Contenu connexe Similaire à PMSpgray (20) 1. 70,
$EVWUDFW²,PDJH UHJLVWUDWLRQ WDVNV DUH RIWHQ IRUPXODWHG LQ
WHUPV RI PLQLPL]DWLRQ RI D IXQFWLRQDO FRQVLVWLQJ RI D GDWD ILGHOLW
WHUP SHQDOL]LQJ WKH PLVPDWFK EHWZHHQ WKH UHIHUHQFH DQG WKH
WDUJHW LPDJH DQG D WHUP HQIRUFLQJ VPRRWKQHVV RI VKLIW EHWZHHQ
QHLJKERULQJ SDLUV RI SL[HOV D PLQVXP SUREOHP 2. 0RVW PHWKRGV
IRU GHIRUPDEOH LPDJH UHJLVWUDWLRQ XVH VRPH IRUP RI LQWHUSRODWLRQ
EHWZHHQ PDWFKLQJ FRQWURO SRLQWV 7KH LQWHUSRODWLRQ PDNHV LW
LPSRVVLEOH WR DFFRXQW IRU LVRODWHG GLVFRQWLQXLWLHV LQ WKH
GHIRUPDWLRQ ILHOG WKDW PD DSSHDU HJ ZKHQ D SKVLFDO VOLFH RI D
PLFURVFRS VSHFLPHQ LV UXSWXUHG E WKH FXWWLQJ WRRO )RU
UHJLVWUDWLRQ RI QHLJKERULQJ SKVLFDO VOLFHV RI PLFURVFRS
VSHFLPHQV ZLWK GLVFRQWLQXLWLHV -DQiþHN SURSRVHG DQ /
GLVWDQFH
GDWD ILGHOLW WHUP DQG D WRWDO YDULDWLRQ 79 4. EDVHG LWHUDWLYH VWHHSHVW GHVFHQW DOJRULWKP
IRU PLQLPL]DWLRQ 7KH /
79 IXQFWLRQDO LV QRQFRQYH[ KHQFH D
VWHHSHVW GHVFHQW DOJRULWKP LV QRW JXDUDQWHHG WR FRQYHUJH WR WKH
JOREDO PLQLPXP 6FKOHVLQJHU SUHVHQWHG WUDQVIRUPDWLRQ RI PD[
VXP SUREOHPV WR PLQLPL]DWLRQ RI D GXDO TXDQWLW FDOOHG SUREOHP
SRZHU ZKLFK LV ± FRQWUDU WR WKH RULJLQDO PD[VXP IXQFWLRQDO ±
FRQYH[ %DVHG RQ 6FKOHVLQJHU
V VROXWLRQ WR PD[VXP SUREOHPV ZH
GHYHORSHG DQ DOJRULWKP IRU /
79 PLQLPL]DWLRQ E LWHUDWLYH
PXOWLODEHO VWHHSHVW GHVFHQW PLQLPL]DWLRQ RI WKH FRQYH[ GXDO
SUREOHP )RU 6FKOHVLQJHUV VXEJUDGLHQW DOJRULWKP ZH SURSRVHG D
QRYHO VWHS FRQWURO KHXULVWLFV WKDW FRQVLGHUDEO HQKDQFHV ERWK
VSHHG DQG DFFXUDF FRPSDUHG ZLWK VWDQGDUG VWHS VL]H VWUDWHJLHV
IRU VXEJUDGLHQW PHWKRGV ,W LV VKRZQ H[SHULPHQWDOO WKDW RXU
VXEJUDGLHQW VFKHPH DFKLHYHV FRQVLVWHQWO EHWWHU LPDJH
UHJLVWUDWLRQ WKDQ * LQ WHUPV RI ORZHU YDOXHV ERWK RI WKH
FRPSRVLWH /
79 IXQFWLRQDO DQG RI LWV FRPSRQHQWV LH WKH /
GLVWDQFH RI WKH LPDJHV DQG WKH WUDQVIRUPDWLRQ VPRRWKQHVV 79
DQG LHOGV YLVXDOO DFFHSWDEOH UHVXOWV HYHQ LQ FDVHV ZKHUH WKH *
EDVHG DOJRULWKP IDLOV 7KH QHZ DOJRULWKP DOORZV HDV
SDUDOOHOL]DWLRQ DQG FDQ WKXV EH VSHG XS E UXQQLQJ RQ PXOWLFRUH
38V RU *UDSKLF 3URFHVVLQJ 8QLWV
RSULJKW F 5. ,((( 3HUVRQDO XVH RI WKLV PDWHULDO LV SHUPLWWHG
+RZHYHU SHUPLVVLRQ WR XVH WKLV PDWHULDO IRU DQ RWKHU SXUSRVHV PXVW EH
REWDLQHG IURP WKH ,((( E VHQGLQJ D UHTXHVW WR SXEVSHUPLVVLRQV#LHHHRUJ
0DQXVFULSW UHFHLYHG -XQH UHYLVHG 'HFHPEHU DFFHSWHG
-DQXDU 7KLV UHVHDUFK ZDV VXSSRUWHG E WKH 0LQLVWU RI (GXFDWLRQ
RXWK DQG 6SRUWV RI WKH ]HFK 5HSXEOLF /+ 8. DQG E WKH 6XSSRUW IRU ORQJWHUP FRQFHSWXDO
GHYHORSPHQW RI UHVHDUFK RUJDQL]DWLRQ 592
-DQ 0LFKiOHN DQG 0DUWLQ ýDSHN DUH ZLWK WKH ,QVWLWXWH RI 3KVLRORJ
$FDGHP RI 6FLHQFHV RI WKH ]HFK 5HSXEOLF YYL 'HSW RI %LRPDWKHPDWLFV
9tGHĖVNi = 3UDJXH ]HFK 5HSXEOLF HPDLO PLFKDOHN#
ELRPHGFDVF] 9. ,QGH[ 7HUPV²,PDJH UHJLVWUDWLRQ FRQYH[ RSWLPL]DWLRQ
VXEJUDGLHQW DOJRULWKP WRWDO YDULDWLRQ
, ,1752'87,21
$1 LPDJH UHJLVWUDWLRQ WDVNV WKDW DULVH LQ PHGLFDO
LPDJH SURFHVVLQJ FDQ EH QDWXUDOO H[SUHVVHG LQ WHUPV RI
PLQLPL]DWLRQ RI VRPH IXQFWLRQDO WKDW NHHSV LQ EDODQFH WZR
LWHPV VLPLODULW EHWZHHQ WKH WZR LPDJHV EHLQJ UHJLVWHUHG DQG
UHVWULFWLRQV RQ WKH GHIRUPDWLRQ QHHGHG WR DOLJQ WKH WZR LPDJHV
,Q PRVW UHJLVWUDWLRQ DOJRULWKPV WKH UHVWULFWLRQV LPSRVHG RQ WKH
GHIRUPDWLRQ ILHOG DVVXPH WKDW WKH PLVPDWFK EHWZHHQ WKH WDUJHW
DQG WKH UHIHUHQFH LPDJH ZDV FDXVHG E VRPH FRQWLQXRXV
SKVLFDO WUDQVIRUPDWLRQ DQG SHQDOL]H GLVFRQWLQXLWLHV LQ EDFN
WUDQVIRUPDWLRQ XVHG IRU UHJLVWUDWLRQ 7KH DVVXPSWLRQ WKDW D
SKVLFDO GHIRUPDWLRQ LV FRQWLQXRXV QHHG QRW EH DOZDV FRUUHFW
2QH VXFK H[DPSOH LV UHJLVWUDWLRQ RI QHLJKERULQJ SKVLFDO VOLFHV
RI ELRORJLFDO VSHFLPHQV LQ PLFURVFRS ZKLFK LV QHHGHG ZKHQ
WKH ' YROXPH LV EHLQJ UHFRQVWUXFWHG IURP VHULHV RI LPDJHV
DFTXLUHG E HJ FRQIRFDO ODVHU VFDQQLQJ PLFURVFRS /60 10. RU RSWLFDO PLFURVFRS 3KVLFDO VOLFHV RI ELRORJLFDO VSHFLPHQV
PD JHW HODVWLFDOO GHIRUPHG RU HYHQ QRQFRQWLQXRXVO
GLVWRUWHG E WKH FXWWLQJ WRRO DV LQ )LJ OHIW LQVLGH WKH RYDO 11. )RU ' YROXPH UHFRQVWUXFWLRQ GLVFRQWLQXLWLHV VXFK DV
ILVVXUHV UXSWXUHV HWF VKRXOG LGHDOO EH UHSDLUHG LQ UHJLVWHUHG
$ 3LHFHZLVH 0RQRWRQH 6XEJUDGLHQW $OJRULWKP
IRU $FFXUDWH /
79 %DVHG 5HJLVWUDWLRQ RI
3KVLFDO 6OLFHV :LWK 'LVFRQWLQXLWLHV LQ
0LFURVFRS
-DQ 0LFKiOHN 0HPEHU ,((( DQG 0DUWLQ ýDSHN
0
)LJ /LJKW PLFURVFRSH LPDJHV RI QHLJKERULQJ SKVLFDO VHFWLRQV RI D WXUWOH
HPEUR KHDG 2Q WKH OHIW LV WKH WDUJHW LPDJH ZKLFK ZLOO EH ZDUSHG E WKH
UHJLVWUDWLRQ DOJRULWKP WR PDWFK DV FORVHO DV SRVVLEOH WKH UHIHUHQFH LPDJH 2Q
WKH ULJKW WKHUH LV WKH UHIHUHQFH LPDJH ZKLFK ZLOO UHPDLQ XQFKDQJHG E
UHJLVWUDWLRQ
12. 70,
LPDJHV DQG WKXV WKH GHIRUPDWLRQ ILHOG XVHG IRU UHJLVWUDWLRQ
PXVW FRQWDLQ GLVFRQWLQXLWLHV 7KHUHIRUH WKH IXQFWLRQDO EHLQJ
PLQLPL]HG PXVW QRW SHQDOL]H LVRODWHG GLVFRQWLQXLWLHV $IILQH RU
HODVWLF UHJLVWUDWLRQ FDQQRW FRSH ZLWK WKLV WDVN VLQFH ERWK
DVVXPH WKDW WKH WUDQVIRUPDWLRQ DOLJQLQJ WKH WDUJHW LPDJH WR WKH
UHIHUHQFH LV FRQWLQXRXV 7R VKRZ WKLV ZH FKRVH IRXU H[DPSOHV
RI LPDJH UHJLVWUDWLRQ VRIWZDUH IUHHO GRZQORDGDEOH IURP WKH
LQWHUQHW DQG DWWHPSWHG UHJLVWUDWLRQ RI WKH LPDJH SDLU LQ )LJ
XVLQJ WKHP ,Q SDUWLFXODU ZH DSSOLHG WKH IROORZLQJ VRIWZDUH
D 15. WKH GHPRQV DOJRULWKP IRU
PXOWLPRGDO QRQULJLG UHJLVWUDWLRQ RI LPDJHV LPSOHPHQWHG LQ
0DWODE @ LQ WKH IRRWVWHSV RI @ DQG G 16. WKH E8QZDUS-
HODVWLF UHJLVWUDWLRQ SOXJLQ RI ,PDJH- @ 5HJLVWUDWLRQ UHVXOWV
DFKLHYHG XVLQJ WKH IRXU VRIWZDUH SDFNDJHV DUH VKRZQ LQ )LJ
,W LV REYLRXV WKDW WKH JDS WKDW VKRXOG EH FORVHG E
UHJLVWUDWLRQ RI )LJ OHIW WR )LJ ULJKW KDV RQO EHFRPH
VRPHZKDW QDUURZHU WKURXJK FRQWLQXRXV UHJLVWUDWLRQ E WKH IRXU
UHJLVWUDWLRQ DOJRULWKPV LQ TXHVWLRQ
,PDJH UHJLVWUDWLRQ LQ SUHVHQFH RI GLVFRQWLQXLWLHV LQ WKH
GHIRUPDWLRQ ILHOG FDQ EH LPSURYHG XVLQJ WRWDO YDULDWLRQ EDVHG
UHJXODUL]HUV DV SURSRVHG LQ @ @ RU @ ,Q @ DQG @ WKH
LPDJHV EHLQJ UHJLVWHUHG DV ZHOO DV WKH GLVSODFHPHQW ILHOG
UHVXOWLQJ IURP UHJLVWUDWLRQ DUH GHILQHG RQ D VXEVHW RI WKH UHDO
FRRUGLQDWH VSDFH 5
DQG DOVR WKH YDOXHV RI WKH GLVSODFHPHQW
ILHOG DUH SDLUV RI UHDO QXPEHUV RQWUDU WR WKDW @ UHOLHV RQ D
GLVFUHWH SUREOHP VWDWHPHQW ZLWK LQWHJHUYDOXHG SL[HO
FRRUGLQDWHV DQG GLVSODFHPHQW ILHOG 7KH GLVFUHWH SUREOHP LV
VROYHG LWHUDWLYHO XVLQJ WKH JUDSKFXWV * 17. DOJRULWKP @ ,Q
WKLV SDSHU ZH GHVFULEH DQ DOWHUQDWLYH PRUH DFFXUDWH
DOJRULWKP VROYLQJ WKH SUREOHP VWDWHPHQW RI @
7KH SDSHU LV EXLOW XS LQ WKH IROORZLQJ PDQQHU ZH ILUVW
IRUPXODWH WKH LPDJH UHJLVWUDWLRQ SUREOHP LQ WHUPV RI
PLQLPL]DWLRQ RI WKH GLVFUHWH /
79 IXQFWLRQDO DQG EULHIO
VNHWFK WKH * EDVHG VWHHSHVW GHVFHQW DOJRULWKP RI @ 7KHQ
ZH SURSRVH D QHZ PXOWLODEHO DOJRULWKP LQ ZKLFK ± LQ
FRQWUDVW WR D VLQJOH GLUHFWLRQ RI SRVVLEOH SL[HO VKLIWV HYDOXDWHG
LQ HDFK LWHUDWLRQ E * ± PXOWLSOH GLUHFWLRQV RI WDUJHW LPDJH
ZDUSLQJ DUH FRPSHWLQJ IRU RSWLPDOLW LQ HDFK VWHHSHVW GHVFHQW
VWHS :H VKRZ KRZ WKH PXOWLODEHO PLQLPL]DWLRQ RI WKH
GLVFUHWH /
79 IXQFWLRQDO FDQ EH FDVW LQWR WKH IUDPHZRUN RI
PD[LPXP VXP RSWLPL]DWLRQ SUHVHQWHG LQ @ 2QH SUREOHP
DGGUHVVHG RQO LQ SDVVLQJ LQ @ LV WKH VHOHFWLRQ RI WKH
JUDGLHQW VWHS VL]H ,Q WKHLU H[DPSOHV WKH DXWKRUV XVHG
KDUPRQLF VHULHV DQG SRLQWHG RXW H[SOLFLWO WKDW RSWLPL]DWLRQ RI
WKH VWHS VL]H ZRXOG UHTXLUH IXUWKHU UHVHDUFK :H H[SHULPHQWHG
ERWK ZLWK WKH KDUPRQLF VHULHV DQG ZLWK RWKHU VWUDWHJLHV RI VWHS
VL]H VHOHFWLRQ IRXQG HJ LQ @ @ DQG @ $OO RI WKHP
OHG WR VORZ FRQYHUJHQFH :H WKHUHIRUH SURSRVHG D QHZ VWHS
FRQWURO VWUDWHJ ZKLFK LQ SUDFWLFH FRQYHUJHV FRQVLGHUDEO
IDVWHU DQG LHOGV PXFK PRUH SUHFLVH UHVXOWV PHDVXUHG E WKH
GLIIHUHQFH EHWZHHQ WKH PD[LPXP VXP DQG LWV GXDO YDOXH WKH
SUREOHP SRZHU ZKLFK VKRXOG EH DV VPDOO DV SRVVLEOH
:H FRPSDUH WKH UHVXOWV REWDLQHG E WKH QHZ VXEJUDGLHQW
VWUDWHJ ZLWK WKRVH DFKLHYDEOH E WKH /
79 SULPDOGXDO
DOJRULWKP @ DQG E WKH JUDSKFXW PLQLPL]DWLRQ @
,, 35(9,286 :25.
2XW RI WKH YDVW OLWHUDWXUH RQ PHGLFDO LPDJH UHJLVWUDWLRQ ZH
UHYLHZ KHUH RQO WKUHH VXEWRSLFV KDYLQJ VRPH FRPPRQ
IHDWXUHV ZLWK WKH SUHVHQW ZRUN
x UHJLVWUDWLRQ RI PLFURVFRS LPDJHV
x PXOWLODEHO GHQVH LPDJH UHJLVWUDWLRQ DSSURDFK E *ORFNHU
@
x LPDJH UHJLVWUDWLRQ LQYROYLQJ D WRWDO YDULDWLRQ 79 18. EDVHG
UHJXODUL]HU
1RQULJLG UHJLVWUDWLRQ RI PLFURVFRS LPDJHV KDV EHHQ
DGGUHVVHG LQ D QXPEHU RI SUHYLRXV SDSHUV 7KH PDMRULW RI WKH
DSSURDFKHV PRGHO WKH KRUL]RQWDO DQG WKH YHUWLFDO FRPSRQHQWV
RI WKH GHIRUPDWLRQ ILHOG WKH YHFWRU ILHOG RI VKLIWV ZKLFK ZRXOG
PRYH SL[HOV RI WKH WDUJHW LPDJH WR WKH SRVLWLRQ RI UHODWHG SL[HOV
LQ D UHIHUHQFH LPDJH 19. XVLQJ FRQWLQXRXV DQG VPRRWK VSOLQH
IXQFWLRQV 3UREDEO WKH ILUVW DSSOLFDWLRQ RI VSOLQH IXQFWLRQV WR
)LJ 7KH IRXU LPDJH UHJLVWUDWLRQ SDFNDJHV GRZQORDGHG IURP WKH LQWHUQHW VHH WH[W 20. SURGXFH FRQWLQXRXV EDFN WUDQVIRUPDWLRQ ILHOGV DQG WKHUHIRUH DUH QRW
DEOH WR FORVH WKH JDS FDXVHG E D WLVVXH UXSWXUH FDXVHG E FXWWLQJ RI WKH VSHFLPHQ 7KH UHJLVWHUHG LPDJHV VKRZ WKH EHVW UHVXOWV ZH ZHUH DEOH WR REWDLQ E
YDULQJ SDUDPHWHUV RI IRXU IUHHZDUH UHJLVWUDWLRQ SDFNDJHV D 23. WKH GHPRQV DOJRULWKP IRU PXOWLPRGDO QRQULJLG
UHJLVWUDWLRQ RI LPDJHV LPSOHPHQWHG LQ 0DWODE @ DV RXWOLQHG LQ @ DQG G 25. 70,
HODVWLF UHJLVWUDWLRQ RI FRQIRFDO LPDJHV ZDV UHSRUWHG E
5RKOILQJ @ ZKHUH WKLUGRUGHU %VSOLQHV ZHUH XVHG WR
WUDQVIRUP WKH ' FRRUGLQDWH VSDFH RI VHJPHQWHG LPDJHV
JHQHUDWHG IURP WZHQW ' FRQIRFDO PLFURVFRS LPDJHV RI EHH
EUDLQV LQWR D FRPPRQ UHIHUHQFH FRRUGLQDWH VVWHP GHILQHG E
DQ DYHUDJH GHIRUPDWLRQ
6WHZDUW HW DO @ LQWURGXFHG D YLHZEDVHG DSSURDFK WR
LPDJH UHJLVWUDWLRQ 7KH DXWKRUV FRPSDUHG IRXU GLIIHUHQW
GHIRUPDWLRQ PRGHOV RXW RI ZKLFK WZR ZHUH QRQOLQHDU
TXDGUDWLF 26. HW FRQWLQXRXV 7KH ILUVW DOLJQHG WKH LPDJHV RQO
LQ D VPDOO UHJLRQ DQG JUDGXDOO LQFUHDVHG WKH UHJLRQ VL]H D
FKDQJH LQ YLHZ 27. 7KH DSSURDFK ZDV DSSOLHG WR UHJLVWHULQJ
FRQIRFDO VWDFNV RI QHXURQDO DQG YDVFXODU UDW EUDLQ 28. LPDJHV
DQJ HW DO @ SURSRVHG D QRQSDUDPHWULF DSSURDFK WR
QRQULJLG UHJLVWUDWLRQ RI PXOWLFKDQQHO ' FRQIRFDO LPDJHV RI
FHOO QXFOHL LQ ZKLFK WKH GHIRUPDWLRQ ILHOG EHWZHHQ WKH
UHIHUHQFH DQG WKH WDUJHW LPDJH LV JHQHUDWHG XVLQJ WKH GHPRQV
DOJRULWKP E 7KLULRQ @ 7KH GHPRQV DOJRULWKP PLQLPL]HV
WKH VTXDUHG VXP RI GLVWDQFHV EHWZHHQ WKH UHJLVWHUHG DQG WKH
UHIHUHQFH LPDJH XVLQJ WKH JUDGLHQW PHWKRG RQWLQXRXV
GHIRUPDWLRQ ILHOG LV DVVXPHG 3ULRU WR UHJLVWUDWLRQ WKH FHOO
QXFOHL LPDJHV DUH VPRRWKHG XVLQJ D *DXVVLDQ ILOWHU
6FKPLWW HW DO @ DSSOLHG HODVWLF UHJLVWUDWLRQ WR DOLJQ
FRQIRFDO LPDJHV RI VHFWLRQHG EUDLQV 7KH IXQFWLRQ WR EH
PLQLPL]HG XVHV VXP RI VTXDUHG GLIIHUHQFHV DV D PHDVXUH RI
VLPLODULW EHWZHHQ WKH LPDJHV DQG WKH HODVWLF SRWHQWLDO DV D
UHJXODUL]HU 7KH DOJRULWKP DVVXPHV DJDLQ WKDW WKH GHIRUPDWLRQ
ILHOG LV FRQWLQXRXV
,Q @ *ORFNHU HW DO SUHVHQWHG DQ LPDJH UHJLVWUDWLRQ
DOJRULWKP ZKLFK PLQLPL]HV D GLVFUHWH FRVW IXQFWLRQDO E
ILQGLQJ D ORZHU ERXQG RQ LWV YDOXH WKURXJK VROYLQJ D GXDO
SUREOHP REWDLQHG E PHWKRGV RI OLQHDU SURJUDPPLQJ GXDOLW
7KH DSSURDFK RI @ DVVXPHV WKDW WKH GHQVH GHIRUPDWLRQ ILHOG
FDQ EH H[SUHVVHG XVLQJ D VPDOOHU QXPEHU RI FRQWURO SRLQWV
UHJLVWUDWLRQ JULG 29. DQG LQWHUSRODWLRQ EHWZHHQ WKHP 7KH
LQWHUSRODWLRQ ZLOO RI FRXUVH SURGXFH FRQWLQXRXV GLVSODFHPHQW
ILHOG DQG VPRRWK DQ GLVFRQWLQXLWLHV EHWZHHQ FRQWURO SRLQWV ,Q
RUGHU WR DFFRXQW IRU ODUJH GHIRUPDWLRQV DQG SURGXFH UHVXOWV RQ
D KLJK UHVROXWLRQ OHYHO D PXOWLVFDOH LQFUHPHQWDO DSSURDFK
ZKHUH WKH RSWLPDO VROXWLRQ LV LWHUDWLYHO XSGDWHG LV FRQVLGHUHG
LQ @ 7KH FRQWURO JULG LV VXFFHVVLYHO UHILQHG E GHFUHDVLQJ
WKH JULG SRLQW VSDFLQJ E D IDFWRU RI WZR ZKLOH DW WKH VDPH WLPH
WKH DOJRULWKP XVHV D *DXVVLDQ SUDPLG IRU WKH LPDJH GDWD )RU
PRVW DSSOLFDWLRQV WKUHH OHYHOV DUH FODLPHG WR EH VXIILFLHQW
/DEHOV LQ @ GHILQH D ILQLWH VHW RI GLVSODFHPHQWV (DFK ODEHO
HQFRGHV ERWK WKH GLUHFWLRQ DQG WKH OHQJWK RI DQ DOWHUQDWLYH
VKLIW ZLWK D VHW RI GLIIHUHQW OHQJWKV DYDLODEOH IRU HDFK VKLIW
GLUHFWLRQ 7ZR WSHV RI VDPSOLQJ FDQ EH FKRVHQ
x 6SDUVH VDPSOLQJ FRQVLGHUV RQO GLVSODFHPHQWV DORQJ WKH
PDLQ D[HV ,I WKHUH DUH 1 SRVVLEOH GLVSODFHPHQWV LQ RQH
GLUHFWLRQ 1' 30. ODEHOV DUH QHHGHG WR HQFRGH DOO
SRVVLEOH VKLIWV LQ ' GLPHQVLRQV )RU WKH GHIDXOW YDOXH RI
1 WKLV UHVXOWV HJ IRU ' LPDJHV LQ DQG IRU ' LQ
ODEHOV HQFRGLQJ DOO SRVVLEOH GLVSODFHPHQWV
x 'HQVH VDPSOLQJ FRQVLGHUV DOO 1 34. FXEH
)RU WKH GHIDXOW YDOXH RI 1 WKLV UHVXOWV HJ IRU '
LPDJHV LQ ODEHOV
7KH QXPEHU RI SRLQWV HYDOXDWHG LQ PLQLPL]DWLRQ RI WKH FRVW
IXQFWLRQDO LQ @ LV UHGXFHG E WKH VHOHFWLRQ RI WKH FRQWURO JULG
7KH DOJRULWKP LV IXUWKHU VSHG XS E XVLQJ D )DVW3' PXOWL
ODEHO PLQLPL]DWLRQ DOJRULWKP $ SULQFLSDO OLPLWDWLRQ RI WKH
)DVW3' DOJRULWKP LV WKDW LW DVVXPHV ELQDU ZHLJKWV LQ WKH
IXQFWLRQDO EHLQJ PLQLPL]HG WR EH D VHPLPHWULF 7KXV WKH
UHJLVWUDWLRQ DOJRULWKP RI @ LV UHVWULFWHG WR FRQWLQXRXV
UHJLVWUDWLRQ E PLQLPL]DWLRQ RI GLVFUHWH IXQFWLRQDOV ZLWK RQO
VHPLPHWULF ELQDU ZHLJKWV
RQWLQXRXV DOEHLW QRQOLQHDU LPDJH UHJLVWUDWLRQ GRHV QRW
SURYLGH D GHILQLWLYH SUREOHP VROXWLRQ IRU WKH DOLJQPHQW RI
PLFURVFRS LPDJHV RI GLIIHUHQW SKVLFDO VOLFHV VLQFH GXULQJ
VHFWLRQLQJ WKH ELRORJLFDO WLVVXH PD EH LUUHYHUVLEO GLVWRUWHG
E WKH FXWWLQJ WRRO 'LIIHUHQW VHFWLRQV PD DVVXPH GLIIHUHQW
VKDSHV GXH WR ILVVXUHV UXSWXUHV RU IROGV KDYLQJ QR FRXQWHUSDUW
LQ WKHLU QHLJKERUV 0DWFKLQJ VXFK LPDJHV WR XQGLVWRUWHG RQHV
ZLOO UHTXLUH GLVFRQWLQXRXV GLVSODFHPHQWV 7KLV WDVN FDQQRW EH
DFFRPSOLVKHG E DOJRULWKPV IRU FRQWLQXRXV UHJLVWUDWLRQ
7R LPSURYH UHJLVWUDWLRQ RI LPDJHV ZLWK GLVSODFHPHQW
GLVFRQWLQXLWLHV YDULRXV DXWKRUV SURSRVHG D QXPEHU RI
UHJLVWUDWLRQ DOJRULWKPV XVLQJ WRWDO YDULDWLRQ DV D UHJXODUL]HU
,Q 79 EDVHG LPDJH UHJLVWUDWLRQ GLVFRQWLQXLWLHV LQ WKH
GLVSODFHPHQW ILHOG DUH QRW SHQDOL]HG EHFDXVH RQ D UHJLRQ RI
PRQRWRQ WKH WRWDO YDULDWLRQ HTXDOV WKH GLIIHUHQFH EHWZHHQ WKH
IXQFWLRQ PD[LPXP DQG PLQLPXP DQG LV QRW DIIHFWHG E
LVRODWHG GLVFRQWLQXWLHV RI WKH ILUVW NLQG $W WKH VDPH WLPH
PLQLPL]DWLRQ RI WKH WRWDO YDULDWLRQ HQIRUFHV VPRRWKQHVV RI WKH
GHIRUPDWLRQ ILHOG VLQFH WKH WRWDO YDULDWLRQ SHQDOL]HV
RVFLOODWLRQV 7KLV LV H[SODLQHG LQ )LJ
)URKQ±6FKDXI HW DO @ SURSRVHG D WRWDO YDULDWLRQ EDVHG
UHJXODUL]DWLRQ ZLWK WKH JRDO WR LPSURYH WKH FRQGLWLRQ RI WKH
UHJLVWUDWLRQ SUREOHP E QRW SHQDOL]LQJ GLVFRQWLQXLWLHV LQ WKH
GLVSODFHPHQW ILHOG ,PDJHV DUH GHILQHG RQ D VXEVHW RI 5
DQG
YDOXHV RI WKH GLVSODFHPHQW ILHOG DUH SDLUV RI UHDO QXPEHUV 7KH
DXWKRUV XVH WKH /
QRUP RI WKH GLIIHUHQFH WR PHDVXUH VLPLODULW
EHWZHHQ WKH UHJLVWHUHG DQG WKH UHIHUHQFH LPDJH DQG FRPSXWH
WKH GLVSODFHPHQW ILHOG LWHUDWLYHO E PLQLPL]LQJ WKH VXP RI D
VHFRQGRUGHU H[SDQVLRQ RI WKH PDWFKLQJ HQHUJ DURXQG WKH
FXUUHQW DSSUR[LPDWLRQ RI WKH GLVSODFHPHQW ILHOG DQG WKH WRWDO
YDULDWLRQ RI WKH FKDQJH RI WKH GLVSODFHPHQW ILHOG LQ WKH FXUUHQW
LWHUDWLRQ VWHS
3RFN HW DO @ SUHVHQWHG DQRWKHU IRUPXODWLRQ RI WKH LPDJH
UHJLVWUDWLRQ WDVN EDVHG RQ PLQLPL]DWLRQ RI D IXQFWLRQDO
FRQVLVWLQJ RI WZR WHUPV WKH /
GLVWDQFH EHWZHHQ WKH UHJLVWHUHG
DQG WKH UHIHUHQFH LPDJH DQG WKH FRQWLQXRXV WRWDO YDULDWLRQ RI
WKH GLVSODFHPHQW ILHOG ,PDJHV DUH GHILQHG RQ D VXEVHW RI 5
ZKLFK LV PDSSHG E WKH GLVSODFHPHQW ILHOG WR 5
7KH
PLQLPL]DWLRQ ZLWK UHVSHFW WR WKH GLVSODFHPHQW ILHOG UHOLHV RQ D
GXDO IRUPXODWLRQ RI WKH WRWDO YDULDWLRQ HQHUJ DQG XVHV WKH
SURMHFWLRQ DOJRULWKP GHVFULEHG LQ @ WR ILQG WKH VROXWLRQ
RQWUDU WR @ ZKHUH WRWDO YDULDWLRQ RI WKH GLVSODFHPHQW ILHOG
FKDQJH LQ LQGLYLGXDO LWHUDWLRQV LV DVVHVVHG WKH SUREOHP
35. 70,
VWDWHPHQW @ XVHV WKH WRWDO YDULDWLRQ RI WKH GLVSODFHPHQW ILHOG
RI WKH UHVXOWLQJ UHJLVWHUHG LPDJH DV UHJXODUL]HU $OVR @ XVHV
WKH /
QRUP UDWKHU WKDQ /
VLQFH /
LV PRUH UREXVW
DJDLQVW RXWOLHUV LQ WKH LQWHQVLW YDOXHV WKDQ WKH TXDGUDWLF QRUP
7KH WUDGHRII EHWZHHQ WKH WUDQVIRUPDWLRQ VPRRWKQHVV DQG WKH
VLPLODULW EHWZHHQ WKH WUDQVIRUPHG WDUJHW DQG WKH UHIHUHQFH
LPDJH H[SUHVVHG E WKH /
WHUP LV FRQWUROOHG E D VHOHFWDEOH
SDUDPHWHU
7R DOORZ IRU UHJLVWUDWLRQ RI GLVFRQWLQXLWLHV LQ SKVLFDO VOLFHV
RI PLFURVFRS VSHFLPHQV VXFK DV UXSWXUHV ILVVXUHV RU JDSV
WKDW PD DULVH GXULQJ WKH FXWWLQJ RI WKH VSHFLPHQ -DQiþHN @
SURSRVHG PLQLPL]DWLRQ RI D GLVFUHWH YDOXHG /
79 IXQFWLRQDO
GHILQHG RQ D GLVFUHWH LPDJH JULG 7KH GLVSODFHPHQW ILHOG
UHVXOWLQJ IURP UHJLVWUDWLRQ LV GLVFUHWH WRR )RU GLUHFW
PLQLPL]DWLRQ RI WKH /
79 IXQFWLRQDO D VWHHSHVW GHVFHQW
DOJRULWKP EDVHG RQ JUDSKFXWV .ROPRJRURY DQG =DELK @ 36. ZDV XVHG 7KH VWHHSHVW GHVFHQW DOJRULWKP VROYHV D VHTXHQFH RI
PD[IORZ SUREOHPV 7KH DGYDQWDJH RI WKH GLVFUHWH VHWWLQJ LQ
@ FRPSDUHG WR WKH DOJRULWKP RI @ OLHV LQ WKH IDFW WKDW WKH *
DOJRULWKP LV JXDUDQWHHG WR WHUPLQDWH ZLWKRXW WKH QHHG IRU DQ
VWRSSLQJ FULWHULRQ DQG LW LV IDVW
,,, 7+( 7(67 '$7$
)RXU LPDJH SDLUV ZLWK GLVFRQWLQXLWLHV LQ WKH GHIRUPDWLRQ
ILHOG ZHUH XVHG WR YDOLGDWH WKH SHUIRUPDQFH RI WKH /
79 EDVHG
UHJLVWUDWLRQ DOJRULWKP SURSRVHG LQ WKLV VWXG DQG IRU LWV
FRPSDULVRQ ZLWK WKH SHUIRUPDQFH RI IUHHO DYDLODEOH LPDJH
UHJLVWUDWLRQ VRIWZDUH SDFNDJHV
7KH ILUVW WHVW SDLU )LJ 37. ZDV FUHDWHG VQWKHWLFDOO ZLWK WKH
DLP WR SURYLGH KLJK FRQWUDVW LPDJHV DOORZLQJ LPPHGLDWH YLVXDO
LQVSHFWLRQ RI WKH UHJLVWUDWLRQ TXDOLW 7KH LPDJHV FRQWDLQ
SHULRGLF VWUXFWXUHV WKDW WR RXU H[SHULHQFH SRVH VLJQLILFDQW
SUREOHPV WR UHJLVWUDWLRQ DOJRULWKPV 7HDULQJ DQ LPDJH
QXPHULFDOO KDV WKH DGYDQWDJH WKDW WKH GHIRUPDWLRQ ILHOG LV
NQRZQ H[DFWO DQG FDQ EH HDVLO FRPSDUHG ZLWK WKH
GLVSODFHPHQW ILHOGV UHFRYHUHG E WKH UHVSHFWLYH UHJLVWUDWLRQ
DOJRULWKP
7KH VHFRQG SDLU RI WHVW LPDJHV )LJ 38. XVHG LQ WKH
LQWURGXFWRU H[DPSOH RI UHJLVWUDWLRQ LQ SUHVHQFH RI
GLVFRQWLQXLWLHV VKRZV LPDJHV RI WZR QHLJKERULQJ VOLFHV RI D
WXUWOH HPEUR KHDG 7KH RYDO LQ WKH WDUJHW LPDJH RQ WKH OHIW
KDQG VLGH RI )LJ PDUNV WKH UHJLRQ ZKHUH WKH SKVLFDO VOLFH
KDV EHHQ WRUQ E WKH FXWWLQJ WRRO LH WKH GHIRUPDWLRQ ILHOG LV
GLVFRQWLQXRXV :H ZLOO XVH WKH LPDJH SDLU LQ )LJ WR
GHPRQVWUDWH WKDW LQ VXFK D FDVH GHIRUPDEOH UHJLVWUDWLRQ ZLWK
LQWHUSRODWLRQ EHWZHHQ UHJLVWHUHG FRQWURO SRLQWV IDLOV WR FORVH
)LJ $UWLILFLDO KRQHFRPE LPDJH UHJLVWUDWLRQ SDLU 7KH UHIHUHQFH LPDJH
ZDV FUHDWHG DUWLILFLDOO XVLQJ LPDJH SURFHVVLQJ VRIWZDUH 7KH WDUJHW LPDJH
ZDV JHQHUDWHG E QXPHULFDOO WHDULQJ WKH UHIHUHQFH LPDJH XVLQJ WKH
GHIRUPDWLRQ ILHOG ZLWK WKH PD[LPXP YHUWLFDO VKLIW E SL[HOV DQG QR
KRUL]RQWDO VKLIW
)LJ 7RWDO YDULDWLRQ GRHV QRW SHQDOL]H GLVFRQWLQXLWLHV )RU WKH
GLVFRQWLQXRXV IXQFWLRQ LQ E 40. 79D 79E II EXW WRWDO YDULDWLRQ SHQDOL]HV
RVFLOODWLRQV F 44. ZKLOH WKH /
79 UHJLVWUDWLRQ LV YHU
DFFXUDWH 7KH VSHFLPHQ ZDV SUHSDUHG DV IROORZV DQ HPEUR RI
KHOGUD VHUSHQWLQD RPPRQ 6QDSSLQJ WXUWOH 45. ZDV IL[HG LQ D
DTXHRXV VROXWLRQ RI IRUPDOGHKGH 3ULRU WR SUHSDUDWLRQ RI
KLVWRORJLFDO VHFWLRQV ERQH WLVVXHV KDG WR EH GHFDOFLILHG WR
HQVXUH SURSHU VHFWLRQLQJ 'HFDOFLILHG VSHFLPHQV ZHUH
HPEHGGHG LQ SDUDSODVW DQG VHULDOO VHFWLRQHG RQ WKH
PLFURWRPH 7UDQVYHUVH KLVWRORJLFDO VHFWLRQV WR —P WKLFN
ZHUH VWDLQHG ZLWK DOFLDQ EOXHKDHPDWR[OLQHRVLQ IRU
UHFRJQLWLRQ RI FDUWLODJH PXVFOH DQG ERQH 'LJLWL]HG LPDJHV RI
KLVWRORJLFDO VHFWLRQV ZHUH DFTXLUHG XVLQJ D /HLFD 0=
VWHUHRPLFURVFRSH HTXLSSHG ZLWK /HLFD ') GLJLWDO
FDPHUD
7KH WKLUG WHVW LPDJH SDLU LQ )LJ VKRZV WZR î PRVDLFV
RI RYHUODSSLQJ /60 RSWLFDO VOLFHV DFTXLUHG IURP DGMDFHQW
SKVLFDO VHFWLRQV RI D GD ROG UDW HPEUR 3KVLFDO VOLFHV RI
WKH VSHFLPHQ ZHUH —P WKLFN LH WKH WDUJHW LPDJH GLVSODV
WLVVXH VWUXFWXUHV —P DSDUW IURP WKHLU FRXQWHUSDUWV LQ WKH
UHIHUHQFH LPDJH ,Q RUGHU WR PLQLPL]H PXWXDO GLVSODFHPHQW RI
VWUXFWXUHV LQ VXFFHVVLYH VHFWLRQV QRQGHSDUDIILQL]HG WLVVXH
VHFWLRQV VWDLQHG ZLWK HRVLQ ZHUH XVHG IRU REWDLQLQJ WKH LQLWLDO
GDWD %HLQJ DFLGLF HRVLQ ELQGV WR FDWLRQLF JURXSV RI WLVVXHV
DQG WKXV VWDLQV FWRSODVP FRQQHFWLYH WLVVXH PXVFOH ILEHUV DQG
HUWKURFWHV 6LQFH HRVLQ DOVR LV D IOXRURSKRUH LW SURYHG
VXLWDEOH WR VWDLQ RXU VDPSOHV IRU /60 2QO VWUXFWXUHV WKDW
DSSHDU EULJKW LQ WKH LPDJHV VWDLQHG VWUXFWXUHV RU VWUXFWXUHV
ZLWK DXWR IOXRUHVFHQFH 46. DUH VXLWHG IRU UHJLVWUDWLRQ 5DZ LPDJHV
RI WKH WHVW VSHFLPHQ ZHUH DFTXLUHG E D /HLFD 63( /60
XVLQJ D VROLGVWDWH QP ODVHU P: 47. 6L[WIRXU
VXFFHVVLYH SKVLFDO VHFWLRQV ZHUH FDSWXUHG XVLQJ D + 3/
)/827$5 GU REMHFWLYH 1$ (PLVVLRQ ZDYHOHQJWKV
UDQJHG IURP WR QP 7R SUHFOXGH ODUJH VKLIWV GXULQJ
QRQULJLG UHJLVWUDWLRQ UDZ LPDJHV ZHUH SUHUHJLVWHUHG ULJLGO
7KH IRXUWK SDLU RI WHVW LPDJHV LQ )LJ GLVSOD SKVLFDO
VOLFHV RI WKH HPEUR RI WKH $PHULFDQ DOOLJDWRU $OOLJDWRU
PLVVLVVLSSLHQVLV 48. 3UHSDUDWLRQ RI WKH VSHFLPHQ DQG LPDJH
DFTXLVLWLRQ ZDV LGHQWLFDO WR WKDW RI )LJ
,9 ,0$*( 5(*,675$7,21 $6 ',65(7( /
79 0,1,0,=$7,21
352%/(0
)RU HDVLHU RULHQWDWLRQ 7DEOH , OLVWV DOO PDWKHPDWLFDO VPEROV
XVHG LQ WKLV ZRUN
7KH LPDJH UHJLVWUDWLRQ SUREOHP ZDV IRUPXODWHG LQ @ LQ
WHUPV RI PLQLPL]DWLRQ RI D GLVFUHWH IXQFWLRQDO ZLWK DQ /
VLPLODULW WHUP DQG D 79 VPRRWKQHVV WHUP
61. ZLWK WKH VHW RI LPDJH SL[HOV DUUDQJHG LQ D UHFWDQJXODU JULG
^ `^ `1F0UFU3L[
WKH VHW RI HGJHV FRQQHFWLQJ QHLJKERULQJ SL[HOV
^ `^ `^ `
^ `^ `^ `
1F0UFUFU
1F0UFUFU(GJ
WKH UHIHUHQFH LPDJH
=o3L[X
WKH WDUJHW LPDJH
=o3L[Y
DQG WKH ILHOG RI YHFWRUV 62. [[ WKDW GHIRUPHG WKH WDUJHW
LPDJH
=o3L[[
0LQLPL]DWLRQ RI WKH /
VLPLODULW WHUP HQIRUFHV SHUIHFW
DOLJQPHQW EHWZHHQ WKH UHIHUHQFH DQG WKH UHJLVWHUHG LPDJH 7KH
79 VPRRWKQHVV WHUP PHDVXUHV WKH GLVFUHWH WRWDO YDULDWLRQ RI
WKH GHIRUPDWLRQ ILHOG RQ WKH UHFWDQJXODU JULG 3L[ DQG WDNHV
LQWR DFFRXQW GHIRUPDWLRQV RI WKH PLFURVFRS VSHFLPHQV GXULQJ
FXWWLQJ WKH GHIRUPDWLRQV DUH PRVWO FRQWLQXRXV HW VRPH
VSHFLPHQ UHJLRQV PD KDYH EHHQ WRUQ DSDUW $V H[SODLQHG LQ
)LJ WKH 79 VPRRWKQHVV WHUP GRHV QRW SHQDOL]H LVRODWHG
)LJ /60 LPDJHV RI QHLJKERULQJ SKVLFDO VHFWLRQV RI UDW HPEUR
PHFKDQLFDOO GDPDJHG GXULQJ SUHSDUDWLRQ 7KH UHJLVWUDWLRQ DOJRULWKP
VKRXOG FORVH WKH ILVVXUH
)LJ 3KVLFDO VOLFHV RI WKH HPEUR RI WKH $PHULFDQ DOOLJDWRU $OOLJDWRU
PLVVLVVLSSLHQVLV 64. 70,
GLVFRQWLQXLWLHV LQ WKH GHIRUPDWLRQ ILHOG PRUH WKDQ DQ HTXDO VXP
RI PRQRWRQH FRQWLQXRXV GHIRUPDWLRQV 7KXV GLVFRQWLQXLWLHV LQ
WKH GLVSODFHPHQW ILHOG JHQHUDWHG IRU UHJLVWUDWLRQ DUH DOORZHG
DQG GLVUXSWHG UHJLRQV LQ WKH WDUJHW LPDJH FDQ JHW FORVHG GXULQJ
UHJLVWUDWLRQ 7KH WUDGHRII EHWZHHQ WKH GDWD ILGHOLW DQG
UHJLVWUDWLRQ VPRRWKQHVV LV FRQWUROOHG E WKH SDUDPHWHUO
7KH IXQFWLRQDO 65. FDQ EH PLQLPL]HG LWHUDWLYHO XVLQJ D
VWHHSHVW GHVFHQW DOJRULWKP ,Q @ -DQiþHN GHVLJQHG D JUDSK
FXW EDVHG VWHHSHVW GHVFHQW 7KH DOJRULWKP VHDUFKHV LWHUDWLYHO
D GLVFUHWH YHFWRU GLVSODFHPHQW ILHOG QHHGHG WR VKLIW WKH SL[HOV
RI WKH WDUJHW LPDJH VXFK WKDW WKH DUH DOLJQHG ZLWK WKH SL[HOV RI
WKH UHIHUHQFH LPDJH ,Q HDFK VWHHSHVW GHVFHQW LWHUDWLRQ DOO
SL[HOV PD EH OHIW LQ SODFH RU VKLIWHG LQ WKH VDPH GLUHFWLRQ E
WKH VDPH DPRXQW WKH ZHOONQRZQ ĮH[SDQVLRQ DOJRULWKP 67. LV DFKLHYHG 7KH VWHHSHVW GHVFHQW LWHUDWLRQ
XVHV WKH JUDSKFXW PHWKRG GHVFULEHG LQ @ )RU WKH JUDSKFXW
PHWKRG WKH PD[LPXPIORZ LQ D GLUHFWHG FDSDFLWDWHG JUDSK
QHHGV WR EH FRPSXWHG
7KH VWHHSHVW GHVFHQW DOJRULWKP RI @ IRU PLQLPL]DWLRQ RI
IXQFWLRQDO 69. GGG DQG , EH WKH LQGLFDWRU IXQFWLRQ ,Q HDFK
VWHS RI WKH PHWKRG ZH ILQG DQ 3L[6 VXFK WKDW
70. 6,) G[ DFKLHYHV D PLQLPXP DQG ZH UHSODFH [ ZLWK
6,G[ 7KH VHW 3L[6 FDQ EH IRXQG E ILUVW FRQVWUXFWLQJ D
GLUHFWHG FDSDFLWDWHG JUDSK RQ WKH VHW RI YHUWLFHV
^ `VLQNVRXUFH3L[ ‰ XVLQJ WKH DSSURDFK RI @ DQG WKHQ
ILQGLQJ WKH PLQLPXPFXW LQ WKLV JUDSK 7KH FXW VHSDUDWHV WKH
SL[HOV WKDW VWD LQ SODFH IURP WKRVH WR EH VKLIWHG $IWHU
PLQLPL]DWLRQ RI 71. 6,) G[ DQG UHSODFHPHQW RI [ ZLWK
6,G[ D QHZ VKLIW FDQGLGDWH 73. 6,) G[ LV PLQLPL]HG DJDLQ
,Q WKH JUDSKFXW H[DPSOHV KHUH VKLIW YHFWRUV G ZHUH
VHOHFWHG VXFFHVVLYHO IURP WKH VHTXHQFH RI YHFWRUV ZLWK
FRPSRQHQW OHQJWKV PRGXOXV 74. EHLQJ D GHFUHDVLQJ SRZHU RI
)LJ *UDSKFXW PHWKRG RI PLQLPL]DWLRQ RI WKH /
79 IXQFWLRQDO VHTXHQFH
RI FDQGLGDWH VKLIWV XVHG LQ D VWHHSHVW GHVFHQW PLQLPL]DWLRQ VWHS IRU PRGXOL
O
O
O
(DFK SL[HO LV HLWKHU PRYHG E WKH FXUUHQW VKLIW YHFWRU RU OHIW LQ
SODFH 7KH UHVXOWLQJ VKLIW RI D SL[HO OHDGLQJ WR UHJLVWUDWLRQ RI WKH WDUJHW LPDJH
WR WKH UHIHUHQFH LPDJH LV WKH VXP RI LQFUHPHQWDO VKLIWV LQ DOO LWHUDWLRQV
7$%/( ,
/,67 2) 0$7+ 60%2/6
) YDOXH RI WKH /
79 IXQFWLRQDO
/
WKH /
QRUP
79 WRWDO YDULDWLRQ
ȟ GLVSODFHPHQW ILHOG
ȟW YDOXH RI GLVSODFHPHQW ILHOG DW WKH SL[HO W
įȟ FKDQJH RI WKH GLVSODFHPHQW ILHOG
X UHIHUHQFH LPDJH
Y WDUJHW LPDJH
3L[ VHW RI LPDJH SL[HOV
(GJ VHW RI LPDJH HGJHV
0 QXPEHU RI LPDJH URZV
1 QXPEHU RI LPDJH FROXPQV
U URZ LQGH[
F FROXPQ LQGH[
W D SL[HO
WW¶ 75. DQ HGJH
= VHW RI LQWHJHUV
=
VHW RI DOO SDLUV RI LQWHJHUV
į VKLIW YHFWRU
, LQGLFDWRU IXQFWLRQ
6 D VXEVHW RI 3L[
. QXPEHU RI ODEHOV
N LQGH[ GHQRWLQJ D ODEHO
NW 76. LQGH[ GHQRWLQJ D ODEHO DW SL[HO W
N D ODEHOLQJ WKH VHW RI ODEHOV DVVLJQHG WR 3L[ 77. N
WKH EHVW ODEHOLQJ
' PRGXOXV RI D VKLIW YHFWRU
O EDVH ORJDULWKP RI WKH PRGXOXV
/ PD[LPXP ORJDULWKP RI WKH PRGXOXV
* SUREOHP TXDOLW FRUUHVSRQGLQJ WR WKH
PD[LPXP DVFHQW )ȟįȟ 79. WWJ c
ELQDU WHUP LQ WKH SUREOHP TXDOLW
Ȝ ZHLJKW RI WKH WRWDO YDULDWLRQ UHJXODUL]HU
4 SUREOHP SRZHU
Ȍ DUUD RI SRWHQWLDOV
ȥWNW 82. NW’ FRPSRQHQW RI VXEJUDGLHQW RI 4 DW SL[HO W IRU
ODEHO N
+ /LSVFKLW] FRQVWDQW
L LWHUDWLRQ LQGH[
Q QXPEHU RI LWHUDWLRQV
ȖL VWHS VL]H LQ VXEJUDGLHQW LWHUDWLRQ
84. 4 DERYH WKH OLQH SDVVLQJ WKURXJK
L ZLWK WKH GLUHFWLRQ GHILQHG E WKH QHJDWLYH
VXEJUDGLHQW LLLL ’˜ J
K VWHS OHQJWK LQ VXEJUDGLHQW LWHUDWLRQ
5Q
QGLPHQVLRQDO (XFOLGLDQ VSDFH
G GLYLVRU XVHG WR UHGXFH VXEJUDGLHQW VWHS VL]H ȖL
104. 7KLV VHTXHQFH RI VKLIW YHFWRUV LV GHSLFWHG LQ )LJ
7KH UHVXOWLQJ DOJRULWKP FDOFXODWHV VKLIWV QHHGHG IRU LPDJH
UHJLVWUDWLRQ LQGLYLGXDOO IRU HDFK LPDJH SL[HO ZLWK QR
LQWHUSRODWLRQ EHWZHHQ WKHP ZKLFK PDNHV UHJLVWUDWLRQ RI
LPDJHV ZLWK LVRODWHG GLVFRQWLQXLWLHV SRVVLEOH
9 1(: $3352$+ 68%*5$',(17 0,1,0,=$7,21 2) 7+(
',65(7( 121219(; /
79 )817,21$/ 86,1* $ 08/7,
/$%(/ 67((3(67 '(6(17 $/*25,7+0
2XU ZRUN XVHV WKH GLVFUHWH /
79 IRUPXODWLRQ RI WKH LPDJH
UHJLVWUDWLRQ SUREOHP LQWURGXFHG LQ @ EXW RIIHUV DQ DOWHUQDWLYH
DOJRULWKP IRU LWV VROXWLRQ
5DWKHU WKDQ XVLQJ WKH /
QRUP DV VLPLODULW WHUP WKH
DOJRULWKP PLJKW MXVW DV ZHOO HYDOXDWH VLPLODULW DV WKH /
QRUP
RI WKH GLIIHUHQFH EHWZHHQ LPDJHV WKLV LV PRUH FRPPRQ LQ
EULJKWQHVVEDVHG VLPLODULW PHDVXUHV 7KH GLVDGYDQWDJH RI /
KRZHYHU LV WKDW LW SHQDOL]HV WKH VTXDUH RI WKH GLIIHUHQFH
EHWZHHQ EULJKWQHVV YDOXHV LH LW LV PXFK PRUH VHQVLWLYH WR
RXWOLHUV WKDQ /
SHQDOL]LQJ VLPSO WKH GLIIHUHQFH
7R RXU NQRZOHGJH WKHUH DUH WZR UHDVRQV ZK /
LV VR
ZLGHO XVHG LQ WKH OLWHUDWXUH
x LQ PD[LPXP D SRVWHULRUL 0$3 106. ZLWK *DXVVLDQ GLVWULEXWLRQ WKH /
QRUP HPHUJHV DV PHDVXUH RI VLPLODULW EHWZHHQ WZR
EULJKWQHVV YDOXHV DIWHU WKH ORJDULWKP RI SURGXFW RI
*DXVVLDQV IURP ZKLFK WKH 0$3 HVWLPDWH LV FDOFXODWHG LV
WDNHQ
x VRPH UHJLVWUDWLRQ DOJRULWKPV HJ @ 107. UHO RQ
GLIIHUHQWLDELOLW RI WKH VLPLODULW WHUP DQG WKHUHIRUH
FDQQRW XVH WKH /
QRUP ZKLFK ± FRQWUDU WR /
± LV QRW
GLIIHUHQWLDEOH DW WKH RULJLQ
2XU SUREOHP VWDWHPHQW GRHV QRW UHO RQ 05)V DQG GRHV QRW
PDNH WKH DVVXPSWLRQ RI SUREDELOLW GLVWULEXWLRQ RI WKH JUD
YDOXH GLIIHUHQFH EHWZHHQ SL[HOV EHLQJ *DXVVLDQ ZKLFK LV ± LQ
DGGLWLRQ ± HYLGHQWO ZURQJ HYHQ IRU VRPH HOHPHQWDU LPDJH
WSHV OLNH HJ EODFNDQGZKLWH LPDJHV 6LPLODUO RXU
DOJRULWKP GRHV QRW UHTXLUH GLIIHUHQWLDELOLW RI WKH VLPLODULW
PHDVXUH HLWKHU VLQFH LW GRHV FRPELQDWRULDO RSWLPL]DWLRQ RQ D
GLVFUHWH JULG 2Q WKH RWKHU KDQG /
RYHUSHQDOL]HV RXWOLHUV )RU
WKHVH UHDVRQV ZH DYRLG XVLQJ WKH /
LQ RXU SUREOHP VWDWHPHQW
7KH IXQFWLRQDO 108. LV PLQLPL]HG E LWHUDWLYHO FDOFXODWLQJ
WKH ILHOG RI VKLIW YHFWRUV
=o3L[[ GHIRUPLQJ WKH WDUJHW
LPDJH Y VXFK WKDW LW EHVW PDWFKHV WKH UHIHUHQFH LPDJH X 7KH
/
79 IXQFWLRQDO LV LQ JHQHUDO QRQFRQYH[ DQG WKXV WKHUH LV
QR JXDUDQWHH WKDW D GLUHFW PLQLPL]DWLRQ DOJRULWKP VXFK DV @
ZLOO FRQYHUJH WR WKH JOREDO PLQLPXP 6FKOHVLQJHU HW DO
SUHVHQWHG LQ @ WKHRU WKDW DOORZV WR FRQYHUW D PD[VXP
SUREOHP WR PLQLPL]DWLRQ RI D GXDO TXDQWLW FDOOHG SUREOHP
SRZHU XVLQJ D VHTXHQFH RI HTXLYDOHQW WUDQVIRUPDWLRQV 7KH
SUREOHP SRZHU LV DQ XSSHU ERXQG RQ WKH PD[VXP IXQFWLRQDO
RQWUDU WR WKH RULJLQDO PD[VXP IXQFWLRQDO WKH SUREOHP
SRZHU LV QRQVPRRWK HW FRQYH[ SLHFHZLVH OLQHDU DQG FDQ EH
PLQLPL]HG XVLQJ DQ LWHUDWLYH VXEJUDGLHQW DOJRULWKP 8QGHU
FHUWDLQ FRQGLWLRQV WKH PLQLPXP RI WKH SUREOHP SRZHU
FRLQFLGHV ZLWK WKH PD[LPXP VXP
:H DSSOLHG 6FKOHVLQJHU
V IUDPHZRUN WR GHVLJQ D VWHHSHVW
GHVFHQW DOJRULWKP IRU LWHUDWLYH PXOWLODEHO PLQLPL]DWLRQ RI WKH
/
79 IXQFWLRQDO 8QOLNH WKH JUDSKFXW EDVHG GLUHFW VWHHSHVW
GHVFHQW DOJRULWKP LQ @ WKH PXOWLODEHO /
79 PLQLPL]DWLRQ
FRQVLGHUV IRU DQ SL[HO PXOWLSOH SRVVLEOH VKLIW GLUHFWLRQV
GHQRWHG E ODEHOV 5DWKHU WKDQ PD[LPL]LQJ GLUHFWO WKH GHVFHQW
RI WKH IXQFWLRQDO 109. LQ HDFK LWHUDWLRQ ZKLFK LV QRW WUDFWDEOH IRU
PXOWLSOH ODEHOV ZH FRQYHUW D VWHHSHVW GHVFHQW VWHS WR D PD[
VXP SUREOHP DQG WKHQ PLQLPL]H LWV FRQYH[ GXDO TXDQWLW
FDOOHG SUREOHP SRZHU ZKLFK LV WKH XSSHU ERXQG RQ WKH PD[
VXP VROXWLRQ LH RQ WKH GHVFHQW VWHS PDJQLWXGH 7KH QRQ
VPRRWK FRQYH[ SUREOHP SRZHU LV PLQLPL]HG XVLQJ D
VXEJUDGLHQW PHWKRG 7KXV WKH VWHHSHVW GHVFHQW PLQLPL]DWLRQ
RI WKH IXQFWLRQDO 110. UHVXOWV LQ VROYLQJ D VHTXHQFH RI QRQ
VPRRWK FRQYH[ PLQLPL]DWLRQ SUREOHPV
,Q D VWHHSHVW GHVFHQW VWHS RI WKH PXOWLODEHO VXEJUDGLHQW
DOJRULWKP ZLWK . ODEHOV DQ SL[HO PD HLWKHU EH OHIW LQ SODFH RU
VKLIWHG E DQ RI D FKRLFH RI . GLIIHUHQW YHFWRUV )RU HDFK
SL[HO D YHFWRU IURP WKLV VHW LV FKRVHQ VXFK WKDW WKH GHFUHDVH RI
WKH IXQFWLRQDO 112. .NNNN
GGG EH WKH NWK RI SRVVLEOH
. VKLIW YHFWRUV LQ DQ LWHUDWLRQ VWHS
:H XVHG WKH IROORZLQJ VHWV RI FDQGLGDWH VKLIW YHFWRUV
^ `.N GGG
LQ RGG LWHUDWLRQV WKH FDQGLGDWH VKLIWV
118. ZHUH DVVLJQHG ODEHOV IURP WKH VHW ^ `.
LQ HYHQ LWHUDWLRQV ODEHOV IURP WKH VHW ^ `.
GHQRWHG WKH FDQGLGDWH VKLIWV
124. 7KH YDOXH O
' LV FDOOHG WKH PRGXOXV RI WKH VKLIW ZLWK
//O 7KH VHTXHQFH RI FDQGLGDWH VKLIW YHFWRUV IRU
PRGXOL O
O
O
LV GHSLFWHG LQ )LJ 7KH PXOWLODEHO
VWHHSHVW GHVFHQW PLQLPL]DWLRQ RI IXQFWLRQDO 128. 70,
$IWHU WKH PLQLPXP KDV EHHQ IRXQG [ LV UHSODFHG ZLWK G[[
D QHZ VHW RI VKLIW FDQGLGDWHV ^ `.N GGG
LV VHOHFWHG DQG
QHZ LWHUDWLRQ LV VWDUWHG 7KHVH VWHSV DUH GHWDLOHG EHORZ WKH
DOJRULWKP FKRRVHV RQH RI WKH VHWV RI ODEHOV GHILQHG E 131. G[[ ) LQWR D PD[
VXP SUREOHP E GHILQLQJ D SUREOHP TXDOLW @
140. G[[ c ¦¦ c
c
)WNWNJWNTN*
(GJWW
WW
3L[W
W
146. N* DQG
WKH FKDQJH G[ RI WKH GLVSODFHPHQW YHFWRU ILHOG LV XQLTXHO
GHILQHG E WKH ODEHOLQJ
N UHVXOWLQJ IURP WKH PD[LPL]DWLRQ RI
157. UHVSHFWLYHO 7KH XQDU ZHLJKWV WT GHSHQG RQO RQ WKH ODEHO N
DVVLJQHG WR WKH SL[HO W ZKLOH WKH SDLUZLVH ZHLJKWV 160. SUREOHPV
RQ WZRGLPHQVLRQDO LPDJHV IRU ZKLFK WKH JUDSK ZLWK WKH
YHUWLFHV 3L[ DQG WKH HGJHV (GJ FDQ EH GHFRPSRVHG LQWR D
KRUL]RQWDO WUHH +
(GJ DQG D YHUWLFDO WUHH 9
(GJ WKH
PD[LPL]DWLRQ RI 263. 4 LV D SLHFHZLVH OLQHDU
FRQYH[ IXQFWLRQ 7KH QRQVPRRWK HW ZUW SRWHQWLDOV
FRQYH[ IXQFWLRQ 264. 4 FDQ EH PLQLPL]HG XVLQJ WKH
VXEJUDGLHQW ’ RI 265. 4 RPSRQHQWV RI WKH VXEJUDGLHQW DUH
FDOFXODWHG XVLQJ WKH RSWLPXP KRUL]RQWDO DQG RSWLPXP YHUWLFDO
ODEHOLQJV
274. )RU D VHTXHQFH RI QXPEHUV LLJ VXFK WKDW
f¦fofo
L
Q
L
Q
L
L
JJ
OLPOLP 276. )LJ 0XOWLODEHO PHWKRG RI /
79 PLQLPL]DWLRQ VHTXHQFH RI FDQGLGDWH
VKLIWV XVHG LQ VWHHSHVW GHVFHQW PLQLPL]DWLRQ RI WKH /
79 IXQFWLRQDO IRU
PRGXOL O
O
O
(DFK SL[HO FDQ EH VKLIWHG E RQH RI WKH IRXU FDQGLGDWH
VKLIW YHFWRUV RU OHIW LQ SODFH GHSHQGLQJ RQ WKH RSWLPXP ODEHOV IRXQG E WKH
LWHUDWLRQ VWHS 7KH UHVXOWLQJ VKLIW RI D SL[HO OHDGLQJ WR UHJLVWUDWLRQ LV WKH VXP
RI VKLIWV LQ DOO LWHUDWLRQV
280. fo
44 L
L
PLQOLP
$ $ 6WHSE6WHS 'HVFULSWLRQ RI WKH $OJRULWKP
6HOHFW WKH PD[LPXP PRGXOXV RI WKH VHDUFK YHFWRUV /
'
VHW WKH LQLWLDO GLVSODFHPHQW ILHOG [ DQG WKH FXUUHQW
HVWLPDWH RI WKH UHJLVWHUHG LPDJH HTXDO WKH WDUJHW LPDJH
FKRRVH WKH VHW RI FDQGLGDWH VKLIW YHFWRUV ^ `.N GGG
XVLQJ 282. WWJ IRU DOO YHUWLFHV
DQG IRU DOO HGJHV RI WKH JUDSK GHILQHG E WKH UHIHUHQFH LPDJH
DQG WKH FXUUHQW HVWLPDWH RI WKH UHJLVWHUHG LPDJH
FDUU RXW WKH PD[LPL]DWLRQ RQ KRUL]RQWDO JULGOLQHV E
GQDPLF SURJUDPPLQJ
299. XVLQJ D VWHS FRQWURO DOJRULWKP FDOFXODWH WKH VWHS VL]H LJ IRU
WKH FXUUHQW VXEJUDGLHQW VWHS
GR RQH VWHS 300. LQ WKH RSSRVLWH VXEJUDGLHQW GLUHFWLRQ
XVLQJ D VWRSSLQJ FULWHULRQ FKHFN LI 301. 4 KDV DFKLHYHG D
PLQLPXP
LI VWRSSLQJ FULWHULRQ QRW VDWLVILHG WKHQ UHWXUQ WR HOVH
FRQWLQXH
RQ WHUPLQDWLRQ WKH VHW RI ODEHOV 3L[
.N GHILQHV WKH
LQFUHPHQW ILHOG G[ RI VKLIW YHFWRUV ZKLFK LHOGV PD[LPXP
GHFUHDVH RI WKH IXQFWLRQDO 302. XSGDWH [[[ G ZKLFK LHOGV QHZ HVWLPDWH RI WKH
UHJLVWHUHG LPDJH
LI RGG LWHUDWLRQ JRWR HOVH / /
LI t/ JRWR HOVH FRQWLQXH
XSGDWH WKH UHJLVWHUHG LPDJH XVLQJ WKH UHVXOWLQJ VKLIW YHFWRU
ILHOG[
7KH DOJRULWKP LV HDVLO SDUDOOHOL]DEOH VLQFH WKH GQDPLF
SURJUDPPLQJ PD[LPL]DWLRQ DORQJ D KRUL]RQWDO UHVS YHUWLFDO 304. JULGOLQHV :H KDYH LPSOHPHQWHG D SDUDOOHO
YHUVLRQ RI WKH DERYH DOJRULWKP ERWK RQ PXOWLSOHFRUH 3V DQG
RQ D 8'$ *UDSKLF 3URFHVVLQJ 8QLW *38 305. % 6WDQGDUG 0HWKRGV IRU 6XEJUDGLHQW 6WHS 6L]H 6HOHFWLRQ
:H EULHIO UHYLHZ VRPH VWDQGDUG UHVXOWV IRU WKH VXEJUDGLHQW
PHWKRG RI XQFRQVWUDLQHG PLQLPL]DWLRQ RI QRQVPRRWK FRQYH[
IXQFWLRQV @ @
/HW 4 EH D QRQVPRRWK /LSVFKLW] FRQWLQXRXV ZLWK WKH
FRQVWDQW + FRQYH[ IXQFWLRQ RQ Q
5 Q
5 DQG 307. LL 4 w’ D VXEJUDGLHQW RI 4 DW
L 7KH VXEJUDGLHQW PHWKRG DWWHPSWV PLQLPL]DWLRQ RI 4 RYHU
Q
5 XVLQJ WKH LWHUDWLYH VFKHPH
LLL ’˜ JL
ZKHUH LJ LV D VWHS VL]H $IWHU WKH LWK LWHUDWLRQ WKH /
VTXDUH
GLVWDQFH RI WKH FXUUHQW LWHUDWLRQ L
WR D
EHORQJLQJ WR WKH
RSWLPDO VHW LV
LLL
7
LLL
LLLL
’’
’˜
JJ
J
/HW 313. LLLLLL 44 ’d JJ
5HSHDWLQJ WKLV SURFHGXUH IRU QL ZH REWDLQ
317. ¦¦ d
Q
L
LLQ
Q
L
LL 44
JJ
ZKLFK LHOGV DQ XSSHU ERXQG IRU WKH GLIIHUHQFH EHWZHHQ WKH
EHVW SDVW LWHUDWLRQ RI WKH REMHFWLYH IXQFWLRQ 320. ,W VKRXOG EH QRWHG WKDW
Q4 LV WKH EHVW YDOXH LQ WKH Q SDVW
LWHUDWLRQV RI WKH REMHFWLYH IXQFWLRQ LW LV QRW QHFHVVDULO WKH
ODWHVW LWHUDWHG YDOXH Q4 ZKLFK PD EH PXFK KLJKHU
9DULRXV WSHV RI FRQYHUJHQFH GHSHQGLQJ RQ D VWHS VL]H UXOH
IRU JHQHUDWLQJ WKH VHTXHQFH ^ `LJ FDQ EH HVWDEOLVKHG EDVHG RQ
322. :H H[SHULPHQWHG ZLWK WKH IROORZLQJ WKUHH
VWHS VL]H UXOHV
x RQVWDQW VWHS VL]H JJL
6LQFH WKH VXEJUDGLHQW LV
ERXQGHG E WKH /LSVFKLW] FRQVWDQW + WKH HVWLPDWH 328. OLP
fo
44Q
Q
x 1RQVXPPDEOH GLPLQLVKLQJ VWHS OHQJWKV :H LQWURGXFH WKH
VWHS OHQJWK E LLLK ’J 'XH WR /LSVFKLW] FRQWLQXLW RI
4 WKH VXEJUDGLHQW LV ERXQGHG E + 7KXV
331. QQ 44 PD EH PXFK KLJKHU WKDQ WKH EHVW YDOXH
DFKLHYHG LQ WKH ODVW Q VWHSV
Q4 LQ WKH HVWLPDWHG GLIIHUHQFH
IURP WKH RSWLPXP 332. 44Q ,Q RXU H[SHULHQFH WKLV OHDGV WR
YHU VORZ FRQYHUJHQFH RI VWDQGDUG VXEJUDGLHQW PHWKRGV LQ
SUDFWLFH ZKLFK PDNHV WKHP LQDGHTXDWH IRU LPDJH UHJLVWUDWLRQ
1RYHO 6WHS 6L]H RQWURO LHOGLQJ 3LHFHZLVH 0RQRWRQH
'HFUHDVH RI WKH 2EMHFWLYH )XQFWLRQ
7KH LWHUDWLRQV LLLL ’˜ J
ZLWK ^ `LJ JHQHUDWHG E
RQH RI WKH DERYH VWHS VL]H UXOHV SURGXFH LQ SUDFWLFH DQ
RVFLOODWLQJ VHTXHQFH RI REMHFWLYH IXQFWLRQ YDOXHV ^ `N4 DQG
KHQFH VORZ FRQYHUJHQFH 7R RYHUFRPH WKH GUDZEDFN RI
RVFLOODWLRQV ZH SURSRVH DQ DOJRULWKP ZLWK SLHFHZLVH
PRQRWRQH GHFUHDVH RI WKH REMHFWLYH IXQFWLRQ DQG ZH VKRZ WKDW
WKH PRQRWRQH DOJRULWKP FRQYHUJHV LQ SUDFWLFH EHWWHU WKDQ WKH
FRQVWDQW RU GLPLQLVKLQJ QRQVXPPDEOH VWHS VL]H UXOH RU WKH
FRQVWDQW RU GLPLQLVKLQJ QRQVXPPDEOH VWHS OHQJWK UXOH
$V VKRZQ LQ @ 333. 4 LV D SLHFHZLVH OLQHDU FRQYH[
IXQFWLRQ 6XSSRVH ZH DUH DW VRPH SRLQW L 9DOXHV RI 334. 4
DORQJ WKH OLQH SDVVLQJ WKURXJK L ZLWK WKH GLUHFWLRQ GHILQHG E
WKH QHJDWLYH VXEJUDGLHQW LLLL ’˜ J
DUH D SLHFHZLVH
OLQHDU FRQYH[ IXQFWLRQ RI RQH YDULDEOH LJ OHW XV FDOO LW 335. LL J
,I WKH YDOXH RI WKH REMHFWLYH IXQFWLRQ DW L 336. LL 4 LV
JUHDWHU WKDQ WKH PLQLPXP RI 337. LL J WKHQ LW LV SRVVLEOH WR ILQG D
VWHS VL]H LJ VXFK WKDW DIWHU WKH VXEJUDGLHQW VWHS
340. LLLL 44 J 7KHUHIRUH LW LV SRVVLEOH WR FRQVWUXFW
D VXEJUDGLHQW DOJRULWKP LQ ZKLFK ± FRQWUDU WR XVXDO
VXEJUDGLHQW DOJRULWKPV ± WKH REMHFWLYH IXQFWLRQ GHFUHDVHV
PRQRWRQLFDOO DV ORQJ DV WKH LWHUDWLRQ VWDUWLQJ SRLQW 341. L4 OLHV
DERYH WKH PLQLPXP RI WKH RQHGLPHQVLRQDO VHDUFK
IXQFWLRQ 342. LL J 7KLV LV LOOXVWUDWHG E )LJ D 348. WKHQ D PRQRWRQLF GHFUHDVH RI WKH
REMHFWLYH YDOXH LQ WKH QHJDWLYH VXEJUDGLHQW GLUHFWLRQ LV QR
ORQJHU SRVVLEOH ,Q VXFK D FDVH DQ RI WKH XVXDO VXEJUDGLHQW
VWHS FRQWURO VWUDWHJLHV FDQ EH DGRSWHG IRU DV ORQJ
DV 350. $V VRRQ DV D VXEJUDGLHQW GLUHFWLRQ
DOORZLQJ IXUWKHU GHFUHDVH RI WKH REMHFWLYH IXQFWLRQ LV
HQFRXQWHUHG WKH SLHFHZLVH PRQRWRQH VWHS VL]H VWUDWHJ LV
UHVXPHG ,I QR VXFK GLUHFWLRQ LV IRXQG XQWLO D VWRSSLQJ FULWHULRQ
LV VDWLVILHG WKH DOJRULWKP WHUPLQDWHV
7KH SUREOHP SRZHU 352. LV WKH XSSHU ERXQG RQ WKH
)LJ 'HSHQGHQFH RI WKH YDOXH RI WKH REMHFWLYH IXQFWLRQ RQ WKH VWHS VL]H
LJ LQ RQH VXEJUDGLHQW LWHUDWLRQ
D 356. LL 44
LH WKH UHTXLUHPHQW WKDW WKH DOJRULWKP EH SLHFHZLVH
PRQRWRQH LV VDWLVILHG DQG WKH LWHUDWLRQ VWHS ZLOO EH DFFHSWHG F 357. WKH
REMHFWLYH IXQFWLRQ KDV QRW GHFUHDVHG GXH WR D WRR ODUJH LWHUDWLRQ VWHS WKH
LWHUDWLRQ ZLOO EH UHMHFWHG DQG D QHZ LWHUDWLRQ ZLOO EH DWWHPSWHG XVLQJ D
UHGXFHG
LJ XQWLO 362. LL J EXW QRW QHFHVVDULO ZLWK D JOREDO PLQLPXP RI 363. 4 QR YDOXH RI
LJ FDQ DFKLHYH 365. LL 44
WKH LWHUDWLRQ VWHS LV DFFHSWHG DQG
LJ LV NHSW
FRQVWDQW XQWLO D 372. DQG LW LV QRQSRVLWLYH ILQLWH VLQFH DOO VXPPDQGV RI 375. L4 LV PRQRWRQH GHFUHDVLQJ LW FRQYHUJHV 7KLV LV WKH FDVH DV
ORQJ DV WKH VLWXDWLRQ LQ )LJ D 379. RFFXUV DQG WKH
DOJRULWKP FRQWLQXHV XVLQJ WKH FRQVWDQW VWHS OHQJWK VWUDWHJ
WKHQ WKH IROORZLQJ DQDOVLV DSSOLHV
7KHUH DUH 10. ˜˜ FRPSRQHQWV RI WKH VXEJUDGLHQW L’ LQ
381. (DFK
VXEJUDGLHQW FRPSRQHQW DVVXPHV YDOXHV RU WKHUHIRUH WKH
PD[LPXP OHQJWK RI WKH VXEJUDGLHQW DQG KHQFH WKH /LSVFKLW]
FRQVWDQW + LV 10.+ L ˜˜’ PD[
7KXV ZLWK FRQVWDQW
VWHS OHQJWK K WKH GLVWDQFH EHWZHHQ WKH SUREOHP SRZHU DQG LWV
RSWLPXP FRQYHUJHV WKHUHIRUH DV
382. OLP
K
10.
K
+44N
N
˜˜˜˜d
fo
([DPSOH )RU D WSLFDO /60 LPDJH ZLWK î ZLWK
. ODEHOV LQYROYHG LQ PLQLPL]DWLRQ WKH /LSVFKLW] FRQVWDQW
DVVXPHV D YDOXH RI ,I D IL[HG VWHS OHQJWK RI K LV
VHOHFWHG WKHQ WKH RSWLPXP SDVW YDOXH 4N
ZLOO FRQYHUJH WR 4
ZLWKLQ DW PRVW 7KLV LV D YHU ORZ YDOXH FRPSDUHG WR
WSLFDO YDOXHV RI WKH IXQFWLRQDO 383. ) WKH ORZHVW YDOXH RI ) ZH
REWDLQHG LQ RXU WHVW VHW RI IRXU WHVW SDLUV LQ WRWDO ZDV
IRU )LJ 384. ,Q WKH IROORZLQJ WKUHH VXESDUDJUDSKV ZH SURYLGH
LPSOHPHQWDWLRQ GHWDLOV RI WKH SLHFHZLVH PRQRWRQH VWHS VL]H
FRQWURO DQG WKH VWRSSLQJ FULWHULD RI WKH DOJRULWKP 9$ $OO
H[DPSOHV RI PXOWLODEHO SLHFHZLVH PRQRWRQH VXEJUDGLHQW
UHJLVWUDWLRQ SUHVHQWHG LQ WKLV SDSHU ZHUH FRPSXWHG XVLQJ WKLV
VWHS VL]H FRQWURO DQG VWRSSLQJ FULWHULD
388. LL 44 t
WKH VXEJUDGLHQW VWHS LV UHMHFWHG
DQG WKH VWHS VL]H LJ LV GHFUHDVHG XVLQJ D VLPSOH UXOH
!G
G
L
L
J
J
LQ ZKLFK G LV DQ DGDSWLYH GLYLVRU DV VSHFLILHG LQ WKH QH[W
VXESDUDJUDSK $IWHU WKH UHGXFWLRQ RI LJ D QHZ VXEJUDGLHQW
VWHS VWDUWLQJ IURP XQFKDQJHG L LV DWWHPSWHG ,I WKURXJK WKH
XSGDWH GLL JJ WKH VWHS EHFRPHV VR VPDOO WKDW DIWHU WKH
VXEJUDGLHQW VWHS WKH QHZ DUUD QXPHULFDOO HTXDOV WKH ROG RQH
LL
WKH VWHS VL]H LV UHSODFHG E WKH ODVW YDOXH WKDW OHG WR
D GHFUHDVH RI WKH REMHFWLYH IXQFWLRQ
390. DIWHU WKH VXEJUDGLHQW LWHUDWLRQ WKH YDOXH RI
WKH REMHFWLYH YDOXH GRHV QRW GHFUHDVH WKH VXEJUDGLHQW VWHS LV
GLVPLVVHG 5HMHFWHG VXEJUDGLHQW LWHUDWLRQV ZDVWH FRPSXWLQJ
WLPH WKHUHIRUH LW LV GHVLUDEOH WKDW RQO IHZ DWWHPSWV XVLQJ WKH
XSGDWH IRUPXOD GLL JJ QHHG WR EH GRQH 7KLV FDQ EH
DFKLHYHG ZKHQ ZH NHHS WUDFN RI WKH ODVW VXFFHVVIXO YDOXH RI WKH
GLYLVRU G ZKHQ WKH XSGDWH GLL JJ GRHV QRW LHOG D GHFUHDVH
RI WKH REMHFWLYH IXQFWLRQ 392. LL 44
WKH GLYLVRU LV
XSGDWHG DFFRUGLQJ WKH VLPSOH UXOH
˜GG
WKH VWHS VL]H LV UHFDOFXODWHG GLL JJ DQG D QHZ VXEJUDGLHQW
LWHUDWLRQ LV DWWHPSWHG ,I DQRWKHU VWHS VL]H XSGDWH EHFRPHV
QHFHVVDU ODWHU LW LV GRQH XVLQJ WKH ODVW VXFFHVVIXO YDOXH RI WKH
GLYLVRU G 7KH LQLWLDO YDOXH RI WKH GLYLVRU LV G
393. 6WRSSLQJ ULWHULRQ
,Q VWHS RI RXU LPSOHPHQWDWLRQ RI WKH DOJRULWKP 9$ ZH
XVHG WKH IROORZLQJ HPSLULFDO VWRSSLQJ FULWHULRQ WKH DOJRULWKP
WHUPLQDWHV LI DQ RI WKH IROORZLQJ LV VDWLVILHG
x 7KH ODEHOLQJ +
N UHVXOWLQJ IURP KRUL]RQWDO PD[LPL]DWLRQ
GLIIHUV IURP WKH ODEHOLQJ 9
N UHVXOWLQJ IURP KRUL]RQWDO
PD[LPL]DWLRQ LQ QR PRUH WKDQ ODEHOV 7KH QXPEHU RI
GLIIHULQJ ODEHOV HTXDOV WKH VTXDUH PDJQLWXGH RI WKH
VXEJUDGLHQW FI 394. )RU DQ LPDJH SDLU WKH PD[LPXP
VTXDUH PDJQLWXGH RI WKH VXEJUDGLHQW HTXDOV WKH QXPEHU RI
SL[HOV LH IRU î LPDJHV ZLWK D PD[LPXP RI
GLIIHULQJ ODEHOV GLIIHULQJ ODEHOV PHDQ WKDW WKH
PLQLPL]DWLRQ RI WKH SUREOHP SRZHU KDV GHFUHDVHG WKH
VTXDUH PDJQLWXGH RI WKH VXEJUDGLHQW WR RI LWV
PD[LPXP YDOXH LH WKDW ZH DUH QHDU WKH RSWLPXP
x 7KH YDOXH RI WKH REMHFWLYH IXQFWLRQ KDV EHHQ HTXDO WR LWV
FXUUHQW PLQLPXP IRU DW OHDVW VXEJUDGLHQW LWHUDWLRQV
x 7KHUH ZHUH PRUH WKDQ LWHUDWLRQV 7KLV LV VLPSO DQ
HPHUJHQF EUDNH
([SHULPHQWDO UHVXOWV LQ WKH QH[W FKDSWHU SURYH WKDW WKH QHZ
SLHFHZLVH PRQRWRQH VXEJUDGLHQW DOJRULWKP SHUIRUPV LQ LPDJH
UHJLVWUDWLRQ WDVNV PXFK EHWWHU WKDQ DQ RI WKH VWDQGDUG VWHS
FRQWURO VWUDWHJLHV IRU WKH VXEJUDGLHQW PHWKRG
' 6LPLODULWLHV DQG 'LIIHUHQFHV EHWZHHQ 0XOWL/DEHO
6XEJUDGLHQW 5HJLVWUDWLRQ $OJRULWKP DQG WKH /LQHDU
3URJUDPPLQJ%DVHG 'HQVH ,PDJH 5HJLVWUDWLRQ $OJRULWKP LQ
WKH 'URS' $OJRULWKP
,Q VSLWH RI VLPLODU QRPHQFODWXUH XVHG LQ WKH GHVFULSWLRQV WKH
SUREOHP VWDWHPHQWV DQG WKH VROXWLRQ RI WKH WZR DOJRULWKPV DUH
HQWLUHO GLIIHUHQW
%RWK WKH DOJRULWKP SUHVHQWHG KHUH DQG WKH UHJLVWUDWLRQ
DOJRULWKP E *ORFNHU @ DUH PXOWLODEHO GLVFUHWH LPDJH
UHJLVWUDWLRQ DOJRULWKPV EDVHG RQ PLQLPL]DWLRQ RI WKH GXDO RI D
GLVFUHWH IXQFWLRQDO FRQVLVWLQJ RI XQDU DQG ELQDU WHUPV EXW
WKHUH DUH WKUHH IXQGDPHQWDO GLIIHUHQFHV
x 7KH UHJLVWUDWLRQ DOJRULWKP @ JHQHUDWHV FRQWLQXRXV
395. 70,
GLVSODFHPHQW ILHOG XVLQJ LQWHUSRODWLRQ ZKLOH RXUV DOORZV
IRU LPDJH UHJLVWUDWLRQ LQ SUHVHQFH RI GLVFRQWLQXRXV
GHIRUPDWLRQV WKXV WKH DOJRULWKP @ FDQQRW UHJLVWHU
LPDJHV ZLWK GLVFRQWLQXLWLHV LQ WKH GHIRUPDWLRQ ILHOG
x 7R DOORZ XVH RI WKH )DVW3' PXOWLODEHO PLQLPL]DWLRQ WKH
ELQDU ZHLJKWV LQ @ PXVW IRUP D VHPLPHWULF ZLWK WKH
SURSHUWLHV
412. ^ `
WWWWWWWW
WW
GGGG
WNWNJ
cccc
c
˜
cc
[[[[[[[[O
7KHUHIRUH WKH VWHHSHVW GHVFHQW /
79 PLQLPL]DWLRQ
SUHVHQWHG KHUH FDQQRW EH VROYHG XVLQJ WKH )DVW3'
DOJRULWKP
7KH VHPLPHWULFV SURSHUW LV QRW UHTXLUHG E WKH PXOWL
ODEHO VXEJUDGLHQW DOJRULWKP LW LV VXIILFLHQW WKDW WKH
ZHLJKWV EH QRQQHJDWLYH ,Q WKLV VHQVH WKH PXOWLODEHO
VXEJUDGLHQW DOJRULWKP LV DSSOLFDEOH WR D PXFK ZLGHU FODVV
RI PLQLPL]DWLRQ SUREOHPV WKDQ )DVW3' EXW )DVW3' LV
PXFK IDVWHU
x /DEHOV LQ RXU DOJRULWKP GHQRWH VKLIW GLUHFWLRQV ZLWK D
JLYHQ OHQJWK RI WKH VKLIW FRPSRQHQWV ZKLOH LQ @ WKH
HQFRGH ERWK VKLIW GLUHFWLRQ DQG OHQJWK
9, 5(68/76
$ RPSDULVRQ RI /
79 5HJLVWUDWLRQ RI WKH 6QWKHWLF
+RQHFRPE 3DLU :LWK 6WDWHRIWKH$UW ,PDJH 5HJLVWUDWLRQ
3DFNDJHV
$Q LOOXVWUDWLYH YLVXDO H[DPSOH RI WKH HIILFLHQF RI WKH
VXEJUDGLHQW PXOWLODEHO /
79 DOJRULWKP LV SURYLGHG LQ )LJ
7KH DUWLILFLDO KRQHFRPE LPDJH UHJLVWUDWLRQ SDLU RI )LJ
ZLWK QXPHULFDOO WRUQ WDUJHW LPDJH DSSHDULQJ DV GLDJRQDO
GDUN ZHGJH LV XVHG 7KH GHIRUPDWLRQ ILHOG RI DQ DUWLILFLDOO
FUHDWHG LPDJH GLVWRUWLRQ FDQ EH HDVLO YLVXDOL]HG VHH )LJ 413. $ FRUUHFWO ZRUNLQJ UHJLVWUDWLRQ DOJRULWKP PXVW EH DEOH QRW
RQO WR PDNH WKH UHJLVWHUHG DQG WKH UHIHUHQFH LPDJH DV VLPLODU
DV SRVVLEOH EXW DOVR WR UHFRYHU WKH WUXH GHIRUPDWLRQ ILHOG DV
FORVHO DV SRVVLEOH :H FRPSDUH D 415. WKH /
79 GXDOLW EDVHG DOJRULWKP
LPSOHPHQWHG E WKH DXWKRU RI @ DQG GRZQORDGHG IURP @
DQG ZLWK WKUHH UHJLVWUDWLRQ DOJRULWKPV JHQHUDWLQJ FRQWLQXRXV
GLVSODFHPHQW ILHOG F 418. WKH GHPRQV DOJRULWKP IRU
PXOWLPRGDO QRQULJLG UHJLVWUDWLRQ RI LPDJHV LPSOHPHQWHG LQ
0DWODE @ DV RXWOLQHG LQ @ 419. 7KHVH UHJLVWUDWLRQ DOJRULWKPV
DUH DPHQDEOH WR FRPSDULVRQ VLQFH WKH GHIRUPDWLRQ ILHOG XVHG
IRU UHJLVWUDWLRQ LV DFFHVVLEOH DIWHU WKH DOJRULWKP KDV WHUPLQDWHG
DQG WKXV FDQ EH FRPSDUHG ZLWK WKH WUXH GHIRUPDWLRQ ILHOG RI
WKH VQWKHWLF WDUJHW LPDJH )LJ 420. 7KH KRUL]RQWDO DQG YHUWLFDO
GLVSODFHPHQW ILHOG FRPSRQHQWV DUH 'UHQGHUHG LQ )LJ
$V H[SHFWHG FRQWLQXRXV UHJLVWUDWLRQ DOJRULWKPV DUH QRW DEOH
WR FORVH GLVFRQWLQXLWLHV LQ WKH WDUJHW LPDJH 7KH RQO
DOJRULWKPV FDSDEOH RI FORVLQJ WKH GLDJRQDO JDS LQ WKH WDUJHW
LPDJH DUH WKH WZR /
79 DOJRULWKPV D 422. 7KLV MXVWLILHV
WKH H[LVWHQFH RI /
79 LPDJH UHJLVWUDWLRQ DV D GLVWLQFWLYH
PHWKRG 7KH PXOWLODEHO VXEJUDGLHQW /
79 DOJRULWKP LHOGV
WKH EHVW UHVXOW LQ WHUPV RI WKH 6$' VXP RI DEVROXWH
GLIIHUHQFHV 423. YDOXH 0RUHRYHU LW LHOGV DOVR WKH EHVW UHVXOWV LQ
WHUPV RI WKH HUURU RI WKH UHFRYHUHG GLVSODFHPHQW ILHOG 7DEOH ,,
FRPSDUHV WKH WRWDO YDULDWLRQ WKH PLQLPD DQG PD[LPD RI WKH
GHIRUPDWLRQ ILHOG FRPSRQHQWV DQG WKH VXPV RI DEVROXWH
GLIIHUHQFHV EHWZHHQ WUXH DQG UHFRYHUHG KRUL]RQWDO DQG YHUWLFDO
GLVSODFHPHQW IRU WKH JURXQG WUXWK )LJ 424. RXU PXOWLODEHO
VXEJUDGLHQW /
79 DOJRULWKP DQG WKH SULPDOGXDO /
79
DOJRULWKP @@ IRU ZKLFK WKH EHVW YDOXHV ZH REWDLQHG IURP
D VHULHV RI H[SHULPHQWV ZLWK WKH ZHLJKWLQJ FRHIILFLHQW EHWZHHQ
WKH /
DQG WKH 79 WHUP DUH TXRWHG ,W VKRXOG EH PHQWLRQHG
KHUH WKDW WKH UHJLVWUDWLRQ DOJRULWKP @ GLYHUJHG IRU TXLWH
VRPH YDOXHV RI ZHLJKWLQJ FRHIILFLHQWV LQ WKH VHQVH WKDW LW
VKLIWHG VRPH RI DOUHDG PDWFKLQJ KRQHFRPE FHOOV
KRUL]RQWDOO RU YHUWLFDOO E RQH FHOO LQVWHDG RI OHDYLQJ WKHP
LQ SODFH WKXV GHVWURLQJ WKH UHJLVWHUHG LPDJH
7KH 79 YDOXH UHFRQVWUXFWHG E WKH PXOWLODEHO VXEJUDGLHQW
DOJRULWKP LV YHU FORVH WR WKH WUXH YDOXH
:LWK WKH H[FHSWLRQ RI WKH PD[LPXP YHUWLFDO VKLIW ZKLFK
VKRXOG EH DV FORVH WR DV SRVVLEOH KRUL]RQWDO PLQLPD DQG
PD[LPD DQG YHUWLFDO PLQLPD IRXQG E D UHJLVWUDWLRQ DOJRULWKP
VKRXOG EH FORVH WR 7KLV UHTXLUHPHQW LV EHVW PHW E WKH PXOWL
ODEHO VXEJUDGLHQW /
79 DOJRULWKP $OVR WKH 6$' HUURU RI WKH
UHFRYHUHG KRUL]RQWDO DQG YHUWLFDO GLVSODFHPHQW LV PXFK ORZHU
IRU WKH VXEJUDGLHQW DOJRULWKP WKDQ IRU WKH SULPDO GXDO
UHJLVWUDWLRQ @
425. 70,
)LJ RPSDULVRQ RI PXOWLODEHO VXEJUDGLHQW /
79 UHJLVWUDWLRQ RI WKH DUWLILFLDO KRQHFRPE LPDJH SDLU ZLWK DQRWKHU /
79 DOJRULWKP @ DQG WKUHH RI
WKH FRQWLQXRXV UHJLVWUDWLRQ DOJRULWKPV XVHG DOVR LQ )LJ 6LPLODULW EHWZHHQ WKH UHJLVWHUHG LPDJH DQG WKH UHIHUHQFH LV HYDOXDWHG XVLQJ WKH 6$' VXP RI
DEVROXWH GLIIHUHQFHV 427. 0XOWLODEHO /
79 LHOGV ERWK YLVXDOO DQG LQ WHUPV RI 6$' WKH EHVW PDWFK EHWZHHQ WKH UHJLVWHUHG DQG WKH UHIHUHQFH LPDJH
0RUHRYHU LWV YHUWLFDO GHIRUPDWLRQ ILHOG FRPSRQHQW PDWFKHV YHU ZHOO WKH JURXQG WUXWK RI )LJ DQG WKH KRUL]RQWDO GHIRUPDWLRQ FRPSRQHQW LV ZLWK WKH
H[FHSWLRQ RI VHYHUDO RXWOLHUV ]HUR DV UHTXLUHG E 428. 3ULPDOGXDO /
79 @ LV WKH VHFRQG EHVW DQG DOVR FORVHV WKH ILVVXUH LQ WKH WDUJHW LPDJH F 429. 'URS' @
LV WKH EHVW RI DOJRULWKPV JHQHUDWLQJ FRQWLQXRXV GLVSODFHPHQW ILHOG 9LVXDOO LW LHOGV D JRRG PDWFK EXW WKHUH DUH FRQVLGHUDEOH HUURUV LQ WKH LGHQWLILFDWLRQ RI
ERWK WKH YHUWLFDO ZKLFK VKRXOG QHYHU EH QHJDWLYH 433. 7KH VSOLQHIXQFWLRQ EDVHG DOJRULWKP IRU
QRQULJLG UHJLVWUDWLRQ RI LPDJHV LPSOHPHQWHG LQ 0DWODE @ DQG WKH GHPRQV DOJRULWKP IRU PXOWLPRGDO QRQULJLG UHJLVWUDWLRQ RI LPDJHV LPSOHPHQWHG LQ
0DWODE @ LQ WKH IRRWVWHSV RI @ LHOG XQVDWLVIDFWRU UHJLVWUDWLRQ LQ SUHVHQFH RI GLVFRQWLQXLWLHV ERWK LQ WHUPV RI VLPLODULW DQG LQ WHUPV RI FRUUHFW
LGHQWLILFDWLRQ RI WKH WUXH GHIRUPDWLRQ ILHOG
434. 70,
% 3DUDPHWHU 6HOHFWLRQ IRU 5HJLVWUDWLRQ $OJRULWKPV
)URP WKH XVHU¶V SRLQW RI YLHZ DQ LPSRUWDQW LVVXH LV WKH HDVH
ZLWK ZKLFK DQ DOJRULWKP¶V SDUDPHWHUV FDQ EH VHW ZLWKRXW WKH
QHHG IRU GHHS FRPSUHKHQVLRQ RI WKH DOJRULWKP )RU WKH
DOJRULWKPV GRZQORDGHG IURP WKH LQWHUQHW DQG FRPSDUHG LQ )LJ
D XVHU KDV WR VHOHFW WKH IROORZLQJ QXPEHUV RI SDUDPHWHUV
E 438. QRQULJLG GHPRQV DOJRULWKP @ SDUDPHWHUV
$ OLIH VFLHQWLVW ZLWK OLWWOH WKHRUHWLFDO EDFNJURXQG LQ LPDJH
SURFHVVLQJ PLJKW ILQG LW GLIILFXOW WR VHOHFW WKDW ODUJH QXPEHU RI
SDUDPHWHUV QHHGHG WR REWDLQ RSWLPXP UHJLVWUDWLRQ UHVXOWV
RPSDUHG WR WKDW WKH /
79 VXEJUDGLHQW DOJRULWKP SUHVHQWHG
KHUH KDV RQO VHOHFWDEOH SDUDPHWHUV ZLWK YHU LQWXLWLYH
PHDQLQJ
x PD[LPXP KRUL]RQWDOYHUWLFDO SL[HO VKLIW ZKLFKHYHU LV
JUHDWHU 439. QHHGHG IRU UHJLVWUDWLRQ 7KLV YDOXH FDQ EH JXHVVHG
YLVXDOO E FRPSDULQJ WKH WDUJHW DQG WKH UHIHUHQFH LPDJH
x WKH ZHLJKWLQJ IDFWRU ʄ NHHSLQJ LQ EDODQFH WKH UHJLVWUDWLRQ
DFFXUDF DQG WKH VPRRWKQHVV RI WKH GHIRUPDWLRQ 7KH
HIIHFW RI ʄ LV YHU VLPSOH
ODUJH YDOXHV RI Ȝ HQIRUFH VPRRWK HW OHVV SUHFLVH
UHJLVWUDWLRQ
VPDOO YDOXHV RI Ȝ ERRVW VLPLODULW EHWZHHQ WKH UHIHUHQFH
DQG WKH WDUJHW LPDJH HW WKH GHIRUPDWLRQ ILHOG EHFRPHV
FRDUVHU
:H EHOLHYH WKDW WKLV VLPSOLFLW RI SDUDPHWHU VHOHFWLRQ FRXOG
FRQWULEXWH WR PDNLQJ WKH PXOWLODEHO VXEJUDGLHQW /
79
UHJLVWUDWLRQ DQ DWWUDFWLYH PHWKRG
5HVXOWV RI /
79 5HJLVWUDWLRQ RI 3KVLFDO 6OLFHV RI
%LRORJLFDO 6SHFLPHQV :LWK 'LVFRQWLQXLWLHV
440. 3KVLFDO 6HFWLRQV RI D 7XUWOH (PEUR +HDG
)LJ VKRZV WKH UHVXOW RI /
79 UHJLVWUDWLRQ RI LPDJHV RI
WZR QHLJKERULQJ VOLFHV RI D WXUWOH HPEUR KHDG RI )LJ 7KH
PDJQLWXGH RI WKH GLVSODFHPHQW ILHOG XVHG WR WUDQVIRUP WKH
WDUJHW LPDJH LV HQFRGHG E FRORU VKDGHV LQ )LJ
441. /60 ,PDJHV RI 3KVLFDO 6OLFHV RI 0RXVH (PEUR
7KH SDLU RI LPDJHV XVHG IRU WKLV H[DPSOH ZDV LQWURGXFHG LQ
)LJ 7KH WDUJHW LPDJH H[SRVHV D UXSWXUH LQ WKH ORZHU ULJKW
FRUQHU 7KH UHVXOW RI UHJLVWUDWLRQ LV VKRZQ LQ )LJ ZLWK WKH
GLVSODFHPHQW ILHOG SORWWHG VHSDUDWHO LQ )LJ
442. 5HJLVWUDWLRQ RI /LJKW 0LFURVFRSH ,PDJHV RI 6OLFHV RI WKH
$PHULFDQ $OOLJDWRU (PEUR 6SHFLPHQ
7KH WHVW LPDJH SDLU ZDV LQWURGXFHG LQ )LJ 7KH UHJLVWHUHG
LPDJH DV ZHOO DV FKHFNHUERDUG SORWV EHIRUH DQG DIWHU
UHJLVWUDWLRQ DUH VKRZQ LQ )LJ WKH GHIRUPDWLRQ ILHOG LQ )LJ
8QOLNH LQ WKH H[DPSOHV RI WKH WXUWOH HPEUR KHDG DQG WKH
PRXVH HPEUR WKH ODUJHVW VKLIWV LQ )LJ GR QRW OLH LQ WKH
GLVFRQWLQXLW UHJLRQ RI WKH WDUJHW LPDJH EXW LQ WKH UHJLRQ RI
FRQWLQXRXV GHIRUPDWLRQ ZKHUH WKHUH LV D PDVVLYH VKLIW EHWZHHQ
FRUUHVSRQGLQJ VWUXFWXUHV RI WKH WZR LPDJHV
7KH JRRG DOLJQPHQW DIWHU UHJLVWUDWLRQ )LJ H 446. VXJJHVWV WKDW WKH /
79 UHJLVWUDWLRQ ZLOO DOVR
SHUIRUP ZHOO IRU FRQYHQWLRQDO UHJLVWUDWLRQ RI VLQJOH PRGDOLW
LPDJH SDLUV
7$%/( ,,
203$5,621 2) $85$ 2) 7+( 5(29(5(' ',63/$(0(17 ),(/'
2) 7+( 68%*5$',(17 $1' 35,0$/'8$/ /
79 $/*25,7+06
JURXQG WUXWK
)LJ 447. PXOWLODEHO
VXEJUDGLHQW
/
79
SULPDOGXDO
/
79 @
WRWDO YDULDWLRQ
PLQLPXP
KRUL]RQWDO VKLIW
PD[LPXP
KRUL]RQWDO VKLIW
PLQLPXP
YHUWLFDO VKLIW
PD[LPXP
YHUWLFDO VKLIW
VXP RI DEVROXWH
GLIIHUHQFHV
EHWZHHQ WUXH DQG
UHFRYHUHG
KRUL]RQWDO
GLVSODFHPHQW
VXP RI DEVROXWH
GLIIHUHQFHV
EHWZHHQ WUXH DQG
UHFRYHUHG
YHUWLFDO
GLVSODFHPHQW
)LJ /
79 UHJLVWUDWLRQ RI LPDJHV RI WZR QHLJKERULQJ VOLFHV RI D WXUWOH HPEUR KHDG D 457. 70,
7KH JDS GHOLQHDWHG E WKH RYDO LQ WKH WDUJHW LPDJH LV FORVHG E
UHJLVWUDWLRQ 7KLV LV DOVR WKH DUHD RI WKH JUHDWHVW ZDUSLQJ LQ )LJ
)LJ 'HIRUPDWLRQ ILHOG UHVXOWLQJ IURP UHJLVWUDWLRQ RI WKH UDW HPEUR
LPDJH SDLU 7KH OLJKWHVW DUHD OLHV LQ WKH UHJLRQ RI WKH UXSWXUH LQ WKH WDUJHW
LPDJH ,W LV DOVR WKLV DUHD ZKHUH WKH SDWFKHV FRUUHVSRQGLQJ WR VTXDUHV RI WKH
UHFWDQJXODU JULG DUH PRVW GLVWRUWHG
)LJ 7KH GLVSODFHPHQW ILHOG XVHG WR WUDQVIRUP WKH WXUWOH HPEUR WDUJHW
LPDJH 7KH VFDOH RQ WKH ULJKW DVVLJQV WKH DEVROXWH YDOXH RI SL[HO VKLIW WR WKH
SDWFK EULJKWQHVV 7KH VKDSH RI WKH SDWFKHV VKRZV KRZ WKH GLVFRQWLQXLW
PDSV WKH UHFWDQJXODU JULG RI WKH UHIHUHQFH LPDJH WR WKH WDUJHW LPDJH 7KH
JUHDWHVW VKLIWV DUH IRXQG LQ WKH ORZHU SDUW RI WKH GLVSODFHPHQW ILHOG ZKHUH
WKHUH LV D UXSWXUH LQ WKH WDUJHW LPDJH
)LJ 5HJLVWUDWLRQ RI /60 LPDJHV RI SKVLFDO VHFWLRQ RI D PRXVH HPEUR RI )LJ D 467. 70,
' RPSDULVRQ RI 6WDQGDUG 6XEJUDGLHQW 6FKHPHV :LWK WKH
1HZ 3LHFHZLVH 0RQRWRQH 6XEJUDGLHQW $OJRULWKP
7R YHULI WKH PHULWV RI WKH SLHFHZLVH PRQRWRQH VXEJUDGLHQW
DOJRULWKP GHVFULEHG DERYH ZH ILUVW FRPSDUHG LW WR D VWDQGDUG
VWHS VL]H UXOH IURP WKH OLWHUDWXUH QDPHO WR WKH RSWLPXP VWHS
OHQJWK IRU D IL[HG QXPEHU RI LWHUDWLRQV E 1HVWHURY @ :H
ILUVW KDG WKH SLHFHZLVH PRQRWRQH VXEJUDGLHQW DOJRULWKP UXQ RQ
WKH WHVW LPDJH SDLU )LJ XQWLO FRQYHUJHQFH D VLWXDWLRQ ZKHUH
WKH YDOXH RI WKH REMHFWLYH IXQFWLRQ GRHV QRW FKDQJH IRU D SUH
VSHFLILHG QXPEHU RI VWHSV 468. ,Q WRWDO VHWV RI VHDUFK YHFWRUV
ZHUH XVHG ZLWK WKH PRGXOL DQG DQG WKH VHDUFK
GLUHFWLRQV DOWHUQDWLQJ EHWZHHQ RGG DQG HYHQ LWHUDWLRQV
DFFRUGLQJ WR 470. DV GHSLFWHG LQ )LJ 7KXV WKH
DOJRULWKP GHVFULEHG XQGHU 9$ ZDV UXQ WZHOYH WLPHV $W WKH
HQG RI HDFK UXQ WKH SDVV¶V QXPEHU RI VWHSV ZDV VDYHG WR EH
XVHG DV WKH IL[HG QXPEHU RI LWHUDWLRQV IRU VWHS VL]H FDOFXODWLRQ
DFFRUGLQJ WR 1HVWHURY¶V RSWLPXP VWHS VL]H OHQJWK
1HVWHURY @ VKRZHG WKDW IRU D IL[HG QXPEHU RI LWHUDWLRQV
1 WKH RSWLPXP VWHS OHQJWK LV
L
1
5
KL
471. ZLWK 5 EHLQJ WKH /
GLVWDQFH RI WKH VWDUWLQJ SRLQW IURP WKH
RSWLPXP VHW 8VLQJ WKLV UHVXOW ZH UDQ WKH WZHOYH SDVVHV RI WKH
DOJRULWKP DQHZ EXW WKLV WLPH ZLWK WKH RSWLPXP VWHS OHQJWK
FDOFXODWHG E 472. IRU WKH IL[HG QXPEHU RI VWHSV QHHGHG E WKH
SLHFHZLVH PRQRWRQH VXEJUDGLHQW DOJRULWKP LQ WKDW SDVV )RU
RXU SUREOHP VWDWHPHQW WKH IRUPXOD 473. LV PHUHO RI
WKHRUHWLFDO YDOXH VLQFH ZH KDYH QR FOXHV FRQFHUQLQJ WKH YDOXH
RI 5 LQ D VSHFLILF FDVH 7KHUHIRUH ZH RSWLPL]HG WKH YDOXH RI 5
PDQXDOO LQ D OHQJWK VHULHV RI FRPSXWDWLRQV DQG XVHG WKH
RSWLPDO 5 IRU FRPSDULVRQ ZLWK WKH SLHFHZLVH PRQRWRQH
DOJRULWKP 7KH WZR DOJRULWKPV EHLQJ FRPSDUHG GLIIHUHG LQ WKH
VWHS VL]H VHOHFWLRQ UXOH DORQH ± DOO RWKHU FRPSRQHQWV LH WKH
KRUL]RQWDO DQG YHUWLFDO GQDPLF SURJUDPPLQJ RSWLPL]DWLRQ
FDOFXODWLRQ RI WKH VXEJUDGLHQW DQG WKH XSGDWH RI WKH SRWHQWLDO
IXQFWLRQV ZHUH LGHQWLFDO
,Q )LJ D 484. (YHQ PRUH LPSRUWDQW LV WKH IDFW WKDW WKH JDS EHWZHHQ WKH
ILQDO YDOXH RI WKH PD[LPXP VXP DQG WKH PLQLPXP SUREOHP
SRZHU YDQLVKHV LQ )LJ D 486. 4 LV DQ XSSHU ERXQG
RQ WKH PD[LPXP VXP WKH VPDOO JDS LQGLFDWHV WKDW WKH VXP
492. LQ WKH FXUUHQW LWHUDWLRQ LV IDU
IURP PD[LPXP
)LJ 'HIRUPDWLRQ ILHOG HVWDEOLVKHG E /
79 UHJLVWUDWLRQ RI VOLFHV RI WKH
$PHULFDQ DOOLJDWRU HPEUR VSHFLPHQ 7KH JUHDWHVW GHIRUPDWLRQV DUH QRW
ORFDWHG LQ WKH DUHD RI WKH UXSWXUH EXW LQ WKH UHJLRQ ZKHUH WKH WDUJHW LPDJH
VWUXFWXUHV DUH VKLIWHG UHODWLYH WR WKH VWUXFWXUHV RI WKH UHIHUHQFH
)LJ /
79 UHJLVWUDWLRQ RI OLJKW PLFURVFRSH LPDJHV RI SKVLFDO VOLFHV RI WKH $PHULFDQ DOOLJDWRU HPEUR VSHFLPHQ D 501. GLVSODV YHU JRRG DOLJQPHQW LPDJH DIWHU UHJLVWUDWLRQ $V VHHQ IURP WKH
FKHFNHUERDUG SORW EHVLGHV WKH UXSWXUH LQ WKH XSSHU ULJKW SDUW RI WKH VSHFLPHQ WKHUH LV DOVR D VLJQLILFDQW VKLIW EHWZHHQ WKH WZR LPDJHV ORZHVW URZ UG
VTXDUH
IURP WKH ULJKW 503. 70,
9DQLVKLQJ JDS EHWZHHQ WKH SUREOHP SRZHU DQG WKH
PD[LPXP VXP VLPLODU WR WKDW LQ )LJ D 504. ZDV REVHUYHG LQ
DOPRVW DOO RI RXU WHVW FDVHV LQGLFDWLQJ YHU JRRG UHJLVWUDWLRQ
UHVXOWV RI WKH PXOWLODEHO SLHFHZLVH PRQRWRQH VXEJUDGLHQW
DOJRULWKP
,Q D IXUWKHU VHULHV RI H[SHULPHQWV ZH FRPSDUHG WKH
FRQYHUJHQFH RI D QRQVXPPDEOH GLPLQLVKLQJ VWHS VL]H UXOH ZLWK
WKH UHVXOWV DFKLHYHG E WKH SLHFHZLVH PRQRWRQH VWUDWHJ 7KH
ILQDO YDOXHV RI WKH PD[LPXP VXP 505. DFKLHYHG LQ HDFK RI WKH
WZHOYH SDVVHV RI WKH SLHFHZLVH PRQRWRQH DOJRULWKP ZHUH XVHG
DV VWRSSLQJ FULWHULRQ IRU VXEJUDGLHQW VWUDWHJLHV ZLWK
GLPLQLVKLQJ VWHS VL]H UXOHV 7KH ILUVW UXOH WHVWHG ZDV D
PRGLILFDWLRQ RI WKH UXOH XVHG LQ @ DQG FDOFXODWHG WKH VWHS
VL]H DV
L
L
U
LJ
:LWK WKH YDOXH U UHFRPPHQGHG LQ @ ZH DUULYHG DIWHU
YHU ORQJ WLPH DW WKH PD[LPXP VXP YDOXHV DFKLHYHG E WKH
SLHFHZLVH PRQRWRQH VXEJUDGLHQW VWHS FRQWURO RQO IRU WKH ILUVW
WHQ RXW RI WRWDOO WZHOYH LWHUDWLRQ QHHGHG IRU WKH PD[LPXP
PRGXOXV YDOXH RI 7KH ODVW WZR LWHUDWLRQV WKRVH IRU WKH
PRGXOXV 506. GLG QRW WHUPLQDWH DIWHU KRXUV DQG ZH EURNH WKH
H[SHULPHQW RII
:H DOVR H[SHULPHQWHG ZLWK WKH KDUPRQLF VHULHV XVHG LQ @
DQG ZLWK WKH QRQVXPPDEOH GLPLQLVKLQJ VWHS OHQJWK UXOH
L
L
U
KL
SURSRVHG E 1HVWHURY @ IRU WKH FDVH ZKHQ WKH QXPEHU RI
LWHUDWLRQV LV QRW IL[HG D SULRUL 1RQH RI WKH VWUDWHJLHV ZDV HYHU
DEOH WR DFKLHYH WKH PD[LPXP VXP YDOXHV RI WKH SLHFHZLVH
PRQRWRQH VWUDWHJ 7KH VDPH KROGV IRU WKH FRQVWDQW VWHS VL]H
VWUDWHJ
( 4XDQWLWDWLYH RPSDULVRQ RI WKH *UDSKXW 0HWKRG :LWK
WKH 3LHFHZLVH 0RQRWRQH 6XEJUDGLHQW $OJRULWKP IRU 0XOWL
/DEHO 0LQLPL]DWLRQ RI WKH /
79 )XQFWLRQDO
0HDVXUH RI UHJLVWUDWLRQ TXDOLW RI SKVLFDO VOLFHV ZLWK
GLVFRQWLQXLWLHV LQ PLFURVFRS LV WKH /
79 IXQFWLRQDO 507. 7KH
UHVXOWV RI UHJLVWUDWLRQ FDOFXODWHG E GLIIHUHQW /
79 PHWKRGV
IRU WKH VDPH ZHLJKWLQJ EHWZHHQ VLPLODULW DQG VPRRWKQHVV FDQ
EH GLUHFWO FRPSDUHG %HVLGHV WKH GLIIHUHQFHV LQ UHJLVWUDWLRQ
SHUIRUPHG E HLWKHU PHWKRG DUH LQ VRPH FDVHV YLVLEOH WR WKH
QDNHG HH
,PSOHPHQWDWLRQ GHWDLOV 7KH PXOWLODEHO /
79 LPDJH
UHJLVWUDWLRQ ZDV LPSOHPHQWHG E XV 7KH SULQFLSDO FRQVWLWXHQWV
DUH WKH GQDPLF SURJUDPPLQJ RSWLPL]DWLRQ RQ KRUL]RQWDO DQG
YHUWLFDO WUHHV FRYHULQJ WKH LPDJH JUDSK LQGLFDWHG LQ 509. DQG WKH QHZ SLHFHZLVH PRQRWRQH
VWHS VL]H VWUDWHJ ZH SURSRVHG XQGHU 9 7KH GQDPLF
SURJUDPPLQJ RSWLPL]DWLRQ RQ D KRUL]RQWDOYHUWLFDO OLQH LV
LQGHSHQGHQW RI RWKHU KRUL]RQWDOYHUWLFDO OLQHV :H H[SORLWHG
WKLV IDFW E LPSOHPHQWLQJ D SDUDOOHO YHUVLRQ RI WKH DOJRULWKP
WKDW PDNHV IXOO XVH DOO 38 FRUHV DYDLODEOH RQ D 3 7KH 38
WLPHV TXRWHG LQ 7DEOH ,,, ZHUH PHDVXUHG RQ D ODSWRS ZLWK IRXU
FRUHV RI DQ ,QWHO RUH L SURFHVVRU UXQQLQJ LQ SDUDOOHO DW
*+] ,Q DGGLWLRQ ZH DOVR LPSOHPHQWHG WKH DOJRULWKP RQ D
8'$ *38 1YLGLD *H)RUFH *7; 511. WKH IUHH +,35
SXVKUHODEHO FRGH GHVFULEHG LQ @ DQG GRZQORDGDEOH IURP
WKH KRPH SDJH RI WKH DOJRULWKP
V LQYHQWRU $QGUHZ 9
*ROGEHUJ ZDV XVHG :H GR QRW NQRZ RI DQ SDUDOOHOL]DEOH
PD[IORZ DOJRULWKP VR WKH DGYDQWDJH RI PXOWLSOH FRUHV FDQQRW
EH H[SORLWHG E * EDVHG RSWLPL]DWLRQ
)LJ RPSDULVRQ RI FRQYHUJHQFH EHWZHHQ D 515. N* ZKLFK LV WR EH PD[LPL]HG WKH
XSSHU GHFUHDVLQJ FXUYH LV WKH FXUUHQW YDOXH RI WKH SUREOHP SRZHU 521. N* LV DFKLHYHG 7KLV LV ZHOO VDWLVILHG
E WKH SLHFHZLVH PRQRWRQH VXEJUDGLHQW VWUDWHJ LQ D 523. ZKHUH WKHUH LV D ODUJH RVFLOODWLQJ JDS EHWZHHQ WKH
SULPDO VROXWLRQ 525. 4 6LQFH WKH JUDSKV VKRZ
WKH ODVW RQH RI WZHOYH VHWV RI VHDUFK YHFWRUV 531. ^ ` PDWFKLQJ YDOXHV RI WKH 535. 7KLV UHVXOW LV DOVR UHIOHFWHG E WKH PXFK ORZHU ILQDO YDOXH RI WKH
IXQFWLRQDO 536. [) DQG FRQVHTXHQWO EHWWHU LPDJH UHJLVWUDWLRQ IRU WKH
SLHFHZLVH PRQRWRQH VWUDWHJ ) 538. 70,
7KH LPDJH SDLUV )LJ )LJ )LJ DQG )LJ ZHUH
UHJLVWHUHG E ERWK WKH * DQG WKH SLHFHZLVH PRQRWRQH
VXEJUDGLHQW DOJRULWKP DQG RQ WHUPLQDWLRQ WKH /
GLVWDQFH
EHWZHHQ WKH UHJLVWHUHG DQG WKH UHIHUHQFH LPDJH DQG WKH WRWDO
YDULDWLRQ RI WKH UHVXOWLQJ GLVSODFHPHQW ILHOG 79 ZDV FRPSXWHG
7KHVH YDOXHV ZHUH XVHG WR FRPSXWH ) /
Ȝ79 9DOXHV RI Ȝ
XVHG IRU HDFK LPDJH SDLU DUH DOVR IRXQG LQ 7DEOH ,,,
/RZHU YDOXHV RI ) /
DQG 79 PHDQ EHWWHU SHUIRUPDQFH LQ
7DEOH ,,, ,W LV VHHQ WKDW ± ZLWK WKH H[FHSWLRQ RI WKH
FRPSXWDWLRQ WLPH ± WKH PXOWLODEHO SLHFHZLVH PRQRWRQH
VXEJUDGLHQW VFKHPH RXWSHUIRUPV WKH JUDSKFXWV LQ DOO RI WKH
WHVW FDVHV 1RW RQO GRHV LW DFKLHYH EHWWHU YDOXHV RI ) RI WKH
IXQFWLRQDO 539. EXW DOVR WKH GLIIHUHQFH /
EHWZHHQ WKH UHJLVWHUHG
LPDJH DQG WKH UHIHUHQFH LPDJH LV VPDOOHU DQG WKH GHIRUPDWLRQ
RI WKH WDUJHW LPDJH LV VPRRWKHU LQ WHUPV RI WKH WRWDO YDULDWLRQ
79
7KH DSSDUHQW VSHHG DGYDQWDJH RI WKH JUDSKFXW DOJRULWKP LV
GHFHSWLYH RPSXWDWLRQ WLPHV LQ 7DEOH ,,, UHIHU WR WLPH QHHGHG
WR DFKLHYH WKH TXRWHG YDOXH RI ) )RU D IDLU FRPSDULVRQ ZH
ZRXOG QHHG WR VWRS WKH PXOWLODEHO DOJRULWKP VRRQHU QDPHO DV
VRRQ DV WKH ) YDOXH RI WKH JUDSKFXW PHWKRG LV DFKLHYHG 7KH
UXQQLQJ WLPHV IRU WKH PXOWLODEHO LPSOHPHQWDWLRQ ZRXOG WKHQ
ORRN PXFK PRUH IDYRUDEOH LI QRW HTXDOO JRRG DV WKRVH IRU
JUDSKFXWV
7KH LPSOHPHQWDWLRQ RQ WKH 8'$ *38 ZDV LQ WKH EHVW FDVH
QRW TXLWH WZLFH DV IDVW DV WKH LPSOHPHQWDWLRQ RQ D IRXUFRUH L
38 *LYHQ WKH PXFK PRUH FRPSOLFDWHG SURJUDPPLQJ GDWD
LQSXWRXWSXW DQG VQFKURQL]DWLRQ EHWZHHQ WKH 38 DQG WKH
*38 ZH UHJDUG WKH HIIRUW QHHGHG WR REWDLQ D VSHHGXS RI OHVV
WKDQ WZR DV XQMXVWLILHG
) 9LVXDO RPSDULVRQ RI $FFXUDF RI /
79 0LQLPL]DWLRQ E
WKH 3LHFHZLVH 0RQRWRQH 6XEJUDGLHQW 6* 540. 0HWKRG DQG E WKH
*UDSK XWV
7KH UHVXOWV LQ 7DEOH ,,, VKRZ WKDW IRU WKH IRXU WHVW H[DPSOHV
SUHVHQWHG KHUH WKH SLHFHZLVH PRQRWRQH 6* DOJRULWKP LHOGV
ZLWKRXW H[FHSWLRQ ORZHU YDOXHV RI WKH UHJLVWUDWLRQ IXQFWLRQDO )
RI WKH VXP RI DEVROXWH GLIIHUHQFHV /
DQG RI WKH WRWDO YDULDWLRQ
79 7KLV LPSOLHV WKDW WKH * PLQLPL]DWLRQ RI WKH QRQFRQYH[
LQ JHQHUDO 542. 6,) G[ DV GHVFULEHG LQ @
WHUPLQDWHV LQ D QRQJOREDO PLQLPXP RQWUDU WR WKDW WKH 6*
DOJRULWKP PD[LPL]HV WKH FRQYH[ GXDO IXQFWLRQ DQG LI WKH
PD[LPXP RI WKH GXDO FRLQFLGHV ZLWK WKH PLQLPXP RI WKH
SULPDO IXQFWLRQDO WKHQ LW LV WKH JOREDO PLQLPXP 7KLV OHG LQ
WKUHH RXW RI WKH IRXU WHVW FDVHV H[DPLQHG KHUH WR YLVXDOO
SHUFHLYDEOH ORZHU TXDOLW RI WKH * UHJLVWHUHG LPDJHV
FRPSDUHG WR PXOWLODEHO VXEJUDGLHQWUHJLVWHUHG LPDJHV DV
VKRZQ LQ )LJ
9,, 21/86,21
,Q WKLV ZRUN ZH SUHVHQWHG D QHZ PXOWLODEHO VXEJUDGLHQW
DOJRULWKP IRU GLVFUHWH /
79 EDVHG UHJLVWUDWLRQ RI LPDJH SDLUV
7KH UHJLVWUDWLRQ LV DFKLHYHG E LWHUDWLYH PLQLPL]DWLRQ RI D
IXQFWLRQDO FRQVLVWLQJ RI WZR WHUPV D GDWD ILGHOLW WHUP
HYDOXDWLQJ WKH VXP RI GLIIHUHQFHV EHWZHHQ WKH UHJLVWHUHG DQG
WKH UHIHUHQFH LPDJH DQG D VPRRWKQHVV WHUP :KLOH WKH UHVXOWV
SUHVHQWHG KHUH UHIHU WR UHJLVWUDWLRQ ZLWK DQ /
GDWD WHUP DQG D
WRWDO YDULDWLRQ VPRRWKQHVV WHUP WKH DOJRULWKP FDQ EH DSSOLHG
WR RWKHU WSHV RI LPDJH UHJLVWUDWLRQ GHILQHG LQ WHUPV RI
PLQLPL]DWLRQ RI D IXQFWLRQDO FRQVLVWLQJ RI ELQDU DQG SDLUZLVH
WHUPV RQ GLVFUHWH LPDJH JULG
:H XVHG WKH LQWHJHU SURJUDP SUREOHP VWDWHPHQW RI @ EXW
SURSRVHG D GLIIHUHQW VROXWLRQ LQ ZKLFK WKH PD[LPXP GHVFHQW RI
WKH /
79 IXQFWLRQDO LV UHSODFHG ZLWK PLQLPL]LQJ D GXDO
TXDQWLW RI D PD[LPXP VXP 2XU LWHUDWLYH VWHHSHVW GHVFHQW
DOJRULWKP UHOLHV RQ WKH IUDPHZRUN RI @ IRU VROXWLRQ RI PD[
VXP ODEHOLQJ SUREOHPV EDVHG RQ WKH PHWKRG RI HTXLYDOHQW
7$%/( ,,,
48$17,7$7,9( 203$5,621 2) 3(5)250$1(
2) 7+( 68%*5$',(17 08/7,/$%(/ $1' *5$3+87 $/*25,7+0
)25 /
79 %$6(' ,0$*( 5(*,675$7,21
LPDJH
SDLU
LPDJH
VL]H
PHWKRG
YDOXH RI
)
/
Ȝ79
/
GLVWDQFH
EHWZHHQ
UHIHUHQFH DQG WDUJHW
LPDJH
WRWDO YDULDWLRQ
RI WKH
GLVSODFHPHQW ILHOG
79
Ȝ FRPSXWDWLRQ
WLPH V@
)LJ
7XUWOH
HPEUR
[ PXOWLODEHO RQ 38 FRUH L
PXOWLODEHO RQ 8'$
JUDSKFXW
)LJ
+RQHFRPE
[ PXOWLODEHO RQ 38 FRUH L
PXOWLODEHO RQ 8'$
JUDSKFXW
)LJ
0RXVH
HPEUR
[ PXOWLODEHO RQ 38 FRUH L
PXOWLODEHO RQ 8'$
JUDSKFXW
)LJ
$OOLJDWRU
HPEUR
[ PXOWLODEHO RQ 38 FRUH L
PXOWLODEHO RQ 8'$
JUDSKFXW
543. 70,
WUDQVIRUPDWLRQV ZKLFK WUDQVIRUPV PD[LPL]DWLRQ RI IXQFWLRQDOV
FRQVLVWLQJ RI VXPV RI ELQDU DQG SDLUZLVH WHUPV RQ VHWV RI
SL[HOV DQG QHLJKERUKRRGV LQWR PLQLPL]DWLRQ RI DQ XSSHU ERXQG
RQ WKH PD[VXP FDOOHG SUREOHP SRZHU E WKH VXEJUDGLHQW
PHWKRG )RU WKH SDUWLFXODU FDVH RI UHFWDQJXODU SL[HO JULGV ZH
FKRVH RQH RI PDQ SRVVLELOLWLHV RI GHILQLQJ WKH VHDUFK
GLUHFWLRQV DV ZHOO DV D VHTXHQFH RI VHDUFK YHFWRU OHQJWKV 7KH
VHDUFK YHFWRUV ZHUH DVVLJQHG ODEHOV ZKLFK DOORZHG WKH XVH RI
WKH VXEJUDGLHQW DOJRULWKP RI @ $ PDMRU GLIIHUHQFH IURP WKH
VROXWLRQ RI @ LV WKDW UDWKHU WKDQ DWWHPSWLQJ WR PLQLPL]H WKH
QRQFRQYH[ IXQFWLRQDO 544. GLUHFWO E WKH VWHHSHVW GHVFHQW
ZLWK WKH ULVN RI JHWWLQJ WUDSSHG DW D ORFDO PLQLPXP ZH LQVWHDG
WDNH WKH QHJDWLYH RI WKH GHVFHQW DQG PLQLPL]H LWV GXDO TXDQWLW
FDOOHG SUREOHP SRZHU WKDW LV JXDUDQWHHG FRQYH[ 7KXV LI WKH
PD[LPXP DVFHQW RI WKH QHJDWLYH GHVFHQW RI IXQFWLRQDO 545. HTXDOV WKH PD[LPXP GHVFHQW RI LWV SUREOHP SRZHU LW ZLOO EH
IRXQG E WKH DOJRULWKP
7KH ZRUN @ OHDYHV RSHQ WKH TXHVWLRQ RI VWHS VL]H FRQWURO
RI WKH VXEJUDGLHQW PLQLPL]DWLRQ +DUPRQLF VHULHV XVHG IRU VWHS
VL]H LQ @ OHDGV WR D YHU VORZ DQG RVFLOODWLQJ FRQYHUJHQFH RI
WKH SUREOHP SRZHU 2WKHU FRPPRQO UHFRPPHQGHG VWHS VL]HV
UXOHV GR QRW SHUIRUP DQ EHWWHU :H WKHUHIRUH SURSRVHG D QHZ
VWUDWHJ RI VWHS VL]H VHOHFWLRQ ZKLFK OHDGV WR SLHFHZLVH
PRQRWRQH FRQYHUJHQFH RI WKH FRQYH[ SUREOHP SRZHU ,W WXUQV
RXW WKDW ZLWK WKLV VWHS VL]H UXOH WKH VXEJUDGLHQW PLQLPL]DWLRQ
FRQYHUJHV PXFK IDVWHU LQ SUDFWLFH DQG WKDW WKH JDS EHWZHHQ
WKH PD[VXP DQG WKH XSSHU ERXQG WKH SUREOHP SRZHU 546. GLVDSSHDUV LQ PRVW FDVHV RU LV PXFK QDUURZHU WKDQ ZLWK
FRPPRQ VXEJUDGLHQW VWHS VL]H UXOHV 7KH YDQLVKLQJ JDS LV D
VDIH LQGLFDWRU RI DFFXUDWH UHJLVWUDWLRQ VLQFH D PD[VXP
IXQFWLRQDO FDQQRW EH KLJKHU WKDQ LWV XSSHU ERXQG
8VLQJ RXU PRGHO H[DPSOH RI KRQHFRPE SDWWHUQ ZLWK D
QXPHULFDOO JHQHUDWHG ILVVXUH ZH FRPSDUHG WKH DFFXUDF RI
RXU LQWHJHU SURJUDP VROXWLRQ ZLWK WKH NQRZQ JURXQG WUXWK DQG
ZLWK WKH VROXWLRQ RI WKH /
79 UHJLVWUDWLRQ @ LPSOHPHQWHG LQ
@ ,W WXUQV RXW WKDW RXU VROXWLRQ LHOGV PRUH DFFXUDWH UHVXOWV
LQ WHUPV RI WKH /
GLVWDQFH RI WKH WRWDO YDULDWLRQ DQG RI WKH VXP
RI GLIIHUHQFHV EHWZHHQ WKH KRUL]RQWDO DQG YHUWLFDO
GLVSODFHPHQW UHFRYHUHG E WKH UHJLVWUDWLRQ DQG WKH JURXQG
WUXWK 7KLV KROGV LQ VSLWH RI WKH IDFW WKDW WKH UHDOYDOXHG
GLVSODFHPHQW ILHOG LQ @ GHILQHG RQ D VXEVHW RI 5
KDV WKH
SRWHQWLDO RI VXESL[HO DFFXUDF LH RI EHLQJ PRUH SUHFLVH WKDQ
RXU UHJLVWUDWLRQ FRQVLGHULQJ LPDJHV GHILQHG RQ D GLVFUHWH SL[HO
JULG DQG DOORZLQJ RQO LQWHJHU SL[HO VKLIWV
)RU PDQ WDVNV LQ LPDJH SURFHVVLQJ JUDSKFXWV DUH D
PHWKRG RI FKRLFH IRU PLQLPL]DWLRQ RI IXQFWLRQDOV FRQVLVWLQJ RI
VXPV RI GDWD WHUPV DQG VPRRWKQHVV WHUPV :H FRPSDUHG WKH
UHVXOWV REWDLQHG E WKH SLHFHZLVH PRQRWRQH VXEJUDGLHQW
PHWKRG ZLWK D VWHHSHVW GHVFHQW JUDSKFXW EDVHG PLQLPL]DWLRQ
RI WKH IXQFWLRQDO 547. DV SURSRVHG LQ @ ,W WXUQV RXW WKDW LQ WKH
IRXU H[DPSOHV SUHVHQWHG KHUH DQG LQ IDFW LQ WRWDOO LPDJH
SDLUV ZH XVHG IRU WHVWLQJ GXULQJ GHYHORSPHQW 549. DQG RI LWV
FRPSRQHQWV ± WKH /
GLVWDQFH EHWZHHQ WKH UHJLVWHUHG DQG WKH
UHIHUHQFH LPDJH DQG WKH WRWDO YDULDWLRQ RI WKH GLVSODFHPHQW
ILHOG *UDSK FXWV REWDLQ WKHLU OHVV DFFXUDWH UHJLVWUDWLRQ DW PRVW
WKUHH WLPHV IDVWHU 7KH WLPH QHHGHG IRU DFFXUDWH UHJLVWUDWLRQ E
WKH VXEJUDGLHQW PHWKRG ZDV HYHQ IRU WKH ELJJHVW LPDJH
H[DPSOH LQ WKLV ZRUN DERXW WHQ PLQXWHV 6LQFH WKH WLPH QHHGHG
IRU WKH SUHSDUDWLRQ RI PLFURVFRS VSHFLPHQV LV E RUGHUV RI
PDJQLWXGH JUHDWHU WKH XVH RI YHU DFFXUDWH UHJLVWUDWLRQ RI
SKVLFDO VOLFHV LQ PLFURVFRS E WKH PXOWLODEHO VXEJUDGLHQW
PHWKRG VHHPV HQWLUHO MXVWLILHG
:H LPSOHPHQWHG RXU DOJRULWKP DOVR RQ D 8'$ *38 7KH
VSHHG JDLQ ZDV LQ WKH EHVW FDVH VOLJKWO XQGHU WZR FRPSDUHG WR
D IRXUFRUH 38 ZKLFK LQ RXU RSLQLRQ LV WRR ORZ WR MXVWLI WKH
DGGLWLRQDO HIIRUW
)LJ ,I WKH QRQFRQYH[ IXQFWLRQDO 550. LV PLQLPL]HG GLUHFWO E LWHUDWLYH
JUDSKFXW PD[LPXP GHVFHQW UHJLVWUDWLRQ UHVXOWV PD JLYH ULVH WR DUWLIDFWV
QRW IRXQG LQ UHJLVWUDWLRQ E WKH VXEJUDGLHQW PLQLPL]DWLRQ RI WKH FRQYH[
GXDO IXQFWLRQ 552. +RQHFRPE LPDJH SDLU RI )LJ WKH JDS DUHD WKH *
IDLOV WR FORVH LQVLGH WKH RYDO LV ODUJHU WKDQ WKDW QRW FORVHG E 6* DQG WKH
ZKROH FHOO LQVLGH WKH UHFWDQJOH LV GLVWRUWHG E 553. WKH WXUWOH HPEUR SDLU RI
)LJ * GHVWURV WKH WLVVXH VHSDUDWLQJ WKH WZR ZKLWH DUHDV F 554. * IDLOV
WR FORVH WKH JDS LQ WKH RXWHU ODHU RI WKH $OOLJDWRU HPEUR LPDJH SDLU RI )LJ
555. 70,
$.12:/('*0(17
7KH DXWKRUV DUH JUDWHIXO WR 'U 59iJQHURYi ,QVWLWXWH RI
+LVWRORJ DQG (PEURORJ VW
)DFXOW RI 0HGLFLQH KDUOHV
8QLYHUVLW 3UDJXH ]HFK 5HSXEOLF 559. )LJ )LJ DQG )LJ DQG
IRU WKH LPDJHV RI WKH $PHULFDQ DOOLJDWRU $OOLJDWRU
PLVVLVVLSSLHQVLV 560. )LJ DQG )LJ 6SHFLDO WKDQNV EHORQJ WR
'U - -DQiþHN IRU IUXLWIXO GLVFXVVLRQ RQ PDWKHPDWLFDO DVSHFWV
RI 79 EDVHG LPDJH UHJLVWUDWLRQ DQG IRU KLV RQJRLQJ
HQFRXUDJHPHQW GXULQJ WKLV ZRUN
5()(5(1(6
@ 'URS ± GHIRUPDEOH LPDJH UHJLVWUDWLRQ VRIWZDUH 2QOLQH@ $YDLODEOH
KWWSZZZPUIUHJLVWUDWLRQQHWGHIRUPDEOHLQGH[KWPO
@ % *ORFNHU 1 .RPRGDNLV * 7]LULWDV 1 1DYDE DQG 1 3DUDJLRV
'HQVH ,PDJH 5HJLVWUDWLRQ WKURXJK 05)V DQG (IILFLHQW /LQHDU
3URJUDPPLQJ 0HGLFDO ,PDJH $QDOVLV YRO SS±
@ %VSOLQH *ULG ,PDJH DQG 3RLQW EDVHG 5HJLVWUDWLRQ 2QOLQH@ $YDLODEOH
KWWSZZZPDWKZRUNVFRPPDWODEFHQWUDOILOHH[FKDQJHEVSOLQH
JULGLPDJHDQGSRLQWEDVHGUHJLVWUDWLRQ
@ 0XOWLPRGDOLW QRQULJLG GHPRQ DOJRULWKP LPDJH UHJLVWUDWLRQ 2QOLQH@
$YDLODEOH
KWWSZZZPDWKZRUNVFRPPDWODEFHQWUDOILOHH[FKDQJH
PXOWLPRGDOLWQRQULJLGGHPRQDOJRULWKPLPDJHUHJLVWUDWLRQ
@ '±- .URRQ DQG + 6OXPS ³05, PRGDOLW WUDQVIRUPDWLRQ LQ GHPRQ
UHJLVWUDWLRQ´ GRZQORDGHG ZLWK WKH VRIWZDUH @
@ E8QZDUS- ,PDJH- SOXJLQ IRU ELGLUHFWLRQDO HODVWLF UHJLVWUDWLRQ RI WZR
LPDJHV 2QOLQH@ $YDLODEOH
KWWSELRFRPSFQEXDPHVaLDUJDQGDE8QZDUS-
@ )URKQ±6FKDXI 6 +HQQ / +|PNH DQG . :LWVFK ´7RWDO 9DULDWLRQ
%DVHG ,PDJH 5HJLVWUDWLRQ´ LQ ,PDJH 3URFHVVLQJ %DVHG RQ 3DUWLDO
'LIIHUHQWLDO (TXDWLRQV 3URF RI WKH ,QW RQI RQ 3'(%DVHG ,PDJH
3URFHVVLQJ DQG 5HODWHG ,QYHUVH 3UREOHPV 0$ 2VOR $XJXVW ±
;K 7DL .$ /LH 7 ) KDQ 6 2VKHU (GV 561. SS±
@ 7 3RFN 0 8UVFKOHU =DFK 5 %HLFKHO DQG + %LVFKRI ³$ GXDOLW
EDVHG DOJRULWKP IRU 79/RSWLFDOIORZ LPDJH UHJLVWUDWLRQ´ LQ WK
,QW RQI RQ 0HGLFDO ,PDJH RPSXWLQJ DQG RPSXWHU $VVLVWHG
,QWHUYHQWLRQ 0,$, 563. /HFWXUH 1RWHV LQ RPSXWHU 6FLHQFH 9RO SS ±
@ - -DQiþHN ³,PDJH 5HJLVWUDWLRQ E 'LVFRQWLQXRXV RUUHVSRQGHQFH
DOFXODWHG ,WHUDWLYHO 8VLQJ *UDSK XWV³ LQ 0LFURVFRS RQI LQ
*UD] 9RO/LIH 6FLHQFHV 0 $ 3DEVW * =HOOQLJ (GV 564. SS ±
@ 9 .ROPRJRURY DQG 5 =DELK ³:KDW HQHUJ IXQFWLRQV FDQ EH
PLQLPL]HG YLD JUDSK FXWV³ ,((( 7UDQV RQ 3$0, YRO QR
SS± 6HS
@ 0 , 6FKOHVLQJHU DQG 9 9 *LJLQDN ³6ROXWLRQ WR VWUXFWXUDO
UHFRJQLWLRQ 0$; 565. SUREOHPV E WKHLU HTXLYDOHQW WUDQVIRUPDWLRQV³
RQWURO 6VWHPV DQG RPSXWHUV 3DUW 1XPEHU ± DQG 3DUW
1XPEHU ± .LHY 8NUDLQH ,QVWLWXWH RI EHUQHWLFV RI
1DWLRQDO $FDGHP RI 6FLHQFHV RI 8NUDLQH
@ 6 %RG DQG $ 0XWDSFLF ³6XEJUDGLHQW 0HWKRGV³ /HFWXUH 1RWHV IRU
((E 6WDQIRUG 8QLYHUVLW $SULO 2QOLQH@ $YDLODEOH
KWWSZZZVWDQIRUGHGXFODVVHHEOHFWXUHVKWPO
@ 1HVWHURY ,QWURGXFWRU /HFWXUHV RQ RQYH[ 2SWLPL]DWLRQ .OXZHU
$FDGHPLF 3XEOLVKHUV SS ±
@ % 6DYFKQVN - .DSSHV 6 6FKPLGW DQG K 6FKQ|UU $ 6WXG RI
1HVWHURY
V 6FKHPH IRU /DJUDQJLDQ 'HFRPSRVLWLRQ DQG 0$3 /DEHOLQJ³
LQ ,((( ,QW RQI RQ RPSXWHU 9LVLRQ DQG 3DWWHUQ 5HFRJQLWLRQ ±
935 3UHSULQW ZLWK VXSSOHPHQWDU PDWHULDO 2QOLQH@ $YDLODEOH
KWWSKFLLZUXQLKHLGHOEHUJGH6WDIIEVDYFKQ
@ 7 5RKOILQJ 5 %UDQGW 5 5 0DXUHU DQG 5 0HQ]HO ³%HH EUDLQV %
VSOLQHV DQG FRPSXWDWLRQDO GHPRFUDF JHQHUDWLQJ DQ DYHUDJH VKDSH
DWODV LQ 3URF ,((( :RUNVKRS RQ 0DWKHPDWLFDO 0HWKRGV LQ
%LRPHGLFDO ,PDJH $QDOVLV±00%,$ /RV $ODPLWRV / 6WDLE
(G 566. SS ±
@ K 9 6WHZDUW K / 7VDL DQG $* $PLWKD 3HUHUD $ 9LHZ%DVHG
$SSURDFK WR 5HJLVWUDWLRQ 7KHRU DQG $SSOLFDWLRQ WR 9DVFXODU ,PDJH
5HJLVWUDWLRQ LQ 3URF WK ,QW RQI RQ ,QIRUPDWLRQ 3URFHVVLQJ LQ
0HGLFDO ,PDJLQJ ,30, SS ±
@ 6 DQJ ' .|KOHU . 7HOOHU 7 UHPHU 3 /H %DFFRQ ( +HDUG 5
(LOV . 5RKU 1RQULJLG 5HJLVWUDWLRQ RI ' 0XOWLFKDQQHO 0LFURVFRS
,PDJHV RI HOO 1XFOHL ,Q 0,$, /16 5 /DUVHQ 0
1LHOVHQ DQG - 6SRUULQJ (GV 567. SS ± 6SULQJHU9HUODJ %HUOLQ
+HLGHOEHUJ
@ - 3 7KLULRQ ,PDJH PDWFKLQJ DV D GLIIXVLRQ SURFHVV DQ DQDORJ ZLWK
0D[ZHOO¶V GHPRQV 0HGLFDO ,PDJH $QDOVLV YRO QR SS ±
@ 2 6FKPLWW - 0RGHUVLW]NL 6 +HOGPDQQ 6 :LUW] DQG % )LVFKHU
,PDJH UHJLVWUDWLRQ RI VHFWLRQHG EUDLQV ,QW -RXUQDO RI RPSXWHU
9LVLRQ YRO SS ±
@ 3ULPDOB'XDOB*8, ± $ 0DWODE WRROER[ WKDW VROYHV VHYHUDO LPDJH
SURFHVVLQJ WDVNV XVLQJ WKH SULPDOGXDO DOJRULWKP 2QOLQH@ $YDLODEOH
KWWSJSXYLVLRQLFJWXJUD]DWLQGH[SKSFRQWHQW GRZQORDGVSKS
@ % 9 KHUNDVVN DQG $ 9 *ROGEHUJ ³2Q ,PSOHPHQWLQJ WKH 3XVK
5HODEHO 0HWKRG IRU WKH 0D[LPXP )ORZ 3UREOHP³ $OJRULWKPLFD YRO
SS±
![70,
$EVWUDFW²,PDJH UHJLVWUDWLRQ WDVNV DUH RIWHQ IRUPXODWHG LQ
WHUPV RI PLQLPL]DWLRQ RI D IXQFWLRQDO FRQVLVWLQJ RI D GDWD ILGHOLW
WHUP SHQDOL]LQJ WKH PLVPDWFK EHWZHHQ WKH UHIHUHQFH DQG WKH
WDUJHW LPDJH DQG D WHUP HQIRUFLQJ VPRRWKQHVV RI VKLIW EHWZHHQ
QHLJKERULQJ SDLUV RI SL[HOV D PLQVXP SUREOHP](https://image.slidesharecdn.com/ed997dac-4c51-497d-b1ae-cd866481901b-160214130748/85/PMSpgray-1-320.jpg)
