Lossless Grey-scale Image Compression Using Source Symbols Reduction and Huffman Coding

C. Saravanan & R. Ponalagusamy
International Journal of Image Processing (IJIP), Volume (3) : Issue (5) 246
Lossless Grey-scale Image Compression using Source
Symbols Reduction and Huffman Coding
C. SARAVANAN cs@cc.nitdgp.ac.in
Assistant Professor, Computer Centre, National Institute of Technology,
Durgapur,WestBengal, India, Pin – 713209.
R. PONALAGUSAMY rpalagu@nitt.edu
Professor, Department of Mathematics, National Institute of Technology,
Tiruchirappalli, Tamilnadu, India, Pin – 620015.
Abstract
Usage of Image has been increasing and used in many applications. Image
compression plays vital role in saving storage space and saving time while
sending images over network. A new compression technique proposed to
achieve more compression ratio by reducing number of source symbols. The
source symbols are reduced by applying source symbols reduction and
further the Huffman coding is applied to achieve compression. The source
symbols reduction technique reduces the number of source symbols by
combining together to form a new symbol. Therefore, the number of Huffman
code to be generated also reduced. The Huffman code symbols reduction
achieves better compression ratio. The experiment has been conducted using
the proposed technique and the Huffman coding on standard images. The
experiment result has analyzed and the result shows that the newly proposed
compression technique achieves 10% more compression ratio than the
regular Huffman coding.
Keywords: Lossless Image Compression, Source Symbols Reduction, Huffman Coding.
1. INTRODUCTION
The image compression highly used in all applications like medical imaging, satellite imaging,
etc. The image compression helps to reduce the size of the image, so that the compressed
image could be sent over the computer network from one place to another in short amount of
time. Also, the compressed image helps to store more number of images on the storage
device [1-4,].
It’s well known that the Huffman’s algorithm is generating minimum redundancy codes
compared to other algorithms [6-11]. The Huffman coding has effectively used in text, image,
video compression, and conferencing system such as, JPEG, MPEG-2, MPEG-4, and H.263
etc. [12]. The Huffman coding technique collects unique symbols from the source image and
calculates its probability value for each symbol and sorts the symbols based on its probability
value. Further, from the lowest probability value symbol to the highest probability value
symbol, two symbols combined at a time to form a binary tree. Moreover, allocates zero to the
left node and one to the right node starting from the root of the tree. To obtain Huffman code
for a particular symbol, all zero and one collected from the root to that particular node in the
same order [13 and 14].
2. PROPOSED COMPRESSION TECHNIQUE
The number of source symbols is a key factor in achieving compression ratio. A new
compression technique proposed to reduce the number of source symbols. The source
symbols combined together in the same order from left to right to form a less number of new
source symbols. The source symbols reduction explained with an example as shown below.

The following eight symbols are assumed as part of an image, 1, 2, 3, 4, 5, 6, 7, 8. By
applying source symbols reduction from left to right in the same sequence, four symbols are
combined together to form a new element, thus two symbols 1234 and 5678 are obtained.
This technique helps to reduce 8 numbers of source symbols to 2 numbers i.e. 2n
symbols
are reduced to 2
(n-2)
symbols. For the first case, there are eight symbols and the respective
Symbols and Huffman Codes are 1-0, 2-10, 3-110, 4-1110, 5-11110, 6-111110, 7-1111110,
8-1111111. The proposed technique reduced the eight symbols to two and the reduced
Symbols and Huffman codes are 1234-0, 5678-1.
The minimum number of bits and maximum number of bits required to represent the new
symbols for an eight bit grayscale image calculated. The following possible combinations
worked out and handled perfectly to ensure the lossless compression. The following are few
different possible situations to be handled by source symbols reduction.
If all symbols in the four consecutive symbols are 0, i.e. 0 0 0 0, then the resulting new
symbol will be 0.
If the four consecutive symbols are 0 0 0 1, then the resulting new symbol will be 1.
If the four consecutive symbols are 0 0 1 0, then the resulting new symbol will be 1000.
If the four symbols are 0 1 0 0, then the resulting new symbol will be 1000000.
If the four symbols are 1 0 0 0, then the resulting new symbol will be 1000000000.
If the four symbols are 255 255 255 255, then the resulting new symbol will be
255255255255.
The average number Lavg of bits required to represent a symbol is defined as,
)()(
1
k
L
k
rkavg rprlL ∑=
=
(1)
where, rk is the discrete random variable for k=1,2,…L with associated probabilities pr(rk). The
number of bits used to represent each value of rk is l(rk). The number of bits required to
represent an image is calculated by number of symbols multiplied by Lavg [5].
In the Huffman coding, probability of each symbols is 0.125 and Lavg = 4.175.
In the proposed technique, probability of each symbol is 0.5 and Lavg=1.0.
The Lavg confirms that the proposed technique achieves better compression than the Huffman
Coding.
From the above different possible set of data, the following maximum and minimum number
of digits of a new symbol formed by source symbols reduction calculated for an eight bits
grey-scale image. The eight bits grey-scale image symbols have values ranging from 0 to
255. The minimum number of digits required to represent the new symbol could be 1 digit and
the maximum number of digits required to represent the new symbols could be 12 digits.
Therefore, if the number of columns of the image is multiples of four, then this technique
could be applied as it is. Otherwise, the respective remaining columns (1 or 2 or 3 columns)
will be kept as it is during the source symbols reduction and expansion.
Four rows and four columns of eight bits grey-scale image having sixteen symbols considered
to calculate required storage size. To represent these 16 symbols requires 16 x 1 byte = 16
bytes storage space. The proposed source symbol reduction technique reduces the 16
symbols into 4 symbols. The four symbols require 4 x 4 bytes = 16 bytes. Therefore, the
source symbols data and the symbols obtained by the source symbols reduction requires
equal amount of storage space. However, in the coding stage these two techniques make
difference. In the first case, sixteen symbols generate sixteen Huffman codes, whereas the

proposed technique generates four Huffman codes and reduces Lavg. Therefore, the
experiment confirms that the source symbols reduction technique helps to achieve more
compression.
The different stages of newly proposed compression technique are shown in figure 1. The
source image applied by source symbols reduction technique then the output undergoes the
Huffman encoding which generates compressed image. In order to get the original image, the
Huffman decoding applied and an expansion of source symbols takes place to reproduce the
image.
FIGURE 1: Proposed Compression Technique
Five different test images with different redundancy developed for experiment from 0% to
80% in step size of 20% i.e 0%, 20%, 40%, 60%, and 80% redundancy. The Huffman coding
could not be applied on data with 100% redundancy or single source symbol, as a result
100% redundancy is not considered for the experiment. The test images with 16 rows and 16
columns will have totally 256 symbols. The images are 8 bit grey-scale and the symbol values
range from 0 to 255. To represent each symbol eight bit is required. Therefore, size of an
image becomes 256 x 8 = 2048 bit. The five different level redundancy images are applied
the Huffman coding and the proposed technique. The compressed size and time required to
compress and decompress (C&D) are noted.
3. EXPERIMENT RESULTS
Following table 1 shows the different images developed for the experiment and corresponding
compression results using the regular Huffman Coding and the proposed technique. The
images are increasing in redundancy 0% to 80% from top to bottom in the table.
Huffman Coding SSR+HC Technique
IMAGE
Compressed size (bits) Compressed size (bits)
2048 384
1760 344
1377 273
944 188
549 118
TABLE 1: Huffman Coding Compression Result
The experiment shows that the higher data redundancy helps to achieve more compression.
The experiment shows that the proposed compression technique achieves more compression
than the Huffman Coding. The first image has 0% redundancy and its compressed image size
is 2048 bit using the Huffman coding whereas the proposed compression technique has
resulted compressed image of size 384 bit. No compression takes place for the first image
using Huffman coding, where as the proposed technique achieved about 81% compression.
Source
Symbols
Reduction
Compressed
Image
Source
Image
Source
Symbols
Expansion
Huffman
Decoding
Reproduced
Image
Huffman
Encoding

For all images the compressed size obtained from the proposed technique better than the
Huffman coding. The proposed compression technique achieves better compression. The
results obtained from the present analysis are shown in figure 2.
FIGURE 2: Compressed Size comparisons
Table 2 shows the comparison between these two techniques. Compression Ratio (CR) is
defined as
sizeCompressed
zeOriginalsi
CR = (2)
Huffman Coding SSR+HC Technique
Redundancy
Compression
Ratio
Compression
Ratio
0% 1.0000 5.3333
20% 1.1636 5.9535
40% 1.4873 7.5018
60% 2.1695 10.8936
80% 3.7304 17.3559
TABLE 2: Compression Ratio versus Time
From the result of the experiment it is found that the two compression techniques are lossless
compression technique, therefore the compression error not considered. The following figure
3 compares the compression ratio of the experiment. From the figure it is observed that the
proposed technique has performed better than the Huffman Coding. The proposed technique
shows better compression ratio for the images having higher redundancy when compared
with the images of lower redundancy.

FIGURE 3: Compression ratio comparisons
In the real time, images are usually having higher data redundancy. Hence, the proposed
technique will be suitable for the user who desires higher compression. Moreover, standard
gray scale images considered for testing. The standard images require 65,536 bytes storage
space of 256 rows and 256 columns. The image is eight bit gray scale image.
The standard images applied using the two the compression techniques and standard JPEG
compression technique. The compression size of the experiment is noted. The following
figure 4 is one of the source image used for the experiment and figure 5 is the reproduced
image using the proposed technique.
FIGURE 4: Source image chart.tif FIGURE 5: Reproduced image chart.tif
Table 3 shows the compression result using Huffman coding, and the proposed technique for
one of the standard image chart.tif. The proposed technique has achieved better compressed
size than the Huffman coding. The source symbols reduction and expansion takes more time
if the number of symbols are higher. Hence, the newly proposed technique is suitable to
achieve more compression.
Source Image
Size (bits)
Huffman Coding
Compressed size (bits)
SSR+HC Technique
Compressed size (bits)
5,128,000 1,015,104 54,207
TABLE 3: Compression test results for chart.tif

4. CONCLUSIONS
The present experiment reveals that the proposed technique achieves better compression
ratio than the Huffman Coding. The experiment also reveals that the compression ratio in
Huffman Coding is almost close with the experimental images. Whereas, the proposed
compression technique Source Symbols Reduction and Huffman Coding enhance the
performance of the Huffman Coding. This enables us to achieve better compression ratio
compared to the Huffman coding. Further, the source symbols reduction could be applied on
any source data which uses Huffman coding to achieve better compression ratio. Therefore,
the experiment confirms that the proposed technique produces higher lossless compression
than the Huffman Coding. Thus, the proposed technique will be suitable for compression of
text, image, and video files.
5. REFERENCES
1. Gonzalez, R.C. and Woods, R.E., Digital Image Processing 2
nd
ed., Pearson Education,
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2. Salomon, Data Compression, 2nd Edition. Springer, 2001.
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using Wavelet Transform, Signal Processing: An International Journal, Volume (2), Issue (5),
2008, pp. 17-26.
4. Singara Singh , R. K. Sharma, M.K. Sharma, Use of Wavelet Transform Extension for
Graphics Image Compression using JPEG2000 Framework, International Journal of Image
Processing, Volume 3, Issue 1, Pages 55-60, 2009.
5. Abramson, N., Information Theory and Coding, McGraw-Hill, New York, 1963.
6. Huffman, D.A., A method for the construction of minimum-redundancy codes. Proc. Inst.
Radio Eng. 40(9), pp.1098-1101, 1952.
7. Steven Pigeon, Yoshua Bengio — A Memory-Efficient Huffman Adaptive Coding Algorithm
for Very Large Sets of Symbols — Université de Montréal, Rapport technique #1081.
8. Steven Pigeon, Yoshua Bengio — A Memory-Efficient Huffman Adaptive Coding Algorithm
for Very Large Sets of Symbols Revisited — Université de Montréal, Rapport technique
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9. R.G. Gallager — Variation on a theme by Huffman — IEEE. Trans. on Information Theory,
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10. D.E. Knuth — Dynamic Huffman Coding — Journal of Algorithms, 6, 1983 pp. 163-180.
11. J.S. Vitter — Design and analysis of Dynamic Huffman Codes — Journal of the ACM,
34#4, 1987, pp. 823-843.
12. Chiu-Yi Chen; Yu-Ting Pai; Shanq-Jang Ruan, Low Power Huffman Coding for High
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13. Lakhani, G, Modified JPEG Huffman coding, IEEE Transactions Image Processing, 12(2),
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14. R. Ponalagusamy and C. Saravanan, Analysis of Medical Image Compression using
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Lossless Grey-scale Image Compression Using Source Symbols Reduction and Huffman Coding

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