Performance enhancement and analysis o f a n adaptive median filter Yanming Zhao, Dongmei L i, a n d Zhaohui L i Abstract-The classical adaptive median filter i s designed t o remove t h e positive a n d negative impulse noise when t h e probability o f noise i s high. B u t simulation shows t h e filtered images remain t h e positive impulse noise i n t h e black background a nd t h e negative impulse noise i n t h e white background. In this paper, t h e classical adaptive median filter i s modified and i t s performance i s improved. Simulation results show t h e new scheme provides t h e better filtering performance. Index Terms-median filter, impulse noise, image restoration I . INTRODUCTION I N image processing, images a r e often corrupted b y th e positive a n d negative impulse noise d u e t o decoding error or noisy channel. S o i t is an important task to filter th e corrupted images. T he median filter ca n remove t h e impulse noise efficiently [1]. B u t i t is difficult t o remove the impulse noise a n d preserve image sharpness concurrently when th e probability o f impulse noise becomes high. To overcome this situation, adaptive median filter i s proposed [2-5]. T h e classical adaptive median filter [ 2 ] c a n efficiently remove the positive a n d negative impulse noise even though t h e probability o f impulse noise is high. B u t this h a s some deficiencies: the filtered images remain t h e positive impulse noise i n th e black background and t h e negative impulse noise i n t h e white background. T o solve the above questions, th e classical adaptive median filter is modified a n d i t s performance is improved. Experimental results show t h e modified scheme provides t h e better filtering performance. I I. T H E CLASSICAL ADAPTIVE MEDIAN FILTER T h e basic difference between t h e adaptive median filter [ 2 ] a n d standard median filter i s that, i n adaptive median filter, the window size i s variable. T h e algorithm i s described a s follows: Adaptive median filter works o n a rectangular region X Y I t changes t h e size o f Sx y during t h e filtering operation depending o n certain conditions a s listed below. T he output o f t h e filter i s a single value which replaces th e current pixel value a t (x, y ) , t h e point o n which S i s centered a t t h e time. T he Y . Zhao, D . L i , a n d Z. L i a r e with t he Information Engineering School, Communication University o f China, P . R. China (phone:+86-10-65779091; fax: +86-10-65779368; e-mail: yanmingzhao(cuc.edu.cn, 1dm(cuc.edu.cn, lizhh(cuc.edu.cn). following notation i s used: Z m n = minimum pixel value i n S Zmax = maximum pixel value i n S X Y Zmed = median pixel value in S X Y x y= pixel value a t coordinates ( x , y ) Smax = maximum allowed size of S X Y T h e adaptive median filter works i n t w o levels, denoted Level A a n d Level B , a s follows: Level A : I f z . < z < z m i n med max G o t o level B Else increasethe window size window size < = Smax repeat level A Else output Z X Y Level B : I f z <Z <Z m i n xy max I output z XY Else ( 1 ) output Zm ed - N o w w e analyze t h e adaptive median filter. Impulse noise c a n b e negative o r positive. Because impulse corruptionusually i s large compared with t h e strength of t h e image signal, negative impulse generally i s digitized a s t h e minimum values and positive impulses generally i s digitized a s t h e maximum values. I f Zmin < Zmed < Zmax Zmed i s n o t an impulse noise. I n this case, w e g o t o Level B . T h e basic idea o f Level B i s a s follows: Z i s evaluated to verify whether i t i s a n impulse o r not. If i t i s a n impulse, i t will b e replaced b y Zmed. Otherwise, Z x y i s n o t a n impulse. z xy i s retained i n t h e filtered image. Thus, unless t h e pixel being considered i s a n impulse, t h e pixel value i n th e filtered image i s t h e same a s that of t h e input image. This ca n avoid unnecessary loss o f detail. Adaptive median filter solves the dual purpose o f removing t h e impulse noise from the image a n d reducing distortion i n t h e Authorized licensed use limited to: PSG College of Technology. Downloaded on January 3, 2010 at 00:05 from IEEE X plore. Restrictions apply.
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Performance enhancement and analysis of an
a d a p t i v emedian
f i l t e rYanming Z h a o , Dongmei L i , a n d Z h a o h u i L i
A b s t r a c t - T h e c l a s s i c a l a d a p t i v e m e d i a n f i l t e r i s d e s i g n e d t or e m o v e t h e p o s i t i v e a n d n e g a t i v e i m p u l s e n o i s e when t h e
p r o b a b i l i t y o f i m p u l s e n o i s e i s h i g h . B u t s i m u l a t i o n s h o w s t h e
f i l t e r e d i m a g e s r e m a i n t h e p o s i t i v e i m p u l s e n o i s e i n t h e b l a c k
b a c k g r o u n d a n d t h e n e g a t i v e i m p u l s e n o i s e i n t h e w h i t e
b a c k g r o u n d . I n t h i s p a p e r , t h e c l a s s i c a l a d a p t i v e m e d i a n f i l t e r i s
m o di f i ed a n d i t s p e r f o r m a n c e i s i m p r o v e d . S i m u l a t i o n r e s u l t s
s h o w t h e new s c h e m e p r o v i d e s t h e b e t t e r f i l t e r i n g p e r f o r m a n c e .
I n d e x Terms-median f i l t e r , i m p u l s e n o i s e , i m a g e r e s t o r a t i o n
I . INTRODUCTION
IN i m a g e p r o c e s s i n g , i m a g e s a r e o f t e n c o r r u p t e d b y t h ep o s i t i v e a n d n e g a t i v e i m p u l s e n o i s e d u e t o d e c o d i n g e r r o r o r
n o i s y c h a n n e l . S o i t i s a n i mp o rt a nt t a s k t o f i l t e r t h e c o r r u p t e di m a g e s . T h e m e d i a n f i l t e r c a n r e m o v e t h e i m p u l s e n o i s ee f f i c i e n t l y [ 1 ] . B u t i t i s d i f f i c u l t t o r e m o v e t h e i m p u l s e n o i s ea n d p r e s e r v e i m a g e s h a r p n e s s c o n c u r r e n t l y w h e n t h ep r o b a b i l i t y o f i m p u l s e n o i s e b e c o m e s h i g h . To o v e r c o m e t h i s
s i t u a t i o n , a d a p t i v em e d i a n f i l t e r i s p r o p o s e d
[ 2 - 5 ] .T h e c l a s s i c a l a d a p t i v e m e d i a n f i l t e r [ 2 ] c a n e f f i c i e n t l yr e m o v e t h e p o s i t i v e a n d n e g a t i v e i m p u l s e n o i s e e v e n t h o u g h
t h e p r o b a b i l i t y o f i m p u l s e n o i s e i s h i g h . B u t t h i s f i l t e r h a s s o m e
d e f i c i e n c i e s : t h e f i l t e r e d i m a g e s r e m a i n t h e p o s i t i v e i m p u l s en o i s e i n t h e b l a c k b a c k g r o u n d a n d t h e n e g a t i v e i m p u l s e n o i s e i nt h e w h i t e b a c k g r o u n d . To s o l v e t h e a b o v e q u e s t i o n s , t h ec l a s s i c a l a d a p t i v e m e d i a n f i l t e r i s m o d i f i e d a n d i t s p e r f o r m a n c e
i s i m pr o v ed . E x p e ri m en t a l r e s u l t s s h o w t h e m o d i f i e d s c h e m e
p r o v i d e s t h e b e t t e r f i l t e r i n g p e r f o r m a n c e .
I I . T HE CLASSICAL ADAPTIVE MEDIAN FILTER
T h e b a s i c d i f f e r e n c e b e t w e e n t h e a d a p t i v e m e d i a n f i l t e r [ 2 ]a n d s t a n d a r d m e d i a n f i l t e r i s t h a t , i n a d a p t i v e m e d i a n f i l t e r , t h ew i n d o w s i z e i s v a r i a b l e . T h e a l g o r i t h m i s d e s c r i b e d a s f o l l o w s :
A d a p t i v e m e d i a n f i l t e r w o r k s o n a r e c t a n g u l a r r e g i o n S X Y . I t
c h a n g e s t h e s i z e o f S x y d u r i n g t h e f i l t e r i n g o p e r a t i o n
d e p e n d i n g o n c e r t a i n c o n d i t i o n s a s l i s t e d b e l o w . T h e o u t p u t o f
t h e f i l t e r i s a s i n g l e v a l u e w h i c h r e p l a c e s t h e c u r r e n t p i x e l v a l u e
a t ( x , y ) , t h e p o i n t o n w h i c h S i s c e n t e r e d a t t h e t i m e . T h e
Y . Z h a o , D . L i , a n d Z . L i a r e w i t h t h e I n f o r m a t i o n E n g i n e e r i n g S c h o o l ,C o m m u n i c a t i o n U n i v e r s i t y o f C h i n a , P . R . C h i n a ( p h o n e : + 8 6 - 1 0 - 6 5 7 7 9 0 9 1 ;
f a x : + 8 6 - 1 0 - 6 5 7 7 9 3 6 8 ; e - m a i l : y a n m i n g z h a o ( c u c . e d u . c n , 1 d m ( c u c . e d u . c n ,l i z h h ( c u c . e d u . c n ) .
f o l l o w i n g n o t a t i o n i s u s e d :
Z m n = m i n i m u m p i x e l v a l u e i n S
Z m a x = maximum p i x e l v a l u e i n S X YZ m e d = m e d i a n p i x e l v a l u e i n S X Y
x y = p i x e l v a l u e a t c o o r d i n a t e s ( x , y )
S m a x = maximum a l l o w e d s i z e o f S X YT h e a d a p t i v e m e d i a n f i l t e r w o r k s i n t w o l e v e l s , d e n o t e d
L e v e l A a n d L e v e l B , a s f o l l o w s :
L e v e l A :
I f z. < z < zm i n med max
Go t o l e v e l BE l s e
i n c r e a s e t h e w i n d o w s i z e
I f w i n d o w s i z e <= S m a xr e p e a t l e v e l A
E l s e
o u t p u t Z X YL e v e l B :
I f z <Z <Zm i n xy max I
o u t p u t z X YE l s e
( 1 )
o u t p u t Zm e d -
Now we a n a l y z e t h e a d a p t i v e m e d i a n f i l t e r . I m p u l s e n o i s ec a n b e n e g a t i v e o r p o s i t i v e . B e c a u s e i m p u l s e c o r r u p t i o n u s u a l l yi s l a r g e c o m p a r e d w i t h t h e s t r e n g t h o f t h e i m a g e s i g n a l ,
n e g a t i v e i m p u l s e g e n e r a l l y i s d i g i t i z e d a s t h e minimum v a l u e sa n d p o s i t i v e i m p u l s e s g e n e r a l l y i s d i g i t i z e d a s t h e maximum
v a l u e s . I f Z m i n < Z m e d < Z m a x Z m e d i s n o t an i m p u l s e n o i s e .
I n t h i s c a s e , we g o t o L e v e l B . T h e b a s i c i d e a o f L e v e l B i s a s
f o l l o w s : Z i s e v a l u a t e d t o v e r i f y w h e t h e r i t i s a n i m p u l s e o r
n o t . I f i t i s a n i m p u l s e , i t w i l l b e r e p l a c e d b y Z m e d . O t h e r w i s e ,
Z x y i s n o t a n i m p u l s e . z x y i s r e t a i n e d i n t h e f i l t e r e d i m a g e .
T h u s , u n l e s s t h e p i x e l b e i n g c o n s i d e r e d i s a n i m p u l s e , t h e p i x e lv a l u e i n t h e f i l t e r e d i m a g e i s t h e s a m e a s t h a t o f t h e i n p u t i m a g e .T h i s c a n a v o i d u n n e c e s s a r y l o s s o f d e t a i l .
A d a p t i v e m e d i a n f i l t e r s o l v e s t h e d u a l p u r p o s e o f r e m o v i n g
t h e i m p u l s e n o i s e f r o m t h e i m a g e a n d r e d u c i n g d i s t o r t i o n i n t h e
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i m a g e . I t can h a n d l e an i m a g e c o r r u p t e d w i t h i m p u l s e n o i s e o f
p r o b a b i l i t y g r e a t e r t h a n 0 . 2 . And g i v e a much b e t t e r o u t p u t
i m a g e t h a n s t a n d a r d m e d i a n f i l t e r .
III. T HE IMPROVED ADAPTIVE MEDIAN FILTER
A . T h e m o d i f i e d a d a p t i v e m e d i a n f i l t e r
T h e r e are some d e f i c i e n c i e s i n t h e a b o v e a l g o r i t h m . I t i s
known t h a t t h e c o n d i t i o n Z m i n l <Zmed Z i s a l w a y s
s a t i s f i e d . When Z m i n < Zmed < Z m a x go t o l e v e l B . O t h e r w i s e ,
when Z m i n M Zmed<max Zmin <Zmed Zmax or
Zmin Zmed =Z m a x . i t i s k e p t i n l e v e l A a n d t h e window s i z e i s
i n c r e a s e d . When Smax i s r e a c h e d , t h e a l g o r i t h m o u t p u t s t h e
v a l u e o f zxy
N e g a t i v e i m p u l s e appears as b l a c k p o i n t ( p e p p e r n o i s e ) i n an
i m a g e a n d p o s i t i v e i m p u l s e appears as w h i t e p o i n t ( s a l t n o i s e ) .When t h e b l a c k i m a g e i n a window i s c o r r u p t e d b y i m p u l s e
n o i s e s , t h e r e are b l a c k a n d w h i t e p i x e l s . F o r an 8 - b i t i m a g e , i t
means t h e p i x e l v a l u e s are 0 or 2 5 5 . B u t most o f t h e p i x e l
v a l u e s are 0 . S o Z m i n = Zmed = 0 Zmax = 255. E v e n t h e
window s i z e i s i n c r e a s e d t o m a x i m u m ,
Zmin = Zmed =°Z =255. In this c a s e , the o u t p u t valuem'n med max
s h o u l d b e 0 . B u t , a c c o r d i n g t o t h e a l g o r i t h m , t h e o u t p u t v a l u e i s
e q u a l t o zX . Z X Y may b e any v a l u e b e t w e e n 0 a n d 2 5 5 . S o t h e
s a l t n o i s e can n o t b e f i l t e r e d i n t h e b l a c k b a c k g r o u n d o f
c o r r u p t e d i m a g e . F o r t h e same reason, t h e pepper n o i s e can n o t
b e r e m o v e d i n t h e w h i t e b a c k g r o u n d .
I f t h e o u t p u t v a l u e i s c h a n g e d f r o m Z x y t o Zmed i n t h e
e x p r e s s i o n ( 1 ) , t h e a b o v e q u e s t i o n s can b e s o l v e d . F o r t h e b l a c k
i m a g e , Z m i n= Z < Zmax o u t p u t i s Z
-Z m i n 0 . F o r, m i nm e d m Z m e d mi
the white image, zmi <Zme =m ,output is
Zmed Zmax 255 F o r t h e g e n e r a l i m a g e ,
Z m i n < Zmed <Z the algorithm goes to level B.min m e d max~teagrtmge olvlB
B . S i m u l a t i o n r e s u l t s
To v a l i d a t e t h e m o d i f i e d a l g o r i t h m , s i m u l a t i o n s are
p e r f o r m e d on an X -r a y i m a g e o f a c i r c u i t b o a r d u s e d i n [ 2 ] a n da f i n g e r p r i n t p i c t u r e . F i g u r e 1 ( a ) i s t h e c o r r u p t e d c i r c u i t b o a r d
i m a g e w i t h t h e i m p u l s e n o i s e p r o b a b i l i t i e s o f 0 . 2 5 . H e r e t h en o i s e l e v e l i s h i g h e n o u g h t o o b s c u r e most o f t h e d e t a i l i n t h e
i m a g e . T h e i m a g e i s f i l t e r e d f i r s t l y u s i n g s t a n d a r d m e d i a n f i l t e r .
T h e r e s u l t i s s h o w n i n f i g u r e 1 ( b ) . A l t h o u g h n o i s e i s e f f e c t i v e l yr e m o v e d , t h e f i l t e r causes s i g n i f i c a n t l o s s o f d e t a i l i n t h e i m a g e .
F i g u r e l ( c ) s h o w s t h e r e s u l t o f u s i n g a d a p t i v e m e d i a n f i l t e r .
N o i s e i s m o s t l y r e m o v e d a n d i m a g e d e t a i l s are p r e s e r v e d .H o w e v e r , pepper n o i s e s t i l l can b e o b s e r v e d i n t h e b l a c k r e g i o n
o f t h e i m a g e , s u c h as t h e c o n n e c t o r s a t t h e l e f t - t o p o f t h e i m a g e .
F i g u r e l ( d ) s h o w s t h e r e s u l t o f t h e m o d i f i e d a d a p t i v e m e d i a n
f i l t e r . P e p p e r n o i s e i n t h e b l a c k r e g i o n o f t h e i m a g e i s r e m o v e d
e f f i c i e n t l y . I m p r o v e m e n t over t h e c l a s s i c a l a d a p t i v e median
f i l t e r i s q u i t e s i g n i f i c a n t . T h e s i m i l a r c o n c l u s i o n can b e d r a w n
f o r t h e f i n g e r p r i n t p i c t u r e .
T h e PSNR r e s u l t s are s h o w n i n T a b l e 1 .
F i g . 1 . C o m p a r i s o n o f t h e d i f f e r e n t m e t h o d s . ( a ) N o i s y image; ( b ) S t a n d a r d
m e d i a n f i l t e r ; ( c ) A d a p t i v e m e d i a n f i l t e r ; ( d ) M o d i f i e d a d a p t i v e m e d i a n f i l t e r .
T A B L E I
PSNR ( D B ) RESULTS FOR SEVERAL M E T H O D S
I V . C O N C L U S I O N
T h e c l a s s i c a l a d a p t i v e m e d i a n f i l t e r h a s some d e f i c i e n c i e s :
t h e f i l t e r e d i m a g e s r e m a i n t h e p o s i t i v e i m p u l s e n o i s e i n t h e
b l a c k b a c k g r o u n d a n d t h e n e g a t i v e i m p u l s e n o i s e i n t h e w h i t e
b a c k g r o u n d . To s o l v e t h e a b o v e q u e s t i o n s , a m o d i f i e d s c h e m e
i s p r o p o s e d . E x p e r i m e n t r e s u l t s s h o w s t h e p r o p o s e d s c h e m e
can i m p r o v e t h e f i l t e r i n g p e r f o r m a n c e s i g n i f i c a n t l y .
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I I
Authorized licensed use limited to: PSG College of Technology. Downloaded on January 3, 2010 at 00:05 from IEEE Xplore. Restrictions apply.
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a p p r o a c h f o r t h e r e m o v a l o f i m p u l s e n o i s e f r o m h i g h l y c o r r u p t e d i m a g e s ,
I E E E T r a n s . I m a g e P r o c e s s i n g , 5 , 1 0 1 2 ( 1 9 9 6 ) .Yanming Z h a o r e c e i v e d t h e P H . D . d e g r e e f r o m S c h o o l o f T e l e c o mm u n i ca t i o n
E n g i n e e r i n g i n B e i j i n g U n i v e r s i t y o f P o s t s a n d T e l e co m m u ni c a t io n s i n 2 0 0 5 .S h e i s now a n a s s i s t a n t p r o f e s s o r i n t h e I n f o r m a t i o n E n g i n e e r i n g S c h o o l ,C o m m u n i c a t i o n U n i v e r s i t y o f C h i n a , P . R . C h i n a . H e r m a i n r e s e a r c h i n t e r e s t sa r e i m a g e p r o c e s s i n g a n d v i d e o c o d i n g .
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