{VERSION 4 0 "IBM INTEL LINUX" "4.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 228 "These are the terms corre sponding with the quadrature filter set. To calculate the dominant ori entation according to article of Freeman & Adelson, use terms with cos (2theta) and with sin(2theta). Use normalization factor (1/5)^2" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 165 "\ncombine\n (\n evalf\n \+ (\n expand\n (\n (1 + 2*c os(2*(theta)) + 2*cos(4*(theta)))^2\n )\n )\n ) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,$\"*++++&!\")\"\"\"*&$\"*++++)F &F'-%$cosG6#,$%&thetaG\"\"#F'F'*&$\"*++++'F&F'-F,6#,$F/\"\"%F'F'*&$\"* ++++%F&F'-F,6#,$F/\"\"'F'F'*&$\"+++++?!\"*F'-F,6#,$F/\"\")F'F'" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 182 "combine\n (\n evalf \n (\n expand\n (\n (1 \+ + 2*cos(2*(theta - (Pi/5))) + 2*cos(4*(theta - (Pi/5))))^2\n \+ )\n )\n );" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,4$\"*0+++ &!\")\"\"\"*&$\")g8sC!\"(F'-%$cosG6#,$%&thetaG\"\"#F'F'*&$\"*&>5a[F&F' -F-6#,$F0\"\"%F'!\"\"*&$\"+pz1OK!\"*F'-F-6#,$F0\"\"'F'F9*&$\"+!*)R.='! #5F'-F-6#,$F0\"\")F'F'*&$\"*<_%3wF&F'-%$sinGF.F'F'*&$\"*_6n_$F&F'-FNF6 F'F'*&$\"+559^BF=F'-FNF?F'F9*&$\"+LI6->F=F'-FNFGF'F9" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 184 "combine\n (\n evalf\n (\n \+ expand\n (\n (1 + 2*cos(2*(the ta - (2*Pi/5))) + 2*cos(4*(theta - (2*Pi/5))))^2\n )\n \+ )\n );" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,4$\"*++++&!\")\"\"\" *&$\"+\"*R.=;!\"*F'-%$cosG6#,$%&thetaG\"\")F'!\"\"*&$\"*&f8skF&F'-F-6# ,$F0\"\"#F'F2*&$\"*-#G-ZF&F'-%$sinGF7F'F'*&$\"*)>5a=F&F'-F-6#,$F0\"\"% F'F'*&$\"*6Rjq&F&F'-F>FCF'F2*&$\"+sz1O7F+F'-F-6#,$F0\"\"'F'F'*&$\"+jgA /QF+F'-F>FNF'F'*&$\"+.0dv6F+F'-F>F.F'F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 187 "combine\n (\n evalf\n (\n \+ expand\n (\n (1 + 2*cos(2*(theta - (3*Pi /5))) + 2*cos(4*(theta - (3*Pi/5))))^2\n )\n )\n \+ );" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,4$\"+2+++]!\"*\"\"\"*&$\"+bf8 skF&F'-%$cosG6#,$%&thetaG\"\"#F'!\"\"*&$\"+m>5a=F&F'-F,6#,$F/\"\"%F'F' *&$\"+%)z1O7F&F'-F,6#,$F/\"\"'F'F'*&$\"+))R.=;F&F'-F,6#,$F/\"\")F'F1*& $\"*.#G-Z!\")F'-%$sinGF-F'F1*&$\"*3Rjq&FJF'-FLF6F'F'*&$\"+ugA/QF&F'-FL F=F'F1*&$\"+/0dv6F&F'-FLFDF'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 187 "combine\n (\n evalf\n (\n expand\n \+ (\n (1 + 2*cos(2*(theta - (4*Pi/5))) + 2 *cos(4*(theta - (4*Pi/5))))^2\n )\n )\n );" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#,4$\"+A+++]!\"*\"\"\"*&$\"+&*)R.='!#5F '-%$cosG6#,$%&thetaG\"\")F'F'*&$\")g8sC!\"(F'-F-6#,$F0\"\"#F'F'*&$\"*8 _%3w!\")F'-%$sinGF7F'!\"\"*&$\"+j>5a[F&F'-F-6#,$F0\"\"%F'F@*&$\"+0:rEN F&F'-F?FEF'F@*&$\"+mz1OKF&F'-F-6#,$F0\"\"'F'F@*&$\"+559^BF&F'-F?FPF'F' *&$\"+KI6->F&F'-F?F.F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 229 "combine\n (\n evalf\n (\n expand\n \+ (\n (1 + 2*cos (2*(theta )) + 2*cos(4*(theta)))\n * (1 + 2*cos (2*(theta-Pi/5)) + 2*cos(4*(theta - Pi/5) ))\n\n )\n )\n );" }}{PARA 12 "" 1 "" {XPPMATH 20 "6 #,4$\"\"\"!\")F%*&$\"*'R.=;F&F%-%$cosG6#,$%&thetaG\"\"#F%F%*&$\")***** ***F&F%-F+6#,$F.\"\"%F%F%*&$\"*++++\"F&F%-F+6#,$F.\"\"'F%!\"\"*&$\"+)) R.=;!\"*F%-F+6#,$F.\"\")F%F>*&$\"*\\qb<\"F&F%-%$sinGF,F%F%*&$\"*`$oxIF &F%-FKF4F%F%*&$\"+KNoxIFBF%-FKF;F%F%*&$\"+/0dv6FBF%-FKFDF%F%" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 227 "combine\n (\n evalf\n \+ (\n expand\n (\n (1 + 2*cos (2* (theta)) + 2*cos(4*(theta)))\n * (1 + 2*cos (2*(t heta-2*Pi/5)) + 2*cos(4*(theta-2*Pi/5)))\n )\n )\n ); " }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,2-%$cosG6#,$%&thetaG\"\")$\"+w)R. ='!#5*&$\")+M!='!\")\"\"\"-F%6#,$F(\"\"#F1!\"\"*&$\"**H6->F0F1-%$sinGF 3F1F6*&$\"*++++\"F0F1-F%6#,$F(\"\"%F1F1*&$\")`UlsF0F1-F;F@F1F6*&$\"*** *******!\"*F1-F%6#,$F(\"\"'F1F6*&$FEF0F1-F;FLF1F6*&$\"+LI6->FJF1-F;F&F 1F6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 223 "combine\n (\n e valf\n (\n expand\n (\n (1 + 2*c os (2*(theta)) + 2*cos(4*(theta)))\n * (1 + 2*cos \+ (2*(theta-3*Pi/5)) + 2*cos(4*(theta-3*Pi/5)))\n )\n )\n );" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,4$\"\"\"!\")F%*&$\"))R.='F&F% -%$cosG6#,$%&thetaG\"\"#F%!\"\"*&$\"*,+++\"F&F%-F+6#,$F.\"\"%F%F%*&$\" *)********!\"*F%-F+6#,$F.\"\"'F%F0*&$\"+)))R.='!#5F%-F+6#,$F.\"\")F%F% *&$\"*/8@!>F&F%-%$sinGF,F%F%*&$\")dUlsF&F%-FLF5F%F%*&$\")aUlsF&F%-FLF= F%F%*&$\"+LI6->F;F%-FLFEF%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 225 "combine\n (\n evalf\n (\n expand\n ( \n (1 + 2*cos (2*(theta)) + 2*cos(4*(theta)))\n * (1 + 2*cos (2*(theta-4*Pi/5)) + 2*cos(4*(theta-4*Pi/5 )))\n )\n )\n );" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,4 $!\"#!\")\"\"\"*&$\")R.=;!\"(F'-%$cosG6#,$%&thetaG\"\"#F'F'*&$\")***** ***F&F'-F-6#,$F0\"\"%F'F'*&$\"*++++\"F&F'-F-6#,$F0\"\"'F'!\"\"*&$\"+*) R.=;!\"*F'-F-6#,$F0\"\")F'F@*&$\"+90dv6FDF'-%$sinGF.F'F@*&$\"*b$oxIF&F '-FMF6F'F@*&$\"+QNoxIFDF'-FMF=F'F@*&$\"+/0dv6FDF'-FMFFF'F@" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 193 "combine\n (\n evalf\n (\n expand\n (\n (1 + 2*cos (2*(theta- Pi/5)) + \+ 2*cos(4*(theta- Pi/5)))\n * (1 + 2*cos (2*(theta-2*Pi/5)) + 2*co s(4*(theta-2*Pi/5)))\n\n)));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,4$\" \"\"!\")F%*&$\")*R.='F&F%-%$cosG6#,$%&thetaG\"\"#F%!\"\"*&$\"*+M!=EF&F %-F+6#,$F.\"\"%F%F0*&$\"+()R.=E!\"*F%-F+6#,$F.\"\"'F%F%*&$\"++*R.='!#5 F%-F+6#,$F.\"\")F%F%*&$\"*.8@!>F&F%-%$sinGF,F%F%*&$\"*08@!>F&F%-FLF5F% F0*&$\"*/8@!>F&F%-FLF=F%F0*&$\"+KI6->F;F%-FLFEF%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 227 "combine\n (\n evalf\n (\n \+ expand\n (\n (1 + 2*cos (2*(theta -Pi/5)) + 2 *cos(4*(theta- Pi/5)))\n * (1 + 2*cos (2*(theta-3*Pi/5)) + 2*cos(4*(theta-3*Pi/5)))\n )\n )\n );" }}{PARA 12 " " 1 "" {XPPMATH 20 "6#,2-%$cosG6#,$%&thetaG\"\")$!+*)R.=;!\"**&$\"*)R. =;!\")\"\"\"-F%6#,$F(\"\"#F1F1*&$\"*^qb<\"F0F1-%$sinGF3F1!\"\"*&$\"),m >QF0F1-F%6#,$F(\"\"%F1F;*&$\"*\\qb<\"F0F1-F:F@F1F1*&$\"*7g'>QF,F1-F%6# ,$F(\"\"'F1F1*&$\"+/0dv6F,F1-F:FKF1F1*&$\"+/0dv6F,F1-F:F&F1F;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 229 "combine\n (\n evalf\n \+ (\n expand\n (\n (1 + 2*cos (2*(th eta -Pi/5)) + 2*cos(4*(theta- Pi/5)))\n * (1 + 2*cos (2 *(theta-4*Pi/5)) + 2*cos(4*(theta-4*Pi/5)))\n )\n )\n \+ );" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,4$\"\"&!\")\"\"\"*&$\"*/+++#F&F '-%$cosG6#,$%&thetaG\"\"#F'!\"\"*&$\"+pz1O7!\"*F'-F,6#,$F/\"\"%F'F1*&$ \"+#*z1O7F5F'-F,6#,$F/\"\"'F'F'*&$\"+++++?F5F'-F,6#,$F/\"\")F'F'*&$\"+ ++Dc:!#F' F1*&$\"+++]7y!#>F'-FMFEF'F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 231 "combine\n (\n evalf\n (\n expand\n (\n \+ (1 + 2*cos (2*(theta-2*Pi/5)) + 2*cos(4*(theta-2*Pi/5) ))\n * (1 + 2*cos (2*(theta-3*Pi/5)) + 2*cos(4*(theta-3* Pi/5)))\n )\n )\n );" }}{PARA 12 "" 1 "" {XPPMATH 20 " 6#,4$!\"%!\"*\"\"\"*&$\"*++++#!\")F'-%$cosG6#,$%&thetaG\"\"#F'!\"\"*&$ \"*)z1OKF+F'-F-6#,$F0\"\"%F'F'*&$\"+*)z1OKF&F'-F-6#,$F0\"\"'F'F2*&$\"+ ********>F&F'-F-6#,$F0\"\")F'F'*&$\"+++v=7!#F'F'*&$\"++++]7FUF'-FMFEF'F2" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 225 "combine\n (\n evalf\n \+ (\n expand\n (\n (1 + 2*cos (2*(thet a-2*Pi/5)) + 2*cos(4*(theta-2*Pi/5)))\n * (1 + 2*cos (2*(t heta-4*Pi/5)) + 2*cos(4*(theta-4*Pi/5)))\n )\n )\n );" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,4-%$cosG6#,$%&thetaG\"\")$!+))R.=;! \"*$\"\"\"!\")F.*&$\"*)R.=;F/F.-F%6#,$F(\"\"#F.F.*&$\"*Zqb<\"F/F.-%$si nGF4F.F.*&$\"*Gg'>QF,F.-F%6#,$F(\"\"%F.!\"\"*&$\"*_qb<\"F/F.-F;F@F.FC* &$\"*3g'>QF,F.-F%6#,$F(\"\"'F.F.*&$\"+10dv6F,F.-F;FLF.FC*&$\"+10dv6F,F .-F;F&F.F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 244 "combine\n \+ (\n evalf\n (\n expand\n (\n \+ (1 + 2*cos (2*(theta-3*Pi/5)) + 2*cos(4*(theta-3*Pi/5)))\n \+ * (1 + 2*cos (2*(theta-4*Pi/5)) + 2*cos(4*(theta-4*Pi/5))) \n )\n )\n );" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#, 4$!\"\"!\")\"\"\"*&$\")+M!='F&F'-%$cosG6#,$%&thetaG\"\"#F'F%*&$\"+vR.= E!\"*F'-F,6#,$F/\"\"%F'F%*&$\"+\"*R.=EF4F'-F,6#,$F/\"\"'F'F'*&$\"+!))R .='!#5F'-F,6#,$F/\"\")F'F'*&$\"*68@!>F&F'-%$sinGF-F'F%*&$\"**H6->F&F'- FLF6F'F'*&$\"*-8@!>F&F'-FLF=F'F'*&$\"+LI6->F4F'-FLFEF'F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 128 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }