NEAR-LOSSLESS COMPRESSION SCHEME USING
HAMMING C O D E S F O R NON-TEXTUAL
IMPORTANT REGIONS IN DOCUMENT IMAGES
Prashant Paikrao
Research Scholar, Department of E&TC, SGGS Institute of Engineering and Technology, Nanded,
(India).
E-mail: plpaikrao@gmail.com; 2019pec201@sggs.ac.in
Dharmapal Doye
Professor, SGGS Institute of Engineering and Technology, Nanded, (India).
Milind Bhalerao
Assistant Professor, SGGS Institute of Engineering and Technology, Nanded, (India).
Madhav Vaidya
Assistant Professor, SGGS Institute of Engineering and Technology, Nanded, (India).
Reception: 27/11/2022 Acceptance: 12/12/2022 Publication: 29/12/2022
Suggested citation:
Paikrao, P., Doye, D., Bhalerao, M., y Vaidya, M. (2022). Near-lossless compression scheme using hamming
codes for non-textual important regions in document images. 3C TIC. Cuadernos de desarrollo aplicados a las
TIC, 11(2), 225-237. https://doi.org/10.17993/3ctic.2022.112.225-237
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ABSTRACT
Working at Bell Labs in 1950, irritated with error-prone punched card readers, R W Hamming began
working on error-correcting codes, which became the most used error-detecting and correcting
approach in the field of channel coding in the future. Using this parity-based coding, two-bit error
detection and one-bit error correction was achievable. Channel coding was expanded further to
correct burst errors in data. Depending upon the use of the number of data bits ‘d’ and parity bits ‘k’
the code is specified as (n, k) code, here ‘n’ is the total length of the code (d+k). It means that 'k' parity
bits are required to protect 'd' data bits, which also means that parity bits are redundant if the code
word contains no errors. Due to the framed relationship between data bits and parity bits of the valid
codewords, the parity bits can be easily computed, and hence the information represented by 'n' bits
can be represented by 'd' bits. By removing these unnecessary bits, it is possible to produce the optimal
(i.e., shortest length) representation of the image data. This work proposes a digital image
compression technique based on Hamming codes. Lossless and near-lossless compression depending
upon need can be achieved using several code specifications as mentioned here. The achieved
compression ratio, computational cost, and time complexity of the suggested approach with various
specifications are evaluated and compared, along with the quality of decompressed images.
KEYWORDS
Hamming code, Parity, Lossless Compression, Near Lossless Compression, Compression Ratio.
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1. INTRODUCTION
Image coding and compression is used mainly for effective data storage and transmission over a
network and in some cases for encryption. Image data is also coded for achieving compression to
optimize the use of these resources. In digital image compression, depending upon the quality of
decompressed image the compression algorithms employed are categorised in the categories like
Lossless compression, Lossy compression, and Near-lossless compression. The data redundancy is a
statistically quantifiable entity, it can be defined as R_D=1-1⁄CR, where the CR is the compression
ratio represents the ratio of number of bits in compressed representation to number of bits in original
representation. A compression ratio of ‘C’ (or ‘C’:1) means that the original data contains ‘C’
information bits for every 1 bit in the compressed data. The associated redundancy of 0.5 indicates that
50% of the data in the first data set is redundant. Three primary data redundancies can be found and
used in digital image compression i.e. coding redundancy, interpixel redundancy, and psychovisual
redundancy. When one or more of these redundancies are considered as a key component for reduced
representation of data and accordingly these redundancies are encoded with some method the
compression is achieved, Sayood (2017). There is no right or wrong decision when deciding between
lossless and lossy image compression techniques. Depending on what suits your application the most,
you can choose. Lossy compression is a fantastic option if you don't mind sacrificing image quality in
exchange for smaller image sizes. However, if you want to compress photographs without sacrificing
their quality or visual appeal, you must choose lossless compression Kumar and Chandana (2009).
Based on a knowledge of visual perception, the irrelevant part of the data may be neglected, a lossy
compression, includes a process for averaging or eliminating this unimportant information to reduce
data size. In lossy compression the image quality is compromised but a significant amount of
compression is possible. When the quality of decompressed image and integrity are crucial then lossy
compression shouldn't be employed Ndjiki-Nya et.al (2007). Not all images react the same way to
lossy compression. Due to the constantly changing nature of photographic images, some visual
elements, including slight tone variations, may result in artefacts (unintended visual effects), but these
effects may largely go unnoticed. While in line graphics or text in document images will more
obviously show the lossy compression artefacts than other types of images. These may build up over
generations, particularly if various compression algorithms are employed, so artefacts that were
undetectable in one algorithm may turn out to be significant in another. So, in this scenario one should
try to bridge the consequences of lossless and lossy compression algorithms. So, the near-lossless
compression algorithm should be practiced in case of document images to optimise the compression
ratio and the quality of reconstruction Ansari et al. (1998). One of the very famous Error detection and
correction technique used in channel coding may be used for the digital image compression Caire et.al
(2004) and Hu et.al (2000). In this paper use of Hamming codes with different specifications for
various compression algorithms mentioned above is done and the compression is achieved.
2. HAMMING CODES
When the channel is noisy or error-prone, the channel encoder and decoder are crucial to the overall
encoding-decoding process. By adding a predetermined amount of redundancy to the source encoded
data, it is possible to minimize the influence of channel noise. As the output of the source encoder is
highly sensitive to transmission noise, it is based on the principle that enough controlled redundant
bits must be added to the data being encoded to guarantee that a specific minimum number of bits will
change during the transmission. Hamming demonstrated, showed that all single-bit errors can be
detected and corrected if 3 bits of redundancy are added to a 4-bit code word, providing the Hamming
distance between any two valid code words 3 bits. The 7-bit Hamming (7, 4) code word P1, P2, D3,
P4, D5, D6, D7 for a 4-bit binary number b1,b2,b3,b4≅
D3,D5,D6,D7 padded with parity bits
p1,p2,p3≅P1,P2,P4 .
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Fig. 1. Hamming Code
2.1. ERROR DETECTION
One of the most popular hamming code specifications used is (7,4); here 7 is total length of codeword
and 4 is number of data bits.
Here (n-k) i.e., 7-4 =3 parity bits are used to encode 4-bit message to detect one bit error and correct
one bit error.
In the following example, the first step of algorithm is to identify the position of the data bits and
parity bits. All the bit positions at powers of 2 are marked as parity bits (e.g., 1, 2, 4, 8). Given below
is the structure of 7-bit hamming code.
Here a data “0 1 0 1” is encoded using (7,4) even parity hamming code and an error is introduced in the
fifth (D5) bit.
Three parity checks and needed to be considered to determine whether there are any errors in the
received hamming code.
Check 1: Here the parity of bits at position 1,3,5,7 should be verified
It is observed that the parity of above codeword is odd, it is concluded that the error is present and
check1 is failed.
Check 2: Here the parity of bits at position 2,3,6,7 should be verified
It is observed that the parity of above codeword is even, then we will conclude the check2 is passed.
Check 3: Here the parity of bits at position 4,5,6,7 should be verified
P1 P2 D3 P4 D5 D6 D7
1 1 0 1 1 0 1
P1 D3 D5 D7
1 0 1 1
P2 D3 D6 D7
1 0 0 1
P4 D5 D6 D7
1 1 0 1
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It is observed that the parity of above codeword is odd, it is concluded that the error is present and
check3 is failed.
So, from the above parity analysis, check1 and check3 are failed so we can clearly say that the received
hamming code has errors.
2.2. ERROR CORRECTION
They must be repaired because it was discovered that the received code contains an error. Use the next
few steps to fix the mistakes:
The error checks word has become:
The error is in the fifth data bit, according to the decimal value of this error-checking word, which was
calculated as "1 0 1" (the binary representation of 5). Simply invert the fifth data bit to make it correct.
So, the correct data will be:
In the same fashion other specifications of code like (3,1), (6,3), (7,3), and so on can be implemented
and error detection and error correction of messages using the parity bits can be accomplished. There
has never been a way for error checking and correcting that is more effective than Hamming codes, so,
it is still widely used channel encoding. It offers an effective balance between error detection and
correction, in addition to that one may verify its application in data compression field, which is being
discussed in the next topic.
3. PROPOSED WORK
The document image compression, if various logical regions of the document image are segmented and
appropriate compression algorithm is used for those regions, then the trade-off between compression
ratio and the quality of decompressed image may be resolved a bit. Lossy compression techniques for
photographs, Near-lossless compression for Figures, Tables and other text-like important regions, and
Lossless compression for the Text contents Shanmugasundaram et.al (2011).
3.1. THE EXISTING LOSSLESS ENCODING ALGORITHM
i. Reshaping: 2D to 1D conversion of image data
ii. Resizing: Divide the data in terms of 7-bit chunks
iii. Checking Hamming encodability of newly formed chunks; valid and invalid hamming codes
(7,4)
iv. Lossless Encoding of data
v. beginning with ‘0’+codeword (7 bit), if the chunk is invalid codeword
vi. beginning with ‘1’+encoded codeword (4 bit), if the chunk is valid codeword
vii. If the size of the coded data is smaller than the input data, then compression is achieved.
The following algorithms are the step by step modification in the existing work of Hu et.al
(2000).
Here, the near-lossless encoding algorithm based on the idea of bit plane slicing is presented as
Algorithm 1. It is presumptive that the least significant bit (LSB) in an image contains the least
check1 check2 check3
1 0 1
P1 P2 D3 P4 D5 D6 D7
1 1 0 1 0 0 1
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significant information, and that if this information is removed from a gray-level image, a little visual
degradation will be caused.
3.2. ALGORITHM 1: BIT PLANE SLICING BASED LOSSY ENCODING
i.
Perform bit-plane slicing: remove LSB (assuming that LSB plane consists of least
information)
ii. Reshaping: 2D to 1D conversion of image data
iii. Resizing: Divide the data in terms of 7-bit chunks
iv. Checking Hamming encodability of new chunks; valid and invalid hamming codes (7,4)
v. Lossless Encoding of data
vi. beginning with ‘0’+codeword (7 bit), if the chunk is invalid codeword
vii. beginning with ‘1’+encoded codeword (4 bit), if the chunk is valid codeword
viii.If the size of the coded data is smaller than the input data, then compression is achieved.
The second approach, which also uses (8,4) Hamming codes for lossless compression, has the
additional capability of detecting and correcting error in the eighth bit, which is set or reset based on the
even or odd parity of the entire 7-bit codeword in (7,4) variant. This technique offers the lossless
compression in addition to the additional 1-bit detection and correction capabilities.
3.3. ALGORITHM 2: LOSSLESS ENCODING USING (8,4) HAMMING
CODE SPECIFICATION
i. Reshaping: 2D to 1D conversion of grey image data
ii. Checking Hamming encodability of newly formed chunks; valid and invalid hamming codes
(8,4)
iii. Lossless Encoding of data
iv. beginning with ‘0’+codeword (8 bit), if the chunk is invalid codeword
v. beginning with ‘1’+encoded codeword (4 bit), if the chunk is valid codeword
vi. If the size of the coded data is smaller than the input data, then compression is achieved.
It is computationally expensive to scan the complete image to determine if the codewords (its grey
levels) are valid or invalid hamming codewords. Therefore, a novel technique for eliminating this
avoidable routine is being tested, which involves discovering the valid codewords beforehand and
simply classifying image gray-levels as valid or invalid codewords by comparing with them. This
process is similar to quantization but here the quantization levels are neither equidistant nor generated
by some programming language function. Even though this quantization inevitably results in
information loss, the compression ratio will be improved Li et.al (2002). These quantized gray-levels
offers spectral compression at the same time the probabilities of the resultant gray-levels also get
changed. The image with changed gray-level probabilities is further feed to probability-based coding
like Huffman’s coding and added compression is achieved Jasmi et.al (2015) and Huffman (1952). The
algorithms 3 is subsequently modified in algorithm 4 and 5 using (8,4) code for lossless compression
with 16 and 32 quantization levels respectively. After the successful compression and decompression,
the quality of decompressed image using quantization approach is computed based on the parameters
like Correlation of input output images Dhawan (2011), its Mean Squared Error (MSE), Signal to Noise
Ratio (SNR), Structural Similarity Index Metric (SSIM) to compute the retainment of structural
properties of the input images, Compression Ratio (CR) achieved and the Computational Time (CT).
3.4. ALGORITHM 3: FAST NEAR-LOSSLESS ENCODING USING (7,4)
HAMMING CODE SPECIFICATION AND QUANTIZATION
i. Reshaping: 2D to 1D conversion of image data
ii.
Perform bit-plane slicing: remove LSB (considering that it LSB plane consists of the least
information) OR
Resizing: Divide the data in terms of 7-bit chunks
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iii. Identify the ‘16’ valid codewords and enlist them in an array valcod
iv. valcod = [0 15 22 25 37 42 51 60 67 76 85 90 102 105 112 127]
v. Lossy step: Quantize the entire image pixels to grey levels in valcod variables
vi. If size of coded data is smaller than input data, then compression is achieved.
3.5. ALGORITHM 4: FAST NEAR-LOSSLESS ENCODING USING (8,4)
HAMMING CODE SPECIFICATION AND 16 LEVEL QUANTIZATION
i. Reshaping: 2D to 1D conversion of image data
ii. Identify the ‘16’ valid codewords and enlist them in an array valcod16
iii. Valcod8 = [0 15 51 60 85 90 102 105 150 153 165 170 195 204 240 255]
iv. Lossy step: Quantize the entire image pixels to grey levels in valcod16 variables
v. If size of coded data is smaller than input data, then compression is achieved.
3.6. ALGORITHM 5: FAST NEAR-LOSSLESS ENCODING USING (8,4)
HAMMING CODE SPECIFICATION AND 32 LEVEL QUANTIZATION
i. Reshaping: 2D to 1D conversion of image data
ii.
Identify the ‘total 32’ valid even, odd conjugate codewords along-with its complements and
enlist them in an array valcod32
iii. valcodeoc = [0 15 23 24 36 43 51 60 66 77 85 90 102 105 119 129 136 142 150 153 165 170
178 189 195 204 212 219 231 232 240 255]
iv. Lossy step: Quantize the entire image pixels using the 32 grey-levels in valcod32 variable
v. If the size of the coded data is smaller than the input data, then compression is achieved.
4. RESULTS
The experimentation carried out on a dataset consisting of three classes of images like graphs,
diagrams, and equations, which are the text-like regions in the document image. As discussed above the
existing Hamming code-based algorithms is implemented and executed over the dataset. Performance
of these algorithms is evaluated by means of the performance metrics like compression ratio and
computation time. The algorithms are implemented using MATLABR2020b software on a 64-bit, 2.11
GHz processor with 8 GB RAM computer system. The algorithm offers compression generally but, in
some times, (4/30) it failed to achieve the compression. The average compression ratio achieved is 1.2 :
1, which is not significant considering the computation cost of the algorithm. The regular scanned
document takes computation time up to 10 min. So, the images in the dataset are resized to 512 X 512
pixel size and further computation time is observed. For this size of images, the computation time
results 21.30 sec./ image. This time is also higher considering the size of image. To improve the CR
and minimizing the computation cost the bit-plane slicing based lossy compression algorithm
(Algorithm 1) is proposed, it has enhanced the CR a bit and the CT is also halved. Further to avoid
information loss a (8,4) and need of image resizing, the Hamming code-based algorithm (Algorithm 2)
is tested. It further enhanced the CR but the CT once again increased up to original algorithm. This
performance of mentioned algorithms is presented using Table 1 below.
Table 1. Comparison of purely Hamming code-based algorithms based on CR and CT.
Sr. No. Algorithm CR (CR:1) CT (sec/
image)
1Algorithm 0 1.20 21.30
2Algorithm 1 1.24 10.32
3Algorithm 2 1.29 19.15
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As both the parameters CR and CT offered by these algorithms are not attractive, the quantization-
based algorithms (Algorithm 3, Algorithm 4, and Algorithm 5) are proposed, avoiding traversing
throughout the image for checking the validity of codewords. These algorithms have achieved the
significant CR along with 100 times less CT. The quality of decompressed image using quantization
approaches is computed based on the parameters like Correlation of input output images, its Mean
Squared Error, Signal to Noise Ratio, Structural Similarity Index Metric to compute the retainment of
structural properties of the images, Compression Ratio achieved and the Computational Time. The
results are presented in Table 2.
Table 2. Comparison of quantization-based algorithms.
It can be observed from the above table that Algorithm 5 performs better than others considering the
mentioned parameters except MSE and CT; the MSE of algorithm 3, that is less 1 bit/image lesser than
Algorithm 5 and CT of Algorithm 4 is least, that is about 0.02 sec lesser than Algorithm 5. The
Correlation and SSIM offered by this algorithm are highest, which is very significant while proposing
the near-lossless algorithm. The performance of quantization-based approach computed over mentioned
three classes using the image quality metrics discussed is presented below. The average values for these
classes are shown to get overall idea about performance of algorithm.
4.1. CORRELATION
The 2D correlation between the input image and the decompressed result is calculated, it ranges from
0-1, where value ‘1’ represent that both the images are identical. The values near to ‘1’ signifies the
near-lossless compression. The performance is displayed using Fig. 2.
Algorithm
3
Algorithm
4
Algorithm
5
Correlation
(0-1) 0.9420 0.9629 0.9658
MSE
(bits/image) 11.22 37.80 12.13
PSNR
(Ratio) 39.19 33.22 39.17
SSIM
(0-1) 0.9295 0.9308 0.9519
CR
(CR:1) 3.04 3.31 3.31
CT
(sec/image) 0.2575 0.1132 0.1314
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Fig. 2. Comparison of algorithms based on Correlation.
4.2. MSE
The most used estimator of image quality is MSE refers to the metric giving cumulative squared error
between the original and compressed image. Near zero values are desirable. The performance is
displayed using Fig. 3.
Fig. 3. Comparison of algorithms based on MSE.
4.3. PSNR
The Peak Signal to Noise Ratio is positive indicator of performance of compression algorithms. The
performance is displayed using Fig. 4, here the Algorithm 5 offers the highest PSNR value, which is a
good indicator of its applicability.
0,8500
0,8875
0,9250
0,9625
1,0000
Algorithm3
Algorithm4
Algorithm5
0,9658
0,9629
0,942
0,9479
0,9261
0,989
0,9723
0,9646
0,9277
graphs diagrams equa<ons average
0,00
12,50
25,00
37,50
50,00
Algorithm3
Algorithm4
Algorithm5
12,1272
37,8001
11,2214
20,4547
40,708
17,7831
6,6826
28,7154
6,1792
9,2443
43,977
9,7019
graphs diagrams equa<ons average
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Fig. 4. Comparison of algorithms based on SNR.
4.4. SSIM
The Structural Similarity Index Measure (SSIM), a perception-based measure, considers image
degradation as a perceived change in structural information. These techniques differ from others like
Mean Squared Error (MSE) and Signal to Noise Ratio that include evaluate absolute errors (SNR).
According to the theory behind structural information, pixels are highly interdependent, when they are
spatially close to one another. These dependencies carry important details about how the elements in an
image are arranged. In our experimentation Algorithm 5 has the highest SSIM, which is another good
indicator of the quality of a compression algorithm. The performance is displayed using Fig. 5.
Fig. 5. Comparison of algorithms based on SSIM.
4.5. COMPRESSION RATIO
Here, the average compression ratio for the considered images, ranges from 3.04 : 1 to 3.31 : 1,
algorithm 5 having the highest value and algorithm 3 having the lowest. The compression ratio is a
useful indicator of decompression effectiveness, the higher value indicates a better algorithm. The
performance is displayed using Fig.6.
30,00
32,50
35,00
37,50
40,00
Algorithm3
Algorithm4
Algorithm5
39,1723
33,2156
39,1873
38,8653
32,8253
38,96
39,1208
33,2439
38,99
39,5308
33,5777
39,6
graphs diagrams equa<ons average
0,8800
0,9075
0,9350
0,9625
0,9900
Algorithm3
Algorithm4
Algorithm5
0,9519
0,9308
0,9289
0,8976
0,8948
0,9841
0,9724
0,9712
0,9226
graphs diagrams equa<ons average
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Fig. 6. Comparison based on Compression Ratio.
4.6. COMPUTATION TIME
Finally, computational time is used to study the time complexity of the algorithm; in this case,
Algorithm 4 tends to be the most efficient and requires the least amount of time. The performance is
displayed using Fig. 7.
Fig. 7. Comparison based on Computation Time.
Algorithm 5 having highest CR, executes faster and performs better in terms of quality of
decompressed image. So, one can conclude that the Algorithm 5 tends to the most optimized algorithm
for Near-lossless compression of Document Images.
5. CONCLUSIONS
Compression offers an attractive option for efficiently storing large amounts of data. Document Images
are multi-tone images, separate algorithm for different regions may improve the compression outcomes.
Lossy algorithms are best for regions like photographs, lossless are necessary in case of sensitive
regions like text and the non-textual but text consisting important regions like figures, plots and
equations needed to be treated with near-lossless techniques. They are advantageous for maintaining the
trade-off between compression ratio and quality of reconstructed image. In this work the channel
coding algorithm like Huffman codes is implemented with its different specifications, the work is
further optimized based on time complexity and quality of decompressed image. Considering the higher
Correlation, PSNR and SSIM values obtained, one can understand that the quality of the decompressed
images is really good, and the algorithms can be considered as near-lossless algorithms. It is also
concluded that the (8, 4) Hamming code with even and odd conjugate complementary codes and based
32 quantization levels works best amongst the other discussed.
0,00
1,00
2,00
3,00
4,00
Algorithm3
Algorithm4
Algorithm5
3,3131
3,0381
3,8392
3,8392
3,6585
2,8406
2,491
3,2596
3,2596
graphs diagrams equa<ons average
0,00
6,50
13,00
19,50
26,00
Algorithm0
Algorithm1
Algorithm2
19,1531
10,3246
21,2962
21,5805
16,6384
25,4826
21,0432
7,3972
21,6251
14,8357
6,938
16,7808
graphs diagrams equa<ons average
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6. FUTURE SCOPE
After observing the performance of various hamming code-based algorithms, one may be encouraged to
practice them and do some modification. So, the first thing that may be tried is to make use of (3,1) and
(4,1) specifications of Hamming code. Further, after the quantization to newly achieved gray levels is
done, one can implement probability-based coding scheme like Huffman or Arithmetic codes to
represent the data more effectively.
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AUTHORS BIOGRAPHY
Mr. Prashant Laxmanrao Paikrao is Ph.D. Research Scholar in Electronics
& Telecommunication Engineering department of SGGSIE&T, Nanded
(M.S.), India. He is an active member of IE, ISTE and IETE. His area
of interest is Image Processing, Digital Logic Design, Fuzzy Logic.
https://doi.org/10.17993/3ctic.2022.112.225-237
3C TIC. Cuadernos de desarrollo aplicados a las TIC. ISSN: 2254-6529
Ed. 41 Vol. 11 N.º 2 August - December 2022
236
Dr. Dharmapal Dronacharya Doye is Professor in Department of
Electronics & Telecommunication Engineering of SGGSIE&T, Nanded
(M.S.), India. He is an active member of IE, ISTE and IETE. His area
of interest is Image Processing, Video Processing, Artificial
Intelligence.
Dr. Milind Vithalrao Bhalerao is Assistant Professor and Head of
Electronics & Telecommunication Engineering Department of
SGGSIE&T, Nanded (M.S.), India. He is an active member of ISTE
and IETE. His area of interest is Image Processing, Robotics, Artificial
Intelligence.
Dr. Madhav Vithalrao Vaidya is Assistant Professor in Information
Technology Department of SGGSIE&T, Nanded (M.S.), India. He is
an active member of IEEE, ISTE and IETE. His area of interest is Data
Mining, Image Processing, Pattern Recognition, Blockchain
Technology, and Internet of Things.
https://doi.org/10.17993/3ctic.2022.112.225-237
3C TIC. Cuadernos de desarrollo aplicados a las TIC. ISSN: 2254-6529
Ed. 41 Vol. 11 N.º 2 August - December 2022
237