Prashant Paikrao
SGGSIET, Nanded, Maharashtra, (India).
Dharmapal Doye
SGGSIET, Nanded, Maharashtra, (India).
Milind Bhalerao
SGGSIET, Nanded, Maharashtra, (India).
Madhav Vaidya
SGGSIET, Nanded, Maharashtra, (India).
Reception: 07/09/2022 Acceptance: 22/09/2022 Publication: 29/12/2022
Suggested citation:
Paikrao, P., Doye, D., Bhalerao, M., and Vaidya, M. (2022). Verification of role of data scanning direction in
image compression using fuzzy composition operations. 3C Tecnología. Glosas de innovación aplicadas a la
pyme, 11(2), 38-49.
3C Tecnología. Glosas de innovación aplicadas a la pyme. ISSN: 2254-4143
Ed. 42 Vol. 11 N.º 2 August - December 2022
A digital image is a numerical representation of visual perception that can be manipulated according
to specifications. In order to reduce the cost of storage and transmission, digital images are
compressed. Depending upon the quality of reconstruction, compression methods are categorized as
Lossy and Lossless compression. The lossless image compression techniques, where the exact recovery
of data is possible, is the most challenging task considering the tradeoff between the compression ratio
achieved and the quality of reconstruction. The inherent data redundancies like interpixel redundancy
and coding redundancy in the image are exploited for this purpose. The interpixel redundancy is
treated by decorrelation using Run-length Encoding, Predictive Coding, and other Transformation
Coding techniques. While entropy-based coding can be achieved using Huffman codes, arithmetic
codes, and the LZW algorithm, which eliminates the coding redundancy. During the implementation of
these sequential coding algorithms, the direction used for data scanning plays an important role. A
study of various image compression techniques using sequential coding schemes is presented in this
paper. The experimentation on 100 gray-level images comprising 10 different classes is carried out to
understand the effect of the direction of scanning of data on its compressibility. Depending upon this
study the interrelation between the maximum length of the Run and compression achieved similarly the
resultant number of Tuples and compression achieved is reported. Considering the fuzzy nature of
these relations, fuzzy composition operations like max-min, min-max, and max-mean compositions are
used for decision-making. In this way, a rational comment on which data scanning direction is
suitable for a particular class of images is made in the conclusion.
Image Compression, Data Scanning Direction, Sequential Coding, Fuzzy Composition.
3C Tecnología. Glosas de innovación aplicadas a la pyme. ISSN: 2254-4143
Ed. 42 Vol. 11 N.º 2 August - December 2022
The digital image is a function of brightness that corresponds to the intensity of pixels. This
representation involves large data associated so that the requirements of storage space, computing
power and the related communication bandwidth are very high. The technique involved is called
image compression to minimize these requirements, so that information can be depicted in a reduced
form (Gonzalez, 2004). The capacity of the compression technique to decrease the data size is called
the compression ratio. To attain lossless and lossy compression respectively, the redundant and
irrelevant data is removed (Holtz, 1993). The techniques of lossy compression have relatively higher
compression ratios than that of lossless compression. Compression ratio and reconstructed image
quality is always a tradeoff.
Nowadays, with the rise in mobile phone popularity, images are becoming an important record form.
Image compression is required for storing and processing large numbers of such images. Depending
upon the requirement of data preservation and accuracy reconstructed data quality, DC techniques can
be divided into lossless and lossy compression. Compressing the data without sacrificing its originality
is the main objective of lossless image compression, the reconstructed data is identical to original data
in lossless compression, and it is suitable primarily for applications in compression of Text, medical
imaging, law forensics, military imagery, satellite imaging, etc. In lossy compression the reconstructed
data is an acceptable approximation of original data, here higher compression ratio can be achieved its
applicable in compression of natural images, audio, video, etc. (Hosseini, 2012).
There is always a limit to the compression ratio that can be achieved in Lossless Compression
(Rehman, 1952). According to Shannon, on the other hand, in lossless compression techniques, the
measure of the amount of information content (Entropy) in the data that can be used to find the
theoretical maximum compression ratio for lossless compression techniques, data can be compressed
into as small as 10 percent of its actual size, and as the compression techniques require less-complex
encoders and decoders as compared to lossless techniques.
The Shannon Entropy concept is explored in the paper to point out different possibilities to increase
the compression ratio to its maximum extent. The paper discusses the different concepts related to
compression techniques. One alternative to deal with the tradeoff between image quality and
compression ratio is to opt for Near-Lossless compression, where difference between the original and
reconstructed data is within user-specified amount called as maximum absolute distortion (MAD).
This may be suitable for compression of medical images, hyper spectral images, videos, etc.
In addition to the storage space requirements and the overhead of processing time, all users on a
specific network are suggested to minimize the size of the data and use the network resources
optimally (Kavitha, 2016). Since compression is both time-effective and cost-effective, it helps to
share network resources to enhance network performance.
In 1999, Holtz gave a review of lossless image compression techniques, saying," Theories are usually the
starting point of any new technology.' There are some lossless compression methods explained, namely
Shannon's theory, Huffman code, Lempel-Ziv (LZ) code and data trees for Self-Learning Autopsy. Hosseini
submitted another review in 2012, which discussed many algorithms with their performances and
applications. It includes Huffman algorithm, Run Length Encoding (RLE) algorithm, LZ algorithm,
Arithmetic coding algorithm, JPEG and MPEG with their applications.
3C Tecnología. Glosas de innovación aplicadas a la pyme. ISSN: 2254-4143
Ed. 42 Vol. 11 N.º 2 August - December 2022
Image Compression deals with the ways in which the data and space needed to represent and store the
digital image are reduced. The elimination of data redundancy may be one of the strategies for achieving
compression. Human Visual System Redundancy is categorized into three categories: Spatial Redundancy,
Spectral Redundancy, and Temporal Redundancy. Spatial redundancy, which is the correlation of
neighborhood image pixels. Spectral redundancy is a correlation measure of an image between different
color planes (Spectral Bands). The Temporal Redundancy deals with the correlation between a video's
consecutive image frames.
In lossless data compression, the removal of data redundancy is the key process, and the data redundancy
(Rd) is given by equation 2.1.
CR (Compression Ratio) = n1/n2,
n1: Size of compressed data, n2: Size of uncompressed data
Types of data redundancy are as follows,
1. Coding Redundancy
2. Inter-pixel Redundancy
3. Psycho-visual Redundancy
A code is a system of symbols used for information representation. The pieces of information are
represented by a combination of symbols called a codeword, and their length is called the number of
symbols in a codeword. The available grey levels in an image are assigned to various codewords. If the
grey levels are coded by using longer codewords than needed, an image is said to have coding redundancy.
An image's gray-level histogram is created to construct codes with reduced coding redundancy. It is
suggested that the most frequent grey levels should be represented by shorter codewords and vice versa to
achieve the shortest representation, i.e., to avoid coding redundancy in the data. This variable length coding
process may result in an image being shorter overall than the representation of the fixed length code. And
when probability-based method(s) are used to design the code, it guarantees the shortest representation. The
present coding redundancy is less than optimal, meaning codewords are used for representation, not as
short as possible. Below is the average number of bits required to represent each pixel, given by equation
2.2 and 2.3.
n – Total number of pixels
– Number of bits used to represent gray level of individual pixel
– Probability of occurrence of gray level .
N – Number of times the nth gray level appears in image
L – Number of gray levels
3C Tecnología. Glosas de innovación aplicadas a la pyme. ISSN: 2254-4143
Ed. 42 Vol. 11 N.º 2 August - December 2022