Affine Invariant Curve Normalization for Shape Based Retrieval

0 downloads 0 Views 323KB Size Report
normalized to the same position; apart from the affine ... of an object is first modeled by a cubic B spline so that the shape is simplified ... translation, scaling, skew, starting point, rotation and reflection ... the curve is normalized so as to coincide with the origin: y x m m. -=. -= ... clockwise rotation by 0 ..... 165 180, 1998.
$IILQH,QYDULDQW&XUYH1RUPDOL]DWLRQIRU6KDSH%DVHG5HWULHYDO @,QWKLVFRQWH[WFRQWHQWLQIRUPDWLRQLQ LVXVXDOO\PRGHOHGLQWHUPVRIORZOHYHOIHDWXUHVVXFKDVFRORU WH[WXUH PRWLRQ DQG VKDSH $V REVHUYHG LQ >@ LW LV QDWXUDO WR UHWDLQ RQO\ WKH REMHFW ERXQGDU\ LI LW FRQWDLQV WKH PDLQ LQIRUPDWLRQ IRU GHVFULSWLRQ ± IRU H[DPSOH LQ FODVVLILFDWLRQ RI VLOKRXHWWHVRIDLUSODQHVRULQFKDUDFWHUUHFRJQLWLRQ7KHVWXG\RI VKDSHIRUJHQHUDOREMHFWGHVFULSWLRQLVFXUUHQWO\DQDFWLYHILHOGRI UHVHDUFK PDLQO\ EHFDXVH L  VKDSH FDQ SURYLGH D SRZHUIXO WRRO IRU YLVXDO LPDJH UHWULHYDO E\ PHDQV RI D TXHU\E\VNHWFK PHFKDQLVP >@ DQG LL  FRQWHQWEDVHG IXQFWLRQDOLWLHV ZLOO EH HPEHGGHG LQ QHZ PXOWLPHGLD FRGLQJ VWDQGDUGV >@ HPSOR\LQJ VHFRQGJHQHUDWLRQVKDSHEDVHGFRGLQJWHFKQLTXHV>@ 6HYHUDO PHWKRGV KDYH EHHQ SURSRVHG LQ WKH OLWHUDWXUH IRU VKDSHDQDO\VLVPRGHOLQJDQGUHSUHVHQWDWLRQUDQJLQJIURPFKDLQ FRGLQJDQGSRO\JRQDODSSUR[LPDWLRQWR%VSOLQHV>@DQG)RXULHU GHVFULSWRUV >@ 0RVW DSSURDFKHV IDFH WKH SUREOHP RI GUDVWLF VKDSH FKDQJHV GXH WR YLHZSRLQW SHUVSHFWLYH  WUDQVIRUPDWLRQV ZKLFKFDQEHZHOODSSUR[LPDWHGE\DIILQHWUDQVIRUPDWLRQVZKHQ REMHFWV DUH IDU IURP WKH FDPHUD 6HYHUDO DIILQH LQYDULDQW WHFKQLTXHVKDYHWKXVEHHQSURSRVHGLQPRVWRIWKHPKRZHYHU LQYDULDQFH LV µHPEHGGHG¶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

VKDSHVDUHQRUPDOL]HGWRDµVWDQGDUG¶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

WKHDUFOHQJWKNQRWSRLQWVDUHUHDOORFDWHGZLWKHTXDOVSDFLQJLQ WHUPVRIWKHHVWLPDWHGSDUDPHWULFYDOXH

&XUYH2UWKRJRQDOL]DWLRQ $FXUYHRUWKRJRQDOL]DWLRQSURFHGXUHLVHPSOR\HGDVWKHILUVW VWDJH RI QRUPDOL]DWLRQ HIIHFWLYHO\ QRUPDOL]LQJ D FXUYH ZLWK UHVSHFW WR SRVVLEOH WUDQVODWLRQ VNHZ DQG VFDOLQJ DQG UHGXFLQJ DIILQHWUDQVIRUPDWLRQVWRRUWKRJRQDORQHV/HWVL >[L\L@7L  « 1 EH 1 FXUYH SRLQWV REWDLQHG WKURXJK %VSOLQH PRGHOLQJ $ ¤1 PDWUL[ QRWDWLRQ V  >V V « V1@ LV XVHG WR UHSUHVHQW WKH SRLQWV ZKLOH WKHLU KRUL]RQWDO DQG YHUWLFDO FRRUGLQDWHVDUHUHSUHVHQWHGE\[ >[[«[1@DQG\ >\\ «\1@7KH ST RUGHUPRPHQWV

P ST V =

 1

1 -

Ñ[

S T L \L



 

L =

RIRUGHUXSWRDUHXVHGIRUWKHFRQVWUXFWLRQRIWKHQRUPDOL]HG FXUYHQD V 7KHSURFHGXUHFRPSULVHVDVHWRIOLQHDURSHUDWLRQV± WUDQVODWLRQ VFDOLQJ DQG URWDWLRQ )LUVW WKH FHQWHURIJUDYLW\ RI WKHFXUYHLVQRUPDOL]HGVRDVWRFRLQFLGHZLWKWKHRULJLQ   [ = [ - m [  \  = \ - m \  ZKHUH  P V  \ P V 7KHFXUYHLVWKHQVFDOHGVRWKDWLWV QGRUGHUPRPHQWVEHFRPHHTXDOWR   [  = s [ [  \  = s \ \   ZKHUH s [ = 

P V  s \ = 

P V  $ FRXQWHU

FORFNZLVHURWDWLRQE\   IROORZV

 Õ[  - \  å V = 5p  V  = Ö æ  ×[  + \  ç

ZKHUH t [ = 

P V   t \ = 

 

P V  7KHQRUPDOL]HG

FXUYHQD V ©VFDQDOVREHZULWWHQDV Q D V = 1 V V - m V 

 

7

ZKHUH V   >P V  P V @  DQG 1 V  GHQRWHV WKH ¤ QRUPDOL]DWLRQPDWUL[RIV,WFDQSURYHG>@WKDWWKHQRUPDOL]HG FXUYHQD V DOZD\VKDVWKHIROORZLQJSURSHUWLHV P Q D V = P Q D V = P Q D V =   D 

P  Q D V = P Q D V =   E  0RUHRYHU WKH DERYH FRQGLWLRQV FDQ RQO\ EH DFKLHYHG LI WKH URWDWLRQDQJOHXVHGLQ  LVHTXDOWRN  N»=7KHWHUP RUWKRJRQDOL]DWLRQ LV MXVWLILHG VLQFH WKHVH FRQGLWLRQV DUH HTXLYDOHQWWRQD V QD V 7 ,/HWXVQRZFRQVLGHUWZRFXUYHVV V¦ UHODWHGWKURXJKDQDIILQHWUDQVIRUPDWLRQ

Õ [ ¦å Õ D E å Õ [ å ÕW [ å V ¦ = $V + W = Ö æ = Ö æ Ö æ+Ö æ × \ ¦ç × F G ç ×\ ç ×W \ ç

  $IILQHWUDQVIRUPDWLRQVDUHUHGXFHGWRRUWKRJRQDORQHVWKDWPD\ FRQWDLQRQO\URWDWLRQDQGRUUHIOHFWLRQKHQFHQRUPDOL]HGFXUYHV DUH LQYDULDQW WR WUDQVODWLRQ VFDOLQJ DQG VNHZ WUDQVIRUPDWLRQV 1RWH WKDW QRUPDOL]DWLRQ LV SHUIRUPHG ZLWKRXW NQRZOHGJH RI WKH DIILQHSDUDPHWHUV$WDQGZLWKRXWRQHWRRQHPDWFKLQJEHWZHHQ FXUYHV V DQG V¦  )XUWKHUPRUH LW FDQ EH VHHQ WKDW WKH VHW RI WUDQVIRUPDWLRQSDUDPHWHUV^  \  \  \`DORQJZLWKQD V  FRQWDLQDOOLQIRUPDWLRQDERXWWKHRULJLQDOFXUYHV

6WDUWLQJ3RLQW1RUPDOL]DWLRQ 6WDUWLQJ SRLQW QRUPDOL]DWLRQ IRU FORVHG FXUYHV LV DSSOLHG DW WKLVSRLQWURWDWLRQDQGUHIOHFWLRQQRUPDOL]DWLRQIROORZVVLQFHLW GHSHQGVRQWKHVWDUWLQJSRLQW%RWKQRUPDOL]DWLRQVDUHEDVHGRQ WKH GLVFUHWH )RXULHU WUDQVIRUP LQVWHDG RI FXUYH PRPHQWV 7KH FRPSOH[YHFWRUQRWDWLRQ] [M\ >]]«]1@7LVWKXVXVHG IRU FXUYH UHSUHVHQWDWLRQ ZKHUH ]L  [L M\L  L  «1 GHQRWHVDVLQJOHFXUYHSRLQW7KH')7 X = ® ] RIFXUYH]LV JLYHQE\

XN =

1 -

Ñ] Z L

- NL

 N =  K  1 -  

 

L =

ZKHUH Z  H M 1 VR WKDW Z l1 =   l » =  (PSOR\LQJ WKH SULPDU\ DUJXPHQW RU SKDVH D N = $UJ X N  ZH FRQVWUXFW WKH SKDVH YHFWRU D = $UJ X = > D  D L D 1 - @  &RQVLGHU QRZ D

VHFRQGFXUYH ] ¦ = > ] ¦ ]¦ L ] ¦1 - @ WKDWLVFLUFXODUO\VKLIWHGZLWK  

)LQDOO\WKHFXUYHLVVFDOHGDJDLQH[DFWO\DVLQ   [  = t [ [  \  = t \ \  

QD V ¦ = 4 QD V 

 

ZKHUH PDWUL[ $ LV DVVXPHG WR EH RI IXOO UDQN 7KHQ V¦ = V ¦ - m V ¦ = $ V - m V = $V  DQG WUDQVODWLRQ LV UHPRYHG 0RUHRYHU ZKHQ D QRUPDOL]HG FXUYH LV URWDWHG RU UHIOHFWHGLQZKLFKFDVH$LVRUWKRJRQDOLWUHPDLQVQRUPDOL]HG ,QYHUVHO\ LI ERWK FXUYHV DUH QRUPDOL]HG WKHQ $ VKRXOG EH RUWKRJRQDO,WLVWKXVVKRZQLQ>@WKDWWKHUHH[LVWVDQRUWKRJRQDO ¤PDWUL[4VXFKWKDW

UHVSHFWWR]E\PVDPSOHVZKHUHP»^«1`

] ¦ = 6 P ]  ] L¦ = ] L + P PRG 1  L =  K  1 -  

 

7KHQLWFDQEHVKRZQWKDW X ¦N = Z NP X N N «1RU

D ¦N = D N + pNP  1 PRG p  N = K  1 -     %DVHGRQWKLVSURSHUW\ZHGHILQHDVWDQGDUGFLUFXODUVKLIWXVLQJ WKHILUVWDQGODVW)RXULHUSKDVHV

Ö1 æ S ] = Ö D - D 1 - æ PRG 1    p  × ç

DQGDSSO\WKHRSSRVLWHVKLIWWRQRUPDOL]HWKHFXUYH Q S ] = 6 - S ] ] 

   

,W LV VKRZQ LQ >@ WKDW WKH DERYH QRUPDOL]DWLRQ LV LQYDULDQW WR VWDUWLQJ SRLQW H[FHSW IRU DQ DPELJXLW\ LQ WKH VWDQGDUG FLUFXODU VKLIWZKLFKPD\FDXVHDQH[WUDVKLIWRI1 S ] ¦ = S ] + P PRG 1    D 

S Q S ] ¦ = S Q S ] =  

E 

  S ] + P < 1   ØQ S ]   Q S ] ¦ = Ù Ú6 1   Q S ]  1    S ] + P < 1

F 

7KH SURSRVHG VHOHFWLRQ RI )RXULHU FRHIILFLHQWV X DQG X1 FDQ GHWHFWUHIOHFWLRQDOFXUYHV\PPHWULHVDQGKDVDOVREHHQHPSOR\HG LQ >@ IRU OLQH SDWWHUQ FXUYHV HJ FKDUDFWHU ERXQGDULHV  ZKLOH WKHXVHRIRWKHUFRHIILFLHQWVLVDOVRSRVVLEOH>@>@

5RWDWLRQ5HIOHFWLRQ1RUPDOL]DWLRQ 5RWDWLRQ QRUPDOL]DWLRQ LV DFKLHYHG E\ VHWWLQJ WKH SKDVHV RI X DQG X1 WR ]HUR VR WKDW WKH\ EHFRPH UHDO DQG SRVLWLYH ,Q SDUWLFXODU DVVXPH WKDW WZR FXUYHV V V¦  KDYH EHHQ

RUWKRJRQDOL]HG DQG QRUPDOL]HG ZUW VWDUWLQJ SRLQW WKXV VDWLVI\LQJ  :HWKHQXQLTXHO\GHFRPSRVHPDWUL[4DV

T å ÕFRV q - VLQ q å Õ V [  å ÕT   4 = Ö  æ æ=Ö æÖ × T  T  ç × VLQ q FRVq ç ×  V \ ç ZKHUH q » > p  V[  › V\  › VR WKDW WKHUH LV RQHWRRQH

QRUPDOL]DWLRQ UHVXOWV DUH GHSLFWHG LQ )LJXUHV  EFG  ,W FDQ EH VHHQ WKDW WKH ILQDO FXUYHV PDWFK YHU\ ZHOO DOWKRXJK QRUPDOL]DWLRQRIHDFKFXUYHLVSHUIRUPHGZLWKRXWNQRZOHGJHRI WKH RWKHUV 7KH VOLJKW GLVFUHSDQFLHV DUH GXH WR GLIIHUHQW VDPSOLQJWKHPDWFKLVSHUIHFWZKHQWKHLQLWLDOFXUYHVDUHDIILQH WUDQVIRUPDWLRQVRIWKHVDPHVDPSOHFXUYH

UHODWLRQ EHWZHHQ URWDWLRQUHIOHFWLRQ SDUDPHWHUV DQG HOHPHQWV RI 4$GRSWLQJWKHFRPSOH[YHFWRUQRWDWLRQ] ] ¦ 

] ¦ = V [ [ + MV \ \ H Mq 

 

7KH URWDWLRQ RI FXUYH ] LV QRUPDOL]HG DFFRUGLQJ WR WKH DYHUDJH YDOXHRI)RXULHUSKDVHVDDQGD1

â Ò U ] = Ó D + D 1 - ã PRG p   ä Ô ]  = ] H - MU ] 

Y ]  = Y [ ]  + MY \ ]  = VJQ P ]  + M VJQ P ]  QU ] = ]  = Y [ ]  [ + MY \ ]  \  

D  E 

ZKHUHVJQGHQRWHVWKHVLJQXPIXQFWLRQ,WLVWKHQSURYHGLQ>@ WKDWQU ] LVLQYDULDQWWRURWDWLRQDQGUHIOHFWLRQWUDQVIRUPDWLRQV

U ] ¦ = lU ] + q PRG p  QU ] ¦ = QU ] 



E 



D 

E  7KHQKRUL]RQWDODQGYHUWLFDOUHIOHFWLRQLVQRUPDOL]HGDFFRUGLQJ WRWKHUGRUGHUPRPHQWVRI] 

D 

  G  F  )LJXUH  D  2ULJLQDO ILVK FRQWRXU DQG D SDLU RI DUELWUDU\ DIILQH WUDQVIRUPDWLRQV XQGHU GLIIHUHQW VDPSOLQJ EFG  FXUYHV DIWHU WUDQVODWLRQ VNHZVFDOLQJ DQG URWDWLRQ QRUPDOL]DWLRQUHVSHFWLYHO\

D  E 

U Q U ] ¦ = U Q U ] =   F  Y [ Q U ] ¦ = Y \ Q U ] ¦ = Y [ Q U ] = Y \ Q U ] =   G  ZKHUH  V[V\ ›1RWHWKDWDVLQFXUYHRUWKRJRQDOL]DWLRQWKH VHW RI SDUDPHWHUV ^U ]  Y ]  Y\ ] `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

D 

F 





E 

G 





)LJXUH  1RUPDOL]DWLRQ UHVXOWV IRU VSDWLDOO\ VLPLODU REMHFW FRQWRXUV D  RULJLQDO FRQWRXUV IRU  GLVWLQFW SODQHV EFG  FXUYHV DIWHU WUDQVODWLRQ VFDOLQJ DQG URWDWLRQ QRUPDOL]DWLRQ UHVSHFWLYHO\

([SHULPHQWDO5HVXOWV 7KH SHUIRUPDQFH RI WKH SURSRVHG DOJRULWKP LV HYDOXDWHG XVLQJ D VKDSH GDWDEDVH FUHDWHG IURP LPDJHV DQG YLGHR VHTXHQFHV 2EMHFW FRQWRXUV KDYH EHHQ REWDLQHG XVLQJ WKH 0 5667 FRORU VHJPHQWDWLRQ DOJRULWKP ZLWK WKH DVVLVWDQFH RI PRWLRQVHJPHQWDWLRQ LQWKHFDVHRIYLGHRVHTXHQFHV SHUIRUPHG RQ WKH EDVLV RI ' SDUDPHWULF PRWLRQ PRGHOV ,Q WKH VHTXHO QRUPDOL]DWLRQ UHVXOWV DUH JLYHQ IRU DOO SURSRVHG QRUPDOL]DWLRQ VWHSV DQG WKH DOJRULWKP¶V HIILFLHQF\ LV GLVFXVVHG IRU DIILQH WUDQVIRUPDWLRQV RI L  WKH VDPH REMHFW XQGHU GLIIHUHQW QRQ XQLIRUP VDPSOLQJ LL  VLPLODU REMHFWV DQG LLL  VXEVWDQWLDOO\ GLIIHUHQWREMHFWV 7KH ILUVW FDVH LV LOOXVWUDWHG LQ )LJXUH  $ FRQWRXU RI D ILVK FRQVLVWLQJRIVDPSOHSRLQWVLVGHSLFWHGLQ)LJXUH D DORQJ ZLWK WZR RWKHU FXUYHV REWDLQHG WKURXJK DUELWUDU\ DIILQH WUDQVIRUPDWLRQV XQGHU GLIIHUHQW QRQXQLIRUP VDPSOLQJ 7KH

D 

F 





E 

G 





)LJXUH  &RQWRXU DOLJQPHQW IRU VXEVWDQWLDOO\ GLIIHUHQW REMHFWV D  RULJLQDO FRQWRXUV RI D KDPPHU D FDU DQG D SODQH EFG  FXUYHV DIWHU WUDQVODWLRQ VFDOLQJ DQG URWDWLRQ QRUPDOL]DWLRQUHVSHFWLYHO\

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

3RLQWV

)'

0)'







5HIHUHQFHV



















>@ @ )6 &RKHQ = +XDQJ DQG = @ ,62,(& -7&6&:* ³03(* &RQWH[W DQG 2EMHFWLYHV Y ´'RF1 >@ ) 0DUTXHV % /ORUHQV DQG $ *DVXOO ³3UHGLFWLRQ RI ,PDJH3DUWLWLRQV8VLQJ)RXULHU'HVFULSWRUV$SSOLFDWLRQWR 6HJPHQWDWLRQ%DVHG &RGLQJ 6FKHPHV´ ,((( 7UDQV 3$0,  SS >@ ( 3HUVRRQ DQG .6 )X ³6KDSH 'LVFULPLQDWLRQ 8VLQJ )RXULHU 'HVFULSWRUV´ ,((( 7UDQV 3$0,    SS   >@ @ ' 6KHQ DQG + ,S ³*HQHUDOL]HG $IILQH ,QYDULDQW ,PDJH 1RUPDOL]DWLRQ´ ,((( 7UDQV 3$0,    SS  



E 

)LJXUH1RUPDOL]DWLRQUHVXOWVLQWKHSUHVHQFHRIQRLVH D  LQLWLDODQG E ILQDOFXUYHVIRUVSDWLDOO\UHODWLYHREMHFWV &RQWRXU

&RQWRXU

















     7DEOH,QGLFDWLYHFRQWRXUFODVVLILFDWLRQGLVWDQFHV



D 

E 





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



D 

RI ILYH YLVXDOO\ GLVWLQFW REMHFW FODVVHV QDPHO\ DLUSODQHV FDUV ILVK KDPPHUV JODVVHV ,Q )LJXUH  UHWULHYDO UHVXOWV DUH LOOXVWUDWHGIRUDQLQSXWLPDJHFRQWDLQLQJDQDLUSODQH,WPXVWEH SRLQWHGRXWWKDWE\XWLOL]LQJRQO\WKHREMHFWFRQWRXUDWWULEXWHD ILVK FRXOG \LHOG KLJKHU UHVHPEODQFH WR DQ ) DLUFUDIW WKDQ D 6WHDOWKDLUFUDIWZRXOG2WKHULPDJHDWWULEXWHVVXFKDVFRORUDQG WH[WXUH VKRXOG WKXV EH LQFOXGHG LQ DQ LQWHJUDWHG FRQWHQWEDVHG UHWULHYDOV\VWHP



F 





 

)LJXUH  ,PDJH UHWULHYDO UHVXOWV TXHU\E\H[DPSOH  EDVHG RQFRQWRXUVLPLODULW\ D LQSXWLPDJH E H[WUDFWHGFRQWRXU F UHWULHYHGLPDJHVLQGHVFHQGLQJFRQWRXUVLPLODULW\ 6RPH LQGLFDWLYH VKDSH FODVVLILFDWLRQ UHVXOWV DUH LQFOXGHG LQ 7DEOH  7KH QRUPDOL]HG FRXQWHUSDUWV RI FRQWRXUV µ¶ DQG µ¶ ZHUH FRPSDUHG RQ WKH EDVLV RI WKUHH VLPSOH PHWULFV QDPHO\ (XFOLGHDQ GLVWDQFH RI L  WKH UHVSHFWLYH SRLQW VHWV LL  WKH HVWLPDWHG )RXULHU GHVFULSWRUV DQG LLL  WKH PRGLILHG )RXULHU GHVFULSWRUV SURSRVHG LQ >@ $V LW ZDV LQWXLWLYHO\ H[SHFWHG DOO WKUHH PHWULFV SURYH WR EH LQGLFDWLYH RI WKH QRUPDOL]HG FXUYH UHVHPEODQFH)LQDOO\WKHSURSRVHGDOJRULWKP¶VSHUIRUPDQFHZDV VXFFHVVIXOO\WHVWHGIRUFRQWHQWEDVHGUHWULHYDOSXUSRVHVEDVHGRQ FRQWRXUVLPLODULW\RQDVPDOOGDWDEDVHFRQWDLQLQJVWLOOLPDJHV

Suggest Documents