VERIFICATION OF ROLE OF DATA SCANNING

DIRECTION IN IMAGE COMPRESSION USING

FUZZY COMPOSITION OPERATIONS

Prashant Paikrao

SGGSIET, Nanded, Maharashtra, (India).

E-mail: plpaikrao@gmail.com

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. https://doi.org/10.17993/3ctecno.2022.v11n2e42.38-49

https://doi.org/10.17993/3ctecno.2022.v11n2e42.38-49

3C Tecnología. Glosas de innovación aplicadas a la pyme. ISSN: 2254-4143

Ed. 42 Vol. 11 N.º 2 August - December 2022

38

ABSTRACT

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.

KEYWORDS

Image Compression, Data Scanning Direction, Sequential Coding, Fuzzy Composition.

https://doi.org/10.17993/3ctecno.2022.v11n2e42.38-49

3C Tecnología. Glosas de innovación aplicadas a la pyme. ISSN: 2254-4143

Ed. 42 Vol. 11 N.º 2 August - December 2022

39

1. INTRODUCTION

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.

2. MACHINE LEARNING METHODS AND FEATURE

IMPORTANCE

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.

https://doi.org/10.17993/3ctecno.2022.v11n2e42.38-49

3C Tecnología. Glosas de innovación aplicadas a la pyme. ISSN: 2254-4143

Ed. 42 Vol. 11 N.º 2 August - December 2022

40

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.

(2.1)

Where,

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

2.1 CODING 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.

(2.2)

Where,

n – Total number of pixels

– Number of bits used to represent gray level of individual pixel

– Probability of occurrence of gray level .

(2.3)

Where,

N – Number of times the nth gray level appears in image

L – Number of gray levels

https://doi.org/10.17993/3ctecno.2022.v11n2e42.38-49

3C Tecnología. Glosas de innovación aplicadas a la pyme. ISSN: 2254-4143

Ed. 42 Vol. 11 N.º 2 August - December 2022

41