**Open Access**-
**Total Downloads**: 19 -
**Authors :**Dr. Sandeep Mathur , Dr. Anjali Mathur , Nitesh Agarwal -
**Paper ID :**IJERTCONV3IS23012 -
**Volume & Issue :**NCETRASECT – 2015 (Volume 3 – Issue 23) -
**Published (First Online):**24-04-2018 -
**ISSN (Online) :**2278-0181 -
**Publisher Name :**IJERT -
**License:**This work is licensed under a Creative Commons Attribution 4.0 International License

#### An Analysis of Variation in Lossless Image Compression using FMM & Threshold Value 10

Dr. Sandeep Mathur1

Department of Mathematics

Jodhpur Institute of Engineering & Technology

Jodhpur, India

Dr. Anjali Mathur2

Department of Mathematics

Jodhpur Institute of Engineering & Technology

Jodhpur, India

Abstract A digital image store its color information in digits format in digital devices. This information store in pixel matrix. Image compression process reduce required storage size of image

r. t to digital device or communication system. Image compression process use two technique to compress image lossless image compression & lossy image compression. Images that provide numerical, secure & financial information compressed using lossless image compression because we required original data back after decompression process. Lossless image compression uses some entropy encoding techniques like RLE, Huffman encoding, LZW encoding etc. Present papers deals with lossless image compression using RLE as entropy encoding, & compare this lossless image compression with some modification by FMM (Five Module Method) & by Threshold value 10. RLE give best compression ratio when image pixel matrix has repeated sequence of pixels. To make repeated sequence in pixel matrix in this paper two method used FMM & TH=10. These method modify pixel original matrix & make repeated sequence in this matrix before RLE to get a good compression ratio.

Key Words: FMM, RLE, MSE, PSNR, TH=10.

INTRODUCTION

There are numerous applications of image processing, such as satellite imaging, medical imaging and video where the image size or image stream size is too large and require a large amount of storage space or high bandwidth for communication in its original form. Every storage device & communication bandwidth cannot satisfy this requirement hence image compression techniques are used in such type of applications where image size is too large to store in digital device & too large for communication purpose. Image compression plays a very important role in application like tele-videoconferencing, remote sensing, document & medical imaging and facsimile transmission, which depends on the efficient manipulation, storage & transmission of binary, gray scale or color images.

Nitesh Agarwal3

Department of Computer Science Jodhpur Institute of Engineering & Technology

Jodhpur, India

Image compression techniques can be classified into two categories lossless image compression & lossy image compression. Images that provide numerical, Secure & financial information compressed using lossless image compression because we required original data back after decompression process. But other images like multimedia images can be compressed using lossy image compression because the human eye is very tolerant of approximation error in an image. Hence we may decide to exploit this tolerance to produce increased compression, at the expense of image quality by reducing some pixel data or information. Lossless image compression use some entropy encoding techniques like Run Length Encoding (RLE), Huffman Encoding, LZW (Lempel Ziv Welch) Encoding, and Area Encoding. This paper deals with RLE as a entropy encoding in lossless image compression. RLE entropy encoding give good compression ratio when image have repeated pixel value sequentially but all the image not have such type of repeated pattern hence present paper use FMM (Five Module Method) & Threshold value before RLE to make repeated sequence.

Lossless Image Compression

In lossless compression, every single bit of data that was

originally in the file remains after the file is uncompressed. All of the information is completely restored. This is generally the technique of choice for text or spreadsheet files, where losing words or financial data could pose a problem. Process of lossless image compression is shown in fig 1 [11].

Image

Entropy Encoding

Image

Entropy Encoding

Channel

Image

Image

Entropy Decoding

Fig 1: Lossless Image Compression Process

Five Module Method (FMM)

In most of images, there is a common feature which is the

After the FMM pixel matrix contain a good no of repeated pixel as shown in table 2. This repeated pixel helps the RLE to compress pixel matrix.

RLE

RLE

neighboring pixels are correlated. Therefore, finding a less correlated representation of image is one of the most important tasks. One of the basic concepts in compression is the reduction of redundancy and Irrelevancy. This can be done by removing duplication from the image. Sometime, Human Visual System (HVS) cannot notice some parts of the signal,

i.e. omitting these parts will not be noticed by the receiver. This is called as Irrelevancy. FMM read each pixel value row by row & divide each pixel value by 5 & add or subtract the reminder from original pixel to get repeated pixel values. The basic idea in FMM is to check the whole pixels metrics and transform each pixel into a number divisible by 5 according to the following conditions.

Image

FMM

Image with Some Pixel modification

Image with Some Pixel modification

Fig 2: Image Compression Using

FMM FMM algorithm

Inverse RLE

Inverse RLE

Channel

if A(i,j) Mod 5 = 4 A(i,j)=A(i,j)+1

else if A(i,j) Mod 5 = 3

A(i,j)=A(i,j)+2

else if A(i,j) Mod 5 = 2

A(i,j)=A(i,j)-2

else if A(i,j) Mod 5 = 1

A(i,j)=A(i,j)-1

For ex.

Input: Pixel matrix of input image. Output: Transformed Pixel Matrix.

{ w = width of pixel matrix; h

= height of pixel matrix;

pixel[h][w] = pixel matrix of original image; for(i=0; i<h; i++)

{ for(j=0; j<w; j++)

{ if pixel(i,j) Mod 5 = 4 pixel(i,j)=pixel(i,j)+1

else if pixel(i,j) Mod 5 = 3

pixel(i,j)=pixel(i,j)+2 else if pixel(i,j) Mod 5 = 2

pixel(i,j)=pixel(i,j)-2 else if pixel(i,j) Mod 5 = 1

pixel(i,j)=pixel(i,j)-1

121

122

122

123

124

125

105

110

130

132

132

131

134

135

133

220

221

222

222

223

224

225

205

300

425

426

427

500

501

502

501

905

521

522

522

523

524

525

555

660

630

632

632

631

634

635

633

633

851

852

852

963

964

965

205

300

425

426

427

500

501

502

501

905

121

122

122

123

124

125

105

110

130

132

132

131

134

135

133

220

221

222

222

223

224

225

205

300

425

426

427

500

501

502

501

905

521

522

522

523

524

525

555

660

630

632

632

631

634

635

633

633

851

852

852

963

964

965

205

300

425

426

427

500

501

502

501

905

Table 1: Input Pixel matrix

Table 1 shows a 2D pixel matrix but this matrix cannot be compressed using RLE because pixel value not repeated sequentially. FMM method convert this matrix so that it can be compressed using RLE

120

120

120

125

125

125

105

110

130

130

130

130

135

135

135

220

220

220

220

225

225

225

205

300

425

425

425

500

500

500

500

905

520

520

520

525

525

525

555

660

630

630

630

630

635

635

635

635

850

850

850

965

965

965

205

300

425

425

425

500

500

500

500

905

Table 2: Transformed Pixel matrix

}

}

}[5].

TH (Threshold) value Method

TH value method take pixel value from 2D pixel matrix row by row. TH value method uses two node 1st node store the 1st pixel & 2nd node move forward row by row in pixel matrix. TH value method take pixel difference between pixel value store in these two node & repeat the pixel value store in node 1 until difference between these two nodes are not greater than threshold value 10. Once a difference greater than 10 occurs node 1 store that pixel & node 2 traverse pixel one by one from neighboring pixel of pixel store in node 1 & same process is follow until complete pixel matrix not traversed. For example

201

200

205

210

301

300

305

310

406

404

407

406

506

504

507

506

602

601

600

602

702

701

700

702

828

829

830

832

928

929

930

932

301

305

302

303

105

104

100

102

655

654

653

650

651

652

657

658

702

705

704

702

701

801

805

809

105

105

105

105

105

106

112

111

Table 3: Pixel matrix of input image

Pixel Value

Repetition

Pixel Value

Repetition

Pixel Value

Repetition

120

3

205

1

630

4

125

3

300

1

635

4

105

1

425

3

850

3

110

1

500

4

965

3

130

4

905

1

205

1

135

3

520

3

300

1

220

1

525

3

425

3

220

3

555

1

500

4

225

3

660

1

905

1

Pixel Value

Repetition

Pixel Value

Repetition

Pixel Value

Repetition

120

3

205

1

630

4

125

3

300

1

635

4

105

1

425

3

850

3

110

1

500

4

965

3

130

4

905

1

205

1

135

3

520

3

300

1

220

1

525

3

425

3

220

3

555

1

500

4

225

3

660

1

905

1

Table 3 metrics cannot be compressed by RLE

201

201

201

201

301

301

301

301

406

406

406

406

506

506

506

506

602

602

602

602

702

702

702

702

828

828

828

828

928

928

928

928

301

301

301

301

105

10

105

105

655

655

655

655

655

655

655

655

702

702

702

702

702

801

801

801

105

105

105

105

105

105

112

112

Table 4: Pixel matrix of After TH value = 10

After the TH value method pixel matrix contain a good no of repeated pixel as shown in table 2. This repeated pixel helps the RLE to compress pixel matrix.

Image TH value=10 RLE Channel

Image with Some Pixel modification Inverse

Table 5: Compressed Data after RLE for Table 2

Table 5 required less storage space as compare to table 1. Table 1 require total 64 values to store but table 3 require only 54 values to store [5].

Pixel Value

Repetition

Pixel Value

Repetition

201

4

301

4

301

4

105

4

406

4

655

8

506

4

702

5

602

4

801

3

702

4

105

6

828

4

112

2

928

4

Pixel Value

Repetition

Pixel Value

Repetition

201

4

301

4

301

4

105

4

406

4

655

8

506

4

702

5

602

4

801

3

702

4

105

6

828

4

112

2

928

4

Compression Ratio (CR) = 64/54 = 1.19 Table 4 by RLE compressed as

RLE

Fig 3: Image Compression Using TH value=10

TH value = 10 algorithm

Input: Pixel matrix of input image. Output: Modified Pixel Matrix.

{ w = width of pixel matrix; h = height of pixel matrix;

pixel[h][w] = pixel matrix of original image; for(i=0; i<h; i++)

{ j=0;

tmp=pixel[i][j]; for(j=0; j<w; j++)

{ if( (difference between tmp & pixel[i][j]) > 10 ) pixel[i][j] = tmp;

else tmp=pixel[i][j];

}}} [1].

THV method used in such type of image where modifying some pixel data does not cause any big problem.

1.1.2 RLE (Run Length Encoding)

This is a very simple compression technique method used for compressing sequential data. Many digital image consist pixel values that are repeats sequentially for such type of image RLE is useful. In TH value method, & in FMM RLE receive sequential data from pixel matrix modified by TH value method & FMM, & store pixel value that repeats & no of time that pixel value repeat sequentially. For example table 2 by RLE compressed as

Table 6: Compressed Data after RLE for Table 4

Table 6 required less storage space as compare to table 3. Table 3 require total 64 values to store but table 6 require only 30 values to store [5].

Compression Ratio (CR) = 64/30 = 2.13

MAIN RESULTS & OUTPUTS

Implementation of lossless Image Compression using RLE Steps involved in this implementation

Create pixel matrix of the image.

Use RLE as entropy encoding on pixel matrix

Store matrix obtain by RLE method in to secondary storage.

To get required image read encoded matrix from secondary storage & apply entropy decoding (Run Length Decoding) on that encoded matrix.

Using this decoded matrix make pixel matrix & then using this pixel matrix to obtain required image.

Now find Compression Ratio by following formula

CR 1

CR 1

Original Im age size Output Im age size

Input image

Compressed size

CR

Size=768 KB Lena.bmp

552

7.46

Size=768 KB Baboon.bmp

624

3.44

Size=768 KB Zelda.bmp

504

7.46

Size=768 KB House.bmp

344

10.68

Size=768 KB Pappers_grey.bmp

424

7.46

Input image

Compressed size

CR

Size=768 KB Lena.bmp

552

7.46

Size=768 KB Baboon.bmp

624

3.44

Size=768 KB Zelda.bmp

504

7.46

Size=768 KB House.bmp

344

10.68

Size=768 KB Pappers_grey.bmp

424

7.46

Implementation of Image Compression using FMM & RLE

Steps involved in this implementation

Create pixel matrix of the image.

Apply FMM method on pixel matrix & apply FMM algorithm.

Use RLE as entropy encoding on pixel matrix obtain from FMM algorithm.

Store matrix obtain by RLE method in to secondary storage.

To get required image read encoded matrix from secondary storage & apply entropy decoding (Run Length Decoding) on that encoded matrix.

Using this decoded matrix make pixel matrix & then using this pixel matrix make required image.

1 H 1 W 1

1 H 1 W 1

Now we Find MSE (Mean Squared Error), PSNR (Peak Signal To Noise Ratio) & CR (Compression Ration) to determine quality of image obtain by proposed method [5] –

MSE

[O(x, y)M (x, y)]2 2

H * W x 0 y 0

PSNR=20*log10 (MAX) – 10*log10 (MSE) (3)

CR can be calculated using eq. (1).

Where H=Height of Image, W= Width of Image, variable MAX shows max value of a pixel for example here image is 8 bit hence MAX=255,

Implementation of Image Compression using TH value = 10 & RLE

Steps involved in this implementation

Create pixel matrix of the image.

Apply TH value =10 method on pixel matrix & apply TH value = 10 algorithm.

Use RLE as entropy encoding on pixel matrix obtain from TH value = 10 algorithm.

Store matrix obtain by RLE method in to secondary storage.

To get required image read encoded matrix from secondary storage & apply entropy decoding (Run Length Decoding) on that encoded matrix.

Using this decoded matrix make pixel matrix & then using this pixel matrix make required image.

Now we Find MSE (Mean Squared Error), PSNR (Peak Signal To Noise Ratio) & CR (Compression Ration) to determine quality of image obtain by proposed method by eq. (2), (3) & (1) respectively.

Outputs

Lossless image compression with RLE only

Lossless Image Compression

Uncompressed Compressed ImageImage Size=768 KB Size=343 KB

Fig 4: Lossless Image compression using RLE

Table 7: Compression Ratio

Image Compression Using FMM & RLE

Input image

Compressed image

MSE

PSNR

CR

Size=768 KB Lena.bmp

Size=296 KB

5.99

40.36

2.59

Size=768 KB Baboon.bmp

Size=432 KB

5.99

40.36

1.78

Size=768 KB Zelda.bmp

Size=280 KB

5.99

40.36

2.74

Size=768 KB House.bmp

Size=176 KB

4.49

41.60

4.36

Size=768 KB Pappers_grey. bmp

Size=296 KB

5.83

40.47

2.59

Table 8: MSE, PSNR & CR value of image after FMM &

RLE

Image Compression Using TH value=10 & RLE

Input image

Compressed image

MSE

PSNR

CR

Size=768 KB Lena.bmp

Size=87.9 KB

20.95

34.92

8.73

Size=768 KB Baboon.bmp

Size=319 KB

15.31

36.28

2.41

Size=768 KB Zelda.bmp

Size=71.9 KB

22.61

34.56

10.68

Size=768 KB House.bmp

Size=63.9 KB

16.56

35.94

12.01

Size=768 KB Pappers_grey. bmp

Size=135 KB

21.05

34.90

5.69

Table 9: MSE, PSNR & CR value of image after TH value = 10 & RLE

CONCLUSION The result presented in this document shows that

The results shows that RLE gives compressed image

without any pixel loss but compression ratio of RLE is not good w.r.t FMM & TH value = 10 .

FMM give good compression ratio than RLE but its compression ratio not god w.r.t. TH value = 10.

By comparing Table 7, Table 8 & Table 9 it is clear TH value = 10 gives best compression ratio.

By comparing Table 7, Table 8 & Table 9 it is clear FMM gives best quality of compressed image because it gives least MSE & high PSNR but CR value less than TH value=10 method. Hence with respect to quality order of best method is RLE > FMM > TH value = 10 & with respect to CR the order of best method is TH value = 10 > FMM > RLE.

Both method can be used in lossy image compression before entropy encoding technique.

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