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Removal of High Density Gaussian Noise in Imageswith Fuzzy Rule Based Filtering Using MA !AB

"rof# $# %# Rai&le'troni's and $ommuni'ation

U%I$ ( Guru Govind %ingh Indra)rastha UniversityDwar*a( New Delhi( India

'srai+i)u#a'#in

,idhi&le'troni's and $ommuni'ation


vidhee-.+gmail#'om

Munish /umar &le'troni's and $ommuni'ation


munish*m0121+gmail#'om

,ee3hore ,arun&le'troni's and $ommuni'ation


vee3hore#varun+gmail#'om

Abstract This paper presents a robust and detailedapproach to design a fuzzy filter for the reduction of additivenoise in colored as well as black and white images. A fuzzy filteris based on a set of IF-T !" rules. The filter consists of twostages. In the first stage# fuzzy derivative values for all the eightdirections that is !# $# "# %# "!# "$# %!# %$ with reference tothe central pi&el are calculated for determining noisy pi&els. Inthe second stage# another fuzzy rule based system is employed. Ituses the output of the previous fuzzy system to perform fuzzysmoothing by weighting the contribution of neighboring pi&els.'oth stages can also be implemented through membershipfunctions using (Fuzzy )ogic* toolbo which is also an inbuilttoolbo& in +AT)A'. For a particular value of an adaptiveparameter ,# the fuzzy logic is iteratively used on the corruptedimage till a desired value of %" comes. 'y the e&perimentalresults# proposed fuzzy rule based filtering providesappro&imately same performance results as that of filters like$einer and +edian filter. The results are compared usingnumerical measures /like %" # and +%!0 and also throughvisual inspection.

KeywordsAdditive noise, histogram, filtering, fuzzification,defuzzification, membership function, edge preserving filtering,noise reduction, Wiener filter, Median filter, correction term, image

processing

I# I N R4DU$ I4N

Noise removal and image smoothing are one of the mostim)ortant )re)ro'essing ste)s in image )ro'essing# Digitalimage )ro'essing fo'uses on two ma5or tas*s #Im)rovement of

)i'torial information for human inter)retation and )ro'essingof image data for storage( transmission and re)resentation for autonomous ma'hine )er'e)tion 678# In re'ent years( manyresear'hers have a))lied the fuzzy set theory to develo) newte'hni9ues for image enhan'ement# Fuzzy set theory is thee:tension of 'onventional ;'ris)< set theory# It handles the'on'e)t of )artial truth ;truth values 3etween 0 ;'om)letelytrue< and . ;'om)letely false8

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Figure 0# Mem3ershi) fun'tions a< %mall 3#< "ositive'#< Negative

II# BA$/GR4UND R &,I& AND " R4"4%&D A""R4A$H

A. PROPOSED FUZZY FILTER

he main aim of the )ro)osed filter is to average a )i:el using

other neigh3oring )i:els# Here we ta*e the neigh3oring )i:els 3ased on the dire'tions su'h as North( &ast( et'# his filter mainly distinguishes lo'al variations due to noise and due toimage stru'tures# In order to a''om)lish this( for ea'h )i:elwe derive a value that e:)resses the degree in whi'h thederivative in a 'ertain dire'tion is small# %u'h a value isderived for ea'h dire'tion 'orres)onding to the neigh3oring

)i:els of the )ro'essed )i:el 3y a fuzzy rule# he further 'onstru'tion of the filter is then 3ased on the o3servation that asmall fuzzy derivative most li*ely is 'aused 3y noise( while alarge fuzzy derivative most li*ely is 'aused 3y an edge in theimage# For ea'h dire'tion we will a))ly two fuzzy rules thatta*e this o3servation into a''ount ;and thus distinguish

3etween lo'al variations due to noise and due to imagestru'ture

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"orth-$estIf an edge is )assing through % @N& dire'tion( then 'al'ulatethe dire'tive value in the N dire'tion for the 'entral )i:eland neigh3oring )i:els#

"orth-!astIf an edge is )assing through N @%& dire'tion( then 'al'ulatethe dire'tive value in the N& dire'tion for the 'entral )i:el andneigh3oring )i:els#

%outh-$estIf an edge is )assing through %&@N dire'tion( then 'al'ulatethe dire'tive value in the % dire'tion for the 'entral )i:eland neigh3oring )i:els#

%outh-!astIf an edge is )assing through % @N& dire'tion( then 'al'ulatethe dire'tive value in the N dire'tion for the 'entral )i:eland neigh3oring )i:els#

"orthIf an edge is )assing through &@ dire'tion( then 'al'ulate thedire'tive value in the N dire'tion for the 'entral )i:el andneigh3oring )i:els#

!astIf an edge is )assing through %@N dire'tion( then 'al'ulate thedire'tive value in the & dire'tion for the 'entral )i:el andneigh3oring )i:els#

%outhIf an edge is )assing through @& dire'tion( then 'al'ulate thedire'tive value in the % dire'tion for the 'entral )i:el andneigh3oring )i:els#

$estIf an edge is )assing through N@% dire'tion( then 'al'ulate thedire'tive value in the dire'tion for the 'entral )i:el and

neigh3oring )i:els#

"$ " "!

$ / y0 !

%$ % %!

"$ " "!

$ / y0 !

%$ % %!

"$ " "!

$ / y0 !

%$ % %!

"$ " "!

$ / y0 !

%$ % %!

"$ " "!

$ / y0 !

%$ % %!

"$ " "!

$ / y0 !

%$ % %!

"$ " "!

$ / y0 !

%$ % %!

"$ " "!

$ / y0 !

%$ % %!

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Ees

No

Figure -# Flow 'hart for a))lying fuzzy rules to noisy image

he algorithm for the fuzzy image filtering 'onsists of thefollowing ste)s@

1. he image on whi'h filtering is 3e )erformed is'hosen# his 'an 3e done 3y using imread inMA !AB#

2. Gaussian noise is added to the image#3. If the image is RGB( then it should 3e first 'onverted

to gray s'ale image# his 'an 3e done as follows6width height dim8 size;image ?different variance

3omparison table of $einer filter# +edian filter and Fuzzy filter on the basis of %" values

"oisy Image Fuzzy 3orrectedImage

istogram of noisyImage

3ameraman.tif

%" ;@.@5@ ,;B# %" ; C.CD

%" ;@.4BBE ,;B# %" ; C.D4B

%" ;@.BB>E5 ,; # %" ; B.>>B

%" ;@. 4E@C ,; # %" ; B. E

%" ;@.> 4E ,;C# %" ; B. >>

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AB!& II# CB 4A % I H GAU%%IAN N4I%& F4R DIFF&R&N ,A!U&% 4F,ARIAN$&

'oats image with

mean;> ? differentvariance


"oisy Image Fuzzy 3orrectedimage

istogram of noisyimage

'oats.Gpg

%" ;@.D EC ,; # %" ; C.5@@

%" ;@.E >5B ,;B# %" ; B.@>

%" ;@. @B5 ,; # %" ; B.D54

%" ;@.B @> ,;B# %" ; .BC

%" ;@.C CD ,;B# %" ; .B>C

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AB!& III# C! &NA I H GAU%%IAN N4I%& F4R DIFF&R&N ,A!U&% 4F,ARIAN$&

)ena image with

mean;> ? differentvariance




)ena.bmp

%" ;@.554DB ,; # %" ; B.>E

%" ;@.EC4B ,; # %" ; B.5B>

%" ;@. C ,; # %" ; .CC>

%" ;@.B>DD ,;B# %" ; .4E

%" ;@. 554CC ,;B# %" ; .5D

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AB!& I,# C $4!4R&D BAB44N I H GAU%%IAN N4I%& F4R DIFF&R&N,A!U&% 4F ,ARIAN$&

3olored 'aboonimage with mean;>? different variance




'aboon.Gpg

%" ;@.DCBCD ,; # %" ; B.>BD

%" ;@.E5CB ,; # %" ; .>BC

%" ;@.4>5 ,;# %" ; . C5

%" ;@.B5D5 ,;B# %" ; .@C5

%" ;@.C@5B ,;B# %" ; .@E

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AB!& ,# C$ 4!4R&D !&NA I H GAU%%IAN N4I%& F4R DIFF&R&N,A!U&% 4F ,ARIAN$&

3olored )ena image

with mean;> ?different variance


"oisy Image Fuzzy 3orrectedImage

istogram of noisyImage

)enaHcoloured.Gpg

%" ;@.5E D5 ,;4# %" ; B.>

%" ;@.E > ,;B# %" ; B.DC5

%" ;@. E C ,;4# %" ; .C E

%" ;@.B ,;B# %" ; .@

%" ;@. E54 D ,;C# %" ; .BD@

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Acknowledgment e would li*e to e:)ress our foremost and sin'ere gratitude to

Dr# $#% Rai( our guide( who has 3een a 'onstant sour'e of *nowledge and ins)iration to us( throughout the 'ourse of thisre)ort#

References608 /erre and M# Na'htegael( &ds#( Fuzzy e'hni9ues in Image"ro'essing# New Eor* %)ringer@,erlag( =...( vol# ?=( %tudies inFuzziness and %oft $om)uting# # $ler* Ma:well( A reatise on&le'tri'ity and Magnetism( -rd ed#( vol# =# 4:ford $larendon( 021=(

))#72@O-#6=8 D# ,an De ,ille( # "hili)s( and I# !emahieu( Fuzzy e'hni9ues in

Image "ro'essing# New Eor* %)ringer@,erlag( =...( vol# ?=( %tudiesin Fuzziness and %oft $om)uting( 'h# Fuzzy@3ased motion dete'tionand its a))li'ation to de@interla'ing( ))# --OJ-71##

6-8 M# Na'htegael and /erre( C$onne'tions 3etween 3inary( gray@s'aleand fuzzy mathemati'al mor)hologies( Fuzzy %ets %yst#( to 3e )u3@

Figure ># "%NR gra)hs of various images for different values of varian'e

PSNR values of Lena_coloured.jpg in presence ofGaussian noise for various values of variance

For variance, 2=0.

For variance, 2=0.!

For variance, 2=0."

For variance, 2=0.#

For variance, 2=0.$

PSNR values of %a&oon_coloured.jpgin presence ofGaussian noise for various values of variance

For variance, 2=0.

For variance, 2=0.!

For variance, 2=0."

For variance, 2=0.#

For variance, 2=0.$

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lished#M# Eoung( he e'hni'al riter s Hand3oo*# Mill ,alley( $AUniversity %'ien'e( 0121#

6>8 CDe'om)osing and 'onstru'ting fuzzy mor)hologi'al o)erations over@'uts $ontinuous and dis'rete 'ase( I&&& rans# Fuzzy %yst# (vol# 2(

))# 70?J7=7( 4't# =...#6?8 B# Reus'h( M# Fathi( and !# Hilde3rand( %oft $om)uting( Multi@media

and Image "ro'essingP"ro'eedings of the orld Automation $ongressAl3u9uer9ue( NM %I "ress( 0112( 'h# Fuzzy $olor "ro'essing for Quality Im)rovement( ))# 2>0J2>2#

678 %ridevi#Ravada et al# International ournal on $om)uter %'ien'e and&ngineering ;I $%&@?00

628 Digital Image "ro'essing@- rd edition ))t# 3y Rafael $# Gonzalez(Ri'hard oods#

618 # Delon and A# Desolneu:( CA )at'h@3ased a))roa'h for random@valuedim)ulse noise removal ( I&&& International $onferen'e on A'ousti's(%)ee'h and %ignal "ro'ess# ;I$A%%"

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