWWULEXWHWKHDYHUDJHRIWKHJUD\OHYHOVRI LWVIRXUDGMDFHQWQHLJKERUV $ [ \
¦ ¦ , [ N \ O N O
:H DOVR FRQVLGHU XVLQJ UHGXQGDQW LQIRUPDWLRQ RQ WKH VFHQH E\ FKDQJLQJ WKH OLJKWLQJ FRQGLWLRQV (DFK OLJKWLQJFRQGLWLRQSURYLGHVDVWHUHRLPDJHSDLU:LWKLQ WKHVDPHVWHUHRSDLUFRUUHVSRQGLQJSRLQWVVKRXOGKDYH VLPLODUJUD\OHYHOYDOXHV:HH[SUHVVWKLVFRQVWUDLQWE\ WKH VTXDUH RI WKH GLIIHUHQFH RI WKH JUD\ YDOXHV DVVRFLDWHG ZLWK WKH PDWFKLQJ FDQGLGDWHV IRU HDFK OLJKWLQJFRQGLWLRQN $ N O [ \
$N
U
[ G[ O [ \ \ G\ O [ \
7KLV WHUP LV ZHLJKWHG ZLWK WKH WHUP UHSUHVHQWLQJ RFFOXVLRQVEHFDXVHLIWKHUHLVDQ\RFFOXVLRQWKHUHZLOO EH QR PDWFKLQJ 7KH HQHUJ\ DVVRFLDWHG ZLWK WKLV FRQVWUDLQWRYHUWKHZKROHLPDJHLV (
5
§ $O [ \ · ¨ ¸ ¦ ¦¨ § [ G[ O [ \ · ¸ U \ [¨$ ¨ ¸¸ ¨ ¨ \ G\ O [ \ ¸ ¸ ¹¹ © ©
2
O
[ \
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
&RQWLQXLW\&RQVWUDLQW :H FRQVLGHU WKH SK\VLFDO VXUIDFHV DV ORFDOO\ FRQWLQXRXV ,Q WKLV FDVH WKHLU (XFOLGHDQ SURMHFWLRQ LV FRQWLQXRXVDVZHOO7KHGLVSDULW\YDULHVDOLWWOHH[FHSW RQ WKH HGJHV 7KH UHDVRQ LV ZH FDQFHO WKH FRQWLQXLW\ FRQVWUDLQW DW WKH HGJHV EHFDXVH ZH FDQFHO WKH FRQVWUDLQW RQ RFFOXVLRQV ZKHUH QR PDWFKLQJ H[LVWV 7KLV FRQVWUDLQW LV H[SUHVVHG E\ WKH HQHUJ\ IXQFWLRQDO JLYHQ KHUHDIWHU +RUL]RQWDO DQG YHUWLFDO HGJHV DUH DQG F\ UHVSHFWLYHO\ GHQRWHG E\ F[ D D F [ [ \ F \ [ \ ^` ZKHUH VWDQGV IRU WKH SUHVHQFHRIDQHGJH D (&
D QD [ Q\ ¦ ¦ [ \ D QD [ Q\ ¦ ¦ [ \ D QD [ Q\ ¦ ¦ [ \ D QD [ Q\ ¦ ¦ [ \
'G[ KD [ \ F [D [ \ 2 D [ \ 2 D [ \ 'G[ YD [ \ F D\ [ \ 2 D [ \ 2 D [ \
'G\ KD [ \ F [D [ \ 2 D [ \ 2 D [ \ 'G\ YD [ \ F D\ [ \ 2 D [ \ 2 D [ \
2FFOXVLRQV&RXQWHUZHLJKW :LWK RFFOXVLRQV DOO RYHU WKH LPDJH WKH HQHUJ\ LV PLQLPDO QXOO EXWWKLVLVQRWDYLDEOHVROXWLRQ7KLVLV ZK\ZHDGGDFRXQWHUZHLJKWLQWKHHQHUJ\IXQFWLRQDO LQ RUGHU WR OLPLW WKH QXPEHU RI RFFOXVLRQV )RU RQH LPDJHWKLVHQHUJ\IXQFWLRQDOLV ( 2D
D ¦ ¦ 2 [ \ [ \
8QLTXHQHVV&RQVWUDLQW (YHU\ SRLQW FDQ RQO\ EH PDWFKHG ZLWK DW PRVW RQH SRLQW IURP WKH RWKHU LPDJH 7KLV FRQVWUDLQW ZDV LQWURGXFHG E\ 0DUU DQG LW LV VWULFWO\ YHULILHG LQ WKH FDVH RI WKH QRQWUDQVSDUHQW REMHFWV 7KLV FRQVWUDLQW VLPSOLILHV WKH FRPSXWDWLRQV DQG HQDEOHV WKH DSSOLFDWLRQ RI WKH YDOLGLW\ FULWHULRQ IRU D JLYHQ PDWFKLQJ$PDWFKLQJLVYDOLGLIERWKGLVSDULWLHV OHIW
$0DUNRY5DQGRP)LHOG0RGHODQG0HWKRGWR,PDJH0DWFKLQJ
WRULJKWDQGULJKWWROHIW HQDEOHXVWRUHDFKWKHSRLQWLQ WKHULJKWKDQGVLGHLPDJHIURPWKHSRLQWLQWKHOHIWKDQG VLGH LPDJH DQG JR EDFN WR WKH OHIW KDQG VLGH LPDJH LQLWLDO SRLQW 7KLV FRQVWUDLQW LV H[SUHVVHG LQ WKH HOHPHQWDU\ WUDQVLWLRQV +RZHYHU LQ FDVH RI IRUHVKRUWHQLQJ FRUUHVSRQGLQJ VXUIDFHV GR QRW H[KLELW WKH VDPH QXPEHU RI SL[HOV $V ZH DUH FRQVLGHULQJ D SRLQWEDVHG PDWFKLQJ DSSURDFK ZH ZLOO HQG XS ZLWK SL[HOV WKDW ZLOO QRW EH PDWFKHG DW DOO 7KH DOJRULWKP ZLOOIRUFHWKHVHSL[HOVWREHRFFOXGHG
(QHUJ\)XQFWLRQDO 7KH HQHUJ\ IXQFWLRQDO RI WKH VWHUHR PDWFKLQJ SUREOHP LV WKH ZHLJKWHG VXP RI WKH HQHUJ\ IXQFWLRQDOV GHULYHG IURPWKHVWHUHRPDWFKLQJFRQVWUDLQWV (
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
O U O U ȡ 5 ( 5 ȡ & ( & ( & ȡ 2 ( 2 ( 2
Selected camera
Epipolar line
Selected pixel corner
Selected element
Elementary transformations
(0)
11 00 00 0 11 11 01 01 01 0 00 11 00 11 0 0 1 0 0 00 11 00 1 11 01 1 00 1 01 1 01 1 1 0
(1A)
11 00 00 11 1 0 0 1 0 1 0 1 0 1 00 11 00 0 0 1 0 0 a11 00 11 00 1 11 01 1 00 1 01 1 01 1 1 0
b
1 0 0 1 00 11 0 1 00 11 00 11 00 11 0 1 0 00 0 1 00 11 00 11 00 11 01 1 011 1 00 11 0 1 00 11 00 11 00 11
11 00 0 1 1 0 0 1 0 1 0 1 0 1 00 11 0 1 0 0 1 0 0 a 00 11 01 1 01 1 00 1 01 1 01 1 1 0
b
1 0 0 1 00 11 00 11 00 11 00 11 00 11 0 1 0 00 11 00 11 00 11 00 11 00 11 01 1 0 1 00 11 00 11 00 11 00 11 00 11
(1B)
11 00 00 1 01 01 01 0 a11 00 11 00 1 11 01 01 01 0
b
11 0 011 00 0 1 00 11 00 11 00 11 01 1 011 00 0 1 00 11 00 11 00 11
11 00 01 1 01 01 01 0 a 00 11 01 1 01 01 01 0
b
11 0 0 00 11 00 11 00 11 00 11 00 11 01 1 0 00 11 00 11 00 11 00 11 00 11
(2A)
11 00 00 1 0 0 0 0 a11 00 11 00 0 11 01 1 01 1 11 0 01 1 0 1
b
1 0 0 0 00 11 0 1 00 00 11 01 1 01 1 0 1 00 11 011 1 00 11 00 11
11 00 0 1 1 0 0 0 0 a 00 11 00 1 01 1 01 1 11 0 01 1 0 1
b
1 0 0 00 11 0 1 00 11 00 11 00 11 01 1 0 1 00 11 0 1 00 11 00 11 00 11
(2B)
11 00 00 11 1 0 0 1 0 1 0 1 0 1 00 11 00 0 0 1 0 0 a11 00 11 00 1 11 01 1 00 1 01 1 01 1 1 0
b
1 0 0 1 00 11 0 1 00 11 00 11 0 1 0 00 0 1 00 00 11 01 1 011 1 00 11 011 1 00 11 00 11
11 00 0 1 1 0 0 1 0 1 0 1 0 1 00 11 0 1 0 0 1 0 0 a 00 11 01 1 01 1 00 1 01 1 01 1 1 0
b
1 0 0 1 00 11 00 11 00 11 00 11 0 1 0 00 11 00 11 00 11 00 11 01 1 0 1 00 11 00 11 00 11 00 11
(2C)
11 00 00 11 0 0 0 0 00 11 00 1 01 1 01 1 01 1 0 1 a11 00 11 00 1 11 01 01 01 0
b
1 0 0 00 0 1 00 00 11 01 1 011 1 00 11 011 1 00 11 00 11 01 1 011 00 011 1 00 00 11
11 00 0 1 0 0 0 0 00 11 01 1 01 1 01 1 01 1 0 1 a 00 11 01 1 01 01 01 0
b
1 0 0 00 11 00 11 00 11 00 11 01 1 0 1 00 11 00 11 00 11 00 11 01 1 0 00 11 00 11 00 11 00 11
empty
occlusion
nothing
no occlusion
1 0 0 1
indifferent
)LJXUH(OHPHQWDU\WUDQVLWLRQV
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`ZKHUH D LVWKHODEHORIWKHUHIHUHQFH LPDJH5LJKW WKHWZRFRQMXJDWHHSLSRODUOLQHVDIWHUWKH WUDQVLWLRQ 'HSHQGLQJ RQ WKH VHOHFWHG SRLQW LQ WKH UHIHUHQFH LPDJH HSLSRODU OLQH WKH WUDQVLWLRQV ^ $ %` DUH SRVVLEOH LI WKH SRLQW LQ WKH UHIHUHQFH LPDJH LV
RFFOXGHG ^$ % &`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`,IWKHFKRLFHLV^ % & `D SRLQW LQ WKH HSLSRODU OLQH LV VHOHFWHG ZLWK HTXDO UDQGRPL]DWLRQ,IWKHVHOHFWHGSRLQWKDVDQRFFOXVLRQ % LV DSSOLHG RWKHUZLVH & LV DSSOLHG :H DOVR
7KH,QWHUQDWLRQDO$UDE-RXUQDORI,QIRUPDWLRQ7HFKQRORJ\9RO 1R1RYHPEHU
JXDUDQWHH WKH VDPH DSSOLFDWLRQ SUREDELOLW\ IRU WUDQVLWLRQV $ % DQG & DV $ LV VHOHFWHG UDQGRPO\WREDODQFHWKHQXPEHURIDSSOLHGHOHPHQWDU\ WUDQVLWLRQV 7UDQVLWLRQV 7KH HOHPHQWDU\ WUDQVLWLRQV DUH GHSLFWHG LQ )LJXUH 7KH OHIW VLGH VKRZV WKH PDWFKLQJ LQ WKH FXUUHQW VWDWH 7KH ULJKW VLGH VKRZV WKH QHZ PDWFKLQJ FRUUHVSRQGLQJ WRWKHQHZVWDWH'HSHQGLQJRQWKHFXUUHQWVWDWHRQHRI WKHHOHPHQWDU\WUDQVLWLRQVLVDSSOLHG7KHGHFLVLRQUXOH LVRXWOLQHGKHUHXQGHU x 'RQRWKLQJ EHFDXVHRIWKHHPSW\HSLSRODUOLQH x $ 0DWFKHVWKHILUVWSRLQWZLWKWKHVHOHFWHGSRLQW LQLWVHSLSRODUOLQH x % $QHZ PDWFKLQJSRLQWEHWZHHQWKHILUVWSRLQW DQGWKHVHOHFWHGSRLQWLQLWVHSLSRODUOLQH WKHIRUPHU FRUUHVSRQGHQWLVRFFOXGHG x $ (VWDEOLVKHV WZR RFFOXVLRQV RQH IRU WKH ILUVW SRLQWDQGWKHRWKHUIRULWVFRUUHVSRQGHQW x % 2FFOXGHV WKH ILUVW SRLQW IRUPHU FRUUHVSRQGHQW DQG HVWDEOLVKHV D QHZ PDWFKLQJ ZLWK WKH VHOHFWHG SRLQWLQWKHHSLSRODUOLQH x & (VWDEOLVKHV WZR RFFOXVLRQV RQH IRU WKH ILUVW SRLQW IRUPHU FRUUHVSRQGHQW DQG WKH RWKHU IRU FRUUHVSRQGHQW RI WKH VHOHFWHG SRLQW LQ WKH HSLSRODU OLQH DQHZPDWFKLQJEHWZHHQWKHILUVWSRLQWDQGWKH VHOHFWHGHSLSRODUOLQHSRLQWLVVHW 7KH HQHUJ\ GLIIHUHQWLDO LV FRPSXWHG ORFDOO\ 7KH FRQILJXUDWLRQ VSDFH FRUUHVSRQGV WR WKH FRQILJXUDWLRQV ZKHUH WKH HSLSRODU OLQH DQG WKH XQLTXHQHVV FRQVWUDLQWV DVZHOODVWKHYDOLGLW\FULWHULRQDUHUHVSHFWHG
6WRFKDVWLF2SWLPL]DWLRQ 5DQGRP ZDON SURFHVVHV DVVRFLDWHG ZLWK *LEEV %ROW]PDQQVDPSOHULVDVWRFKDVWLFDSSURDFKIRUJHQHUDO QRQOLQHDURSWLPL]DWLRQSUREOHPV,WLVVXLWDEOHIRUODUJH VL]HSUREOHPVZKHUHWKHJOREDOPLQLPXPLVKLGGHQE\ VHYHUDO ORFDO PLQLPD DQGZKHUHWKH QRWLRQ RI JUDGLHQW KDV QR VLJQLILFDWLRQ 7KLV DSSURDFK LV DSSOLHG WR D FRPELQDWRULDO GLVFUHWH SUREOHP 6HYHUDO FRQGLWLRQV DUH UHTXLUHG >@ D GHVFULSWLRQ RI DOO SRVVLEOH V\VWHP FRQILJXUDWLRQV [ ^[L ` ZKLFKDUHWKHJHQHUDWHGVWDWHV WR EH H[SORUHG LQFOXGLQJ WKH RSWLPDO VWDWHV DQ LQLWLDOL]DWLRQ [ [L WKHLQLWLDOVWDWH DJHQHUDWRURI
^ `
UDQGRP VWDWHV [ o [ c DQ HQHUJ\ IXQFWLRQDO - [ WKDW GHVFULEHV WKH SUREOHP DQG ZKLFK PLQLPL]DWLRQ LV WKH JRDO RI WKH SURFHGXUH D FRQWURO SDUDPHWHU ZLWK LWV LQLWLDOYDOXH7 DQGILQDOO\DGHFUHDVHUXOH 7 o 7 c
$OJRULWKP 7KHDQQHDOLQJLVDZHOONQRZQIUDPHZRUNLQVWRFKDVWLF RSWLPL]DWLRQ :H DUH RQO\ LQWHUHVWHG LQ WKH SDUWLFXODU
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nitalization dx(x), dy(), O()
Evaluate J(x) the system total energy
Shake the system by making a small change to dx(), dy(), O()
Evaluate the energy differential dJ Yes
dJ < 0
Accept new state with Boltzmann probability
Accept new state
No
No
System stable
Yes
Stop
)LJXUH%ORFNGLDJUDP
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
$0DUNRY5DQGRP)LHOG0RGHODQG0HWKRGWR,PDJH0DWFKLQJ
KHOSV WKH V\VWHP IUHH LWVHOI LI WUDSSHG LQ D ORFDO PLQLPXP YDOOH\ 7KH SURFHGXUH LV UHSHDWHG XQWLO QR VWHSVGHFUHDVLQJWKHHQHUJ\DUHSRVVLEOH ,QSUDFWLFHZHFRPSDUHDUDQGRPQXPEHUEHWZHHQ DQG ZLWK WKH *LEEV%ROW]PDQQ H[SRQHQWLDO H¨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
([SHULPHQWDO5HVXOWV $ VLPSOH PHWKRG LV XVHG WR FRPSXWH WKH ZHLJKWLQJ FRHIILFLHQWVLQWKHHQHUJ\IXQFWLRQ,IDWROHUDQFHRI LVDOORZHGRQWKHUHVHPEODQFHFRQVWUDLQWWKHPDWFKLQJ LV FDQFHOOHG LI WKH JUD\ OHYHO GLIIHUHQFH LV KLJKHU WKDQ WKLV YDOXH îȡ5îȡ2 :LWK ȡ2 ZH KDYH ȡ5 )XUWKHUPRUH ZH DVVXPH IRU D VPRRWK VXUIDFH WKDW WKH ORFDOGLIIHUHQFHLQGLVSDULWLHVLVQRWKLJKHUWKDQ,IWKH DFFXPXODWHGGLVSDULWLHVGLIIHUHQFHVLQGLUHFWLRQVIRUD SDLU RI PDWFKHG SRLQWV DUH ODUJHU WKDQ WKH HQHUJ\ SURYLGHG E\ RFFOXVLRQV WKH RFFOXVLRQV DUH VHW îîȡ&îȡ2 :LWK ȡ2 ZH KDYH ȡ& )LQDOO\ DV ZH KDQGOH WKH WZR FDVHV OHIW WR ULJKW DQG ULJKW WR OHIW DOWRJHWKHU ZH VKRXOG VHW ȡ2 7KLV DOORZV WR EDODQFH EHWZHHQ WKH IXQFWLRQDO WHUPV RU WR JLYH PRUH LPSRUWDQFHWRRQHWHUPZLWKUHVSHFWWRWKHRWKHUV7KH UHVXOWV REWDLQHG ZLWK WKH ZHLJKWLQJ JDLQV JLYHQ DERYH DUH DOUHDG\ EHWWHU WKDQ WKH RQHV REWDLQHG ZLWK WKH LQLWLDOL]DWLRQ(YHQEHWWHUUHVXOWVFRXOGEHREWDLQHGZLWK WKRURXJKH[SHULPHQWDWLRQVRQWKHZHLJKWLQJJDLQV7KH VWDUWLQJ FRQWURO SDUDPHWHU 7 LV VHW WR ZKLFK FRUUHVSRQGV WR WKH V\VWHP V VWDWH ZKHUH YLUWXDOO\ DOO WKHHOHPHQWDU\WUDQVLWLRQVDUHDFFHSWHG7KHSDUDPHWHU W LV VHW WR 7KLV SDUDPHWHU¶V YDOXH KDV SURYHQ WR JLYHJRRGUHVXOWV7RSURYLGHDQDFFHSWDEOHLQLWLDOVWDWH ZH FRQVLGHUHG XVLQJ WKH 6XP RI 6TXDUHG 'LIIHUHQFHV EDVHG FRUUHODWLRQ 66' ZH KDYH XVHG WKH VDPH UHVHPEODQFHFRQVWUDLQWHSLSRODUFRQVWUDLQWXQLTXHQHVV FRQVWUDLQW DQG YDOLGLW\ FULWHULRQ 7KH FRUUHODWLRQ
D OHIWDQGULJKWJUD\OHYHOLPDJHV
E OHIWDQGULJKWGLVSDULW\PDSV JURXQGWUXWK
)LJXUH6\QWKHVL]HGGDWDVHW
,Q )LJXUH ZH VKRZ WKH LQLWLDOL]DWLRQ XVLQJ WKH 66' FRUUHODWLRQEDVHG PDWFKLQJ DQG WKH HUURU DJDLQVW WKH JURXQGWUXWK 7KH FRUUHODWLRQ SURGXFHG D ODUJHQXPEHURIRFFOXVLRQVGXHWRDODUJHQXPEHURI LQYDOLGPDWFKHV7KHGLVSDULW\PDSFRQWDLQVWRRPDQ\ HUURUV7KHHUURUPDSVDUHFRPSXWHGDVWKHGLIIHUHQFH EHWZHHQWKHSURGXFHGGLVSDULW\PDSVDQGWKHJURXQG WUXWK ,Q WKH HUURU PDSV EODFN SL[HOV VWDQG IRU DUHDV ZKHUH QR PHDVXUHPHQWV FRXOG KDYH EHHQ GRQH GDUN DUHDV UHSUHVHQW ODUJH HUURUV ZKLOH OLJKWHU RQHV UHSUHVHQWVPDOORUQRHUURUV
D /OHIWDQGULJKWGLVSDULW\PDSVFRPSXWHGZLWK66'FRUUHODWLRQ
7KH,QWHUQDWLRQDO$UDE-RXUQDORI,QIRUPDWLRQ7HFKQRORJ\9RO 1R1RYHPEHU
E /HIWDQGULJKWHUURUPDSVFRPSXWHGDVWKHGLIIHUHQFHEHWZHHQWKH LQLWLDOL]DWLRQDQGJURXQGWUXWK
E /HIWDQGULJKWGLVSDULW\PDSV
)LJXUH5HDOLPDJHU\
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
)LQDOO\ WKH HYROXWLRQ RI WKH HQHUJ\ IXQFWLRQDO LV VKRZQ LQ )LJXUH :H QRWH WKDW WKH FRQWLQXLW\ DQG QXPEHU RI RFFOXVLRQV IXQFWLRQDO DUH GHFUHDVLQJ DQG FRQYHUJLQJ WRZDUGV VPDOO YDOXHV +RZHYHU WKH JUD\ OHYHO IXQFWLRQDO VRPHKRZ LQFUHDVHV DOWKRXJK LW UHDFKHVDVWDELOLW\SODWHDX7KLVLVGXHWRWKHIDFWWKDW FRUUHVSRQGLQJSL[HOVGRQRWKDYHQHFHVVDULO\WKHVDPH JUD\ OHYHO DQG DOVR WKH FRQWLQXLW\ ZHLJKW FRHIILFLHQW WKDW IDYRUV ORFDO FRQWLQXLW\ RYHU JUD\ OHYHO UHVHPEODQFH 5HVHPEODQFHWHUP 800 4
1 lighting condition lighting conditions
700
600
(QHUJ\
)LJXUH 6\QWKHVL]HG GDWD ,QLWLDOL]DWLRQ DQG HUURU PDS FRPSXWHG DJDLQVWWKHJURXQGWUXWK
500
400
300
200
100
0 0
20
40 60 iterations
80
,WHUDWLRQV
D
100
0DWFKLQJHQHUJ\
&RQWLQXLW\WHUP
D /HIWDQGULJKWGLVSDULW\PDSV IRXUOLJKWLQJFRQGLWLRQVVWHUHRSDLUVZHUH FRQVLGHUHGDWWKHVDPHWLPH
1400 1 lighting condition 4 lighting conditions
1200
(QHUJ\
1000
E /HIWDQGULJKWHUURUPDSVFRPSXWHGDVWKHGLIIHUHQFHEHWZHHQWKH GLVSDULW\PDSVDQGJURXQGWUXWK
)LJXUH 6\QWKHVL]HG GDWD ,PDJH PDWFKLQJ XVLQJ 05) DQG VWRFKDVWLFDSSURDFK
800
600
400
200
0 0
20
40
60
80
100
80
100
,WHUDWLRQV
E &RQWLQXLW\HQHUJ\
([SHULPHQWDO UHVXOWV RQ UHDO LPDJHU\ DUH VKRZQ LQ )LJXUH 6LPLODUO\ ZH FRQVLGHUHG IRXU OLJKWLQJ FRQGLWLRQV GXULQJ WKH LPDJH DFTXLVLWLRQ 7KH IRXU OLJKWLQJ FRQGLWLRQV VWHUHR SDLUV ZHUH XVHG DW WKH VDPH WLPH WR JHQHUDWH WKH GLVSDULW\ PDSV )LUVW URZ VKRZV RQH RI WKH IRXU VWHUHRLPDJH SDLUV 6HFRQG URZ VKRZV WKHGLVSDULW\PDSVFRPSXWHGE\WKHVWRFKDVWLFDSSURDFK RQWKH05)
2FFOXVLRQVWHUP 4000 1 lighting condition 4 lighting conditions 3500
(QHUJ\
3000
2500
2000
1500
1000
500
0 0
20
40
60
,WHUDWLRQV
D *UD\OHYHOVWHUHRSDLU
F 1XPEHURIRFFOXVLRQVHQHUJ\
)LJXUH(YROXWLRQRIWKHHQHUJ\IXQFWLRQDOFRPSRQHQWV
$0DUNRY5DQGRP)LHOG0RGHODQG0HWKRGWR,PDJH0DWFKLQJ
1RWH WKDW ERWK WKH QXPEHU RI RFFOXVLRQV DQG FRQWLQXLW\ HQHUJLHV GHFUHDVH DQG FRQYHUJH WRZDUGV D VPDOO YDOXH 7KH PDWFKLQJ HQHUJ\ DOVR FRQYHUJHV WR D VWDEOHYDOXH7KLVYDOXHLVKLJKHUWKDQWKHLQLWLDOYDOXH DVWKHPDWFKHGSL[HOVGRQRWKDYHQHFHVVDULO\WKHVDPH JUD\OHYHO
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
5HIHUHQFHV >@ $DUWV ( DQG /DDUKRYHQ 3 6LPXODWHG $QQHDOLQJ DQG $SSOLFDWLRQV .OXZHU $FDGHPLF 3XEOLVKHUV +ROODQG >@ %HQDPHXU : ³&RPSXWLQJ WKH ,QLWLDO 7HPSHUDWXUH RI 6LPXODWHG $QQHDOLQJ´ &RPSXWDWLRQDO 2SWLPL]DWLRQ DQG $SSOLFDWLRQV YRO QRSS >@ %HQ$UL 5 DQG 6RFKHQ 1 ³$ *HRPHWULF $SSURDFKIRU5HJXODUL]DWLRQRIWKH'DWD7HUPLQ 6WHUHR9LVLRQ´-RXUQDORI0DWKHPDWLFDO,PDJLQJ DQG9LVLRQYROQRSS >@ %HUWHUR 0 3RJJLR 7 DQG 7RUUH 9 ³,OO3RVHG 3UREOHPVLQ(DUO\9LVLRQ´LQ3URFHHGLQJVRIWKH ,(((SS >@ %R\NRY @ &DVWHOODQL 8 )XVLHOOR $ *KHUDUGL 5 DQG 0XULQR9³$XWRPDWLF6HOHFWLRQRI05)&RQWURO 3DUDPHWHUVE\5HDFWLYH7DEX6HDUFK´,PDJHDQG 9LVLRQ&RPSXWLQJYROQRSS
>@ &RUVR - 7X = DQG <XLOOH $ ³05) /DEHOLQJ ZLWKD*UDSK6KLIWV$OJRULWKP´LQ3URFHHGLQJV RI /HFWXUH 1RWHV LQ &RPSXWHU 6FLHQFH %HUOLQ SS >@ )DXJHUDV 2 DQG .HULYHQ 5 ³&RPSOHWH GHQVH 6WHUHR 9LVLRQ XVLQJ /HYHO 6HW 0HWKRGV´ LQ 3URFHHGLQJV RI /HFWXUH 1RWHV LQ &RPSXWHU 6FLHQFHSS > @ *HPDQ 6 DQG *HPDQ ' ³6WRFKDVWLF 5HOD[DWLRQ *LEEV 'LVWULEXWLRQV DQG WKH %D\HVLDQ 5HVWRUDWLRQ RI ,PDJHV´ ,((( 7UDQVDFWLRQV RQ 3DWWHUQ $QDO\VLV DQG 0DFKLQH ,QWHOOLJHQFHYROQRSS >@ +XDQJ - DQG /LX + ³6WHUHR 9LVLRQ XVLQJ 0LFURFDQRQLFDO 0HDQ)LHOG $QQHDOLQJ 1HXUDO 1HWZRUN´ 1HXUDO &RPSXWDWLRQV YRO QR SS >@ +XT 6 $ELGL % DQG $ELGL 0 ³6WHUHR%DVHG ' )DFH 0RGHOLQJ XVLQJ $QQHDOLQJ LQ /RFDO (QHUJ\ 0LQLPL]DWLRQ´ LQ 3URFHHGLQJV RI WK ,QWHUQDWLRQDO&RQIHUHQFHRQ,PDJH$QDO\VLVDQG 3URFHVVLQJ0RGHQDSS >@ ,VKLNDZD + ³([DFW 2SWLPL]DWLRQ IRU 0DUNRY 5DQGRP )LHOGV ZLWK &RQYH[ 3ULRUV´ ,((( 7UDQVDFWLRQV RQ 3DWWHUQ $QDO\VLV DQG 0DFKLQH ,QWHOOLJHQFH YRO QR SS >@ -LD @ .RPRGDNLV 1 7]LULWDV * DQG 3DUDJLRV 1 ³3HUIRUPDQFH YV &RPSXWDWLRQDO (IILFLHQF\ IRU 2SWLPL]LQJ 6LQJOH DQG '\QDPLF 05)V 6HWWLQJ WKH6WDWHRIWKH$UWZLWK3ULPDO'XDO6WUDWHJLHV´ &RPSXWHU 9LVLRQ DQG ,PDJH 8QGHUVWDQGLQJ 6SHFLDO ,VVXH RQ 'LVFUHWH 2SWLPL]DWLRQ LQ &RPSXWHU 9LVLRQ YRO QR SS >@ 1H¶PD % DQG $OL + ³0XOWLSXUSRVH &RGH *HQHUDWLRQ XVLQJ )LQJHUSULQW ,PDJHV´ ,QWHUQDWLRQDO $UDE -RXUQDO RI ,QIRUPDWLRQ 7HFKQRORJ\YROQRSS >@ 5DGKDNULVKQDQ 6 6XEEDUD\DQ * DQG 9LNUDP . ³:DYHOHWV %DVHG 9LGHR (QFRGHU XVLQJ .&'6´ 7KH ,QWHUQDWLRQDO $UDE -RXUQDO RI ,QIRUPDWLRQ 7HFKQRORJ\ YRO QR SS >@ 5DG]LV]HZVNL 0 DQG $OGD : ³)DPLO\ RI (QHUJ\ &RQVHUYLQJ *ORVV\ 5HIOHFWLRQ 0RGHOV´ LQ 3URFHHGLQJV RI /HFWXUH 1RWHV LQ &RPSXWHU 6FLHQFH%HUOLQSS >@ 6FKOLFN & ³$Q ,QH[SHQVLYH %5') 0RGHO IRU 3K\VLFDOO\%DVHG 5HQGHULQJ´ &RPSXWHU *UDSKLFV )RUXP YRO QR SS
7KH,QWHUQDWLRQDO$UDE-RXUQDORI,QIRUPDWLRQ7HFKQRORJ\9RO 1R1RYHPEHU
> @ 6XQ\RWR + 0DUN : DQG *DYULOD ' ³$ &RPSDUDWLYH 6WXG\ RI )DVW 'HQVH 6WHUHR 9LVLRQ $OJRULWKPV´ ,QWHOOLJHQW 9HKLFOHV 6\PSRVLXP ,(((YROQRSS >@ 6]HOLVNL 5 =DELK 5 6FKDUVWHLQ ' 9HNVOHU 2 .ROPRJRURY 9 $JDUZDOD $ 7DSSHQ 0 DQG 5RWKHU & ³$ &RPSDUDWLYH 6WXG\ RI (QHUJ\ 0LQLPL]DWLRQ 0HWKRGV IRU 0DUNRY 5DQGRP )LHOGV´ LQ 3URFHHGLQJV RI /HFWXUH 1RWHV LQ &RPSXWHU6FLHQFHSS >@ :DQJ / @ :HUGD , &KDRXFK + 6DPHW $ %HQ$\HG 0 DQG 0DVPRXGL 1 ³2SWLPDO '63 %DVHG ,QWHJHU 0RWLRQ (VWLPDWLRQ ,PSOHPHQWDWLRQ IRU +$9&%DVHOLQH(QFRGHU´7KH,QWHUQDWLRQDO $UDE -RXUQDO RI ,QIRUPDWLRQ 7HFKQRORJ\ YRO QRSS 0RKDPPHG2XDOLUHFHLYHGKLV3K' LQ UHDOWLPH URERWLFV DQG FRQWURO IURP 0LQHV 3DULV7HFK)UDQFH LQ +H KDV RYHU \HDUV RI H[SHULHQFH LQ GHYHORSLQJ HPEHGGHG V\VWHPV LQ DHURQDXWLFV DXWRPRWLYH LQGXVWU\DQG&$'V\VWHPVIRU9/6, UHYHUVH HQJLQHHULQJ +LV PDLQ UHVHDUFK LQWHUHVWV DUH LQ FRPSXWHUYLVLRQDQGSDWWHUQUHFRJQLWLRQ
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
$0DUNRY5DQGRP)LHOG0RGHODQG0HWKRG WR,PDJH0DWFKLQJ 0RKDPPHG2XDOL+ROJHU/DQJHDQG.KHLUHGGLQH%RXD]]D /,7,2/DE8QLYHUVLW\RI2UDQ$OJHULD 5 '*URXS*HQHUDO'\QDPLFV&DQDGD&DQDGD 'HSDUWPHQWRI&RPSXWHU6FLHQFH7DLI8QLYHUVLW\.6$ 'HSDUWPHQWRI&RPSXWHU6FLHQFH8PP$O4XUD8QLYHUVLW\.6$ $EVWUDFW ,Q WKLV SDSHU WKH FRUUHVSRQGHQFH SUREOHP LV VROYHG E\ PLQLPL]LQJ DQ HQHUJ\ IXQFWLRQDO XVLQJ D VWRFKDVWLF DSSURDFK 2XU SURFHGXUH JHQHUDOO\ IROORZV *HPDQ DQG *HPDQ¶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¶ SDUDPHWHUV IRFDO GLVWDQFH SL[HO VL]H &&' JULG VL]H LPDJH FRRUGLQDWHV RI WKH FHQWHU RI SURMHFWLRQ DQG WKH H[WULQVLFFDPHUDV¶SDUDPHWHUV PDLQO\WKHFRPSXWDWLRQ RI WKH URWDWLRQ DQG WUDQVODWLRQ PDWULFHV EHWZHHQ WKH FDPHUDV &DPHUDV¶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
$0DUNRY5DQGRP)LHOG0RGHODQG0HWKRGWR,PDJH0DWFKLQJ
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¶V S\UDPLGV WR FUHDWH VPDOOHU YHUVLRQV RI WKH RULJLQDO LPDJHV 0DWFKLQJ LV XVXDOO\ HDVLHU DW ORZ UHVROXWLRQ DQG WKH FRPSXWHG GLVSDULW\ PDSV DUH SURSDJDWHG WR KLJKHU UHVROXWLRQV 3UHYLRXV ZRUNV DGGUHVVHG HQHUJ\ PLQLPL]DWLRQEDVHG GHQVH VWHUHR PDWFKLQJ DQG VHYHUDO PHWKRGV ZHUH SURSRVHG $PRQJ WKHVH ZH FLWH OHYHO VHW PHWKRGV >@ DQG PHDQ ILHOG
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
7KH,QWHUQDWLRQDO$UDE-RXUQDORI,QIRUPDWLRQ7HFKQRORJ\9RO 1R1RYHPEHU
[ \ ^ Q` GHQRWH FROXPQV DQG OLQHV UHVSHFWLYHO\ DQG , O DQG , U EHLQJWKHOHIWKDQGDQGULJKWKDQGVLGH LPDJHV7ZRFDPHUDVDQGREVHUYHWKHVDPHVFHQHKDYH D FRPPRQ ILHOG RI YLVLRQ $ SRLQW LQ WKH VFHQH LV SURMHFWHGRQWKHWZRLPDJHVLQWZRSRLQWVZKLFKKDYH GLIIHUHQWFRRUGLQDWHVGXHWRWKHGLIIHUHQWSRLQWVRIYLHZ RI WKH FDPHUDV :H H[SUHVV WKLV VKLIWLQJ E\ KRUL]RQWDO DQG YHUWLFDO GLVSDULWLHV LQ WKH WZR GLUHFWLRQV OHIW ZLWK UHVSHFW WR ULJKW DQG ULJKW ZLWK UHVSHFW WR OHIW G[ D [ \ [E [ D DQG G\ D [ \ \ E \ D ZKHUH
D E ^ O U U O ` 7KH WZR FDPHUDV GR QRW REVHUYH H[DFWO\ WKH VDPH SK\VLFDO SRLQWV LQ WKH VFHQH EHFDXVHVRPHSRLQWVFDQEHRXWRIWKHFRPPRQILHOGRI YLVLRQ RU KLGGHQ E\ REMHFWV $ SRLQW REVHUYHG E\ D VLQJOHFDPHUDLVGHFODUHGDVDQRFFOXVLRQLQWKHLPDJH ZKHUH LW DSSHDUV 2FFOXVLRQV DUH QRWHG 2O [\ DQG 2U [ \ ^` ZKHUH VWDQGV IRU DQ RFFOXVLRQ 3RLQWV WKDW DUH VHHQ E\ ERWK FDPHUDV FDQ EH PDWFKHG 'LVSDULWLHV FDQ EH FDOFXODWHG E\ WKLV SRLQW PDWFKLQJ 7KH GLVSDULWLHV D GHSWK FDQ HDVLO\ EH FRPSXWHG E\ WULDQJXODWLRQ XVLQJ WKH FDPHUDV DQG WKH VWHUHR ULJ SDUDPHWHUV
5HVHPEODQFH&RQVWUDLQW 7KLVFRQVWUDLQWDOORZVWKHPDWFKLQJRIWZRSRLQWVRQO\ LI WKH\ KDYH WKH VDPH JUD\ OHYHO ,Q WKH FDVH RI ODPEHUWLDQ VXUIDFHV D SRLQW LQ WKH VFHQH KDV WKH VDPH JUD\OHYHOLQERWKLPDJHV$SRLQWLVDFRUQHURIDSL[HO IRUZKLFKZHDWWULEXWHWKHDYHUDJHRIWKHJUD\OHYHOVRI LWVIRXUDGMDFHQWQHLJKERUV $ [ \
¦ ¦ , [ N \ O N O
:H DOVR FRQVLGHU XVLQJ UHGXQGDQW LQIRUPDWLRQ RQ WKH VFHQH E\ FKDQJLQJ WKH OLJKWLQJ FRQGLWLRQV (DFK OLJKWLQJFRQGLWLRQSURYLGHVDVWHUHRLPDJHSDLU:LWKLQ WKHVDPHVWHUHRSDLUFRUUHVSRQGLQJSRLQWVVKRXOGKDYH VLPLODUJUD\OHYHOYDOXHV:HH[SUHVVWKLVFRQVWUDLQWE\ WKH VTXDUH RI WKH GLIIHUHQFH RI WKH JUD\ YDOXHV DVVRFLDWHG ZLWK WKH PDWFKLQJ FDQGLGDWHV IRU HDFK OLJKWLQJFRQGLWLRQN $ N O [ \
$N
U
[ G[ O [ \ \ G\ O [ \
7KLV WHUP LV ZHLJKWHG ZLWK WKH WHUP UHSUHVHQWLQJ RFFOXVLRQVEHFDXVHLIWKHUHLVDQ\RFFOXVLRQWKHUHZLOO EH QR PDWFKLQJ 7KH HQHUJ\ DVVRFLDWHG ZLWK WKLV FRQVWUDLQWRYHUWKHZKROHLPDJHLV (
5
§ $O [ \ · ¨ ¸ ¦ ¦¨ § [ G[ O [ \ · ¸ U \ [¨$ ¨ ¸¸ ¨ ¨ \ G\ O [ \ ¸ ¸ ¹¹ © ©
2
O
[ \
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
&RQWLQXLW\&RQVWUDLQW :H FRQVLGHU WKH SK\VLFDO VXUIDFHV DV ORFDOO\ FRQWLQXRXV ,Q WKLV FDVH WKHLU (XFOLGHDQ SURMHFWLRQ LV FRQWLQXRXVDVZHOO7KHGLVSDULW\YDULHVDOLWWOHH[FHSW RQ WKH HGJHV 7KH UHDVRQ LV ZH FDQFHO WKH FRQWLQXLW\ FRQVWUDLQW DW WKH HGJHV EHFDXVH ZH FDQFHO WKH FRQVWUDLQW RQ RFFOXVLRQV ZKHUH QR PDWFKLQJ H[LVWV 7KLV FRQVWUDLQW LV H[SUHVVHG E\ WKH HQHUJ\ IXQFWLRQDO JLYHQ KHUHDIWHU +RUL]RQWDO DQG YHUWLFDO HGJHV DUH DQG F\ UHVSHFWLYHO\ GHQRWHG E\ F[ D D F [ [ \ F \ [ \ ^` ZKHUH VWDQGV IRU WKH SUHVHQFHRIDQHGJH D (&
D QD [ Q\ ¦ ¦ [ \ D QD [ Q\ ¦ ¦ [ \ D QD [ Q\ ¦ ¦ [ \ D QD [ Q\ ¦ ¦ [ \
'G[ KD [ \ F [D [ \ 2 D [ \ 2 D [ \ 'G[ YD [ \ F D\ [ \ 2 D [ \ 2 D [ \
'G\ KD [ \ F [D [ \ 2 D [ \ 2 D [ \ 'G\ YD [ \ F D\ [ \ 2 D [ \ 2 D [ \
2FFOXVLRQV&RXQWHUZHLJKW :LWK RFFOXVLRQV DOO RYHU WKH LPDJH WKH HQHUJ\ LV PLQLPDO QXOO EXWWKLVLVQRWDYLDEOHVROXWLRQ7KLVLV ZK\ZHDGGDFRXQWHUZHLJKWLQWKHHQHUJ\IXQFWLRQDO LQ RUGHU WR OLPLW WKH QXPEHU RI RFFOXVLRQV )RU RQH LPDJHWKLVHQHUJ\IXQFWLRQDOLV ( 2D
D ¦ ¦ 2 [ \ [ \
8QLTXHQHVV&RQVWUDLQW (YHU\ SRLQW FDQ RQO\ EH PDWFKHG ZLWK DW PRVW RQH SRLQW IURP WKH RWKHU LPDJH 7KLV FRQVWUDLQW ZDV LQWURGXFHG E\ 0DUU DQG LW LV VWULFWO\ YHULILHG LQ WKH FDVH RI WKH QRQWUDQVSDUHQW REMHFWV 7KLV FRQVWUDLQW VLPSOLILHV WKH FRPSXWDWLRQV DQG HQDEOHV WKH DSSOLFDWLRQ RI WKH YDOLGLW\ FULWHULRQ IRU D JLYHQ PDWFKLQJ$PDWFKLQJLVYDOLGLIERWKGLVSDULWLHV OHIW
$0DUNRY5DQGRP)LHOG0RGHODQG0HWKRGWR,PDJH0DWFKLQJ
WRULJKWDQGULJKWWROHIW HQDEOHXVWRUHDFKWKHSRLQWLQ WKHULJKWKDQGVLGHLPDJHIURPWKHSRLQWLQWKHOHIWKDQG VLGH LPDJH DQG JR EDFN WR WKH OHIW KDQG VLGH LPDJH LQLWLDO SRLQW 7KLV FRQVWUDLQW LV H[SUHVVHG LQ WKH HOHPHQWDU\ WUDQVLWLRQV +RZHYHU LQ FDVH RI IRUHVKRUWHQLQJ FRUUHVSRQGLQJ VXUIDFHV GR QRW H[KLELW WKH VDPH QXPEHU RI SL[HOV $V ZH DUH FRQVLGHULQJ D SRLQWEDVHG PDWFKLQJ DSSURDFK ZH ZLOO HQG XS ZLWK SL[HOV WKDW ZLOO QRW EH PDWFKHG DW DOO 7KH DOJRULWKP ZLOOIRUFHWKHVHSL[HOVWREHRFFOXGHG
(QHUJ\)XQFWLRQDO 7KH HQHUJ\ IXQFWLRQDO RI WKH VWHUHR PDWFKLQJ SUREOHP LV WKH ZHLJKWHG VXP RI WKH HQHUJ\ IXQFWLRQDOV GHULYHG IURPWKHVWHUHRPDWFKLQJFRQVWUDLQWV (
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
O U O U ȡ 5 ( 5 ȡ & ( & ( & ȡ 2 ( 2 ( 2
Selected camera
Epipolar line
Selected pixel corner
Selected element
Elementary transformations
(0)
11 00 00 0 11 11 01 01 01 0 00 11 00 11 0 0 1 0 0 00 11 00 1 11 01 1 00 1 01 1 01 1 1 0
(1A)
11 00 00 11 1 0 0 1 0 1 0 1 0 1 00 11 00 0 0 1 0 0 a11 00 11 00 1 11 01 1 00 1 01 1 01 1 1 0
b
1 0 0 1 00 11 0 1 00 11 00 11 00 11 0 1 0 00 0 1 00 11 00 11 00 11 01 1 011 1 00 11 0 1 00 11 00 11 00 11
11 00 0 1 1 0 0 1 0 1 0 1 0 1 00 11 0 1 0 0 1 0 0 a 00 11 01 1 01 1 00 1 01 1 01 1 1 0
b
1 0 0 1 00 11 00 11 00 11 00 11 00 11 0 1 0 00 11 00 11 00 11 00 11 00 11 01 1 0 1 00 11 00 11 00 11 00 11 00 11
(1B)
11 00 00 1 01 01 01 0 a11 00 11 00 1 11 01 01 01 0
b
11 0 011 00 0 1 00 11 00 11 00 11 01 1 011 00 0 1 00 11 00 11 00 11
11 00 01 1 01 01 01 0 a 00 11 01 1 01 01 01 0
b
11 0 0 00 11 00 11 00 11 00 11 00 11 01 1 0 00 11 00 11 00 11 00 11 00 11
(2A)
11 00 00 1 0 0 0 0 a11 00 11 00 0 11 01 1 01 1 11 0 01 1 0 1
b
1 0 0 0 00 11 0 1 00 00 11 01 1 01 1 0 1 00 11 011 1 00 11 00 11
11 00 0 1 1 0 0 0 0 a 00 11 00 1 01 1 01 1 11 0 01 1 0 1
b
1 0 0 00 11 0 1 00 11 00 11 00 11 01 1 0 1 00 11 0 1 00 11 00 11 00 11
(2B)
11 00 00 11 1 0 0 1 0 1 0 1 0 1 00 11 00 0 0 1 0 0 a11 00 11 00 1 11 01 1 00 1 01 1 01 1 1 0
b
1 0 0 1 00 11 0 1 00 11 00 11 0 1 0 00 0 1 00 00 11 01 1 011 1 00 11 011 1 00 11 00 11
11 00 0 1 1 0 0 1 0 1 0 1 0 1 00 11 0 1 0 0 1 0 0 a 00 11 01 1 01 1 00 1 01 1 01 1 1 0
b
1 0 0 1 00 11 00 11 00 11 00 11 0 1 0 00 11 00 11 00 11 00 11 01 1 0 1 00 11 00 11 00 11 00 11
(2C)
11 00 00 11 0 0 0 0 00 11 00 1 01 1 01 1 01 1 0 1 a11 00 11 00 1 11 01 01 01 0
b
1 0 0 00 0 1 00 00 11 01 1 011 1 00 11 011 1 00 11 00 11 01 1 011 00 011 1 00 00 11
11 00 0 1 0 0 0 0 00 11 01 1 01 1 01 1 01 1 0 1 a 00 11 01 1 01 01 01 0
b
1 0 0 00 11 00 11 00 11 00 11 01 1 0 1 00 11 00 11 00 11 00 11 01 1 0 00 11 00 11 00 11 00 11
empty
occlusion
nothing
no occlusion
1 0 0 1
indifferent
)LJXUH(OHPHQWDU\WUDQVLWLRQV
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`ZKHUH D LVWKHODEHORIWKHUHIHUHQFH LPDJH5LJKW WKHWZRFRQMXJDWHHSLSRODUOLQHVDIWHUWKH WUDQVLWLRQ 'HSHQGLQJ RQ WKH VHOHFWHG SRLQW LQ WKH UHIHUHQFH LPDJH HSLSRODU OLQH WKH WUDQVLWLRQV ^ $ %` DUH SRVVLEOH LI WKH SRLQW LQ WKH UHIHUHQFH LPDJH LV
RFFOXGHG ^$ % &`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`,IWKHFKRLFHLV^ % & `D SRLQW LQ WKH HSLSRODU OLQH LV VHOHFWHG ZLWK HTXDO UDQGRPL]DWLRQ,IWKHVHOHFWHGSRLQWKDVDQRFFOXVLRQ % LV DSSOLHG RWKHUZLVH & LV DSSOLHG :H DOVR
7KH,QWHUQDWLRQDO$UDE-RXUQDORI,QIRUPDWLRQ7HFKQRORJ\9RO 1R1RYHPEHU
JXDUDQWHH WKH VDPH DSSOLFDWLRQ SUREDELOLW\ IRU WUDQVLWLRQV $ % DQG & DV $ LV VHOHFWHG UDQGRPO\WREDODQFHWKHQXPEHURIDSSOLHGHOHPHQWDU\ WUDQVLWLRQV 7UDQVLWLRQV 7KH HOHPHQWDU\ WUDQVLWLRQV DUH GHSLFWHG LQ )LJXUH 7KH OHIW VLGH VKRZV WKH PDWFKLQJ LQ WKH FXUUHQW VWDWH 7KH ULJKW VLGH VKRZV WKH QHZ PDWFKLQJ FRUUHVSRQGLQJ WRWKHQHZVWDWH'HSHQGLQJRQWKHFXUUHQWVWDWHRQHRI WKHHOHPHQWDU\WUDQVLWLRQVLVDSSOLHG7KHGHFLVLRQUXOH LVRXWOLQHGKHUHXQGHU x 'RQRWKLQJ EHFDXVHRIWKHHPSW\HSLSRODUOLQH x $ 0DWFKHVWKHILUVWSRLQWZLWKWKHVHOHFWHGSRLQW LQLWVHSLSRODUOLQH x % $QHZ PDWFKLQJSRLQWEHWZHHQWKHILUVWSRLQW DQGWKHVHOHFWHGSRLQWLQLWVHSLSRODUOLQH WKHIRUPHU FRUUHVSRQGHQWLVRFFOXGHG x $ (VWDEOLVKHV WZR RFFOXVLRQV RQH IRU WKH ILUVW SRLQWDQGWKHRWKHUIRULWVFRUUHVSRQGHQW x % 2FFOXGHV WKH ILUVW SRLQW IRUPHU FRUUHVSRQGHQW DQG HVWDEOLVKHV D QHZ PDWFKLQJ ZLWK WKH VHOHFWHG SRLQWLQWKHHSLSRODUOLQH x & (VWDEOLVKHV WZR RFFOXVLRQV RQH IRU WKH ILUVW SRLQW IRUPHU FRUUHVSRQGHQW DQG WKH RWKHU IRU FRUUHVSRQGHQW RI WKH VHOHFWHG SRLQW LQ WKH HSLSRODU OLQH DQHZPDWFKLQJEHWZHHQWKHILUVWSRLQWDQGWKH VHOHFWHGHSLSRODUOLQHSRLQWLVVHW 7KH HQHUJ\ GLIIHUHQWLDO LV FRPSXWHG ORFDOO\ 7KH FRQILJXUDWLRQ VSDFH FRUUHVSRQGV WR WKH FRQILJXUDWLRQV ZKHUH WKH HSLSRODU OLQH DQG WKH XQLTXHQHVV FRQVWUDLQWV DVZHOODVWKHYDOLGLW\FULWHULRQDUHUHVSHFWHG
6WRFKDVWLF2SWLPL]DWLRQ 5DQGRP ZDON SURFHVVHV DVVRFLDWHG ZLWK *LEEV %ROW]PDQQVDPSOHULVDVWRFKDVWLFDSSURDFKIRUJHQHUDO QRQOLQHDURSWLPL]DWLRQSUREOHPV,WLVVXLWDEOHIRUODUJH VL]HSUREOHPVZKHUHWKHJOREDOPLQLPXPLVKLGGHQE\ VHYHUDO ORFDO PLQLPD DQGZKHUHWKH QRWLRQ RI JUDGLHQW KDV QR VLJQLILFDWLRQ 7KLV DSSURDFK LV DSSOLHG WR D FRPELQDWRULDO GLVFUHWH SUREOHP 6HYHUDO FRQGLWLRQV DUH UHTXLUHG >@ D GHVFULSWLRQ RI DOO SRVVLEOH V\VWHP FRQILJXUDWLRQV [ ^[L ` ZKLFKDUHWKHJHQHUDWHGVWDWHV WR EH H[SORUHG LQFOXGLQJ WKH RSWLPDO VWDWHV DQ LQLWLDOL]DWLRQ [ [L WKHLQLWLDOVWDWH DJHQHUDWRURI
^ `
UDQGRP VWDWHV [ o [ c DQ HQHUJ\ IXQFWLRQDO - [ WKDW GHVFULEHV WKH SUREOHP DQG ZKLFK PLQLPL]DWLRQ LV WKH JRDO RI WKH SURFHGXUH D FRQWURO SDUDPHWHU ZLWK LWV LQLWLDOYDOXH7 DQGILQDOO\DGHFUHDVHUXOH 7 o 7 c
$OJRULWKP 7KHDQQHDOLQJLVDZHOONQRZQIUDPHZRUNLQVWRFKDVWLF RSWLPL]DWLRQ :H DUH RQO\ LQWHUHVWHG LQ WKH SDUWLFXODU
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nitalization dx(x), dy(), O()
Evaluate J(x) the system total energy
Shake the system by making a small change to dx(), dy(), O()
Evaluate the energy differential dJ Yes
dJ < 0
Accept new state with Boltzmann probability
Accept new state
No
No
System stable
Yes
Stop
)LJXUH%ORFNGLDJUDP
6KRZLQJ WKH VWHSV SHUIRUPHG IURP LQLWLDOL]DWLRQWR V\VWHP HTXLOLEULXP 7KH V\VWHP VWDWH YHFWRU QDPHO\ WKH RFFOXVLRQV KRUL]RQWDO DQG YHUWLFDO GLVSDULWLHV DUH LQLWLDOL]HG 7KH LQLWLDOL]DWLRQ PD\ EH UDQGRP RU RQH FDQ XVH D SUHOLPLQDU\ HYHQ DQ LQDFFXUDWH UHVXOW SURYLGHG E\ D IDVW PDWFKLQJ DOJRULWKP 7KH WRWDO HQHUJ\ RI WKH V\VWHP LV HYDOXDWHG 7KHQ WKH V\VWHP SHUIRUPVDVPDOOVWHSLQWKHFRQILJXUDWLRQVSDFH7KLV GHVWLQDWLRQLVDFFHSWHGDVWKHQHZVWDWHLIWKHV\VWHP V HQHUJ\GHFUHDVHV)URPWLPHWRWLPHHYHQQHZVWDWHV LQFUHDVLQJ WKH V\VWHP V HQHUJ\ DUH DFFHSWHG 7KLV
$0DUNRY5DQGRP)LHOG0RGHODQG0HWKRGWR,PDJH0DWFKLQJ
KHOSV WKH V\VWHP IUHH LWVHOI LI WUDSSHG LQ D ORFDO PLQLPXP YDOOH\ 7KH SURFHGXUH LV UHSHDWHG XQWLO QR VWHSVGHFUHDVLQJWKHHQHUJ\DUHSRVVLEOH ,QSUDFWLFHZHFRPSDUHDUDQGRPQXPEHUEHWZHHQ DQG ZLWK WKH *LEEV%ROW]PDQQ H[SRQHQWLDO H¨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
([SHULPHQWDO5HVXOWV $ VLPSOH PHWKRG LV XVHG WR FRPSXWH WKH ZHLJKWLQJ FRHIILFLHQWVLQWKHHQHUJ\IXQFWLRQ,IDWROHUDQFHRI LVDOORZHGRQWKHUHVHPEODQFHFRQVWUDLQWWKHPDWFKLQJ LV FDQFHOOHG LI WKH JUD\ OHYHO GLIIHUHQFH LV KLJKHU WKDQ WKLV YDOXH îȡ5îȡ2 :LWK ȡ2 ZH KDYH ȡ5 )XUWKHUPRUH ZH DVVXPH IRU D VPRRWK VXUIDFH WKDW WKH ORFDOGLIIHUHQFHLQGLVSDULWLHVLVQRWKLJKHUWKDQ,IWKH DFFXPXODWHGGLVSDULWLHVGLIIHUHQFHVLQGLUHFWLRQVIRUD SDLU RI PDWFKHG SRLQWV DUH ODUJHU WKDQ WKH HQHUJ\ SURYLGHG E\ RFFOXVLRQV WKH RFFOXVLRQV DUH VHW îîȡ&îȡ2 :LWK ȡ2 ZH KDYH ȡ& )LQDOO\ DV ZH KDQGOH WKH WZR FDVHV OHIW WR ULJKW DQG ULJKW WR OHIW DOWRJHWKHU ZH VKRXOG VHW ȡ2 7KLV DOORZV WR EDODQFH EHWZHHQ WKH IXQFWLRQDO WHUPV RU WR JLYH PRUH LPSRUWDQFHWRRQHWHUPZLWKUHVSHFWWRWKHRWKHUV7KH UHVXOWV REWDLQHG ZLWK WKH ZHLJKWLQJ JDLQV JLYHQ DERYH DUH DOUHDG\ EHWWHU WKDQ WKH RQHV REWDLQHG ZLWK WKH LQLWLDOL]DWLRQ(YHQEHWWHUUHVXOWVFRXOGEHREWDLQHGZLWK WKRURXJKH[SHULPHQWDWLRQVRQWKHZHLJKWLQJJDLQV7KH VWDUWLQJ FRQWURO SDUDPHWHU 7 LV VHW WR ZKLFK FRUUHVSRQGV WR WKH V\VWHP V VWDWH ZKHUH YLUWXDOO\ DOO WKHHOHPHQWDU\WUDQVLWLRQVDUHDFFHSWHG7KHSDUDPHWHU W LV VHW WR 7KLV SDUDPHWHU¶V YDOXH KDV SURYHQ WR JLYHJRRGUHVXOWV7RSURYLGHDQDFFHSWDEOHLQLWLDOVWDWH ZH FRQVLGHUHG XVLQJ WKH 6XP RI 6TXDUHG 'LIIHUHQFHV EDVHG FRUUHODWLRQ 66' ZH KDYH XVHG WKH VDPH UHVHPEODQFHFRQVWUDLQWHSLSRODUFRQVWUDLQWXQLTXHQHVV FRQVWUDLQW DQG YDOLGLW\ FULWHULRQ 7KH FRUUHODWLRQ
D OHIWDQGULJKWJUD\OHYHOLPDJHV
E OHIWDQGULJKWGLVSDULW\PDSV JURXQGWUXWK
)LJXUH6\QWKHVL]HGGDWDVHW
,Q )LJXUH ZH VKRZ WKH LQLWLDOL]DWLRQ XVLQJ WKH 66' FRUUHODWLRQEDVHG PDWFKLQJ DQG WKH HUURU DJDLQVW WKH JURXQGWUXWK 7KH FRUUHODWLRQ SURGXFHG D ODUJHQXPEHURIRFFOXVLRQVGXHWRDODUJHQXPEHURI LQYDOLGPDWFKHV7KHGLVSDULW\PDSFRQWDLQVWRRPDQ\ HUURUV7KHHUURUPDSVDUHFRPSXWHGDVWKHGLIIHUHQFH EHWZHHQWKHSURGXFHGGLVSDULW\PDSVDQGWKHJURXQG WUXWK ,Q WKH HUURU PDSV EODFN SL[HOV VWDQG IRU DUHDV ZKHUH QR PHDVXUHPHQWV FRXOG KDYH EHHQ GRQH GDUN DUHDV UHSUHVHQW ODUJH HUURUV ZKLOH OLJKWHU RQHV UHSUHVHQWVPDOORUQRHUURUV
D /OHIWDQGULJKWGLVSDULW\PDSVFRPSXWHGZLWK66'FRUUHODWLRQ
7KH,QWHUQDWLRQDO$UDE-RXUQDORI,QIRUPDWLRQ7HFKQRORJ\9RO 1R1RYHPEHU
E /HIWDQGULJKWHUURUPDSVFRPSXWHGDVWKHGLIIHUHQFHEHWZHHQWKH LQLWLDOL]DWLRQDQGJURXQGWUXWK
E /HIWDQGULJKWGLVSDULW\PDSV
)LJXUH5HDOLPDJHU\
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
)LQDOO\ WKH HYROXWLRQ RI WKH HQHUJ\ IXQFWLRQDO LV VKRZQ LQ )LJXUH :H QRWH WKDW WKH FRQWLQXLW\ DQG QXPEHU RI RFFOXVLRQV IXQFWLRQDO DUH GHFUHDVLQJ DQG FRQYHUJLQJ WRZDUGV VPDOO YDOXHV +RZHYHU WKH JUD\ OHYHO IXQFWLRQDO VRPHKRZ LQFUHDVHV DOWKRXJK LW UHDFKHVDVWDELOLW\SODWHDX7KLVLVGXHWRWKHIDFWWKDW FRUUHVSRQGLQJSL[HOVGRQRWKDYHQHFHVVDULO\WKHVDPH JUD\ OHYHO DQG DOVR WKH FRQWLQXLW\ ZHLJKW FRHIILFLHQW WKDW IDYRUV ORFDO FRQWLQXLW\ RYHU JUD\ OHYHO UHVHPEODQFH 5HVHPEODQFHWHUP 800 4
1 lighting condition lighting conditions
700
600
(QHUJ\
)LJXUH 6\QWKHVL]HG GDWD ,QLWLDOL]DWLRQ DQG HUURU PDS FRPSXWHG DJDLQVWWKHJURXQGWUXWK
500
400
300
200
100
0 0
20
40 60 iterations
80
,WHUDWLRQV
D
100
0DWFKLQJHQHUJ\
&RQWLQXLW\WHUP
D /HIWDQGULJKWGLVSDULW\PDSV IRXUOLJKWLQJFRQGLWLRQVVWHUHRSDLUVZHUH FRQVLGHUHGDWWKHVDPHWLPH
1400 1 lighting condition 4 lighting conditions
1200
(QHUJ\
1000
E /HIWDQGULJKWHUURUPDSVFRPSXWHGDVWKHGLIIHUHQFHEHWZHHQWKH GLVSDULW\PDSVDQGJURXQGWUXWK
)LJXUH 6\QWKHVL]HG GDWD ,PDJH PDWFKLQJ XVLQJ 05) DQG VWRFKDVWLFDSSURDFK
800
600
400
200
0 0
20
40
60
80
100
80
100
,WHUDWLRQV
E &RQWLQXLW\HQHUJ\
([SHULPHQWDO UHVXOWV RQ UHDO LPDJHU\ DUH VKRZQ LQ )LJXUH 6LPLODUO\ ZH FRQVLGHUHG IRXU OLJKWLQJ FRQGLWLRQV GXULQJ WKH LPDJH DFTXLVLWLRQ 7KH IRXU OLJKWLQJ FRQGLWLRQV VWHUHR SDLUV ZHUH XVHG DW WKH VDPH WLPH WR JHQHUDWH WKH GLVSDULW\ PDSV )LUVW URZ VKRZV RQH RI WKH IRXU VWHUHRLPDJH SDLUV 6HFRQG URZ VKRZV WKHGLVSDULW\PDSVFRPSXWHGE\WKHVWRFKDVWLFDSSURDFK RQWKH05)
2FFOXVLRQVWHUP 4000 1 lighting condition 4 lighting conditions 3500
(QHUJ\
3000
2500
2000
1500
1000
500
0 0
20
40
60
,WHUDWLRQV
D *UD\OHYHOVWHUHRSDLU
F 1XPEHURIRFFOXVLRQVHQHUJ\
)LJXUH(YROXWLRQRIWKHHQHUJ\IXQFWLRQDOFRPSRQHQWV
$0DUNRY5DQGRP)LHOG0RGHODQG0HWKRGWR,PDJH0DWFKLQJ
1RWH WKDW ERWK WKH QXPEHU RI RFFOXVLRQV DQG FRQWLQXLW\ HQHUJLHV GHFUHDVH DQG FRQYHUJH WRZDUGV D VPDOO YDOXH 7KH PDWFKLQJ HQHUJ\ DOVR FRQYHUJHV WR D VWDEOHYDOXH7KLVYDOXHLVKLJKHUWKDQWKHLQLWLDOYDOXH DVWKHPDWFKHGSL[HOVGRQRWKDYHQHFHVVDULO\WKHVDPH JUD\OHYHO
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
5HIHUHQFHV >@ $DUWV ( DQG /DDUKRYHQ 3 6LPXODWHG $QQHDOLQJ DQG $SSOLFDWLRQV .OXZHU $FDGHPLF 3XEOLVKHUV +ROODQG >@ %HQDPHXU : ³&RPSXWLQJ WKH ,QLWLDO 7HPSHUDWXUH RI 6LPXODWHG $QQHDOLQJ´ &RPSXWDWLRQDO 2SWLPL]DWLRQ DQG $SSOLFDWLRQV YRO QRSS >@ %HQ$UL 5 DQG 6RFKHQ 1 ³$ *HRPHWULF $SSURDFKIRU5HJXODUL]DWLRQRIWKH'DWD7HUPLQ 6WHUHR9LVLRQ´-RXUQDORI0DWKHPDWLFDO,PDJLQJ DQG9LVLRQYROQRSS >@ %HUWHUR 0 3RJJLR 7 DQG 7RUUH 9 ³,OO3RVHG 3UREOHPVLQ(DUO\9LVLRQ´LQ3URFHHGLQJVRIWKH ,(((SS >@ %R\NRY @ &DVWHOODQL 8 )XVLHOOR $ *KHUDUGL 5 DQG 0XULQR9³$XWRPDWLF6HOHFWLRQRI05)&RQWURO 3DUDPHWHUVE\5HDFWLYH7DEX6HDUFK´,PDJHDQG 9LVLRQ&RPSXWLQJYROQRSS
>@ &RUVR - 7X = DQG <XLOOH $ ³05) /DEHOLQJ ZLWKD*UDSK6KLIWV$OJRULWKP´LQ3URFHHGLQJV RI /HFWXUH 1RWHV LQ &RPSXWHU 6FLHQFH %HUOLQ SS >@ )DXJHUDV 2 DQG .HULYHQ 5 ³&RPSOHWH GHQVH 6WHUHR 9LVLRQ XVLQJ /HYHO 6HW 0HWKRGV´ LQ 3URFHHGLQJV RI /HFWXUH 1RWHV LQ &RPSXWHU 6FLHQFHSS > @ *HPDQ 6 DQG *HPDQ ' ³6WRFKDVWLF 5HOD[DWLRQ *LEEV 'LVWULEXWLRQV DQG WKH %D\HVLDQ 5HVWRUDWLRQ RI ,PDJHV´ ,((( 7UDQVDFWLRQV RQ 3DWWHUQ $QDO\VLV DQG 0DFKLQH ,QWHOOLJHQFHYROQRSS >@ +XDQJ - DQG /LX + ³6WHUHR 9LVLRQ XVLQJ 0LFURFDQRQLFDO 0HDQ)LHOG $QQHDOLQJ 1HXUDO 1HWZRUN´ 1HXUDO &RPSXWDWLRQV YRO QR SS >@ +XT 6 $ELGL % DQG $ELGL 0 ³6WHUHR%DVHG ' )DFH 0RGHOLQJ XVLQJ $QQHDOLQJ LQ /RFDO (QHUJ\ 0LQLPL]DWLRQ´ LQ 3URFHHGLQJV RI WK ,QWHUQDWLRQDO&RQIHUHQFHRQ,PDJH$QDO\VLVDQG 3URFHVVLQJ0RGHQDSS >@ ,VKLNDZD + ³([DFW 2SWLPL]DWLRQ IRU 0DUNRY 5DQGRP )LHOGV ZLWK &RQYH[ 3ULRUV´ ,((( 7UDQVDFWLRQV RQ 3DWWHUQ $QDO\VLV DQG 0DFKLQH ,QWHOOLJHQFH YRO QR SS >@ -LD @ .RPRGDNLV 1 7]LULWDV * DQG 3DUDJLRV 1 ³3HUIRUPDQFH YV &RPSXWDWLRQDO (IILFLHQF\ IRU 2SWLPL]LQJ 6LQJOH DQG '\QDPLF 05)V 6HWWLQJ WKH6WDWHRIWKH$UWZLWK3ULPDO'XDO6WUDWHJLHV´ &RPSXWHU 9LVLRQ DQG ,PDJH 8QGHUVWDQGLQJ 6SHFLDO ,VVXH RQ 'LVFUHWH 2SWLPL]DWLRQ LQ &RPSXWHU 9LVLRQ YRO QR SS >@ 1H¶PD % DQG $OL + ³0XOWLSXUSRVH &RGH *HQHUDWLRQ XVLQJ )LQJHUSULQW ,PDJHV´ ,QWHUQDWLRQDO $UDE -RXUQDO RI ,QIRUPDWLRQ 7HFKQRORJ\YROQRSS >@ 5DGKDNULVKQDQ 6 6XEEDUD\DQ * DQG 9LNUDP . ³:DYHOHWV %DVHG 9LGHR (QFRGHU XVLQJ .&'6´ 7KH ,QWHUQDWLRQDO $UDE -RXUQDO RI ,QIRUPDWLRQ 7HFKQRORJ\ YRO QR SS >@ 5DG]LV]HZVNL 0 DQG $OGD : ³)DPLO\ RI (QHUJ\ &RQVHUYLQJ *ORVV\ 5HIOHFWLRQ 0RGHOV´ LQ 3URFHHGLQJV RI /HFWXUH 1RWHV LQ &RPSXWHU 6FLHQFH%HUOLQSS >@ 6FKOLFN & ³$Q ,QH[SHQVLYH %5') 0RGHO IRU 3K\VLFDOO\%DVHG 5HQGHULQJ´ &RPSXWHU *UDSKLFV )RUXP YRO QR SS
7KH,QWHUQDWLRQDO$UDE-RXUQDORI,QIRUPDWLRQ7HFKQRORJ\9RO 1R1RYHPEHU
> @ 6XQ\RWR + 0DUN : DQG *DYULOD ' ³$ &RPSDUDWLYH 6WXG\ RI )DVW 'HQVH 6WHUHR 9LVLRQ $OJRULWKPV´ ,QWHOOLJHQW 9HKLFOHV 6\PSRVLXP ,(((YROQRSS >@ 6]HOLVNL 5 =DELK 5 6FKDUVWHLQ ' 9HNVOHU 2 .ROPRJRURY 9 $JDUZDOD $ 7DSSHQ 0 DQG 5RWKHU & ³$ &RPSDUDWLYH 6WXG\ RI (QHUJ\ 0LQLPL]DWLRQ 0HWKRGV IRU 0DUNRY 5DQGRP )LHOGV´ LQ 3URFHHGLQJV RI /HFWXUH 1RWHV LQ &RPSXWHU6FLHQFHSS >@ :DQJ / @ :HUGD , &KDRXFK + 6DPHW $ %HQ$\HG 0 DQG 0DVPRXGL 1 ³2SWLPDO '63 %DVHG ,QWHJHU 0RWLRQ (VWLPDWLRQ ,PSOHPHQWDWLRQ IRU +$9&%DVHOLQH(QFRGHU´7KH,QWHUQDWLRQDO $UDE -RXUQDO RI ,QIRUPDWLRQ 7HFKQRORJ\ YRO QRSS 0RKDPPHG2XDOLUHFHLYHGKLV3K' LQ UHDOWLPH URERWLFV DQG FRQWURO IURP 0LQHV 3DULV7HFK)UDQFH LQ +H KDV RYHU \HDUV RI H[SHULHQFH LQ GHYHORSLQJ HPEHGGHG V\VWHPV LQ DHURQDXWLFV DXWRPRWLYH LQGXVWU\DQG&$'V\VWHPVIRU9/6, UHYHUVH HQJLQHHULQJ +LV PDLQ UHVHDUFK LQWHUHVWV DUH LQ FRPSXWHUYLVLRQDQGSDWWHUQUHFRJQLWLRQ
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
