PERFORMANCE EVALUATION OF JPEG IMAGE COMPRESSION USING SYMBOL REDUCTION TECHNIQUE

Natarajan Meghanathan, et al. (Eds): ITCS, SIP, JSE-2012, CS & IT 04, pp. 217–227, 2012.
© CS & IT-CSCP 2012 DOI : 10.5121/csit.2012.2120
PERFORMANCE EVALUATION OF JPEG IMAGE
COMPRESSION USING SYMBOL REDUCTION
TECHNIQUE
Bheshaj Kumar1
,Kavita Thakur2
and G. R. Sinha3
1,2
DSchool of Studies in Electronics, Pt. R. S. University,Raipur,India
bheshaj.dewangan@rediffmail.com
kavithakur@rediffmail.com
3
Shri Shankarachrya College of Engineering & Technology, Bhilai, India
ganeshsinha2003@gmail.com
ABSTRACT
Lossy JPEG compression is a widely used compression technique. Normally the JPEG technique
uses two process quantization, which is lossy process and entropy encoding, which is considered
lossless process. In this paper, a new technique has been proposed by combining the JPEG
algorithm and Symbol Reduction Huffman technique for achieving more compression ratio. The
symbols reduction technique reduces the number of symbols by combining together to form a new
symbol. As a result of this technique the number of Huffman code to be generated also reduced.
The result shows that the performance of standard JPEG method can be improved by proposed
method. This hybrid approach achieves about 20% more compression ratio than the Standard
JPEG.
KEYWORDS
Image Compression, JPEG, Source Reduction, Entropy Encoder, Huffman coding.
1. INTRODUCTION
Image compression has a fundamental importance in image communication and storage. A
typical image compression scheme first manipulates the input image data in a way to obtain more
compact and/or uncorrelated representation. This manipulation may be in the form of a mapping,
transformation, quantization or a combination of these. The manipulated data is then fed to an
entropy encoder [1-2]. Recent research in the field of image compression focuses more on data
manipulation stage, and a growing number of new techniques concerning this stage are
introduced in the recent year. Conventional technique used in the entropy encoding stage and
there are relatively less innovation in this stage. Thus the performance of most image
compression scheme can be improved by utilizing an entropy encoder.
In most general terms, an entropy coder is an invertible mapping from a sequence of events to a
sequence of bits. The objective of entropy coding is the minimization of the number of bits in the
bit sequence, while maintaining the invertibility of the mapping. The way of defining the

218 Computer Science & Information Technology (CS & IT)
particular events can also be considered a part of entropy coding. The entropy coding can be
considered to define its own set of intermediate events, based on the input sequence of events as
define externally. Entropy coding has been extensively studies in the literature, particularly under
the discipline of information theory.
Let X = x1x2x3…………..xn be a sequence of independent input symbols, each symbol taking on
values from a finite alphabet A = { a1,a2,……….am). Let pij denote the probability that xi, the ith
symbol in the sequence, takes the value aj. Thus the entropy of the sequence is defined as
(1)
Shannon’s source coding theorem [1] states that the entropy of the sequence is the lower bound
on the expected value of the number of bits that is required to encode the sequence [2].
It’s well known that the Huffman’s algorithm is generating minimum redundancy codes
compared to other algorithms [3-7]. 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.
.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 [8-11].
There are numerous amount of work on image compression is carried out both in lossless and
lossy compression [11-14]. Very limited research works are carried out for Hybrid Image
compression[21-27]. Hsien Wen Tseng and Chin-Chen Chang proposed a very low bit rate image
compression scheme that combines the good energy-compaction property of DCT with the high
compression ratio of VQ-based coding[15]. Lenni Yulianti and Tati R.Mengko proposed a hybrid
method to improve the performance of Fractal lmage Compression (FIC) technique by combining
FIC (lossy compression) and lossless Huffman coding[16].A novel hybrid image compression
technique for efficient storage and delivery of data is proposed by S.Parveen Banu and
Dr.Y.Venkataramani based on decomposing the data using daubechies-4 wavelet in combination
with the lifting scheme and entropy encoding[17].
In the proposed work, for image compression, symbol reduction technique is applied in Standard
JPEG lossy method. The results provide better compression ratio compare to JPEG technique.
2. BACKGROUND OF OUR WORK
2.1. Joint Photographic Expert Group (JPEG)
A common characteristic of most images is that the nearby pixels are associated and therefore
comprise redundant information. The primary task then is to find less associated representation of
the image. Two essential attributes of compression are redundancy and irrelevancy reduction.
Redundancy reduction aims at removing repetition from the signal source. Irrelevancy reduction
omits parts of the signal that will not be discerned by the signal receiver, namely the Human
Visual System (HVS). JPEG Compression method is one of the commonly recognized and used
procedures for image compression. JPEG stands for Joint Photographic Experts Group. JPEG
standard has been established by ISO (International Standards Organization) and IEC

Computer Science & Information Technology (CS & IT) 219
(International Electro-Technical Commission) [18]. The JPEG Image compression system
consists of three closely connected constituents specifically
• Source encoder (DCT based)
• Quantizer
• Entropy encoder [18]
Figure 1shows the block diagram of a JPEG encoder, which has the following components [18]
Figure 1. Block Diagram of JPEG Encoder [18]
2.1.1 Forward Discrete Cosine Transform (FDCT)
The still images are first partitioned into non-overlapping blocks of size 8x8 and the image
samples are shifted from unsigned integers with range [0 to 2p
-1] to signed integers with range [-
2p-1
to 2p-1
], where p is the number of bits.It should however be mentioned that to preserve
freedom for innovation and customization within implementations, JPEG neither specifies any
unique FDCT algorithm, nor any unique IDCT algorithms[18]. Because adjacent image pixels are
highly correlated, the `forward' DCT (FDCT) processing step lays the foundation for achieving
data compression by concentrating most of the signal in the lower spatial frequencies. In
principle, the DCT introduces no loss to the source image samples; it merely transforms them to a
domain in which they can be more efficiently encoded [20].
2.1.2 Quantization
After output from the FDCT, each of the 64 DCT coefficients block is uniformly quantized
according to a quantization table. Since the aim is to compress the images without visible
artifacts, each step-size should be chosen as the perceptual threshold or for “just noticeable
distortion”. Psycho-visual experiments have led to a set of quantization tables and these appear in
ISO-JPEG standard as a matter of information, but not a requirement [18]. At the decoder, the
quantized values are multiplied by the corresponding QT elements to recover the original
unquantized values. After quantization, all of the quantized coefficients are ordered into the
zigzag sequence. This ordering helps to facilitate entropy encoding by placing low-frequency
non-zero coefficients before high-frequency coefficients. The DC coefficient, which contains a
significant fraction of the total image energy, is differentially encoded [20].
2.1.3 Entropy Coder
This is the final processing step of the JPEG encoder. Entropy Coding (EC) achieves additional
compression lossless by encoding the quantized DCT coefficients more compactly based on their
statistical characteristics. The JPEG standard specifies two entropy coding methods – Huffman
and arithmetic coding. The baseline sequential JPEG uses Huffman only, but codecs with both
methods are specified for the other modes of operation. Huffman coding requires that one or more
sets of coding tables are specified by the application. The same table used for compression is used
Compressed
Image Data
FDC
T
Entropy
EncoderQuantizer
Table
Specification
Table
Specification
Source Image
Data
8X8 Sub-
Image Block

needed to decompress it. The baseline JPEG uses only two sets of Huffman tables – one for DC
and the other for AC. Figure 2 shows the block diagram of the JPEG decoder. It performs the
inverse operation of the JPEG encoder [18].
Figure 2. Block Diagram of JPEG Decoder
The use of uniformly sized blocks simplified the compression system, but it does not take into
account the irregular shapes within the real images[20]. Degradation occurs which is known as
blocking effect and it depends on the block size. A larger block leads to more efficient coding but
requires more computational power. Image distortion is less annoying for small than for large
DCT blocks. Therefore more existing systems use blocks of 8x8 or 16x16 pixels as a compromise
between coding efficiency and image quality [28-29].
2.2 Symbol Reduction Method
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, A, B, C, D, E, F, G, H. 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 ABCD and EFGH are obtained[8]. 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 A-0, B-10,
C-110, D-1110, E-11110, F-111110, G-1111110, H-1111111. The proposed technique reduced
the eight symbols to two and the reduced Symbols and Huffman codes are ABCD-0, EFGH-1.
The average number Lavg of bits required to represent a symbol is defined as,
. (2)
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) [9]. The number of bits required to
represent an image is calculated by number of symbols multiplied by Lavg [1-2].In the Huffman
coding, probability of each symbols is 0.125 and Lavg = 4.375.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.
8 rows and 8 columns of eight bits grey-scale image having 64 symbols considered to calculate
required storage size. In the coding stage these two techniques make difference [9]. In the first
case, 64 symbols generate 64 Huffman codes, whereas the proposed technique generates 16
IDCT
Entropy
Decoder Dequantizer
Table
Specificatio
n
Table
Specification
Recovered
Image
Data
Compressed
Image Data

Huffman codes and reduces Lavg. Therefore, the experiment confirms that the source symbols
reduction technique helps to achieve more compression [9].
Since the source images firstly divided in 8x8 sub-block, will have totally 64 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 [9]. Therefore, size of an image becomes 64 x 8 = 512 bit.
3. PROPOSED JPEG IMAGE COMPRESSION METHOD
The image is subdivided into non-overlapping 8x8 sub-image blocks and DCT coefficients are
computed for each block. The quantization is performed conferring to quantization table. The
quantized values are then rearranged according to zigzag arrangement. After getting zigzag
coefficients the remaining coefficients are compressed by the proposed entropy encoder. The
block diagram of our proposed method is shown in figure 3.
Figure 3. Block Diagram of Proposed JPEG Encoder
3.1 Algorithm
1. Input the image data to be compressed.
1. Divide the image into non-overlapping 8x8 sub images blocks.
2. Shift the gray-levels in the range between [-128, 127].
3. Apply DCT on the each sub-image.
4. Quantize the coefficients and the less significant coefficients are set to zero.
5. Order the coefficients using zigzag ordering and the coefficients obtained are in order of
increasing frequency.
6. Compress remaining quantized values by applying proposed entropy encoder.
To reconstruct the image, reverse process of our proposed algorithm are carried out.
As an example, let us consider the 8 X 8 block of pixel value component samples shown in Table
1. This block is extracted from one of the images used in the experiments. Table 2 shows the
corresponding coefficients obtained by applying the DCT transform to the block in Table 1.
Table 1. An example of pixel values of 8X8 image block
58 45 29 27 24 19 17 20
62 52 42 41 38 30 22 18
48 47 49 44 40 36 31 25
FD
PROPOSED ENTROPY
Quantizer
Table
Specification
Table
Specification
Source
Image Data
8X8 Sub-
Image Block
Zigzag
Coefficient
Coefficient
Reduction
Huffman
Encoding
Compresse
d Image

59 78 49 32 28 31 31 31
98 138 116 78 39 24 25 27
115 160 143 97 48 27 24 21
99 137 127 84 42 25 24 20
74 95 82 67 40 25 25 19
Table 2. DCT coefficients corresponding to the 8X8 block in Table 1
421.00 203.33 10.65 -45.19 -30.25 -13.83 -14.15 -7.33
-107.82 -93.43 10.09 49.21 27.72 5.88 8.33 3.28
-41.83 -20.47 -6.16 15.53 16.65 9.09 3.28 2.52
55.94 68.58 7.01 -25.38 -9.81 -4.75 -2.36 -2.12
-33.50 -21.10 16.70 8.12 3.25 -4.25 -4.75 -3.39
-15.74 -13.60 8.12 2.42 -3.98 -2.12 1.22 0.73
0.28 -5.37 -6.47 -0.58 2.30 3.07 0.91 0.63
7.78 4.95 -6.39 -9.03 -0.34 3.44 2.57 1.93
Now we apply the quantization processes to the DCT coefficients in Table 2. To compute the
quantized values, we adopt the JPEG standard default quantization table as shown in Table 3.
Table 4 reports the quantized DCT coefficients.
Table 3. Default Quantization Table
16 11 10 16 24 40 51 61
12 12 14 19 26 58 60 55
14 13 16 24 40 57 69 56
14 17 22 29 51 87 80 62
18 22 37 56 68 109 103 77
24 35 55 64 81 104 113 92
49 64 78 87 103 121 120 101
72 92 95 98 112 100 103 99
Table 4. The quantized DCT coefficients corresponding to the block in Table 1
After quantization, we can observe that there usually are few nonzero and several zero-valued
DCT coefficients. Thus, the objective of entropy coding is to losslessly compact the quantized
DCT coefficients exploiting their statistical characteristics. The quantized 64 coefficients are
formatted by using the zigzag scan preparation for entropy coding.
[ 26 18 -9 -3 -8 1 -3 1 -2 4 -2 4 0 3 -1 0 1 1 0 -1 -1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
26 18 1 -3 -1 0 0 0
-9 -8 1 3 1 0 0 0
-3 -2 0 1 0 0 0 0
4 4 0 -1 0 0 0 0
-2 -1 0 0 0 0 0 0
-1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0

Since many of the coefficients are negative and zero after quantization, each coefficient is
checked for either non-zero or zero coefficient, if coefficient is nonzero, add 128 to the
coefficient to make a positive integer.
[154 146 119 125 120 129 125 128 126 132 126 132 0 131 127 0 129 129 0 127 127 0 0 0 127 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
Now according to proposed reduction method, from left to right in the same sequence, four
symbols are combined together to form a new string, thus these 64 symbols are reduced in 16
symbols.
[(154146119125) (120129125128) (126132126132) (01311270) (1291290127) (127000)
(127000) (0000) (0000) (0000) (0000) (0000) (0000) (0000) (0000) (0000)]
This string is encoded using a predetermined Huffman coding process and finally, it generates
compressed JPEG image data.
4. RESULT AND DISCUSSION
For evaluating the performance of the proposed algorithms, we used 256x256 grayscale versions
of the well-known Cameraman, Rice, Coin and Tree images, shown in Figure 4.
Figure 4. Test images for evaluating the performance of proposed method
Intermediate Images of Cameraman during processing are shown below
Figure 5. Original Test images

Figure 6. After applying DCT
Figure 7. After applying IDCT
Figure 8. Reconstructed image
The results obtained from the implementation of the proposed algorithm are shown in the table 5.
The compressed ratio of the four test images are calculated and presented in table 5.

Table 5. Compression Ratio of Standard JPEG and Proposed Method
Test Images JPEG
Method
Proposed
Method
Cameraman 4.13 4.94
Rice 5.68 6.45
Coin 3.84 4.73
Tree 2.53 3.08
The result shows that for all test images the compressed size obtained from the proposed
technique better than the Standard JPEG method. The proposed compression technique achieves
better compression. The results obtained from the present analysis are shown in figure 5.
Figure 5. Compression Ratio of Standard JPEG and Proposed Method
Since it is found that the two compression techniques are lossless compression technique,
therefore the compression error not considered. So the picture quality (PSNR) values are common
to both Standard JPEG method and Proposed JPEG compression method.
5. CONCLUSION
The experimentation in present paper reveals that the compression ratio of the proposed technique
achieves better than the standard JPEG method. The proposed entropy encoding technique
enhances the performance of the JPEG technique. Therefore, the experiment confirms that the
proposed technique produces higher lossless compression than the Huffman Coding and this
technique will be suitable for compression of all type of image files.
6. REFERENCES
[1] C. E. Shannon, “A Mathematical Theory of Communication”, in Bell System Technical Journal, vol.
27, July, October 1948, pp. 379–423,623–656.
[2] Gonzalez, R.C. and Woods, R.E., “Digital Image Processing”, 2nd ed., Pearson Education, India,
2005.

[3] Huffman, D.A., “A method for the construction of minimum-redundancy codes”, Proc. Inst.Radio
Eng. 40(9), pp.1098-1101, 1952.
[4] Steven Pigeon, Yoshua Bengio,”A Memory-Efficient Huffman Adaptive Coding Algorithm for Very
Large Sets of Symbols”, Université de Montréal, Rapport technique #1081.
[5] Steven Pigeon, Yoshua Bengio,”A Memory-Efficient Huffman Adaptive Coding Algorithm for Very
Large Sets of Symbols Revisited” ,Université de Montréal, Rapport technique#1095.
[6] R.G. Gallager,”Variation on a theme by Huffman”, IEEE. Trans. on Information Theory, IT-24(6),
1978, pp. 668-674.
[7] D.E. Knuth,”Dynamic Huffman Coding”,Journal of Algorithms, 6, 1983 pp. 163-180.
[8] C. Saravanan & R. Ponalagusamy,’Lossless Grey-scale Image Compression using Source Symbols
Reduction and Huffman Coding” International Journal of Image Processing , Vol. 3,Issue 5,pp. 246-
251.
[9] Jagdish H. Pujar and Lohit M. Kadlaskar, “A New Lossless Method of Image Compression and
Decompression Using Huffman Coding Techniques”, Journal of Theoretical and Applied Information
Technology,pp. 18-23.
[10] Chiu-Yi Chen; Yu-Ting Pai; Shanq-Jang Ruan, “Low Power Huffman Coding for High
Performance”, Data Transmission, International Conference on Hybrid Information Technology,
2006, 1(9-11), 2006 pp.71 – 77.
[11] Lakhani, G, “Modified JPEG Huffman coding”, IEEE Transactions Image Processing, 12(2), 2003
pp. 159 – 169.
[12] K. Rao, J. Hwang, “Techniques and Standards for Image, Video, and Audio Coding”, Prentice-Hall,
Inc., Upper Saddle River, NJ, USA, 1996.
[13] W.B. Pennebaker, J.L. Mitchell, “JPEG Still Image Data Compression Standard,” 2nd ed., Kluwer
Academic Publishers, Norwell, MA, USA, 1992.
[14] B. Sherlock, A. Nagpal, D. Monro, “A model for JPEG quantization”, Proceedings of the
International Symposium on Speech, Image Processing and Neural Networks (ISSIPNN-94), vol. 1,
13–16 April, IEEE Press, Piscataway, NJ, 1994.
[15] Hsien-Wen Tseng, Chin-Chen Chang, “ A Very Low Bit Rate Image Compressor Using Transformed
Classified Vector Quantization”, Informatica ,29 (2005) ,pp. 335–341.
[16] Lenni Yulianti and Tati R.Mengko, “Application of Hybrid Fractal Image Compression Method for
Aerial Photographs”, MVA2OOO IAPR Workshop on Machine Vision Applications, Nov. 28-
30.2000,pp. 574-577.
[17] S.Parveen Banu, Dr.Y.Venkataramani,“An Efficient Hybrid Image Compression Scheme based on
Correlation of Pixels for Storage and Transmission of Images”,International Journal of Computer
Applications (0975 – 8887) Volume 18– No.3, 2011,pp. 6-9.
[18] http://nptel.iitm.ac.in/courses /Webcourse contents / IIT % 20Kharagpur /Multimedia % 20Processing
/pdf ssg_m6l16.pdf.
[19] GRGIC et al., “Performance analysis of image compression using wavelets”, IEEE Trans.
Indus.Elect., Vol. 48, No. 3, June 2001,pp. 682-695.

[20] Kamrul Hasan Talukder and Koichi Harada,“Haar Wavelet Based Approach for Image Compression
and Quality Assessment of Compressed Image”, International Journal of Applied Mathematics, 36:1,
IJAM_36_1_9,2007.
[21] Rene J. van der Vleuten, Richard P.Kleihorstt, Christian Hentschel ,“Low-Complexity Scalable DCT
Image Compression”, 2000 IEEE.
[22] S. Smoot, L. Rowe, “Study of DCT coefficient distributions”, Proceedings of the SPIE Symposium
on Electronic Imaging, vol. 2657, SPIE, Bellingham, WA, 1996.
[23] D. Monro, B. Sherlock, “Optimum DCT quantization”, Proceedings of the IEEE Data Compression
Conference (DCC-93), IEEE Press, Piscataway, NJ, 1993.
[24] F. Muller, “Distribution shape of two-dimensional DCT coefficients of natural images”, Electron.
Lett. 29 (October (22)) (1993), pp. 1935–1936.
[25] Hong, S. W. Bao, P., “Hybrid image compression model based on subband coding and edge
preserving regularization”, Vision, Image and Signal Processing, IEE Proceedings, Volume: 147,
Issue: 1, Feb 2000,pp. 16-22.
[26] Zhe-Ming Lu, Hui Pei ,”Hybrid Image Compression Scheme Based on PVQ and DCTVQ”, IEICE -
Transactions on Information and Systems archive, Vol E88-D , Issue 10 ,October 2006.
[27] Charles F. Hall., “A Hybrid Image Compression Technique” CH2I 18-8/85/0000-0149 © 1985, IEEE.
[28] Ms.Mansi Kambli1 and Ms.Shalini Bhatia,”Comparison of different Fingerprint Compression
Techniques”, Signal & Image Processing: An International Journal(SIPIJ) Vol.1, No.1, September
2010, pp. 27-39.
[29] M.Mohamed Sathik , K.Senthamarai Kannan , Y.Jacob Vetha Raj, “Hybrid JPEG Compression
Using Edge Based Segmentation”, Signal & Image Processing : An International Journal(SIPIJ)
Vol.2, No.1, March 2011,pp.165-176.

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