Optimization Of Fractal Compression Using Genetic Algorithm

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Image compress pace for storing ransmission of equires image ensing etc. Frac for better image within the same higher compress echnique. Usua complexity in en applied to reduce encoding. The e method will redu preserving the im Keywords: Fr algorithm, encod

1. Intro

mage compres number of bits compression h

nformation tra of data canno capacity. Henc plays a very

ransmission. F mage coding t Micheal Barns principle of F similar portion self similar po fractals are use his was impro Encoding and feature in sto majority of compression m

echnique, whi approximation from higher c encoding time had been propo still it takes lon

his FIC is that at the same tim

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sion is a method g images and v

the same. Som compression is ctal image comp e compression, e image to rem sion ratio. FIC i ally fractal com ncoding. In this

e the search tim experimental res uce the time requ mage quality wel

ractals, Iterated ding time, compr

oduction

ssion is conce which is used has become a ansmission and ot be stored i ce the compre important ro Fractal image

technology wh sley in 1987 FIC. This type ns which exist ortions are cal ed in order to oved by Arnau decoding of a oring and tran the methods methods. FIC ich means that

of the original complexity in but lesser dec osed to speed u nger encoding t it achieves th me keeping the r

ional Journal of In

of Fracta

PG Student, Depa RajaRajes ciate Professor,

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ract:

d in which we c ideo which will me of the appl multimedia, in pression (FIC) i it exploits the move the redund is a lossy imag mpression suffe paper the genet me and speed up

sults shows that uired to encode a ll.

d function sys ression ratio, PS

erned with mi to represent an a very vital d storage [13]. H

if there is a ession of bits

le in storage compression hich was first

[1], who intro e encoding u

in the same i lled as fractal compress an ud. E. Jacqin an image has nsmitting the which exis is a lossy t the decoded l image [3], [4] encoding; it oding time. M up the encodin g time. The ma

he higher comp reconstructed i

novative Science,

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Veena K K 1 ,

artment of Elect swari College of Department of E eswari College o

can reduce the l be helpful in lication which nternet, remote is an approach self similarity dancy and get ge compression ers from high tic algorithm is

the process of t the proposed an image while

stem, Genetic SNR

inimizing the n image. Data concept for Huge amount

low storage in an image as well as (FIC) is an projected by oduced basic ses the self-image. These ls, and these

image. Later in 1992 [2]. been a vital image. The t are lossy

compression image is an ]. FIC suffers takes longer Many methods

ng process but ain benefit of pression ratio image quality

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The rest o gives the Section 3 4 tells ab follows th implemen finally in

2. F

Fractal Im Michael principle encode th storage sp image. FI image, ba of the im these sel fractals a algorithm geometric codes’ wh of the im resolution can obser part of the

echnology, Vol. 2

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mmunication Eng angalore, India,, Communication Bangalore, India

of the paper is brief descripti explains the I bout the proper he Genetic Al ntation of the section 7 conc

Fractal Ima

mage Compres Barnsley in of FIC. FIC he image in s pace by using IC is a lossy c ased on fractal mage resemble

f similar part are used in or ms converts the c shapes into m hich are later u mages is conve n independent rve that whole e same image.

Fig 1 E

Issue 5, May 2015

Genetic

ineering, ,

Engineering,

s organized as ion of fractal im Iterative functi rty of self – si lgorithm. Sect proposed syst clusions are pro

age Compre

ssion (FIC) wa 1987, who is a technique such a way t self-similar p compression te ls. In certain i the other par ts are called rder to compr ese parts (refer

mathematical used to reconst erted into fract [5], [6]. In the image is repe

Example of fractal

5.

ISSN 2348

Algorith

follows; Secti mage compres ion system. Sec imilarity, Secti tion 6 explains tem using GA ovided.

ession

as first propose introduced b e which is use that it reduces portion of the s echnique for di images, some rts of same im

fractals and t ess image. Fr rred as fractal data called ‘fr truct an image. tal code it bec e below figure eated pattern o

fern

8 – 7968

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3. Itera

According t represented this idea of t code forms impractical improvemen using partitio

PIFS c

domain Di, mappings W IFS are c transformatio rotation an transformatio

1

Where a, b, c rotate, shrin produce cert transformatio fractals. The 2 1. Begin 2. Divide 3. Discar 4. Repea

4

.

Self- Sim

The object wh similar to a par his feature is mages we can more number o when some tran

ated Functio

to Michael Ba as a set of m taking an imag the basis

because o nt is made to oned iterated fu

consists of met I=1…..n and Wi: Di X, I=1 called affine ons can be c nd scaling. L

on on I I2 th

1

c, d, e, f are co nk, and transl tain kind of se ons are used

example of IF

Fig 2 Illus

with a Square e the square int

rd the center sq at step two

milarity Pro

hich is exactly rt of itself is ca

called as self n get similar of similar portio

nsformations ar

on System

arnsley, an im mathematical e

ge and express of FIC, but of its com

it by Arnaud unction system

tric space X, a d a group of 1…..n. The im

transformati combination o Let Wi be at

o-efficient whic late the imag

elf similar pat to map these FS is shown in

strating IFS

to four equal-s

quare

operty

y similar or a alled self simila f similar prope portions and ons when rotat re done. In the

mage can be equations and it as an IFS

this found mplexity, an

d Jacquin, by m(PIFS).

group of sub f contractive ages with the ions. Affine

f translation, the affine

ch are used to e. IFS can tterns. Affine e self similar below figure

sized squares

approximately ar objects and erty. In many

we even get te, shrink and e below figure

3 of tajma resembles part whic other part called sel

But images i get the transform

Step 1: Id

Step2: Or Step3: Or Step4: Or Step5: Or Step6: Ro Step7: Ro Step8: Ro .

5

Genetic search me principles optimizat applied in [7], [8], mechanic requires o to perfo crossover range blo searched, applied. ordinates

ahal we can se s the smaller p ch is highlighte

t of the pillar. f similarity.

the exact sim in such cases t

similar portio mations are appl

dentity rthogonal refle rthogonal refle rthogonal refle rthogonal refle otation through otation through otation through

Fig 3 Illust

5. Genetic A

c algorithm (G ethod develope s in natural tion methods u n our project in [9]. GA is cs of natural se only a binary re orm the gen

r and mutation ock the matc and eight The GA para and the isome

ee that larger p ortion of the sa ed in the figur

These kinds o

milarity is not the transformat ons. In this lied, they are [

ction on mid-v

ction on mid-h

ction on first d

ction on secon

h +900 _{with cen}

h +1800 with ce

h +2700 with ce

trating similar por

Algorithm

GA) is one of th ed by mimickin

legacy. The used for differe n order to redu

a search rou election and na epresentation o etic operation n [10], [11]. In ching domain isometric tra ameters are d tric flip [12].

portion of the d ame and the p re 3 is same a of similar part

t found in all tions are applie

paper eight 14] vertical axis horizontal axis diagonal nd diagonal

nter as referenc

enter as referen

rtions

he optimization ng the evolutio ere are nume ent domains. G ce the search s ute based on atural genetics of domain varia

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co-IJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 2 Issue 5, May 2015.

www.ijiset.com ISSN 2348 – 7968

A. Chromosome:

It is constituted by three genes in our work, which are submitted to genetic modification which are optimized by genetic search. The following figure shows one chromosome format of the IFS, this will improve both speed and reconstructed quality.

X domain Y domain Flip

Fig 4 Chromosome type

B. Fitness function

The fitness function assign to each individual in numeric value that conveys its quality. The fitness denotes the ability of an individual to survive and to produce its offspring.

C. Genetic operators:

The principle operator in our work is

 Selection

 Crossover

 Mutation

Selection: It selects the parent block to produce its

offspring to create the new generation.

Crossover: It combines two individual in the population

to produce two offspring.

Eg, Parent A 10110001 Parent B 00111110 Child A 10111110 Child B 00010011

Crossover operation can be done in three ways i.e. single point crossover; two point crossover and uniform crossover.

Single point crossover: In this type, randomly a position

is chosen in the chromosome to produce the offspring. The child 1 or offspring 1 is head of chromosome of parent 1 with the tail of chromosome of parent 2 and offspring 2 (child 2) is vice versa.

Two point crossover: In this type two random positions

are selected from the chromosome to produce its offspring’s.

Uniform crossover: In this type a mask is generated

randomly and based on the mask created the offspring’s will be produced accordingly.

Mutation: It modifies the chromosome randomly

according to the mutation probability. The genes Xdomain, Ydomain and flip are changed with a random value respectively.

10111110

10101110

5. Implementation

The proposed algorithm has been tested on various images of png image formats of grey scale and color images. These were implemented using the software MatlabR2010a. The original image is preprocessed of Lena, Pepper, Barbara, Rose and . Genetic algorithm is applied to optimize the search criteria of matching domain block. Experimental results of grey images are shown in figure 6-10 with original and reconstructed image. Table 1 shows the results corresponding to images with the design metrics of compression ratio, Encoding time and PSNR. Figure 11- 15 shows the results of color images

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5.1 Experimental Results for Grey Images

Original image Reconstructed image.

Fig 6 Lena

Fig 7 Pepper

Fig 8 Barbara

Original image Reconstructed image

Fig 9 Rose

Fig 10 Taj mahal

Table 1

Results obtained for different grey images

Image Compression Ratio (CR)

Encoding time(ET) in sec

PSNR in db

Lena 32.10 17.41 38.51

Pepper 23.79 14.2 40.24

Barbara 37.5 17.5 38.46

Rose 15.9 18.03 37.79

Taj mahal 28.06 18.7 39.3

Graph 1

Comparison of CR, Encoding time and PSNR for different images

5.2 Experimental Results for Color

0

10 20 30 40 50

CR

ET

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IJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 2 Issue 5, May 2015.

www.ijiset.com ISSN 2348 – 7968

Images

Fig 11 Lena Color

Fig 12 Pepper Color

Fig 13 Barbara Color

Fig 14 Rose color

Fig 15 Tajmahal color

Table 2

Results obtained for different color images

Image Compression Ratio (CR)

Encoding time (ET) in sec

PSNR in DB

Lena 33.38 51.53 42.83

Pepper 28.87 52.46 43.43

Barbara 43.67 48.57 42.18

Rose 22.3 50.92 40.9

Taj mahal 31.35 53.43 42.86

Graph 2

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7. Conclusion

In this paper, genetic algorithm is applied for improved fractal compression. In fractal compression the search of range and matching domain block plays an important role in reduction in encoding process. Hence a new searching process is proposed using GA in order to speed up the encoding process. The proposed Genetic algorithm greatly reduces the time taken for compression while preserving the image quality well with better PSNR than any traditional methods. This algorithm is best suitable for png and bmp image formats.

References

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[2] Jianji Wang, Student Member, IEEE, and Nanning Zheng, , IEEE ”A Novel Fractal Image Compression Scheme with Block Classification and Sorting Based on Pearson’s Correlation Coefficient” IEEE transactions on image processing, vol. 22, no. 9, september 2013

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[11] A. R. Nadira Banu Kamal and Priyanga “ Parallel fractal coding for color image compression using genetic algorithm and simulated annealing “ IJCSIT International journal of computer science and information technologies, vol4, 2013. 1017-1022 [12] Y. Chakrapani and K. Soundara Rajan “ genetin

algorithm applied t fractal compression” ARPN journal of engineering and applied sciences vol 4, no.1, February 2009

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IEEE, vol. 81, no. 10, pp. 1451–1465, Oct. 1993. 0

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ET