Image compression by self-organized Kohonen map

IEEE TRANSACTIONS ON NEURAL NETWORKS,VOL.9,NO.3,MAY 1998503
Image Compression by Self-Organized Kohonen Map
Christophe Amerijckx,Associate Member,IEEE,Michel Verleysen,Member,IEEE,
Philippe Thissen,Member,IEEE,and Jean-Didier Legat,Member,IEEE
Abstract—This paper presents a compression scheme for digital still images,by using the Kohonen’s neural network algorithm,not only for its vector quantization feature,but also for its topological property.This property allows an increase of about 80%for the compression pared to the JPEG standard,this compression scheme shows better performances (in terms of PSNR)for compression rates higher than 30.
Index Terms—Discrete cosine transforms,entropy coder,image processing,JPEG,self-organizing feature maps,variable length codes,vector quantization.I.I NTRODUCTION
I
N the context of image processing,compression schemes are aimed to reduce the transmission rate for still (or fixed images),while maintaining a good level of visual quality.One of the main common methods to compress images is to code them through vector quantization (VQ)techniques [1],[2].The principle of the VQ techniques is simple.At first,the image is splitted into square blocks
of 4or
8)o f v e c t o r s (c o d e w o r d s )i n t h i s s p a c e i s s e l e c t e d i n o r d e r t o a p p r o x i m a t e a s m u c h a s p o s s i b l e t h e d i s t r i b u t i o n o f t h e i n i t i a l v e c t o r s e x t r a c t e d f r o m t h e i m a g e ;i n o t h e r w o r d s ,m o r e c o d e w o r d s w i l l b e p l a c e d i n t h e r e g i o n o f t h e s p a c e w h e r e t h e r e a r e m o r e p o i n t s i n t h e i n i t i a l d i s t r i b u t i o n (i m a g e ),a n d v i c e -v e r s a .T h i r d ,e a c h v e c t o r f r o m t h e o r i g i n a l i m a g e i s r e p l a c e d b y i t s n e a r e s t c o d e w o r d (u s u a l l y a c c o r d i n g t o a s e c o n d -o r d e r d i s t a n c e m e a s u r e ).F i n a l l y ,i n a t r a n s m i s s i o n s c h e m e ,t h e i n d e x o f t h e c o d e w o r d i s t r a n s m i t t e d i n s t e a d o f t h e c o d e w o r d i t s e l f ;t h e c o m p r e s s i o n i s a c h i e v e d i f t h e n u m b e r o f b i t s u s e d t o t r a n s m i t t h i s i n d e x ()i s l e s s t h a n t h e n u m b e r o f i n i t i a l b i t s o f t h e b l o c k
(i s t h e r e s o l u t i o n o f e a c h p i x e l ).M a n y a u t h o r s u s e d t h e K o h o n e n ’s a l g o r i t h m [3]o r s e l f -o r g a n i z e d f e a t u r e m a p (K S O M )[4]t o a c h i e v e t h e v e c t o r q u a n t i z a t i o n p r o c e s s o f i m a g e c o m p r e s s i o n .K o h o n e n ’s a l g o -r i t h m i s a r e l i a b l e a n d e f fic i e n t w a y t o a c h i e v e V Q ,a n d h a s s h o w n t o b e u s u a l l y f a s t e r t h a n o t h e r a l g o r i t h m a n d t o a v o i d
t h e p r o b l e m o f “d e a d u n i t s ”t h a t c a n a r i s e f o r e x a m p l e w i t h
t h e L B G a l g o r i t h m [5].
K o h o n e n ’s a l g o r i t h m h a s h o w e v e r a n o t h e r i m p o r t a n t p r o p -e r t y b e s i d e s v e c t o r q u a n t i z a t i o n :i t r e a l i z e s a m a p p i n g b
e t w e e n M a n u s c r i p t r e c e i v e d N o v e m b e r 2,1996;r e v i s e d A u g u s t 10,1997a n d
J a n u a r y 7,1998.
C .A m e r i j c k x ,M .V e r l e y s e n ,a n d J .-
D .L e g a t a r e w
i t h U n i v e r s i t ´e c a t h o l i q u e d e L o u v a i n ,M i c r o e l e c t r o n i c s L a b o r a t o r y ,B -1348L o u v a i n -l a -N e u v e ,B e l -g i u m .
P .T h i s s e n i s w i t h V L S I T e c h n o l o g y ,S o p h i a A n t i p o l i s ,F r a n c e
.P u b l i s h e r I t e m I d e n t i fie r S 1045-9227(98)02770-2.a n i n p u t a n d a n o u t p u t s p a c e t h a t p r e s e r v e s t o p o l o w o r d s ,i f v e c t o r s a r e n e a r f r o m e a c h o t h e r i n t h e i t h e i r p r o j e c t i o n i n t h e o u t p u t s p a c e w i l l b e c l o s e I n t h e p r o p o s e d c o m p r e s s i o n s c h e m e ,w e w i l l u d i m e n s i o n a l K o h o n e n m a p c o r r e s p o n d i n g t o a g r i w o r d s (i n s t e a d o f a o n e -d i m e n s i o n a l t a b l e i n s t a n d
t h e p r o j e c t i o n o f a n i n i t i a l s p a c e i n c l u d i n g a l l v e f r o m b l o c k s o f t h e i n i t i a l i m a g e .T h e m a i n a s p e c t o f t h i s p a p e r i s t o u s e t h e t
p r e s e r v i n g p r o p e r t y o f K S O M .I n a s t a n d a r d i m a g e c a n m a k e t h e h y p o t h e s i s t h a t t w o c o n s e c u t i v e b l o
t h e h o r i z o n t a l o r v e r t i c a l d i r e c t i o n s ,w i l l b e s i m
c a s e s ,j u s t b e c a u s e u n i f o r m r e g i o n s i n t h e i m a g e a m u c h l a r g e r t h a n t h e s i z e o f t h e b l o c k s .A c c o r
d i n g o r g a n i z a t i o n p r o p
e r t y o
f K S O M ,t w o c o n s e c u t i v e b l o c k s w i l l b e c o d e d i n t o s i m i l a r c o d e w o r d s ;t h d i f f e r e n t i a l e n t r o p i c s c h e m e t o e n c o d e c o n s e c u t i v t h u s i m p r o v e t h e c o m p r e s s i o n r a t i o .O t h e r a u t h o r s a l r e a d y u s e d t h e t o p o l o
g y -p r e s e r v
o f K S O M ’s f o r d i f f e r e n t r e a s o n s .I n [6],t h i s p r o p
f o r p r o
g r e s s i v e t r a n s m i s s i o n o f t
h e
i m a g e .I n [7
f o r f u r t h e r d i f f e r e n t i a l c o d i n
g ,a s i n t
h
i s p a p e r ,b w i t h o u t d i s c r e t e c o s i n e t r a n s f o r m (D C T )t r a n s f o r a l e s s -p e r f o r m a n t z e r o t h -o r d e r p r e d i c t o r (i n s t e a d i n t h i s p a p e r ).I n [8],a n o r i g i n a l n e u r a l n e t w o r k m i n s t e a d o f a fir s t -o r d e r p r e d i c t o r ,b u t o n i m a g e s w t r a n s f o r m .F i n a l l y i n [9],t h e t o p o l o g y -p r e s e r v i n u s e d t o m i n i m i z e t h e e f f e c t o f t r a n s m i s s i o n e r r o c h a n n e l s .I n t h i s p a p e r ,w e p r e s e n t a c o m p r e s s i o n s c h e m e D C T t r a n s f o r m o f t h e o r i g i n a l i m a g e ,v e c t o r q u
b y K o h o n e n m a p ,d i f f e r e n t i a l
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n t r o p i c c o d i n g o f t h e d i f f e r e n c e s .S i m u l a t i o p r o v i d e d ,t o g e t h e r w i t h c o m p a r i s o n s w i t h s i m i l a r s c h e m e (D C T /V Q )w i t h o u t d i f f e r e n t i a l c o d i n g ,a s t a n d a r d J P E G a l g o r i t h m .I I .T H E G L O B A L
C O M P R E S S I O N S C H E M E T h e g l o b a l c o m p r e s s i o n s c h e m e f o r l o s s y c o m p d e s c r i b e d i n F i g .1.A f t e r a v e c t o r i z a t i o n (t r a n s f i m a g e b l o c k s i n t o v e c t o r s ),a
D C T [10]a n d a fil t e r fir s t r e d u c e t h e q u a n t i t y o f i n f o r m a t i o n b y k
t h e l o w -f r e q u e n c y c o e f fic i e n t s .T h e n ,t h e v e c t o r i s p e r f o r m e d ,w i t h a n o t h e r l o s s o f i n f o r m a t i o n .i n d e x e s o f t h e c o d e w o r d s f o u n d b y t h e v e c t o r a r e t r a n s f o r m e d b y a d i f f e r e n t i a l c o d i n g ,a n d t h e c o m p r e s s e d b y a n e n t r o p i c c o d e r [11];t h e s e t w o l
1045–9227/98$10.00©1998I E E E
504IEEE TRANSACTIONS ON NEURAL NETWORKS,VOL.9,NO.3,MAY
1998
Fig.1.Global compression scheme for lossy compression.
not introduce any loss in the information.The decompression scheme performs the same operations in the opposite way.A.Image Preprocessing
The image is first decomposed into blocks
(48pixels as usual);the DCT transform is applied on each block,in order to eliminate a part of the information contained in the image,that is,high frequencies not visible to human eyes.The DCT transform of
a pixels block is again
a block.However,in the transformed block,low-frequency coefficients are grouped in the upper-left corner,while high-frequency ones are grouped in the lower-right corner.The low-pass filter on the transformed block will thus keep only
the
-neighborhoods on
the grid,which include all neurons whose distance (on the grid)from one (central)neuron is less or equal
to
codewords is represented by its
weight is the dimension of the space
(
in the compression scheme).For each presentation of an input
vector
of the codeword nearest
from
-neighborhood
of neuron
,according to the
relation
(2)
where
-neighborhood of neuron
the learning
factor.
and
and
and
and ,will be,respectively,in the same
direction
(
and
and
and
AMERIJCKX et al.:IMAGE COMPRESSION BY SELF-ORGANIZED KOHONEN MAP505
Fig.4.Coding the difference between indexes.
Fig.5.Decoding the difference between indexes.
and
to
,the direction of the minimal difference between them
can be computed with the already existing blocks,and not
being transmitted.
The coding of a block is summarized in Fig.4.The best
direction isfirst computed according to the above scheme,and
block is selected.The new block
to decode,and is converted again in
an image block by the look-up table created with Kohonen’s
algorithm.
It must be mentioned that the scheme proposed in Fig.3is
only valid when the twofirst lines have already been encoded.
For the twofirst lines,a classical differential scheme is used.
D.Entropic Coder:UVLC
Run length coding(RLC)and variable length coding(VLC)
are widely used techniques for lossless data compression.
We used an entropy coding system combining these two
techniques in order to achieve a higher compression ratio.This
system is similar to the one described in[11].
III.S IMULATIONS AND R ESULTS
For the simulation of the whole compression process(see
Fig.1),we used4
,where each
bit of the image is coded on eight bits,and is the number
506IEEE TRANSACTIONS ON NEURAL NETWORKS,VOL.9,NO.3,MAY1998
parison of PSNR for the proposed lossy compression scheme
and the JPEG algorithm.
of bits necessary to code all codewords(seven for
AMERIJCKX et al.:IMAGE COMPRESSION BY SELF-ORGANIZED KOHONEN MAP 507
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[10]N.Ahmed,T.Natarajan,and K.R.Rao,“Discrete cosine transform,”
IEEE put.,vol.C-23,pp.90–93,Jan.1974.
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ACM ,vol.34,no.4,pp.32–34,Apr.
1991.
Christophe Amerijckx (S’95–A’95)received the bachelor’s degree in electrical engineering from the Catholic University of Louvain,Louvain-la-Neuve,Belgium .
He is working under the frame of the European Community’s ESPRIT Mivip project in rehabilita-tion of vision for blind people and working toward the Ph.D.degree in this field in the Microelectronics Laboratory at the Catholic University of Louvain.His research activities and interests include image processing,RISC architectures,FPGA architectures,
and VLSI
implementations.
Michel Verleysen (S’87–M’92)received the bach-elor’s degree in engineering and the Ph.D.degree in microelectronics from the Catholic University in Louvain,Louvain-la-Neuve,Belgium,in 1987and 1992,respectively.
He is a Research Associate of the Belgian Na-tional Fund for Scientific Research,and Invited Lecturer at the Catholic University in Louvain.He was an Invited Professor at the usanne in 1992.He has been an author and coauthor of more than 50publications in the field,and wrote a book
in the “Que Sais-je?”series (in French).
Dr.Verleysen organizes the European Symposium on Artificial Neural Networks,and is the Editor-in-Chief of Neural Processing Letters .He is a member of the International Neural Network
Society.
Philippe Thissen (S’90–M’92)received the bach-elor’s degree in electrical engineering from the Universite catholique de Louvain,Belgium,in 1992and the Ph.D.degree in microelectronics from the same university in 1996.His doctoral research con-cerned digital and mixed signal implementations of neural networks for classification purposes.
Since 1996,he joined VLSI Technology,Sophia Antipolis,France,where he is involved in analog and mixed-signal designs for wireless products in submicron
technology.
Jean-Didier Legat (S’79–M’81)was born in Brus-sels,Belgium,on April 15,1957.He received the bachelor’s and master’s degrees in engineering from the Universit´e Catholique de Louvain,Louvain-la-Neuve,Belgium in 1981.He received the Ph.D.degree in February 1987.
From 1981to September 1984,he was granted a Belgian fellowship to undertake research in the field of document processing at the Microelectronics laboratory at the Universit´e Catholique de Louvain.At the end of 1984,he joined the Belgian Company
Anfima with the proposal of creating a new company which would design and commercialize integrated devices for image processing.In April 1987a company called Image Recognition Integrated Systems (I.R.I.S.)was formed.He was cofounder of I.R.I.S.and was Vice-President.In October 1990,he came back to the Microelectronics Laboratory of Louvain-la-Neuve.He is presently a full Professor.His current interests are computer architecture,parallel and distributed systems,and design of embedded integrated circuits in the areas of artificial neural networks,digital signal processing,computer vision,and pattern recognition.。