International Journal of Engineering Trends and Technology (IJETT) – Volume 29 Number 4 - November 2015
A review on fuzzy image compression
Linsa v u#1, Dr.T.M Amarunnishad*2
#
M.Tech T.K.M College of Engineering
Kollam, Kerala, India
Abstract — Image compression is a technique to
reduce the data of representation of images. Different
methods are available for compression of images.
Digital image compression used in number of
applications, like satellite communication, huge
storage and transformation. The good compression
method should be fast and memory efficient. It also
reduces storage and transmission space and reduces
transmission bandwidth. The fuzzy based image
compression consists three steps .fuzzification; modify
the pixel value and defuzzification. In compression the
modification means reduce the number of bits to
represent the pixel or reduce the number of pixels. In
this study discuss various fuzzy image compression
techniques that reduce the size of image without affect
the visual quality of image.
Keywords — fuzzy image processing ; fuzzy
image compression;fuzzy relational equations; fuzzy
transform; vector quantization,
.
I. INTRODUCTION
Digital image compression are useful in many field
such as satellite images, medical images ,huge data
transfer and sharing ,storage etc .Hence we need
efficient very fast and memory efficient(highly
compressed) image compression. Image compression
reduces the data of representation of images. it reduces
the irrelevant data in the image .Image compression
reduces [1]either
 inter pixel redundancy
 psycho visual redundancy
 coding redundancy
Basically image compression is classified into lossy
and lossless [1]. Lossy image compression cannot
reconstruct the exact copy of the original image. This
reconstructs the image with loss of some information
compare to the original one. so lossy image
compression is suitable in exact information is not
needed applications. Important lossy image
compression methods are transform coding, vector
quantization ,block truncation coding etc. compression
methods
are
transform
coding,
vector
quantization ,block truncation coding etc.
But in lossless image compression that produce or
decode the exact copy of the original image. That
cannot loss the information of the input image.
Lossless image compression is But in lossless image
compression that produce or decode the exact copy of
ISSN: 2231-5381
the original image. That cannot loss the information of
the input image. Lossless image compression is useful
in
medical
image
processing
like
applications .example of lossless image compression
methods are Huffman coding, arithmetic coding, run
length coding etc.
II. COMPONENTS OF IMAGE COMPRESSION
The componets of image compression are encoder
and decoder.The basic block diagram of compression
shows in Fig.1.Fig.2 shows the reverse of compression
(reconstuction) processs.The encode perform the
compression operations and decoder perform the
decompression process.
Input
image
Compressi
on
Compresse
d image
Fig.1. Block diagram of compression
Compress
ed image
Decompr
ession
Reconstruct
ed image
Fig.2. Block diagram of decompression
III.FUZZY IMAGE COMPRESSION
Fuzzy image processing means the fuzzy logic is
applied to the image processing for better processing.
it is a collection of different fuzzy techniques applied
to the image processing. All the approaches
understand, represent and process the images; the
features are the fuzzy sets. The representation and
processing depends the image processing applications.
Basically fuzzy image processing has 3
steps .Fuzzification, modify the membership function
and defuzzification. Fig.3 shows the basic block
diagram of fuzzy image processing. Fuzzification is
the change the pixel values for processing in fuzzy
logic. The main power of fuzzy image processing
depends the second step, modify the membership
function. The modification is the actual process in
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International Journal of Engineering Trends and Technology (IJETT) – Volume 29 Number 4 - November 2015
image processing. Last one is defuzzification. It
converts into the original form.
Image
Intermediate
level
Segmentation
Representation
Description
Low level
Preprocessing
Geometrical
fuzziness
Grayness
ambiguity
compression we try to reduce the redundancy like
inter pixel, psycho visual, coding redundancy.
We reduce the number pixel in the second step or
reduce number bits to represent the pixel in second
step.
Fuzzificati
on
Modificat
ion
Defuzzifi
cation
Fig.3. Fuzzy image processing
IV. MEASURES
Uncertainty
Fig.4. block diagram of uncertainty
There are so many reasons why we should use fuzzy
image processing .the important reasons are
 It is a powerful tool for knowledge
representation and processing.

It manages
efficiently.
uncertainty
and
vagueness
Fuzzy logic and fuzzy set theory provides a better
method for image processing using if the rules. Other
one is many difficulties occurs due to data /task/results
are uncertain.
Basically we can distinguish three kinds of
imperfections in image processing.
 grayness
 geometrical
 vagueness
High level
Analysis
Interpretation
Recognition
Result
 compression ratio
 time of processing
 memory need
Compression ratio indicates how much compress
particular image. For example if the compression rate
0.111 indicates the compressed image is 0.111 of the
original image. The compression ratio is calculated by
compressed image size/original image size.
Computation time is the time required to transmit
the original image into the coded image .that depends
the different techniques. Objective quality of the
image coding method is measured by following
parametric.
Memory requirement is the storage space need to
store the image.
Normally used measures for measuring objective
quality of image in image compression are
 MSE
 PEN
 PSNR
MSE(mean square error) is the cumulative squared
error between the reconstructed(decoded) image and
the original image .if the MSE less that indicate the
good compression result .Equation(1) is the standard
equation for calculate the MSE.
Vague
knowledge
Fig.4 represents the block diagram of uncertainty in
fuzzy image processing
In fuzzy image compression, fuzzified by using
any Fuzzification method that is applicable all fuzzy
image processing. Only the difference in the main step
modification of the membership functions. In fuzzy
ISSN: 2231-5381
All title and author details must be in single-column
format and must be centered. Different performance
metrics are selected for measuring the objective and
subjective quality of the coding/decoding system. The
suitable method is selected based on
PSNR (peak signal to noise ratio) is the ratio of
signal to noise .it is calculated based on MSE.PSNR is
high that indicate the good compression method.
Equation for determine the PSNR is (2).
PEN (penalty function) is the penalty function.
Equation (3) specifies the equation for PEN. it is
useful in color image processing.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 29 Number 4 - November 2015
N
i 1
 cR,G ,B  
MSE 
M
j 1
P (i, j)  P
E
c NM
c
(i, j)
frame (predictive frame).I frame is the original frame
of motion .P- frame has slight difference from the Iframe. Similarity between P-frame and I-frame is
calculated by equation(6) .if it has greater than a
particular value the two frames are different-frame is
compressed higher rate than the I-frame.the frame are
compressed same like image compression .

2
3MN
(1)

 iN1  Mj1  cR,G ,B Pc (i, j )  PcENM (i, j)
PEN 

2
3MN
SimL ( F , G ) 
1 m n
  1  maxFij , Gij  min Fij , Gij 
( m  n) i 1 j 1
(2)
(6)
 max x , y I ( x, y ) 
PSNR  10 * log10 

RMSE


2
(3)
V. DIFFERENT FUZZY IMAGE
COMPRESSION TECHNIQUES
A. Fuzzy relation equation for compression
In fuzzy relation equations based compression
the Fuzzification of input pixel values same as
fuzzy transform based compression. The input
(source) image pixels are fuzzified by Original
pixel value divided by 255, 255 is the maximum
gray level value the fuzzified values are
compressed by Equations of fuzzy relation (4).
M N

C pq    A pi tBqj   t S ij
i 1 j 1

(4)
The table 1 shows the image compression by fuzzy
relational equations. The compressed image are
reconstructed by Equation of fuzzy relation (5).
K
H

Dij    A pi tB qj tG pq
p 1 q 1

(5)
Basically the Images are compressed by fuzzy
relational equation. From the equation of compression
we can see different type fuzzy relational equation for
compression is possible depends the norms. In [3]
fuzzy relational equation is selected for compression of
gray scale images. After that this method is extend to
color images. In color images the pixels are
transformed into the YUV space (RGB to YUV), using
equations .then apply the fuzzy relation equation in
each domain separately as same as the in [5].
In [22] fuzzy relational equations for coding and
decoding process of images and videos. The gray scale
images are coded by fuzzy relation equations like in
[12].Using Gödel, goguen ,lukasiewicz t-norm. The
case RGB images each component are separated then
apply the fuzzy relation equation like gray images.
Then combine the components. In video compression
frames are separated as I-frame (intra frame) and P-
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In [23] find the efficient decomposition method
of fuzzy relation equations .one optimization method
improve the cost function. Another one improves the
decomposition process. The PSNR value of this
method (fuzzy relation equation) is compare with the
JPEG and MPEG.
B. Fuzzy transform based compression
Fuzzy transform based compression is better than
some other existing methods. It is lossy image
compression method. so the reconstructed image is not
a exact copy of the original image.
In fuzzy transform based compression fuzzy
transform of two variables is selected for
compression .in this method the input values are
image pixels or intensity values. The input pixel
values are fuzzified in the first step .In[1,2]the pixels
are divided by 255(maximum gray level value. the
fuzzified value )for Fuzzification.
Equation (7) denotes the fuzzy transform of two
variables. The two input parameter are membership
functions (normally use standard member ship
functions sinusoidal, triangular membership functions)
that represent in (8),(9),(10) .All[233] this techniques
the selected membership functions are (8).The two
variable fuzzy transform is applied in the output of
Fuzzification .then get the compressed representation.
Ckl 
 Mj1  iN1 R(i, j ) Ak (i) B l ( j )
 Mj1  iN1 Ak (i) B l ( j )
(7)


0.5(1  cos ( x  x1 )) ifx  x1 , x2 
A1 ( x)  
h

0 otherwise
(8)
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International Journal of Engineering Trends and Technology (IJETT) – Volume 29 Number 4 - November 2015
equation(6).In[12]segmentation process is used before
compression. FGFCM (fast generalized fuzzy c-mean)
clustering is used. The compressed by fuzzy transform.


0.5(1  cos ( x  xk )) ifx  xk 1 , xk 1 
Ak ( x)  
h
C. Fuzzy vector quantization for image compression

0 otherwise
(9)


0.5(1  cos ( x  x n )) ifx  x n1 , x n 
An ( x)  
h

0 otherwise
(10)
The reduction of color images by fuzzy
transform [7] .In image reduction the reduced
(compressed) images via image compression
techniques compare with the original image .but in
image compression the reconstructed (decompressed)
image is compare with the original image. The image
are compressed by f-transform are magnified for
comparing with the source or initial image.
The compressed images are reconstructed by using
inverse discrete F-transform for comparing with the
original one. After comparison the efficiency
(subjective and objective) of the techniques are
determined. Equation (11) is the reconstruction
equation in fuzzy transform.
n
m
Dnm (i, j )    C kl Ak (i ) Bl ( j )
k 1
(11)
l 1
The discrete F-transform is selected for compression
in[9] and inverse fuzzy transform is selected for
compression in[10].it is similar to the fuzzy transform
based compression only the slight variation in
equation. The objective measures are comparing with
the JPEG method.
Vector quantization is a type of lossy image
compression. Normally it includes four steps. Vector
formation, training vector selection, codebook
generation and quantization. The input image pixels
are divided and generate the vectors. From the set of
vectors some vectors are selected for training purpose.
Codebooks of codeword’s are generated based on
standard clustering algorithms. Then the input vectors
are selected and corresponding codeword selected
form the codebook. Likewise reduce the total storage
and transmission space.
In [21] generate codebook using fuzzy c-mean
clustering operates image histogram, is used to
generate good codebook. In [16] improve the fuzzy cmean clustering. It reduces certain problems. it change
the objective function of fuzzy c-mean clustering.
Then change the overall training procedure. In [18]
generate fast vector quantization procedures. For that
reduce the number of codebooks that are affected by
specific pattern. Also reduce the number of patterns in
the design process. Sequential implementation above
two method reduce the computational cost.
In [17] combine the fuzzy clustering with
competitive agglomeration and novel codebook
migration strategy. It reduce the when using the fuzzy
clustering method. In [19] use FPSO (fuzzy particle
swarm optimization, itself extract the near optimum
codebook of vector quantization.
D. Other methods
Wavelet transform coding is applicable for image
compression. In [23] embedded zero wavelets coding
is selected for compression. Fuzzy clustering applied
In [8] discuss the theory and application of fuzzy to quantizing the wavelet coefficients after coded by
transform. It includes fuzzy transform of two variables, wavelet transform.
one variable, discrete and continues fuzzy
In [22] region oriented compression of color images
transforms .In [14] fragile water marking tamper
using
fuzzy inference and fast merging. Splitting
detection with images compressed by fuzzy transform.
based
on watershed transform and merging using
The image are compressed by fuzzy transform then
fuzzy color preserving rule based system and novel
the compressed image used in watermarking process.
one dimensional graph structure.
In [13] color image compression with fuzzy
transform in YUV space. The RGB
images are
converted into the YUV space similar to the previous
method. Then the converted image compressed. In[15]
fuzzy transform for compression and decompression
of color video .separate I-frame and P-frame and
compress each frame using the fuzzy transform Pframe is more compressed compare to I-frame.the
frames
are
separated
by
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VI. CONCLUSIONS
Here we discuss about various fuzzy image
compression techniques. Fuzzy relational equation
based, fuzzy transform based and vector quantization
based. Fuzzy transform based compression provides
better results than fuzzy relational equation based
compression. in image compression we focus the
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International Journal of Engineering Trends and Technology (IJETT) – Volume 29 Number 4 - November 2015
higher compression rate with high quality of the
output image.
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