$WKLUD69LMD\
Dept. of Electronics and Communication, SCT College Of Engineering, Pappanamcode,
Thiruvananthapuram-18
1HOZLQ5DM15 Assistant Professor,
Dept. of Electronics and Communication, SCT College of Engineering, Pappanamcode,
Thiruvananthapuram-18
$EVWUDFW²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
.H\ZRUGV²0RWLRQEOXU3LHFHZLVHOLQHDUFXUYH.HUQHOHVWLPDWLRQ'HEOXUULQJ6LPXODWHGDQQHDOLQJDOJRULWKP36)
,,1752'8&7,21
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
2QHRIWKHVROXWLRQVWRUHGXFHWKHGHJUHHRIEOXULVWRFDSWXUHLPDJHVZLWKVKRUWHUH[SRVXUHWLPH%XWUHGXFLQJWKH H[SRVXUHWLPHZLOOLQFUHDVHWKHDPRXQWRIQRLVHLQWKHLPDJHV$QDOWHUQDWLYHDSSURDFKLVWRWU\WRUHPRYHWKHEOXU RIIOLQH$PRWLRQEOXULVXVXDOO\GHVLJQHGDVWKHFRQYROXWLRQRIDODWHQWLPDJHZLWKDPRWLRQEOXUNHUQHO7KHQ GHFRQYROXWLRQRSHUDWLRQLVSHUIRUPHGWRUHFRYHUWKHODWHQWLPDJHIURPWKHEOXUU\YHUVLRQ
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
EX JXNXQX«««««
ZKHUHEXJXNXDQGQXUHSUHVHQWVWKHEOXUUHGLPDJHODWHQWLPDJHEOXUNHUQHODQGDGGLWLYHQRLVH UHVSHFWLYHO\
7KHDXWKRUVLQ>@KDYHGHPRQVWUDWHGDXQLILHGYDULDWLRQDODSSURDFKEDVHGRQLWHUDWLYHDOJRULWKPDQGGHEOXUULQJ DOJRULWKP LV LQWURGXFHG IRU LPDJH GHEOXUULQJ DQG LPSXOVH QRLVH UHPRYDO ,W LV KLJKO\ UREXVW EXW KDV OLPLWHG SHUIRUPDQFH0RWLRQEDVHGPRWLRQGHEOXUULQJ>@H[SORLWHGWKHWUDGHRIIEHWZHHQVSDWLDOUHVROXWLRQDQGWHPSRUDO UHVROXWLRQWRJHQHUDWHDK\EULGFDPHUDZKLFKPHDVXUHVLWVRZQPRWLRQ7KLVLQIRUPDWLRQDERXWWKHPRWLRQLVXVHG WRFRPSXWHDSRLQWVSUHDGIXQFWLRQ36)ZKLFKLVXVHGWRGHEOXUWKHLPDJH
0RWLRQEOXULGHQWLILFDWLRQIURPLPDJHJUDGLHQWV>@LQWURGXFHGWKHLGHDRIVSHFWUDODQDO\VLVRILPDJHJUDGLHQWV ZKLFKOHDGVWRHIILFLHQWLGHQWLILFDWLRQRIEOXUNHUQHO+HUHWKHEOXUSDUDPHWHUVDUHHVWLPDWHGXVLQJK\EULG)RXULHU UDGRQWUDQVIRUP,QWKHDSSURDFKHVEDVHGRQWKHSLHFHZLVHOLQHDUPRGHOVVXFKDV>@DQG>@PRWLRQFRPSRQHQWV DUHHVWLPDWHGLQLWLDOO\7KHQWKHFRPSRQHQWVDUHDVVHPEOHGWRIRUPDFRPSOHWHNHUQHO
A. Problem Formulation
7KHIRFDOSODQHWUDQVODWLRQGXULQJWKHSHULRGRIH[SRVXUHFDQEHH[SUHVVHGDVDUDQGRPSDUDPHWULFFXUYH4VN ZKHUHV¼>1F@DQGN >FL[FL\@7LVD1FYHFWRU7KXV4VLVHTXLYDOHQWWRWKHFRQFDWHQDWLRQRI1F±
OLQHVHJPHQWV/FRQQHFWHGXVLQJFRQWUROSRLQWVFL >FL[FL\@7>@
8VLQJWKHSURMHFWLRQRSHUDWRU3WKHUDQGRPSDUDPHWULFFXUYHLVPDSSHGLQWRDFRQWLQXRXVEOXUNHUQHOKȥN7KLV FRQWLQXRXVNHUQHOLVWKHQVDPSOHGXVLQJWKHGLVFUHWL]DWLRQRSHUDWRU'WRREWDLQDGLVFUHWHNHUQHOKXN)LQDOO\ GHEOXUULQJ FDQ EH DFKLHYHG E\ SHUIRUPLQJ RSWLPL]DWLRQ EHWZHHQ NHUQHO HVWLPDWLRQ DQG GHFRQYROXWLRQ DV
VXPPDUL]HGLQ$OJRULWKP7KHHQHUJ\WHUP-.KLQ$OJRULWKPLVJLYHQE\
-.K -'K-5K«««««
:KHUH-'K ^JXKXN±EX`UHSUHVHQWVWKHGDWDILWWLQJWHUPDQG-5KUHSUHVHQWVUHJXODUL]DWLRQWHUP
-5K Į-6UKȕ-&UK«««««
:KHUH-6UKDQG-&UKUHSUHVHQWVVSDFLQJDQGFXUYDWXUHUHJXODUL]DWLRQUHVSHFWLYHO\
6SDFLQJDQGFXUYDWXUHUHJXODUL]DWLRQLVWKHQDSSOLHGDIWHUIL[LQJDFRQVWDQWYDOXHIRUĮDQGȕLQRUGHUWRLPSURYHWKH OHYHORIPLQLPL]DWLRQ%XWHIILFLHQWPLQLPL]DWLRQFDQQRWEHDFKLHYHGDVH[SHFWHG7KHUHIRUHDSURSHURSWLPL]DWLRQ RIWKHUHJXODUL]DWLRQWHUPLVQHFHVVDU\6HFWLRQ,,,GHVFULEHVWKHRSWLPL]DWLRQLQGHWDLO
7KHUHVWRIWKHSDSHULVRUJDQL]HGDVIROORZV7KH3LHFHZLVHOLQHDUUHSUHVHQWDWLRQRIWKHQRQOLQHDUEOXUNHUQHOLV EULHIO\LQWURGXFHGLQ6HFWLRQ,,,Q6HFWLRQ,,,WKHSURSRVHGUHJXODUL]DWLRQXVLQJVLPXODWHGDQQHDOLQJDOJRULWKPDQG NHUQHOXSGDWLQJLVGHVFULEHGLQGHWDLO6HFWLRQ,9JLYHVWKHUHVXOWVDQGGLVFXVVLRQV)LQDOO\FRQFOXVLRQVDUHJLYHQLQ 6HFWLRQ9
$OJRULWKP'HEOXUULQJSURFHVV J[/DWHQW,PDJH
K[%OXU.HUQHO K¶ KLQLWJ¶ JLQLW
)RULWHU WR1LWHUGR
.HUQHO(VWLPDWLRQK¶[ DUJPLQ-.K
'HFRQYROXWLRQJ¶[ K¶[J[E[ J¶ SUHGLFWJ¶[
(QGIRU
5HWXUQJ¶DQGK¶
,,352326('6<67(0
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
)LJXUH2YHUYLHZRIWKHGHEOXUULQJSURFHVV
A. Piecewise Linear Representation Of Blur Kernel
)URPWKHJLYHQEOXUUHGLPDJHPRWLRQEOXUNHUQHOLVSUHGLFWHG7KHNHUQHOLVDVVXPHGWREHDQRQOLQHDUSDUDPHWULF
FXUYH4VNZKLFKLVJLYHQLQ)LJXUH7KLVDUELWUDU\FXUYHLVPDSSHGWRDFRQWLQXRXVNHUQHOKȥNFĺ5
XVLQJDSURMHFWLRQRSHUDWRU3DQGLVVDPSOHGE\WKHGLVFUHWL]DWLRQRSHUDWRU'WRREWDLQWKHGLVFUHWHNHUQHOKXN Gĺ5>@
KXN '>3>4VN@@«««««««
ZKHUH 3>4VN@4VNĺKȥN '>KȥN@KȥNĺKXN
ZKHUHȥ >ȥȗ@7DQGX >XY@DUHWKHFRQWLQXRXVDQGGLVFUHWHVSDWLDOGRPDLQFRRUGLQDWHV1
FOLQHVHJPHQWVDUH
SUHVHQWLQ4VNKȥNFDQEHVDPSOHGDV
KȥN >1F@KLȥN««««««
ZKHUH1FLVWKHQRUPDOL]LQJFRQVWDQWDQGL1FKLȥNLVWKHIUDFWLRQRIKȥNREWDLQHGE\WKH
FRQFDWHQDWLRQRISDUDPHWULFOLQHVHJPHQWV/FRQQHFWHGXVLQJFRQWUROSRLQWVFL
KࣜN /ȡFLFL«««««««
)LQDOO\
KXN '>KࣜN@««««««
,QPRVWRIWKHSUHH[LVWLQJWHFKQLTXHVWKHDUELWUDU\FXUYHVZHUHFRQVLGHUHGWREHOLQHDU%XWKHUHRQQRWLFLQJWKH )LJXUHLWVHOILWLVFOHDUWKDWWKHHVWLPDWLRQLVQRQOLQHDU
)LJXUH)RFDOSODQHWUDQVODWLRQGXHWRFDPHUDVKDNHVDQGEOXUVNHUQHOUHSUHVHQWDWLRQIRU1S >@
,, %/85.(51(/(67,0$7,21
A. Regularization Using Simulated Annealing Algorithm
7KHVSDFLQJDQGFXUYDWXUHUHJXODUL]DWLRQHQHUJLHVDUHDSSOLHGLQRUGHUWRDOLJQWKHFRQWUROSRLQWVKRUL]RQWDOO\DQG YHUWLFDOO\WREULQJRIIDEHVWHVWLPDWHRIWKHNHUQHO7KHUHJXODUL]DWLRQVFKHPHFDQEHUHSUHVHQWHGDV
-5K Į-6UKȕ-&UK««««««««
ZKHUH-6UDQG-&UUHSUHVHQWVKRUL]RQWDOVSDFLQJDQGYHUWLFDOFXUYDWXUHUHJXODUL]DWLRQHQHUJLHVUHVSHFWLYHO\DQGĮ
DQGȕDUHWKHSDUDPHWHUVWRFRQWUROWKHHQHUJ\IXQFWLRQ7KHHQHUJ\WHUPVDUHXVHGWRUHIOHFWWKHGLYHUJHQFHVRI NHUQHOIURPWKHGHVLUHGFRQILJXUDWLRQ>@
&RQVLGHUWZRDX[LOLDU\YHFWRUVșDQGȦLQRUGHUWRUHDGMXVWWKHFRQWUROSRLQWVRIWKHGLVFUHWHNHUQHOVXFKWKDW HDFKFRQWUROSRLQWVZLOOEHHTXLGLVWDQWIURPWKHLUQHLJKERULQJSRLQWVZKHQۅșۅ DQGDOOWKHFRQWUROSRLQWVVKRXOG OLHRQWKHVDPHOLQHVHJPHQWZKHQۅȦۅ
ș >«FL´[TL[FL´\TL\«@
Ȧ >«FL´[SL[FL´\SL\«@«««««««
ZKHUHSLTLDQGFL´DUHWKHXQLWQRUPDOYHFWRUXQLWWDQJHQWLDOYHFWRUDQGVHFRQGGHULYDWLYHRI4VN
)LJXUH5HJXODUL]DWLRQRISLHFHZLVHOLQHDUPRGHOE\UHDGMXVWLQJWKHFRQWUROSRLQWV>@
)URPWKH)LJXUH
FL´ FLFLFLSL ULFL
TL >SL\SL[@7«««««««««
ZKHUHTLLVREWDLQHGE\SHUSHQGLFXODUO\URWDWLQJSLۅșۅDQGۅȦۅDUHHTXLYDOHQWWRWKHQRUPVRILQQHUSURGXFWV
ۅșۅ >FL´TL@ۅȦۅ >FL´SL@«««««««««
:KHQۅșۅDQGۅȦۅEHFRPHVSDFLQJDQGFXUYDWXUHUHJXODUL]DWLRQFDQEHDFKLHYHGVLQFH-6KDQG-&KDUHWKH
VTXDUHGVXPRIۅșۅDQGۅȦۅ
-6K òۅșۅ-&K òۅȦۅ«««««««««
$ORQJZLWKVSDFLQJDQGFXUYDWXUHUHJXODUL]DWLRQWKHFRQWUROSDUDPHWHUVĮDQGȕXVHGWRUHIOHFWWKHGHIOHFWLRQRI NHUQHOIURPWKHDFWXDOFRQILJXUDWLRQLVRSWLPL]HGXVLQJVLPXODWHGDQQHDOLQJDOJRULWKP6$
7KH6$DOJRULWKPDOORZVWRHVFDSHIURPWKHWUDSRIORFDORSWLPDDQGWRUHDFKWKHJOREDORSWLPD2SWLPL]DWLRQXVLQJ VLPXODWHGDQQHDOLQJDOJRULWKPLVJLYHQLQ$OJRULWKP
$OJRULWKP>@2SWLPL]DWLRQXVLQJ6$DOJRULWKP $WDIL[HGWHPSHUDWXUH7
*HQHUDWHDUDQGRPVROXWLRQDQGLWVFRVWXVLQJVRPHFRVWIXQFWLRQDVGHILQHG *HQHUDWHDUDQGRPQHLJKERULQJVROXWLRQDQGFDOFXODWHWKHQHZVROXWLRQ¶VFRVW &RPSDUHWKHP
,IFQHZFROGPRYHWRWKHQHZVROXWLRQ
,IFQHZ!FROGDFFHSWHGQHZVROXWLRQZLWKSUREDELOLW\
H[SFROGFQHZ7
7KHDFFHSWDQFHSUREDELOLW\LVFRPSDUHGZLWKDUDQGRPQXPEHUEHWZHHQDQG ,IWKHDFFHSWDQFHSUREDELOLW\LVODUJHUWKDQWKHUDQGRPQXPEHUVZLWFK
'HFUHPHQWWHPSHUDWXUH7 7İZKHUHİ
5HSHDWVWHSVDERYHXQWLODQDFFHSWDEOHVROXWLRQLVUHDFKHG
2Q PLQLPL]LQJ UHJXODUL]DWLRQ HQHUJLHV DV ZHOO DV FRQWURO SDUDPHWHUV -5 FDQ EH PLQLPL]HG 7KXV LW SURYLGHV
HORQJDWHGDQGHTXDOO\VSDFHGFRQILJXUDWLRQRIFRQWUROSRLQWVWRIRUPFXUY\VKDSHIRUNHUQHOLQVWHDGRIVSUHDGRXW RQH >@ $IWHU WKLV RSWLPL]DWLRQ D ORFDO PLQLPXP RI WKH HQHUJ\ IXQFWLRQ ( LV UHDFKHG ZKRVH YDOXH ZLOO EH SURSRUWLRQDOWRWKHGLVWDQFH
B. Optimization of the Energy Function
7RRSWLPL]HWKHHQHUJ\IXQFWLRQ%UHJPDQLWHUDWLRQLVSHUIRUPHG,WLVDQLWHUDWLYHDOJRULWKPWRVROYHFHUWDLQFRQYH[ RSWLPL]DWLRQSUREOHPV>@7KHDOJRULWKPLVDURZDFWLRQPHWKRGDFFHVVLQJFRQVWUDLQWIXQFWLRQVRQHE\RQHDQGWKH PHWKRGLVSDUWLFXODUO\VXLWHGIRUODUJHRSWLPL]DWLRQSUREOHPVZKHUHFRQVWUDLQWVFDQEHHIILFLHQWO\HQXPHUDWHG>@ 7KHRULJLQDO%UHJPDQLWHUDWLRQ>@ZDVGHVLJQHGWRVROYHSUREOHPRIWKHIRUP
N DUJPLQ-N««««««««««««
VXEMHFWWR+N -DQG+DUHFRQYH[IXQFWLRQV%UHJPDQ,WHUDWLRQVDUHJLYHQLQ$OJRULWKP $OJRULWKP%UHJPDQ,WHUDWLRQ
N
:KLOH³1RWFRQYHUJHG´GR
NL DUJPLQ-NSLN!ȝ+N
ZKHUHSL¼-NL
SL SN±ȝǻ+NL
(QGZKLOH
B. Coarse to Fine Approach
2QFHWKHILQDOHVWLPDWHRIODWHQWLPDJHKDVEHHQREWDLQHGDWDFRDUVHOHYHOLWLVXSVDPSOHGE\ELOLQHDULQWHUSRODWLRQ DQGWKHQXVHGIRUWKHLQSXWIRUNHUQHOHVWLPDWLRQDWWKHQH[WILQHUOHYHO>@
,,, $'$37,9('(%/855,1*$/*25,7+0
:HVXPPDUL]HWKHPDLQVWHSVRIDGDSWLYHGHEOXUULQJE\SLHFHZLVHOLQHDUDSSUR[LPDWLRQRIPRWLRQEOXUNHUQHODORQJ ZLWKVLPXODWHGDQQHDOLQJDOJRULWKPDVIROORZV
,QLWLDOO\DEOXUUHGLPDJHLVJLYHQDVWKHLQSXW
,QWHQVLW\WUDQVIRUPDWLRQLQWKHEOXUUHGLPDJHLVUHSUHVHQWHGDVDQDUELWUDU\SDUDPHWULFFXUYHDQGZKLFKLVWKHQ DSSUR[LPDWHGE\XVLQJDSLHFHZLVHOLQHDUPRGHO
7KHVSDFLQJDQGFXUYDWXUHDVZHOODVFRQWUROSDUDPHWHUVĮDQGȕDUHWKHQUHJXODUL]HGWRPLQLPL]HWKHHQHUJ\ IXQFWLRQ
$FXUY\VKDSHGNHUQHOREWDLQHGDIWHUUHJXODUL]DWLRQLVXSGDWHGXVLQJEUHJPDQLWHUDWLRQDOJRULWKPWRREWDLQD EHVWHVWLPDWH
7KLVHVWLPDWHGNHUQHOLVGHFRQYROYHGZLWKWKHJLYHQEOXUUHGLPDJHWRREWDLQDGHEOXUUHGLPDJH
,IWKHEHVWHVWLPDWHRIWKHGHEOXUUHGLPDJHLVQRWREWDLQHGWKHNHUQHOREWDLQHGGXULQJWKHSUHYLRXVLWHUDWLRQLV XVHGDVWKHSUHVHQWNHUQHODQGUHSHDWIURPVWHS
2QFHWKHEHVWHVWLPDWHLVREWDLQHGWKHDOJRULWKPFRQYHUJHV
,9(;3(5,0(17$/5(68/76
7RYDOLGDWHWKHSHUIRUPDQFHRIWKHSURSRVHGPHWKRGDQGLWVLPSDFWRQWKHTXDOLW\RIWKHGHEOXUUHGLPDJHVDVHWRI EOXUUHGLPDJHVZDVFUHDWHGPDQXDOO\6XSSRVHWKDWIRUDJLYHQLPDJHIWKHEOXUUHGQRLV\LPDJHLVJHQHUDWHGE\ FRQYROYLQJWKHEOXUNHUQHOVKZLWKWKHLGHDOLPDJHVIDQGVRPHQRLVHQZHUHDGGHGLHE IKQ7KHEOXU NHUQHOVZHUHWKHQHVWLPDWHGIURPWKHEOXUUHGLPDJHDQGWKLVHVWLPDWHGNHUQHOLVGHFRQYROYHGZLWKEOXUUHGLPDJHE LQRUGHUWRUHFRYHUWKHODWHQWLPDJHI
7KH H[SHULPHQW LV LPSOHPHQWHG LQ 0$7$% 7KH EOXU NHUQHO PRGHOV WR EH HYDOXDWHG DUH WKH IDVW PRWLRQ GHEOXUULQJ E\ &KR DQG /HH >@ WKH SLHFHZLVH OLQHDU PRGHO E\ 6XQJFKDQ DQG *\HRQJKZDQ DQG WKH SURSRVHG PRGHO )RU WKH IDVW PRWLRQ GHEOXUULQJ PRGHO >@ LPDJH JUDGLHQWV DUH FRPSXWHG IRU SUHGLFWLQJ WKH RULJLQDOLPDJH)RUWKHSLHFHZLVHOLQHDUPRGHOĮ DQGȕ ZHUHFKRVHQ,QWKHSURSRVHGPHWKRGĮDQGȕ ZHUHIRXQGRXWLWHUDWLYHO\XVLQJVLPXODWHGDQQHDOLQJDOJRULWKP
DE
FG
HI
)LJXUHD%OXUUHG,PDJHRIVL]H[E3DUDPHWULF&XUYHF3LHFHZLVHOLQHDUDSSUR[LPDWLRQRIWKHSDUDPHWULFFXUYHG5HJXODUL]DWLRQ RISDUDPHWULFFXUYHH(VWLPDWHG.HUQHOI'HEOXUUHG,PDJH
3615LVXVHGDVDVWDWLVWLFDOPHWKRGWRFRPSDUHWKHGHEOXUUHGRXWSXWRIWKHSLHFHZLVHOLQHDUPRGHOZLWKWKHRULJLQDO LPDJH
3615 ORJ0$;,06(««««««««««
ZKHUH0$;,LVWKHPD[SRVVLEOHSL[HOYDOXHRIWKHLPDJHDQG06(LVWKH0HDQ6TXDUH(UURU
3615 YDOXHV RI WKH &KR /HH 0RGHO 3LHFHZLVH OLQHDU PRGHO DQG 3LHFHZLVH OLQHDU PRGHO ZLWK VLPXODWHG DQQHDOLQJDOJRULWKPZHUHHYDOXDWHGRQGDWDVHWLPDJHVDQGYDOXHVZHUHJLYHQLQ7DEOH7KHGLIIHUHQWSDUDPHWHUV HYDOXDWHGXVLQJ3LHFHZLVHOLQHDUPRGHODQG3LHFHZLVHOLQHDUPRGHOZLWKVLPXODWHGDQQHDOLQJDOJRULWKPRQDGDWDVHW LPDJHRIVL]H;LVVXPPDUL]HGLQWKH7DEOH
7DEOH,3615YDOXHVRI&KR$QG/HH>@3LHFHZLVH/LQHDU0RGHO$QG3LHFHZLVH/LQHDU0RGHO6$$OJRULWKP
7DEOH,,3DUDPHWHUV(VWLPDWHG8VLQJ3LHFHZLVH/LQHDU0RGHO$QG3LHFHZLVH/LQHDU0RGHO6$$OJRULWKP
0HWKRGV &KR /HH 3LHFHZLVH/LQHDU 3LHFHZLVH/LQHDU6$
,PDJH
,PDJH
,PDJH
,PDJH
9&21&/86,216
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
5()(5(1&(6
>@/%DU1.LU\DWLDQG16RFKHQ³,PDJHGHEOXUULQJLQWKHSUHVHQFHRILPSXOVLYHQRLVH´Int. J. Comput. VisYROQR'HFSS
>@0%HQ(]UDDQG6.1D\DU³0RWLRQEDVHGPRWLRQGHEOXUULQJ´IEEE Trans. Pattern Anal. Mach. Intell.,YROQR-XQSS
>@-+XLDQG/&KDRTLDQJ³0RWLRQEOXULGHQWLILFDWLRQIURPLPDJHJUDGLHQWV´in Proc. IEEE Conf. Comput. Vis. Pattern Recognit.-XQ
SS
>@%.DQJ-:6KLQDQG33DUN³3LHFHZLVHOLQHDUPRWLRQEOXULGHQWLILFDWLRQXVLQJPRUSKRORJLFDOILOWHULQJLQIUHTXHQF\GRPDLQ´in Proc.
ICCAS-SICESS
>@.3DWDQXNKRPDQG$1LVKLKDUD³,GHQWLILFDWLRQRISLHFHZLVHOLQHDUXQLIRUPPRWLRQEOXU´in Proc. IEEE Region 10 Conf1RYSS
>@6XQJFKDQ2KDQG*\HRQJKZDQ.LP³5REXVW(VWLPDWLRQRI0RWLRQ%OXU.HUQHO8VLQJ$3LHFHZLVH/LQHDU0RGHO´IEEE Transactions on
Image Processing9ROQR0DUFK
>@.DWULQD(OOLVRQ Simulated Annealing Algorithm[Online}.$YDLODEOHKWWSNDWULQDHJFRPVLPXODWHGDQQHDOLQJKWPO
>@DS Gleich (2012) Bregman Iteration Algorithm [online]. Available: https://en.wikipedia.org/wiki/bregman iteration
>@-LDQ)HQJ &DL 6WDQOH\ 2VKHU DQG =XRZHL 6KHQ ³6SOLW EUHJPDQ PHWKRGV DQG IUDPH EDVHG LPDJHUHVWRUDWLRQ´Multiscale Modeling and
SimulationYROQR
>@6&KRDQG6/HH³)DVWPRWLRQGHEOXUULQJ´ACM Trans. GraphYROQRSS
3DUDPHWHUV 3LHFHZLVH/LQHDU 3LHFHZLVH/LQHDU6$
3615 G% G%
06(
506(
8QLYHUVDO,PDJH4XDOLW\,QGH[
(0(RULJLQDOLPDJH
(0(ZDWHUPDUNLPDJH
615 G% G%
0$(