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UNIVERSITY OF ENGINEERING AND TECHNOLOGY, TAXILA

FACULTY OF TELECOMMUNICATION AND INFORMATION ENGINEERING

SOFTWARE ENGINEERING DEPARTMENT

COMPUTER GRAPHICS&

IMAGE PROCESSING

LAB MANUAL 6

PREPARED BY:: ENGR. ALI JAVED

Computer Graphics & Image Processing 7thTerm-SE UET Taxila


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IMAGE FILTERING IN FREQUENCY DOMAIN

LAB OBJECTIVE:

The objective of this !b is to "#$e%st!#$ & i'(e'e#t

)* I'!+e e#h!#ce'e#t i# f%e"e#c- $o'!i#*

.* Lo/ 0!ss Fite%s

G!"ssi!# o/ (!ss fite%

1"tte%/o%th o/ (!ss fite%

I$e! o/ (!ss fite%

2* Hi+h 0!ss Fite%s

G!"ssi!# hi+h (!ss fite%

1"tte%/o%th hi+h (!ss fite%

I$e! hi+h (!ss fite%

BACKGROUND MATERIAL:

Dis!"#" F$%!i"! T!'s($!)

W*# is #*" Dis!"#" F$%!i"! T!'s($!)+

The +e#e%! i$e! is th!t the i'!+e 3f(x,y)of si4e M 5N6 /i be %e(%ese#te$ i# the f%e"e#c- $o'!i#3F(u,v)6* The e"!tio# fo% the t/o7$i'e#sio#! $isc%ete Fo"%ie% t%!#sfo%' 3DFT6 is8

The co#ce(t behi#$ the Fo"%ie% t%!#sfo%' is th!t !#- /!vefo%' th!t c!# be co#st%"cte$ "si#+ ! s"' ofsi#e !#$ cosi#e /!ves of $iffe%e#t f%e"e#cies* The e5(o#e#ti! i# the !bove fo%'"! c!# be e5(!#$e$i#to si#es !#$ cosi#es /ith the v!%i!bes u!#$ v$ete%'i#i#+ these f%e"e#cies*

The i#ve%se of the !bove $isc%ete Fo"%ie% t%!#sfo%' is +ive# b- the foo/i#+ e"!tio#8



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Th"s, if /e h!ve F(u,v), /e c!# obt!i# the co%%es(o#$i#+ i'!+e 3f(x,y)6 "si#+ the i#ve%se, $isc%eteFo"%ie% t%!#sfo%'*

Thi#+s to #ote !bo"t the $isc%ete Fo"%ie% t%!#sfo%' !%e the foo/i#+8

the v!"e of the t%!#sfo%' !t the o%i+i# of the f%e"e#c- $o'!i#, !t F(0,0), is c!e$ the $c

co'(o#e#to F(0,0)is e"! to MNti'es the !ve%!+e v!"e of f(x,y)

o i# 9ATLA1, F(0,0)is !ct"!- F(1,1)bec!"se !%%!- i#$ices i# 9ATLA1 st!%t !t ) %!the%

th!# :

the v!"es of the Fo"%ie% t%!#sfo%' !%e co'(e5, 'e!#i#+ the- h!ve %e! !#$ i'!+i#!%- (!%ts*

The i'!+i#!%- (!%ts !%e %e(%ese#te$ b- i, /hich is the s"!%e %oot of 7)

/e vis"!- !#!-4e ! Fo"%ie% t%!#sfo%' b- co'("ti#+ ! F$%!i"! s,"#!%)3the '!+#it"$e of

F(u,v)6 !#$ $is(!- it !s !# i'!+e*

o the Fo"%ie% s(ect%"' is s-''et%ic !bo"t the o%i+i#

the f!st Fo"%ie% t%!#sfo%' 3FFT6 is ! f!st !+o%ith' fo% co'("ti#+ the $isc%ete Fo"%ie%

t%!#sfo%'*

9ATLA1 h!s th%ee f"#ctio#s to co'("te the DFT8

1. fft 7fo% o#e $i'e#sio# 3"sef" fo% !"$io6

2. fft. 7fo% t/o $i'e#sio#s 3"sef" fo% i'!+es6

3. fft# 7fo% # $i'e#sio#s 9ATLA1 h!s th%ee f"#ctio#s th!t co'("te the i#ve%se DFT8

1. ifft

2. ifft.

3. ifft#

H$- $"s #*" Dis!"#" F$%!i"! T!'s($!) !"/#" #$ S,#i/ D$)i' Fi/#"!i'0

The foo/i#+ co#vo"tio# theo%e' sho/s !# i#te%esti#+ %e!tio#shi( bet/ee# the s(!ti! $o'!i# !#$f%e"e#c- $o'!i#8

!#$, co#ve%se-,

the s-'bo ;


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Bsi S#",s i' DFT Fi/#"!i'0

The foo/i#+ s"''!%i4e the b!sic ste(s i# DFT Fite%i#+

)* Obt!i# the (!$$i#+ (!%!'ete%s "si#+ f"#ctio# (!$$e$si4e80=>(!$$e$si4e3si4e3f66?

.* Obt!i# the Fo"%ie% t%!#sfo%' /ith (!$$i#+8F>fft.3f, 0=3)6, 0=3.66?

2* Ge#e%!te ! fite% f"#ctio#, H, of si4e 0=3)6 5 0=3.6****@* 9"ti(- the t%!#sfo%' b- the fite%8

G>H*%e!3ifft.3G66?

B* C%o( the to(, eft %ect!#+e to the o%i+i#! si4e8+>+3)8si4e3f, )6, )8si4e3f, .66?

L$-,ss ' Hi0*,ss F!"1%"'2 D$)i' Fi/#"!s

1!se$ o# the (%o(e%t- th!t '"ti(-i#+ the FFT of t/o f"#ctio#s f%o' the s(!ti! $o'!i# (%o$"ces theco#vo"tio# of those f"#ctio#s, -o" c!# "se Fo"%ie% t%!#sfo%'s !s ! f!st co#vo"tio# o# !%+e i'!+es*As ! #ote, o# s'! i'!+es, it is f!ste% to /o% i# the s(!ti! $o'!i#*

Ho/eve%, -o" c!# !so c%e!te fite%s $i%ect- i# the f%e"e#c- $o'!i#* The%e !%e t/o co''o#-$isc"sse$ fite%s i# the f%e"e#c- $o'!i#8

Lo/(!ss fite%s, so'eti'es #o/# !s s'oothi#+ fite%s

Hi+h(!ss fite%s, so'eti'es #o/# !s sh!%(e#i#+ fite%s

L$-,ss F!"1%"'2 D$)i' Fi/#"!s

Lo/(!ss fite%s8

c%e!te ! b"%%e$ 3o% s'oothe$6 i'!+e

!tte#"!te the hi+h f%e"e#cies !#$ e!ve the o/ f%e"e#cies of the Fo"%ie% t%!#sfo%' %e!tive-

"#ch!#+e$

Th%ee '!i# o/(!ss fite%s !%e $isc"sse$ i# Digital Image Processing Using MA!A"8

)* i$e! o/(!ss fite% 3IL0F6.* 1"tte%/o%th o/(!ss fite% 31L0F62* G!"ssi!# o/(!ss fite% 3GL0F6

The co%%es(o#$i#+ fo%'"!s !#$ vis"! %e(%ese#t!tio#s of these fite%s !%e sho/# i# the t!be beo/* I#the fo%'"!e, D0is ! s(ecifie$ #o##e+!tive #"'be%* D(u,v) is the $ist!#ce f%o' (oi#t (u,v) to thece#te% of the fite%*

http://www.cs.uregina.ca/Links/class-info/425/Lab4/M-Functions/paddedsize.mhttp://www.cs.uregina.ca/Links/class-info/425/Lab4/M-Functions/paddedsize.m


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Hi0*,ss F!"1%"'2 D$)i' Fi/#"!s

Hi+h(!ss fite%s8

sh!%(e# 3o% sho/s the e$+es of6 !# i'!+e

!tte#"!te the o/ f%e"e#cies !#$ e!ve the hi+h f%e"e#cies of the Fo"%ie% t%!#sfo%' %e!tive-

"#ch!#+e$

The hi+h(!ss fite% 3#$%6 is ofte# %e(%ese#te$ b- its %e!tio#shi( to the o/(!ss fite% 3#l%68



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1ec!"se hi+h(!ss fite%s c!# be c%e!te$ i# %e!tio#shi( to o/(!ss fite%s, the foo/i#+ t!be sho/s theth%ee co%%es(o#$i#+ hi+h(!ss fite%s b- thei% vis"! %e(%ese#t!tio#s8



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IMPLEMENTATION DETAILS WITH RESULTS:

G%ssi' L$- Pss Fi/#"!

MATLAB CODE

i'!+e>i'%e!$3c!'e%!'!#*tif6?

i'sho/3i'!+e6?

',#>si4e3i'!+e6?

i'!+e>i'.$o"be3i'!+e6?

F>fft.3i'!+e6?

F>fftshift3F6?

Si+'!>):?

H>fs(eci!3+!"ssi!#,' #,si+'!6?

G>H*ifftshift3G6?

+>%e!3ifft.3G66?

fi+"%e,i'sho/3+,6

OUTPUT

Si0)3Dis#'"457



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ORIGINAL IMAGE IMAGE AFTER G%ssi' LPF

OUTPUT

Si0)3Dis#'"487



9/12




ORIGINAL IMAGE IMAGE AFTER G%ssi' LPF

G%ssi' L$- Pss Fi/#"!

MATLAB CODE 9%si'0 (%'#i$' /,(i/#"!

i'!+e>i'%e!$3c!'e%!'!#*tif6?

i'sho/3i'!+e6?

',#>si4e3i'!+e6?

i'!+e>i'.$o"be3i'!+e6?

F>fft.3i'!+e6?

F>fftshift3F6?

si+'!>):?

H4/,(i/#"!9;0%ssi';


10/12




i'!+e>i'%e!$3c!'e%!'!#*tif6?

i'sho/3i'!+e6?

',#>si4e3i'!+e6?

i'!+e>i'.$o"be3i'!+e6?

F>fft.3i'!+e6?

F>fftshift3F6?

si+'!>):?

H4*,(i/#"!9;0%ssi';i'%e!$3c!'e%!'!#*tif6?

i'sho/3i'!+e6?

',#>si4e3i'!+e6?

i'!+e>i'.$o"be3i'!+e6?

F>fft.3i'!+e6?

F>fftshift3F6?

O%$e%>.?

H4/,(i/#"!9;=#-;i'%e!$3c!'e%!'!#*tif6?



11/12




i'sho/3i'!+e6?

',#>si4e3i'!+e6?

i'!+e>i'.$o"be3i'!+e6?

F>fft.3i'!+e6?

F>fftshift3F6?

O%$e%>.?

H4*,(i/#"!9;=#-;i'%e!$3c!'e%!'!#*tif6?

i'sho/3i'!+e6?

',#>si4e3i'!+e6?

i'!+e>i'.$o"be3i'!+e6?

F>fft.3i'!+e6?

F>fftshift3F6?

H4/,(i/#"!9;i"/;


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i'!+e>i'.$o"be3i'!+e6?

F>fft.3i'!+e6?

F>fftshift3F6?

H4*,(i/#"!9;i"/;

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