Using Wavelets for Texture Classification - wseas

4 downloads 0 Views 439KB Size Report
together the standard, median absolute and mean absolute deviations of horizontal, vertical and diagonal wavelet detail coefficients were appropriate wavelet ...
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

SDSHU WKH ZDYHOHWV DUH XVHG WR DQDO\]H WKH WH[WXUHGLPDJHV6HYHUDOWH[WXUHVDPSOHVZHUH DQDO\]HG DQG REWDLQHG VWDWLVWLFDO SURSHUWLHV RI ZDYHOHW GHWDLO FRHIILFLHQWV 7KHQ ZH FODVVLILHG WKHWH[WXUHFODVVHV XVLQJWKHVHVWDWLVWLFDOYDOXHV VXFK DV VWDQGDUG PHGLDQ DEVROXWH DQG PHDQ DEVROXWH GHYLDWLRQV RI KRUL]RQWDO YHUWLFDO DQG GLDJRQDOZDYHOHWGHWDLOFRHIILFLHQWV

7H[WXUH$QDO\VLV

7H[WXUH FDQ EH GHILQHG DV WKH VHW RI ORFDO VWDWLVWLFDO SURSHUWLHV RI WKH FRHIILFLHQWV SL[HO JUD\ OHYHOV  ZKLFK FRQVWLWXWH WKH LPDJH¶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

WH[WXUHVHJPHQWDWLRQ RUDFROOHFWLRQRISL[HOV LPDJHFODVVLILFDWLRQ >@

:DYHOHW7UDQVIRUP

7KH FRQWLQXRXV  ZDYHOHW WUDQVIRUP RI D ' VLJQDOI [ LVGHILQHGDV :I D E

³ I W \ D E W GW

¢I  \ D E ² D z 



\

ZKHUHWKHZDYHOHW D E LVFRPSXWHGIURPWKH PRWKHUZDYHOHW \ E\WUDQVODWLRQDQGGLODWLRQ \ D E W

§WE· \¨ ¸ D © D ¹





7KH PRWKHU ZDYHOHW \ KDV WR VDWLVI\ WKH DGPLVVLELOLW\ FULWHULRQ WR HQVXUH WKDW LW LV D ORFDOL]HG]HURPHDQIXQFWLRQ>@  &DQEHGLVFUHWL]HGE\UHVWUDLQLQJD Q

DQG E WR D GLVFUHWH ODWWLFH D  *E  =  7\SLFDOO\ VRPH PRUH FRQVWUDLQWV DUH LPSRVHG RQ \ WRHQVXUHWKDWWKHWUDQVIRUPLVFRPSOHWH QRQUHGXQGDQW  DQG FRQVWLWXWHV D PXOWLUHVROXWLRQ UHSUHVHQWDWLRQ RI WKH RULJLQDO VLJQDO 7KLV KDV OHG WR DQ HIILFLHQW UHDOVSDFH LPSOHPHQWDWLRQ RI WKH WUDQVIRUP XVLQJ TXDGUDWXUHPLUURUILOWHUV 7KH H[WHQVLRQ WR WKH ' FDVH LV XVXDOO\ SHUIRUPHG E\ XVLQJ D SURGXFW RI ' ILOWHUV ,Q SUDFWLFH WKH WUDQVIRUP LV FRPSXWHG E\ DSSO\LQJ D VHSDUDEOH ILOWHU EDQN WR WKH LPDJH / Q E L  E M >+ [ >+ \ / Q  @ p @ p E L  E M



' Q E L  E M >+ [ >* \ / Q  @p  @ p E L  E M



' Q  E L  E M >* [ >+ \ / Q  @p  @p E L  E M



' Q  E L  E M >* [ >* \ / Q  @p @p E L  E M



*





GHQRWHVWKHFRQYROXWLRQRSHUDWRU p  p VXEVDPSOLQJ DORQJ WKH URZV FROXPQV  DQG /

, [

LV WKH RULJLQDO LPDJH + DQG * DUH D ORZ DQG EDQGSDVV ILOWHU UHVSHFWLYHO\ /Q LV

REWDLQHGE\ORZSDVVILOWHULQJDQGLVWKHUHIRUH UHIHUUHGWRDVWKHORZUHVROXWLRQLPDJHDWVFDOH Q7KH'QL DUHREWDLQHGE\EDQGSDVVILOWHULQJLQ DVSHFLILFGLUHFWLRQDQGWKXVFRQWDLQGLUHFWLRQDO GHWDLO LQIRUPDWLRQ DW VFDOH Q WKH\ DUH UHIHUUHG WRDVWKHGHWDLOLPDJHV7KHRULJLQDOLPDJH,LV WKXV UHSUHVHQWHG E\ D VHW RI VXELPDJHV DW ^/  ' `

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

0' QL

¦ 'QL E M EN M N



ZKHUH 1 LV WKH WRWDO QXPEHU RI ZDYHOHW FRHIILFLHQWVLQ'QL ZKLFKLVDVXELPDJH $Q DOWHUQDWLYH PHDVXUH ZKLFK LV XVHG DVDWH[WXUHIHDWXUHLVWKHHQHUJ\RIDVXELPDJH 'QLDQGLVGHILQHGDV ( QL

 1

¦ 'QL E M EN  MN

&ODVVLILFDWLRQ([SHULPHQWV



:H PDGH VHYHUDO FODVVLILFDWLRQ H[SHULPHQWV ZLWKYDULRXVWH[WXUHV6SHFLILFDOO\ZHJRWHLJKW UHDO ZRUOG [ LPDJHV IURP GLIIHUHQW QDWXUDOVFHQHVIURPWKH9LV7H[GDWDEDVHZKLFK DUHSUHVHQWHGLQ)LJXUH>@

H[SHULPHQWV 7KHUH DUH VHYHUDO PHWKRGV IRU FODVVLILFDWLRQ SXUSRVHV 7KH PRVW NQRZQV DUH WKHED\HVFODVVLILHUSDUDPHWULFFODVVLILHU QRQ SDUDPHWULF FODVVLILHU QHXUDO QHWZRUNV DQG WKH .QQFODVVLILHU ,Q WKLV ZRUN ZH XVHG WKH .QQ FODVVLILHU ,Q WKH . QHDUHVW QHLJKERU FODVVLILHU .QQFODVVLILHU  RQH DVVXPHV WKDW WKH IHDWXUH VSDFH LV D PHWULF VSDFH LH WKHUH H[LVW VRPH IXQFWLRQ G [ \ ZKLFK H[SUHVVHV WKH GLVWDQFH EHWZHHQWZRSRLQWV[DQG\LQIHDWXUHVSDFH$ IUHTXHQWO\ XVHG RQH LV WKH (XFOLGLDQ GLVWDQFH >@ G [  \

)LJXUH   6HOHFWHG LPDJHV IURP OHIW WR ULJKW DQG WRS WR ERWWRP )ORZHUV %ULFN )DEULF 0HWDO )RRG*UDVV6DQG/HDYHV

:H VXEGLYLGH HDFK [ LPDJH LQWR  QRQRYHUODSSLQJ [ VXELPDJHV 7KDW¶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

¦ [ L  \ L  G

L 



7KLV OHDGV WR D YHU\ VLPSOH FODVVLILFDWLRQ SURFHGXUH WKH VDPSOH [ VKRXOG EHDVVLJQHGWRWKDWFODVVWRZKLFKPRVWRILWV. QHDUHVW QHLJKERUV EHORQJ 6LQFH WKLV UXOH LV GHULYHG IURP %D\HV UXOH LW LV RSWLPDO LQ WKH VHQVHWKDWLWPLQLPL]HVWKHFRQGLWLRQDOULVN (UURU HVWLPDWLRQ LV DOVR LPSRUWDQW LQ FODVVLILFDWLRQ SURFHGXUHV $ µJRRG¶ FODVVLILHU VKRXOGDFFXUDWHO\FODVVLI\DQ\SRVVLEOHSDWWHUQ IRU ZKLFK LW LV GHVLJQHG (UURU UDWH LV XVXDOO\ SHUIRUPHG E\ HUURU FRXQWLQJ 6XSSRVH WKDW WKHUHDUH1W WHVWVDPSOHVDQGOHWWLEHDYDULDEOH ZKLFKWDNHVWKHYDOXHLIWKHL WK WHVWVDPSOHLV FODVVLILHG FRUUHFWO\ DQG  RWKHUZLVH 7KH FODVVLILFDWLRQ SHUIRUPDQFH RI WKH FODVVLILHU LV WKHQHVWLPDWHGE\WKH REVHUYHG HUURUUDWH> @ HU

 1W

¦ WL 1W

L 



$QG ILQDOO\WKHUHVXOWLQJHUURUUDWHVRI  FODVVLILFDWLRQ H[SHULPHQWV DUH SUHVHQWHG LQ WDEOHV

7DEOH&(VWDQGDUGGHYLDWLRQ&(PHGLDQ DEVROXWH GHYLDWLRQ &( PHDQ DEVROXWH GHYLDWLRQ &( VWDQGDUG PHGLDQ DQG PHDQ DEVROXWHGHYLDWLRQVDUHXVHG (UURU5DWHVLQKRUL]RQWDO 7H[WXUH ZDYHOHWGHWDLOFRHIILFLHQWV &ODVVHV &( &( &( &(  )ORZHUV      %ULFN      )DEULF      0HWDO      )RRG      *UDVV      6DQG      /HDYHV     0HDQ    

7DEOH&( VWDQGDUG GHYLDWLRQ&( PHGLDQ DEVROXWH GHYLDWLRQ &( PHDQ DEVROXWH GHYLDWLRQ &( VWDQGDUG PHGLDQ DQG PHDQ DEVROXWHGHYLDWLRQVDUHXVHG (UURU5DWHVLQYHUWLFDO 7H[WXUH ZDYHOHWGHWDLOFRHIILFLHQWV &ODVVHV &( &( &( &(  )ORZHUV      %ULFN      )DEULF      0HWDO      )RRG      *UDVV      6DQG      /HDYHV     0HDQ     7DEOH  &( VWDQGDUG GHYLDWLRQ &( PHGLDQ DEVROXWH GHYLDWLRQ &( PHDQ DEVROXWH GHYLDWLRQ &( VWDQGDUG PHGLDQ DQGPHDQDEVROXWHGHYLDWLRQVDUHXVHG (UURU5DWHVLQGLDJRQDO 7H[WXUH ZDYHOHWGHWDLOFRHIILFLHQWV &ODVVHV &( &( &( &(  )ORZHUV      %ULFN      )DEULF      0HWDO      )RRG      *UDVV      6DQG      /HDYHV     0HDQ    

7DEOH  6WDQGDUG PHGLDQ DQG PHDQ GHYLDWLRQV RI &( KRUL]RQWDO DQG YHUWLFDO &( KRUL]RQWDODQGGLDJRQDO&( YHUWLFDO DQG GLDJRQDO &( KRUL]RQWDO YHUWLFDO DQG GLDJRQDOZDYHOHWGHWDLOFRHIILFLHQWVDUHXVHG 7H[WXUH (UURU5DWHV &ODVVHV &( &( &( &(  )ORZHUV      %ULFN      )DEULF      0HWDO      )RRG      *UDVV      6DQG      /HDYHV     0HDQ    

&RQFOXVLRQVDQG'LVFXVVLRQV

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

5HIHUHQFHV

 0 0LVLWL

Suggest Documents