Digital image compression techniques

IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
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Volume: 03 Issue: 10 | Oct-2014, Available @ http://www.ijret.org 285
DIGITAL IMAGE COMPRESSION TECHNIQUES
Gomathi.K.V1
, Lotus.R2
1
Centre for Information Technology and Engineering, Manonmaniam Sundaranar University, Tirunelveli, Tamil
Nadu, India
2
Centre for Information Technology and Engineering, Manonmaniam Sundaranar University, Tirunelveli, Tamil
Nadu, India
Abstract
In today’s world of electronic revolution, digital images play an important role in consumer electronics. The need for storing
images grows day to day. Compression of digital images plays an important role in storing the images. Due to compression the
memory occupied by the images gets reduced and so that we can store more images in the available memory space. Also
compression results in encoding of images which itself offer a security on transaction. This paper deals with a clear note on
various aspects regarding compression and various compression techniques used and their implementation.
Keywords: digital image, compression, data redundancy, compression techniques.
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1. INTRODUCTION
Image: An image is the result of a visual signal of any
object captured by optical devices such as human eyes,
camera lenses etc., Image is the two dimensional
representation of the object.
Digital image: Image when stored in electronic devices
such as computers, it is known as the digital image. Thus a
digital image is the numeric representation of an image.
Digital images are of two types – raster and vector. Raster
images refers to the images built using a finite set of digital
values, called picture elements or pixels. Pixel is the
smallest element in an image. The value that is equivalent to
the colour of that specific pixel is stored in the place of the
pixel. Images stored in electronic devices fall under this
category. Vector images refer to the images that are resulted
from mathematical calculations. Vector refers to the
elements that have both magnitude and direction (Raster
images have only magnitude). In electronic devices, vector
type is used to refer texts stored as images or to store images
that require more accuracy even in zoomed level. Vectors
have both magnitude and direction. So the images are clear
even when zoomed. Usually the term digital image refers to
raster images.
Need for Compression: The need for storage of digital
information increases rapidly with the growth of internet
technology. Images are widely used in applications like
medical, army and satellite images. Everyday an enormous
amount of information is stored, processed and transmitted
digitally [4]. The unprocessed or raw digital images occupy
more space. This necessitates compression of data. Image
compression is the process of representing the required
information with the possible minimal amount of data.
Hence it is useful for reducing the amount of memory space
need for the file. Thus for the growing requirements of
image storage and digital technology, storing the
compressed images allows us to store more images in the
given disk space. Also transmission rate of images gets
increased due to compression. This paper deals with the
process of compression in the second part, Compression
types in the Third part, Compression techniques in the
Fourth part and gets concluded in the fifth part.
2. COMPRESSION PROCESS
Compression
Compression is achieved by removing one or more of the
three basic data redundancies. They are
 Coding Redundancy
 Interpixel Redundancy
 Psychovisual Redundancy.
Data redundancy refers to the data that are in the state of
being not or no longer needed.
2.1 Coding Redundancy
A code is a set of symbols that represents some information
in the image. As a method of compression, codes occurring
many times are represented with lesser bits and other codes
are represented with more number of bits. In that, coding
redundancy is the form of data redundancy that is present
when less than optimal code words are used to represent any
information[1] and so this redundancy deals with the data
representation of the image. Let us consider that we have a
gray image which is represented as R then the average
number of bits or optimal value of codes required to
represent each pixel is given by
Where represents the kth gray level in the image.
is the number of occurrence of , - probability of
to occur and N is the total number of gray levels in the
image. Coding redundancy is removed using Huffman
coding.

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2.2 Interpixel Redundancy:
Interpixel redundancy is the form of data redundancy that
is related to interpixel correlation within an image [11].
While storing an image, it is not necessary to store all the
details of pixels in the image. This is allowed due to the
reason that the value of any pixel can be calculated from the
values of the neighboring pixels. This is known as interpixel
dependency. Interpixel correlation is the difference between
the information content and the information capacity of the
image. In an image, consequent pixels may contain same
colour or relative shades of same colfour. Instead storing the
full details of all the pixels the values of correlated pixels
may be calculated from the details of a single pixel for
which full details are stored. Thus this data redundancy
works on image representation.
Let us consider any two pixels which are represented as
functions f(r) and g(r) respectively. The formula used to find
the correlation between those two pixels is given by the
convolution theorem,
Depending upon the value of the equation (B) we can say
that the two pixels are correlated or not. A Threshold T is
fixed and if the value of (B) is greater than T then the pixels
are not correlated else the pixels are correlated. If the pixels
are auto-correlated then we have . The value of
correlated pixels can be calculated based on two operations
namely repetition and prediction. Repetition is used for
auto-correlated pixels and prediction is used for other
correlated pixels. This means the relatively or equally
valued pixels are calculated. This method can be applied for
both colour and grayscale images. Interpixel redundancy is
of two types – spatial and Interframe.
Spatial Redundancy:Spatial redundancy refers to
redundancy in still images. Consider any pixel, A having
coordinates (x,y), then Value(x,y) always depends on (x’,y’)
and the Value(x’,y’), for all (x’,y’) belongs to the
neighbourhood of (x,y).
Interframe redundancy: Interframe redundancy refers to
the redundancy present in videos. Consider the set of frames
(x,y,ti), for all i=0,1,2,… then Value(x,y,ti) is related to each
other.
Interpixel redundancy is removed using compression
techniques like Constant area coding, Run length encoding.
2.3 Psychovisual Redundancy:
Psychovisual redundancy is the data redundancy that works
with respect to image content. The psychovisual redundancy
refers to the information that is not noticed or processed by
the human eyes. This is because certain information has
more importance for Human Visual System(HVS) than
others based upon the fact that Human eye has the effect of
recognizing only low frequencies and neglecting high
frequencies. Thus its function as a low pass filter is used by
compression algorithms, to reduce the probably high
frequency signal.
By removing the psychovisually redundant information, the
compression achieved is lossy but the end user who is a
human being, cannot find the difference.
To find the psychovisually redundant information, a
discrimination threshold ( ) is found for all the pixels and
this value is added to the initial value of the pixel . After
that, the pixel having smallest value is the psychovisually
redundant information.
Discrimination threshold is calculated using the Weber’s
Law
where Kw is a constant known as the Weber’s fraction. i.e
the value of always depends upon the .
The equation (C) may be rewritten as
which is similar to the equation of a straight line
with Kw as the slope and b value as 0. Thus we can see all
the values of lies in a straight line when plotted using a
graph. Lossy compression algorithms like JPEG
compression works to remove this type of redundancy.
3. COMPRESSION TYPES
Compression process always results in encoding of the
input. Then to retrieve the original image decompression is
used. Based on whether the original image can be retrieved
from the compressed file, the types of compression are
1. Lossless compression
2. Lossy compression
3.1 Lossless Compression Technique:
In lossless compression technique, the original image is
perfectly retrieved from the compressed image. This is also
known as noiseless coding. The lossless compression
techniques follow the entropy encoding schemes. In entropy
encoding, the nature of the input data is analyzed and the
encoding or further process is performed based on it.
3.1.1 Basic Steps in Lossless Compression
Technique:
Lossless compression is done in following steps:
1. Analysis and grouping of data.
2. Encoding.

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Fig-1: Lossless compression process
Analysis and Grouping of data:
The input data is analyzed and grouped together based on
the compression technique involved.
Encoding:
The compression technique is applied in this step to the
previously grouped or analyzed data.
3.2 Lossy Compression Technique
In lossy compression technique the original images are not
exactly reconstructed after decompression. But the output
produced will be reasonably close to the original image.
Only data that is considered trivial is deleted. The remaining
data will be sufficient to represent the required information.
Also in lossy compression schemes there are more
possibilities for higher compression ratios. The lossy
compression techniques follow source encoding schemes. In
source encoding, the nature of the input data is not needed to
be analyzed.
3.2.1 Basic Steps in Lossy Compression:
Any lossy compression process is done in three steps:
1. Matrix Transformation
2. Quantization
3. Encoding
Fig-2: Lossy compression process
Matrix transformation: Matrix transformation is
performed for the transformation of input data to the
required approach. Algorithms like DCT is used in this step.
The output of this algorithm is lossless when compared with
its input.
Quantization: Quantization is the rounding – off process.
Quantization is a step that has its results as lossy when
compared with its input. Quantization process is
irreversible. So it is not present in decompression.
Encoding: This step encodes the quantized input to be
suitable to store. The output of this step is compressed when
compared with its input. Encoding is the key step in any
compression process. Other steps are preprocesses to
encoding.
4. COMPRESSION TECHNIQUES
There are a large number of encoding techniques separately
for lossy and lossless compressions, in which, the following
are most important and used in many compression
algorithms
Fig-3: Lossless and Lossy compression techniques
4.1 Lossless Compression Techniques
4.1.1 Run Length Encoding
Run Length Encoding (RLE) is an entropy encoding
compression technique that works on interpixel redundancy.
This compression proceeds by first, finding the runs of data
in the image. Runs of data refer to sequences in which same
value occurs in many consecutive elements [16]. When such
runs of data are identified, they are stored as a set of two
values – one value being the original value that composes
the run and the number of times the value is repeated. This
compression algorithm is suitable for line drawings, logos
and small animation files. For example consider the
following example of a binary image of ‘I’ in black, with a
white background. This is a stored in the memory as zeros
and ones. 0 for white and 1 for black.

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000000 {0,6}
011110 {0,1},{1,4},{0,1}
001100 {0,2},{1,2},{0,2}
001100 {0,2},{1,2},{0,2}
001100 {0,2},{1,2},{0,2}
011110 {0,1},{1,4},{0,1}
000000 {0,6}
Total number of symbols in Original Image: 42
Total number of symbols in Compressed Image: 34
But this encoding scheme will not be optimal for the images
without more runs.
4.1.2 Huffman Encoding
This is an entropy encoding technique that works on coding
redundancy. This data compression algorithm encodes the
data based on their probability of occurrence in the image.
The elements of the image that is, the pixels are considered
as symbols. All the images that contain the repetition of any
particular value, does not contain it as runs. For the
compression of those images, Huffman Coding is suitable
rather than Run Length Encoding. For symbols that occur
more frequently, smaller number of bits are assigned and
others are assigned with relatively larger number of bits.
For example, in a text file we consider five symbols:
A,E,I,O,U with their probability of occurrence and number
of bits allotted for each of them:
Table 1: Bit allocation for various symbols
Symbols Frequency of
occurrence
Number of
bits allotted
to encode
A 12 6
E 30 2
I 6 7
O 17 5
U 22 3
4.1.3 LZW Coding:
This entropy encoding technique works in the way that,
various patterns in the image are noted in a dictionary and
then the original image is encoded by linking the pattern in
the dictionary. Once a pattern is created, whenever any
pattern is encountered, the algorithm checks for whether that
pattern is present already in the dictionary. If yes, then a link
to that pattern in the dictionary is given. If no then that
pattern is included in the dictionary and then it is linked in
the original file. Hence this algorithm is known as
“dictionary based compression algorithm”. This encoding
scheme is optimal for images having a large number of
repeated patterns and not suitable for images having less
number of repeated patterns since the dictionary occupies a
large amount of memory space which in turn makes the file
bigger.
For example Consider the occurrence of patterns “en, op,
ng, co, tr, to, di” , in the text “entzropy encoding”
Table 2: Dictionary of patterns
1 2 3 4 5 6 7
en Op Ng Co Tr to di
The encoded text is: “152y 1473”. The size of a pattern is
taken as two. While grouping the texts, when a single
element resides unable to be grouped, then that element is
written as it is.
4.1.4 Area Coding
Area coding is an entropy encoding scheme which works on
binary images. This works in the way that the whole image
is divided into some blocks of same size so the resulting
block may be of three types – blocks having only white
pixels, blocks having only black pixels and blocks having
both black and white pixels. Then the block that occurs
frequently, is assigned with a 1-bit code word and the others
are assigned with 2-bit code words. Thus by replacing
blocks with 1-bit or 2-bit code words the file size gets
reduced and thus the compression is achieved.
4.2 Lossy Compression Techniques
4.2.1 Transformation Coding
This source encoding scheme works in such a way that, the
pixels in the original image is transformed into frequency
domain coefficients. These frequency domain coefficients
are known as transform coefficients. These coefficients have
certain useful properties. For example: it has the energy
compaction property due to which maximum amount of
energy in the original data gets concentrated in few of the
transform coefficients. These coefficients alone are selected,
the remaining are deleted to achieve compression. To the
selected coefficients, further processing is applied.DCT
coding has been the most common approach to perform
transform coding. It is also adopted in the JPEG image
compression standard.
4.2.2 Vector Quantization
This source encoding technique is otherwise known as block
quantization or pattern matching quantization[16]. The input
image which contains various amplitude levels is divided
into various blocks. The amplitude levels present in the
input are in the form of vectors since they have both
magnitude and direction. Consider an i-dimensional vector
. It is matched to a of j-dimensional vectors
with j < i . Vector space y contains the
quantized values of the vector space x. In quantization
phase, the vectors are quantized in whole as a block instead
of quantizing each sample. Thus this has the density
matching property due to which some errors occur and these
errors are inversely proportional to the density of the blocks.
The quantized values of the vector space are stored as code
words in a codebook. Only the index of the codeword in the
codebook is used and thus compression is achieved through
this also.

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4.2.4 Fractal Coding
This source encoding technique is useful in encoding
bitmaps. Fractal coding works on the principle that real
world input data contains many fractals. The similar patterns
in the images getting repeated itself are known as fractals.
Mapping of fractals does not require exact matches but is
based on approximate matches. Thus replacing fractals
occupy less memory space and due to approximate matching
of fractals the compression achieved is lossy. This gives a
good quality of compression even in higher compression
ratios when compared with other lossy compression
techniques because other techniques aim in discarding the
redundant data while fractal encoding does not aim in
discarding data. Fractal coding is an asymmetric technique
which needs more time for compression then decompression
because the process of compression needs to find the various
fractals in the image using millions of iterations and the
process of decompression simply needs to translate back the
fractals into bitmaps. The parameters that affect the
compression time and the output file size are resolution of
input image, compression ratio, quality of output image.
Fractal image representation is described mathematically as
an Iterated Function System(IFS). Let us consider a binary
image as a subset of . Now we want to find the IFS of
the image. IFS can be described as a set of mappings
{f1,f2,…,fN} such that . The IFS
defines a 2D set S as a fixed point of the H operator. H
operator stands for Hutchinson operator
S is the unique set satisfying H(S) = S. This shows that
.So it is clear that IFS is
the fractal representation of S. Set S can be recovered using
Fixed point iteration (FPI). FPI says that for any nonempty
initial set , the iteration = gives the value of
S. In case of grayscale images, same steps are followed but
the image R is considered as the subset of .
4.2.4 Block Truncation Coding:
In this source encoding technique, image is divided into non
overlapping blocks of pixels. Threshold value is determined
for every block. Here the threshold value is the mean of the
values in the block. It is denoted as
is the gray value of the pixels, N is the total number of
pixels in the block.
The values greater than are replaced by 1, the values less
than are replaced by 0 and the pixels having same value as
are replaced by either 0 or 1 based on the requirement of
the compression algorithm implementing this. Now we have
partial output. We have the image which is separated as
segments. Each segment now contains zeros and ones.
Reconstruction value of these blocks is found out.
Reconstruction is made using two values, k and l
And
Where q is the number of pixels having their value as one
and is the standard deviation, computed using the formula,
4.2.5 Subband Coding
In this source encoding technique, the input frequency band
is divided into different sub-bands using digital filter bank.
Consider an input . Then it is
separated into and Ry
Where
for all 2 . We have and
n is the number of frequency bands
Again can be recovered using the formula
This digital filtration is based on the separation of low and
high frequencies. Thus these filters act as the low pass and
high pass filters. For further separation, each of the sub-
bands is applied with low pass and high pass filters. This
compression technique works to remove the psychovisually
redundant information and hence some of the high
frequency data is removed. Then each of the sub-bands is
quantized separately. As the final step, the encoding of the
bands is performed. The encoding technique that is suitable
for each of the sub-bands is applied without being
interrupted by others.
5. CONCLUSION
Thus from this study on digital image compression, we are
able to get an idea of various types of redundancies that
must be handled while compressing an image, various
compression techniques followed and their approach to
compress an image. Each technique follows its own way of
compression and so they have specific application area. The
selection of compression type plays an important role in the
success of any image based application.

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Digital image compression techniques

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