Lossy and lossless compression using combinational methods

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Lossy and lossless compression using

combinational methods

Ms. C.S Sree Thayanandeswari,M.E, MISTE, Assistant Professor, Department of ECE, PET Engineering College, Vallioor.

J Jeya Christy Bindhu Sheeba, Dept of ECE, IIndM.E(C.S) PET Engineering College, Vallioor .

Abstract—Image compression is the process of reducing the amount of data required to represent an image. Image Compression is used in the field of Broadcast TV, Remote sensing, Medical Images. Many common file formats are surveyed and the experimental results of various states of lossy and lossless compression algorithms are given .In the proposed method, image is compressed by using lossy and lossless methods for different types of images. Here, the lossy compression is done by the fractal decomposition code and lossless compression is done by using the LZW algorithm. LZW is the dictionary based algorithm, which is simple and can be used for the hardware applications. Fractal compression represents the image in a contractive form. Inspite of its lossy nature it can be used for the case of lossless compression. A general comparison is done based on analyzing the parameters such as Peak Signal to Noise Ratio (PSNR), Mean Square Error(MSE), Image fidelity (IF), Absolute Difference (AD) to the different types of images.

IndexTerms Image compression, LZW, Fractal decomposition, mean square error.

1. INTRODUCTION

In the digitized world of today, the role played by computer and its applications are mandatory in each and every field. There are many fields which has the wide variety applications of the audio, image and digital video processing. In order to handle more number of data (images, videos) there is a requirement of large amount of space and a huge bandwidth for the process of transmission. The good solution for this problem is the compression of the images which reduce the redundant information and increase the space.

In this paper, LZW algorithm is capable of producing compressed images without having an effect on the quality of the image. This can be successfully brought about by reducing the total number of bits needed to constitute each pixel of an image. Thus, in

succession which minimize the memory space needed to store images and transmission can be done with little amount of time. There are two types of image compression. They are lossy and lossless image compression. Depending on the application and the degree of compression any one of the two types can be chosen. Lossless compression is used where the exact replica of the original image is to be produced. Lossy compression can be affected by the loss of data compared to the original image. The improvement of this type is that it provides a scope for high compression ratios than the lossless compression

Fig1.Block diagram of image compression system

The most common characteristics of the images are the nearby pixels are compared and then they have the unwanted information. The first quest is to find reduced number of similar depiction of the image. The two major elements of compression are redundancy and reduction in irrelevancy.

Reduction in redundancies aims in getting rid of the mimeo from the source signal. Reduction in the irrelevancy neglects the part of the signal that is not seen by the receiver or the Human Visual Display System.

Original image

Encoder

Channel

Recreated image

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Fig.2Block diagram for the proposed system

The block diagram consists of the input image. At first the input image is to be compressed by the LZW algorithm. In order to be compressed by LZW it must be transformed to binary image. The grey scale image is to be converted from the decimal value to binary value. The binary image which is compressed by LZW is then divided into blocks which have 7 bits each; since it wants only 7 bits to depict a byte. This is known by the term decoding by BCH. Thus the compressed image is obtained.

Then the reverse process of decoding is to be done to delete the extra added 7 bits. Then the result so obtained is to be decompressed to get the binary image. To obtain the original image, the binary image is to be transformed to grey scale image.

3. PROPOSED METHOD

The proposed method uses a compression methodology using the two lossless techniques LZW along with Huffman coding and then the Discrete Cosine Transform (DCT). Next, along with these lossless techniques the proposed method also has the lossy algorithm as fractal compression. Fractal compression algorithm removes some information from the input image and the output given by the fractal method is not so clear. DCT algorithm produces a blurred output. LZW algorithm produces the result which is same as that of the original image. The LZW algorithm is superior to other compression techniques.

3.1 LZW ALGORITHM

The LZW algorithm is named after the scientists Lempel, Ziv and Welch. It is a simple dictionary based algorithm used for the lossless compression of images. Dictionary based algorithms are nothing but they are arranged in the form of dictionary. The algorithm first searches the file and then it arranges the dates in sequences of strings which occur repeatedly. The LZW algorithm then replaces the repeated text omitting the incoming text. If any one of the data is found to be new then it will add to the dictionary. These words are then saved in the dictionary and the references are added where the data gets repeated. Each word in the dictionary has a particular code. The repeated words are replaced with another code. The length of the code must be a constant one. The LZW algorithm is used where the file have more repeated strings. It s a computationally fast algorithm and is very effective, since the decompression does not need the strings to be passed to the table. LZW encoding is based on the multiplication of the encoded pixels. The principle involves in building the dictionary by substituting the patterns for the image given as input. The LZW algorithm can be applied to different types of image formats which are used to remove the repeated strings. The BCH algorithm used along with the LZW algorithm is to correct the errors or to find the errors. The size of the image file which is compressed by LZW algorithm along with BCH increased because it has monochrome images.

Input Image Compress by

LZW

Decode by BCH

Compressed image

Original image

Decompress by LZW

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DFT has a good computational efficiency but the designing of DFT is difficult and has poor energy compaction. Energy compaction is nothing but the capacity to collect the energy of the spatial coordinates in the frequency domain. Energy compaction is very much important for image compression. Since the DCT does not save any bits and also doesnot introduce any distortion hence it can be quantized and used in lossless compression.

The DCT works well in separating the image into different pixels of differing frequencies. So that it can be compressed without losing the major information. The edges and borders in the images compressed by DCT are clearly visible without any blurs and distortion. In the processing of the image by DCT, the image is first broken into 8*8 blocks of pixels. Then from the top to bottom or left to right DCT is applied to each and every block of pixels. The blocks of pixels are compressed by the process of quantization. The compressed block of array which has the image is stored in less space than the original image. To obtain the original image is done by the process of decompression which can be done by Inverse Discrete Cosine Transform (IDCT). DCT and ICDT are symmetric in nature.

Before applying DCT to the image the pixels are to be divided based in the black and white pixels. The black and white pixels range from 0 to 255. The pure black pixels are denoted by 0 and pure white pixels are given by 255. This is the reason why the image looks like black and white or grey in color. An image contains thousands of 8*8 blocks in which the compression is done in each and every block. By this way each and every block is to be compressed and the resultant image is obtained.

4 FRACTAL DECOMPOSITION ALGORITHM

The Fractal image compression is given by Integrated Function System (IFS). Here in this method it has a source image and the designation image. The source image is known as the attractor. The designation image is the output or the recreated image. At first the image is partitioned into small parts which are known as blocks. Those subdivided blocks should not overlap with other blocks. Each destination block is to be mapped with other block which is assembled after the removal of repeated bits. It has a transforming operator is known as contracting function. It transforms the compressed image but the visual effect does not change. This point is reached when the transformation is done to N points in the image which can be done by elementary transformations. This has the basic

approaches needed to compress the image known as contacting transformation. Then by dividing and contacting the image by a transformation it is named as fractal transformation or fractal decomposition. It is advantageous since it depicts the image in a contractive form. Fractal compression is a recent method on lossy compression based on the use of fractals which degrades the likeliness of different parts of an image.

5 PERFORMANCE CRITERIA FOR IMAGE COMPRESSION

SNR:

The standardized quantity of measuring the image quality is the signal-to-noise ratio. It is given by ratio of the power of the signal to the power of noise in the signal. SNR is given in decibels by

𝑆𝑁𝑅 𝑑𝑏 = 10 log10

σx2

MSE⁡

PSNR:

The most common case of representing the picture of the input image is given by the Peak value of SNR. It is defined as the ratio of the maximum power of the signal to the power of the corrupted noise signal.

𝑃𝑆𝑁𝑅 𝑑𝑏 = 10 log10

2552

𝑀𝑆𝐸

Where the value 255 is the peak in image signal.

MSE:

Mean square error is defined as the measure of average of square of ratio of estimator output to the estimated output. it is also known as the rate of distortion in the retrieved image. Mean square error is given in decibels by

𝑀𝑆𝐸 𝑑𝑏 = 1

𝑥𝑦 𝑋 𝑚, 𝑛 − 𝑌(𝑚, 𝑛)

2 𝑦−1

𝑛=0 𝑥−1

𝑚 =0

6 RESULTS AND DISCUSSION

The performance comparison between lossy and lossless images is done using MATLAB. The lossy compression is done by using fractal decomposition method and lossless compression is done by two compression algorithms DCT and LZW.

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This loaded image is further preceded to the next stage of lossy compression. The next stage gives the compressed image by fractal decomposition method. The loaded input image is converted to grayscale values and then the binary values are obtained from it, then the binary values are converted to compressed image. Next upcoming step gives; the image which is compressed by the fractal decomposition method is then compressed by the lossless compression technique of DCT algorithm. This provides a better result than the fractal compression method. The image which is compressed by the DCT algorithm is then compressed by LZW algorithm which is a lossless method. This provides a better result than the DCT algorithm. Further, image which is compressed by the DCT algorithm is then compressed by LZW algorithm which is a lossless method. This provides a better result than the DCT algorithm.

This algorithm based on the combinational method has the combination of fractal decomposition for lossy method and DCT, LZW for the lossless compression. Here in this thesis different image types such as bmp, tif, png, jpg formats are used .those image formats are black and white type. The given colored images are processed in the form of gray scale images only.

Input Image Image obtained by fractal method

Image by DCT Image by LZW

Fig3 Result of Compressed Image of bmp Type

Fig4 Result of Compressed Image of tif Type

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Fig6 Result of Compressed Image of jpeg Type

PARAMETERS VALUES OBTAINED

LOSSY COMPRESSION BY FRACTAL

DECOMPOSTION

Average absolute

difference

0.2198

Image fidelity 0.1851

SNR 7.3152

PSNR 9.8407

MSE -0.0717

LOSSLESS COMPRESSION BY LZW

Average absolute

difference

0.0105

Image fidelity 0.0004

SNR 3.1696

PSNR 5.7365

MSE -0.0001

Table1: Summarized Result

IMAGE TYPE

IMAGE NAME

PSNR SNR MSE

bmp bird 5.73 3.16 0.0001

tif women -20.23 -25.39 0.10

png balloon -22.64 -22.91 0.18

[image:5.612.72.289.385.702.2]

jpeg penguin 9.87 7.35 0.07

Table 2 Comparison of different image types

7 CONCLUSION

Thus the compression is a theme which gains much significance and it can be used in many applications. This thesis presents the lossy and lossless image compression on different file format of images. Many different types of methods have been assessed in account of quantity of compression that they offer, effectiveness of the method used and the sensitivity of error. The effectiveness of the method used and the sensitivity to error are sovereign of the feature of the group of source. The level of the compression attained greatly depends on the source file. It is terminated that the higher data redundancy favors to reach more compressed image. The proposed method has the advantage of LZW algorithm which is combined with the fractal decomposition method is known for the clarity and fastness. The major goal is to reduce the computational time and minimize the space occupancy.

The tests were carried on the different types of image sets and their results were assessed by the clarity and then by bits per pixel. The demonstrational rating gives that the proposed method has improvement while comparing with other conventional methods.

8 FUTURE WORKS

The future works aims in achieving a better compression ratio by using various new techniques. The proposed method is on various image types but it is limited to the videos. New algorithms can be merged and resolved that reduced the computational time which occurred by the creation of dictionary in LZW method.

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Sree Thayanandeswari received the B.E degree in Electronics and communication from Anna University ,Chennai, 2007 and M.E degree from Anna University ,Chennai, 2013. She is currently working as an Assistant Professor in the PET Engg college,Department of Electronics and Communication, Vallioor. Her research areas include digital image processing.