A Review on Different Techniques of Fractal Image...

International Journal of Advanced Research in Computer Engineering & Technology (IJARCET)

Volume 6, Issue 8, August 2017, ISSN: 2278 – 1323

1164 All Rights Reserved © 2017 IJARCET

A Review on Different Techniques of Fractal Image Compression

Manish Joshi Dr. RajendraBelwal Dr. Bhumika Gupta

Assistant Professor, Professor, Assistant Professor,

Teerthanker Mahaveer University Amrapali College of Tech.& Sc., G.B.PantEngg. College,

Moradabad(U.P.) Haldwani(Uttrakhand) Pauri,Garhwal(Uttrakhand)

Abstract

The prime concern about an image is it‟s size. Fractal Image Compression is an emerging technique which may represent an

image by a contractive transform on an image space for which the settled point is near the first picture.This wide standard envelops a wide assortment of coding plans, a hefty portion of which have been investigated in the quickly developing

assemblage of distributed research. While certain hypothetical parts of this portrayal are entrenched, generally little

consideration has been given to the development of an intelligible basic picture demonstrate that would legitimize its utilization.

Most simply fractal-based plans are not aggressive with the present best in class, yet half breed plans fusing fractal compression

and option procedures have made extensively more noteworthy progress. This audit speaks to a study of the most critical

advances, both functional and hypothetical in unique fractal coding plan. In this paper, we review the essential standards of the

development of fractal objects with iterated work frameworks (IFS) using ICA and DBSCAN algorithms.

Keywords—Fractal, contractive, iterated function system.

1. INTRODUCTION

Data Compression has turned into a vital issue for

information storage and transmission. This is particularly

valid for databases comprising of countless PC pictures. As

of late, a substantial amount of strategies has showed up in

the writing for accomplishing high compression ratio for

compacted image storage and among them, the fractal

approach turn into a possible and promising compression

procedure. The field of picture coding (or compression)

manages effective methods for speaking to pictures for

transmission and capacity purposes. The essential goal of

video coding is to pack the information rate by evacuating excess data. There are two noteworthy classes of coding

plans (i.e. source coding and entropy coding). Mixed media

information requires extensive capacity limit and

transmission data transfer capacity. The information are as

designs, sound, video and picture. These sorts of

information must be compacted amid the transmission

procedure. Vast measure of information can't be put away

if there is low stockpiling limit show. Compression

facilitates a way to decrease the cost of capacity and

enhance the speed of transmission. Image compression is

utilized to limit the size in bytes of an illustrations record without degrading the pixel quality of the picture. There are

two kind of image compression approaches exist. They are

lossy and lossless. In lossless pressure, the recreated picture

after pressure is numerically indistinguishable to the first

picture. In lossy compression method, the recreated picture

contains degradation with respect to the first. Lossy

strategy causes picture quality degradation in every

pressure or decompression step. All in all, lossy strategies

accommodate more noteworthy compression ratios than

lossless procedures i.e. Lossless compression gives great

nature of packed pictures, yet yields just less compression

whereas the lossy compression strategies prompt loss of information with higher pressure proportion.The

methodologies for lossless picture pressure incorporate

variable-length encoding, Adaptive word reference

calculations, for example, LZW, bit-plane coding, lossless

prescient coding, and so forth. The methodologies for lossy

pressure incorporate lossy prescient coding and change

coding. Change coding, which applies a Fourier-related

change, for example, DCT and Wavelet Transform, for

example, DWT are the most normally utilized approach. In

the course of recent years, an assortment of capable and

complex Fractal image compression technique for image

compression have been produced and actualized. The emphasis work framework gives a superior quality in the

pictures. Source coding manages source material and yields

comes about which are lossy (i.e. picture quality is

degraded). Entropy coding accomplishes pressure by

utilizing the measurable properties of the signs and is, in

principle, lossless. Various video pressure methods have

been proposed over the most recent two decades and new

ones are being produced each day. For adequate picture

quality, these methods can just accomplish direct

diminishment in the source information not surpassing 25

and 200 times with still and persistent pictures, individually (for instance by using a versatile discrete cosine

transform(ADCT) coding plans). Unfortunately this is

turned out to be not adequate to adapt to the expanding

request in the utilization of transmission channels and

capacity media. Therefore, there is a ceaseless requirement

for assist diminishment in picture information keeping in

mind the end goal to profit by the quick advancement in

present day correspondence innovation in the most

effective way. This presumption is moved down by seeing

its consideration into end client items, for example,

Microsoft's Encarta or as a Netscape module by Iterated

Systems Inc.. Fractal picture pressure misuses the normal relative excess present in run of the mill pictures to




accomplish high pressure proportions in a lossy pressure arrange. The primary thought of the strategy comprises in

finding a development decide that delivers a fractal picture,

approximating to the first one. Fractal imagecoding has its

underlying foundations in the numerical hypothesis of

iterated work frameworks (IFS) created by Barnsley while

the primary completely mechanized calculation was

produced by Jacquin .Fractal picture coding comprises of

finding an arrangement of changes that delivers a fractal

picture which approximates the first picture. Repetition

decrease is accomplished by portraying the first picture

through littler duplicates or parts of the picture. Iterated

capacities frameworks (IFS) hypothesis, firmly identified with fractal geometry, has as of late discovered a

fascinating application in picture pressure. Barnsley and

Jacquin spearheaded the field, trailed by various

commitments .The approach comprises of communicating

a picture as the attractor of a contractive capacities

framework, which can be recovered essentially by

emphasizing the arrangement of capacities beginning from

any underlying discretionary picture. The type of repetition

abused is named piece-wise self-transformability. This

term alludes to a property that each section of a picture can

be legitimately communicated as a basic change of another piece of higher determination. Uncertainties based still-

picture pressure systems can claim to have great execution

at high pressure proportions (around 70–80). The

significant issue with fractal-based coding methods is that

of multifaceted nature at the encoding stage. However, the

intricacy of the decoder stays sensible when contrasted

with the encoding. Fractal-based systems deliver

extraordinary outcomes as far as compression in images,

holding a high level of self-likeness. Another fascinating

component of fractal-based strategies is their capacity to

create a decent quality rendered picture for a subjective

scaling factor. Fractal picture pressure is tedious in the encoding procedure. The time is basically spent on the scan

for the best-coordinate piece in an expansive space pool.

In this paper, we review the fundamental principles of the

development of fractal objects with iterated function

systems(Uncertainties), at that point we clarify how such a

system has been embraced by Jacquin for the coding

(pressure) of computerized pictures.

1.1 ITERATED FUNCTION SYSTEMS

The essential instrument utilized as a part of portraying

pictures with iterated work frameworks is the relative

change. This change is utilized to express relations between

various parts of a picture. Relative changes can be depicted

as blends of revolutions, scalings and interpretations of

facilitate tomahawks in n-dimensional space [9]. For

instance, in two measurements a point (x, y) on the picture

can be spoken to by (xn, yn) under relative change.This

change can be portrayed as takes after: The parameters a, b,

c and d play out a revolution, and their sizes result in the

scaling. For the entire framework to work appropriately;

the scaling must dependably bring about shrinkage of the separations between focuses; generally rehashed cycles will

bring about the capacity exploding to interminability. The

parameters e and f cause a straight interpretation of the fact

being worked upon. In the event that this change is connected to a geometric shape, the shape will be meant

another area and there turned and contracted to another,

littler size. Keeping in mind the end goal to delineate

source picture onto a coveted target picture utilizing

iterated work frameworks, more than one change is

frequently required and every change, i, must have a

related likelihood, 9, deciding its relative significance

regarding alternate changes. The irregular emphasis

calculation given by Barnsley [9] can be utilized to

decipher an IFS code with a specific end goal to reproduce

the first picture. This calculation is given in the

accompanying pseudo code:

(1) Set x=0 and y=0,

(2) Select transformation wi depending on its probability pi

apply transformation wi to the point (x, y) to obtain (xn,

yn),

(3) set x=xn, y=yn and plot (x, y),

(4) go to step (2) and repeat as many times as

required. Fractal has the following properties:

1. It has a fine structure, i.e., details on arbitrarily small

scales.

2. 2.It is too irregular to be described in a traditional

geometrical language, both locally and globally.

3. It usually has some form of self-similarity, perhaps

approximate or statistical.

4. Its fractal dimension (Hausdorff dimension) is usually

higher than its Euclidean dimension. 5. In most cases of interest, a fractal is defined in a very

simple way, perhaps, recursively. Most fractal

compression algorithms require the segmentation of

the image into blocks

Partition Scheme Virtual codebook

(Range Block) (Domain Block)

Figure 1 Block mappings in a PIFS

representation.

1.2 SELF-SIMILARITY PROPERTY

To encode a picture as indicated by self-likeness property. Each piece to be encoded must hunt in an extensive pool to

locate the best match For the standard full pursuit

technique, the encoding procedure is tedious in light of the

fact that a lot of calculations of comparability measure are

required. here the picture will be shaped by duplicates of

legitimately changed parts of the first. These changed parts




don't fit together, when all is said in done, to frame a precise of the first picture, thus it must permit some

blunder in our portrayal of a picture as an arrangement of

changes.

1.3 FRACTAL IMAGE COMPRESSION

1.3.1 Definition of Fractal

Fractal Geometry is another science. It was an

outcome to the advances in numerical representation of

conditions utilizing PCs. It was given its name by the math

researcher Benoit B. Mandelbrot of IBM. The name

originates from the Latin word fractus which implies

unpredictably broken. In spite of the fact that the

Mandelbrot set is not considered as a fractal Benoit B. Mandelbrot is viewed as the father of fractals. Nobody can

deny the nearby connection amongst bedlam and fractals,

that would be clarified later.

Definition: Fractals are self-comparable geometric

shapes which imply that in the wake of amplifying any part

of the first shape we get the same shape once more.

Fractals seem both in scientific conditions and in nature.

For instance in nature they show up in lightning, plants, mountains and a large portion of the unpleasant surfaces. A

portion of the numerical case of fractals are: Cantor set,

Koch bend and Julia set.

1.3.2Fractal Dimension:

Before portraying the most settled instance of

fractals, let us look at an examination by metrologist Lewis

Richardson. He endeavored to evaluate the length of the

edge of the west-shore of England and found that the result

depends immovably upon the span of the guide he used.

Repeating the investigation using just a single guide with

each one of the inconspicuous components on it, however

decreasing the unit of measure without fail, we would find

that for each decay, the length of the drift would increase

showing that the perpetual length of the West – Coast of

England. So it creates the impression that the length is not an uncommonly profitable system for portraying a

coastline and that a measure of twirliness would be better.

Mandelbrot called this twirliness, a number something

close to 1 and 2, the fractal estimation. Fractals, before that

word was established, were fundamentally thought to be

above logical appreciation, until the point when

examinations were done in the 1970's by Benoit Mandelbrot, the "father of fractal geometry" see

[Mandelbrot, B. B.; Cannon, J. W 1984].Mandelbrot

developed a procedure that viewed fractals as a bit of

standard Euclidean geometry, with the estimation of a

fractal being a case. Fractals pack immeasurability into "a

grain of sand". This immeasurability shows up when one

tries to gage them. The assurance lies in considering them

to be falling between estimations. The estimation of a

fractal when all is said in done is not a whole number, not

an entire number. So a fractal twist, a one-dimensional

thing in a plane which has two-estimations, has fractal

estimation that falsehoods something close to 1 and 2. Thus, a fractal surface has estimation something close to 2

and 3. The quality depends on upon how the fractal is

produced. The closer the estimation of a fractal is to its

possible most extreme cutoff which is the estimation of the

space in which it is introduced, the rougher, the

furthermore filling of that space it is. Fractal Dimensions

are an attempt to measure, or portray the case, in fractals. A

zero-dimensional universe is one point. A one-dimensional

universe is a single line, intensifying unfathomably. A two-

dimensional universe is a plane, a level surface connecting

all over, and a three-dimensional universe, for instance, our own, extends all over.

These dimensional values are characterized by a

whole number. What, at that point, would a 2.5 or 3.2

dimensional universe resemble? This is replied by fractal

geometry, the word fractal originating from the idea of

fragmentary dimensions. A fractal lying in a plane has a

measurement in the vicinity of 1 and 2. The nearer the

number is to 2, say 1.9, the more space it would fill. Three-dimensional Fractal Mountains can be produced utilizing

an irregular number succession, and those with a

measurement of 2.9 (near the furthest reaches of 3) are

unbelievably spiked. Fractal Mountains with a

measurement of 2.5 are less rough, and a measurement of

2.2 presents a model of about what is found in nature. The

investigation of non-whole number measurement and a few

essential properties of fractal objects were examined by

Georg Cantor, David Hilbert, G. Peano, Helge von Koch,

W. Sirpinski, Gaston Julia and Flex Hausdroff.

Let us consider „a‟ as unit of measurement and if it require

to use N times obtain the approximation of the length of a

line for which we are evaluating the fractal dimensions(so

that the estimated length becomes Na),the fractal

dimension can be represent as,

0

loglim

1log

a

ND

a

There are various summed up implication of estimation,

used as a piece of unadulterated number-crunching:

Hausdorff (1919), Cantor and Minkowski, Bouligand,

Kolmogorov, et cetera. These implications of estimations, which were used similarly as a piece of unadulterated

number juggling, however every one of them, contrast with




the techniques for measuring the length of the coastline. The most prepared definition has a place with Hausdorff,

and it furthermore is the most "expressive" one (from the

geometric perspective).In 1987, a mathematician named

Michael F. Barnsley made a PC program called the Fractal

Transform, which recognized fractal codes in certifiable

pictures, for instance, pictures, which have been registered

and changed over with a modernized gathering. This

delivered fractal picture pressure, which is used as a piece

of an a lot of PC applications, especially in the locales of

video, virtual reality, and outline. The major method for

fractals is the thing that makes them so significant. If some

individual was rendering a virtual reality condition, each leaf on each tree and each stone on every mountain would

should be secured. Or maybe, a fundamental condition can

be used to make any level of unpretentious component

required. A complicated scene can be secured as a few

conditions in less than 1 kilobyte, rather than a similar

scene being secured as 2.5 megabytes of picture data.

Fractal image compression is a main issue for making the

"mixed media upheaval".

1.3.3 Categories of Fractals

Cantor Set: It's viewed as one of the least difficult

and most well-known fractals. It was named after George

Cantor who imagined it.It's framed by evacuating the

center third interim of any interim (i.e. [0, 1]) then

rehashing the same operation again and again on the rest of

the components which gives the succession:

0, 1, 1/3,2/3, 1/9, 2/9, 7/9, 8/9,…..

In type of numbers it doesn't generally mean

anything interestingly. In any case, in the wake of plotting

its realistic representation of it, it's conspicuous how The

Cantor Set is a fractal as every part of the set is a reiteration

of the fundamental set. For instance the interim [0, 1/3] is a

down scaled variant of the primary interim (verification

[7]). The interim [0, 1] has the same cardinality as The

Cantor Set. It could be demonstrated as there exists a

bijective capacity that maps components from The Cantor Set to the interim [0, 1] that function1 is:

1 1

3 22

k kkk

k k

af a

FIGURE 1: CANTOR SET

Koch Curve: Its significance lies in that it speaks to the

importance of a fractal structure and a portion of the

standards made by Mandelbrot to characterize fractals. It's developed by a straightforward line called the initiator. The

bend is developed by supplanting the center third part of

the line by an equilateral triangle without its base then

rehashing the same operation on the produced lines fit as a

fiddle. In the wake of doing that operation ordinarily we

get what may resemble a bend yet does not have any

smooth bends which implies that this bend is not

differentiable (as no digression could be set on the curve)

The Pascal Triangle: It's gotten from the popular triangle

used to speak to the coefficients of the development of the

polynomial (1 + x)n, n speaks to the line number beginning

from 0 and the quantity of coefficients are n+2 beginning from 0. The estimation of any cell of the triangle could be

gotten from the condition:

!

!( )!k

nb

k n k

where n is the row number and k is the number of the

element in the row.

That equation was derived from the binomial theorem

which states that:

( )

0

!

! !

kn

n n k y

k

nx y x

k n k

The fractal is seen by coloring a group of numbers that

have the same qualities like coloring odd numbers in dark and even numbers in white, coloring mutiples of 3 in black

and other numbers in white, and so forth.




2. LITERATURE REVIEW

Jaseela C C and Ajay James in their research paper

entitled “A New Approach to Fractal Image Compression

Using DBSCAN” suggested to use DBSCAN algorithm to

pack a picture with fractal compression strategy. The

change is connected to decline encoding time by decreasing

the successive pursuits through the entire picture to its

neighbors. This strategy packs and decompresses the

shading pictures rapidly. The execution time of the

compression algorithm is diminished essentially contrasted

with the customary fractal picture compression. In web picture database is exceptionally large.So putting away

pictures in less space is a test. Picture compression gives a

potential cost investment funds connected with sending less

information over exchanged phone system where expense

of call is truly generally based upon its duration.It

diminishes capacity necessities as well as general execution

time.The proposed strategy pack pictures in square by

piece premise, rather than checking in pixel by pixel. This

strategy pack the shading pictures and interpret them

rapidly by considering their RGB values independently.

This strategy is exceptionally helpful for putting away

pictures in picture

Ali Nodehi,Ghazali Sulong,Mznaah al

rodhaan,Abdullah-Al-dheelan,Amjad Rehmaan and

Tanjila Sabain their research paper entitled “Intelligent

fuzzy approach for fractal image compression “suggested a

two–phase algorithm to perform fractal picture

compression which decreases the MSE computations. In

first phase, all picture pieces were partitioned into three

classes as indicated by picture squares edge property

utilizing DCT coefficients. From the spatial domain, a

square of picture could be changed to the recurrence domain by method for DCT transformation. Within the

recurrence domain, the DCT coefficients that is arranged in

the upper left of the picture piece implies the picture piece's

low recurrence data and it's harsh shape where as the DCT

that is arranged in the lower right of the picture piece

means the picture piece's high recurrence data and it's fine

texture. Therefore we can rexplore the class of picture

square by thinking of it's lower-higher recurrence DCT

coefficients. In second stage, the ICA algorithm found the

reasonable domain pieces utilizing the outcome acquired as

a part of the principal phase.it is discernible that the measure of MSE calculations in boolean picture has been

502 times more than that of the fundamental FIC algorithm while the PSNR worth is only 0.41 not as much as that of

essential FIC algorithm.ICA additionally works the idea of

least optima in the entire locale.

Yuanyuan Sun, Rudan Xu1, Lina Chen and Xiaopeng

Hu in their research paper entitled “Image compression

and encryption scheme using fractal dictionary and Julia

set “recommended a novel compression–encryption plan

utilizing a fractal word reference and Julia set. For the compression in this plan, fractal word reference encoding

decreases time utilization, as well as gives great quality

picture reproduction. For the encryption in the plan, the key

has extensive key space and high affectability, even to little

annoyance. In addition, the stream figure encryption and

the dispersion procedure received in this study spread

bother in the plaintext, accomplishing high plain

affectability and giving a successful imperviousness to

picked plaintext assaults. In the encryption procedure, the

key has almost 2272 key space with a 10 × 10 Julia set. As

examined in Section 4.3, the encryption framework has a

high plaintext affectability and key affectability to a minor bother. Consequently, we completed a point by point

investigation of the Julia set size, and the exploratory

results demonstrate that when K is equivalent to 8 or 10, it

has a high affectability for figure to both key and plaintext.

Also, the cipher text breezed through the sp800–22 test

suite, demonstrating that the ciphertext has a decent

arbitrariness. At last, we tried the encryption/decoding time

utilization of various pictures. The test results show that the

encryption operation is < 15% of compression procedure,

implying that it doesn't postpone the compression

procedure and this makes it simple to acknowledge continuous compression and encryption.

SarabjeetKaur and Er. Anand Kumar Mittal in his

paper entitled “Improved Fractal Based Image

Compression for Grayscale Using Combined Shear and

Skew Transformations” proposed that The force of fractal

encoding is appeared by its capacity to outflank utilizing

the DCT, which shapes the premise of picture compression.

The shear and skew based fractal picture compression is another algorithm yet is not without issues. Most

fundamentally, quick encoding is required for it to discover

wide use in mixed media applications. The outcomes

procured demonstrate that the proposed approach uses

between pixel redundancies to render fabulous de-

relationship for characteristic pictures. The higher measure

of the applicable pixels is related to the expansion of the

shear and skews changes. These changes permit to frame

lesser no. of the reach obstructs in the montage thus the

compression result is higher. In this way, all the

uncorrelated change coefficients can be encoded autonomously without trading off coding proficiency.

Additionally, a portion of the high recurrence substance

can be disposed of without noteworthy quality debasement.

Fractal picture compression gives speedier compression in

dark scale when contrasted with RGB because of single

plane multifaceted nature when contrasted with the three

plane many-sided quality in the shading picture.




Joan Puate and Fred Jordan in their research paper entitled “Using fractal compression scheme to embed a

digital signature into an image “recommended another

plan taking into account fractal coding and decoding. As a

rule terms, a fractal coder misuses the spatial repetition

inside the picture by building up a relationship between its

diverse parts. We depict an approach to utilize this

relationship as a method for inserting a Watermark. Tests

have been performed with a specific end goal to quantify

the heartiness of the procedure against JPEG change and

low pass sifting. In both cases, exceptionally encouraging

results have been gotten. An element of this method is that

it doesn't permit, once the picture has been decoded, to discover the area of the mark (truth be told, it doesn't

permit to figure out if a mark has been installed or not).

Since a Local Iterated Function Systems based algorithm

searches for an arrangement of changes ready to give a

decent estimation to the picture to encode, it doesn't make a

difference what these changes are if the guess is adequate.

What the algorithm does, truth be told, is to recognize

distinctive arrangement of changes by providing for one of

them the component of constituting a mark. Identified with

the last point would be the way that we let completely

opened the decision of seeking locales shapes. The streamlining of these shapes may expand the power of the

signature and additionally the recovering unwavering

quality.

A R NadiraBanu Kamal in her research paper entitled

“Iteration Free Fractal Image Compression For Color

Images Using Vector Quantization, Genetic Algorithm And

Simulated Annealing” suggested that vector quantization,

genetic algorithm and simulated annealing can be utilized for FIC. The systems Vector Quantization, Genetic

Algorithm and Simulated Annealing are utilized to decide

the best domain hinder that matches the extent pieces. The

proposed algorithm has the better execution as far as

picture quality, piece rate and coding time for Color

pictures. Just the encoding expends additional time yet the

decoding is quick. To start with the reach pieces were

named either smooth or harsh relying upon the fluctuation

of the square. This arrangement was exceptionally valuable

when the picture had parcel of smooth pieces. So relying

upon the picture and the parcel, a high compression proportion was accomplished. Just the encoding expends

additional time yet the decoding is quick. GA strategy for

cycle free fractal coding is favored for better picture quality

though VQ is favored for decreased coding time and SA is

ideal for ideal picture quality and time. The proposed

techniques utilizing VQ, GA and SA are found to give

computational productivity, in this way radically lessening

the expense of coding. The execution time can further be

diminished by actualizing the proposed strategy in parallel

for encoding. Shading pictures are generally utilized as a

part of the majority of the application now-a-days.

Applications where pictures can be put away in a compacted structure, which require speedier recovery,

similar to restorative pictures and photos for ID can utilize

the proposed strategy.

D.Sophin Seeli, Dr.M.K.Jeyakumar in their research

paper entitled” A Study on Fractal Image Compression

using Soft Computing Techniques “suggested a near investigation of existing Fractal Image Compression

techniques to look at the exhibitions of such existing

strategies as far as their compression proportion. The near

investigation demonstrates that the current techniques are

have to improve to achieve the higher compression

proportion. This lower execution in near examination

process has propelled to do another powerful heuristic FIC

procedure for achieve the higher compression proportion.

The new created fractal picture compression strategy used

most famous technique to play out the picture compression

process. These FIC methods ordinarily used the

enhancement procedures to locate the ideal best coordinating pieces. Each of the FIC procedures and their

execution are dissected as far as their compression

proportion, encoding time and PSNR (Peak Signal-to Noise

Ratio) esteem. Taking into account these parameters the

execution of the FIC methods were concentrated on and a

similar investigation of these strategies was given.

Hitashi,GaganpreetKaur and Sugandha Sharma in their

research paper entitled „Fractal Image Compression-A Review’ suggested that the field of fractal compression is

relatively new, as is the study of fractals, and as such

there is no standardized approach to this technique. The

main concept in this compression scheme is to use Iterated

Function Systems ( IFS ) to reproduce images. An

important property of fractals is that they exhibit self -

similarity. By partitioning an image into blocks, typically

8x8 or 16x16 pixels, it becomes possible to map small

portions of an image to larger portions. In addition, the

smaller portions are reproduced by use of affine

transformations. These transformations effectively map squares to parallelograms through translation, scaling,

skewing, rotation, etc. In this way an image can be stored

as a collection of affine transformations that can be used to

compress as lossless reproduce a near copy of the original

image. The process is iterative in that detail is added after

each pass through the function set. The process is

computationally intensive but can yield much improved

compression ratios.Fractal compression area is great. It

should be possible to take advantage of the large

compression ratios achieved from fractal compression and

produce a trade-off of compression ratios for information loss to achieve a lossless result. This could be achieved

through a post comparison of a fractally compressed file

and its original data. By then using a traditional

compression scheme, encoding of the differences could be

implemented in such a way that a lossless representation of

the original data can be reproduced.

Dan Liu, Peter K Jimack in his paper titled A Survey of

Parallel Algorithms forFractal Image Compression review

the various techniques associated with parallel approach

using fractal image compression.It is introduced due to the

high encoding cost of fractal image compression. Thesetechniques have been discussed from the viewpoints

of granularity, load balancing, data partitioning and

complexity reduction. It merits watching however that

large portions of the properties of the present parallel

hardware are not reliable with presumptions made in a

portion of the past work. Specifically, it is




incomprehensible today that a parallel processor would not have adequate of its own primary memory to store its own

duplicate of the whole uncompressed picture. The

advantages from parallel fractal image decoding are not

prone to be so incredible as with the coding algorithm,

since the decoding algorithm is proved to be fastest in any

case. this is one of the primary attractions of fractal image

compression after all considerations.

D.Sophin Seeli1, Dr. M. K. Jeyakumar in his paper titled

A Study on Fractal Image Compression using Soft

Computing Techniquesanalyze the current FIC techniques

that has been developed with the end goal of expanding compression ratio and shorten the computational time.

generally these FIC techniques used the optimization

methods to locate the ideal best matching blocks. Each of

the FIC procedures and their execution are analyzed as far

as their compression ratio, encoding time and PSNR(Peak

Signal-to Noise Ratio) esteem. In view of these parameters

the execution of the FIC systems were contemplated and a

comparative study of these procedures was given. The

analysis demonstrates that the current techniques need to

improve to accomplish the higher compression ratio. This

lower execution in similar investigation process has roused to do another powerful heuristic FIC procedure for achieve

the higher compression ratio. The new developed fractal

image compression method used most eminent technique to

play out the image compression process. The execution of

the most prestigious technique gave higher image

compression ratio than the techniques discussed.

Gaurish Joshi in his paper titled Fractal Image

Compression and its Application in Image Processing

proposed two methods RDPS and ERB to make changes in

the encoding time of fractal image compression. RDPS

primarily focused on diminishing the encoding time and ERB concentrate on expanding compression ratio alongside

slight change in encoding time. Thus the two techniques

are consolidated to frame new strategy RDPS-ERB to

acquire the best outcomes. It has been demonstrated that

compression ratio expanded to twofold that of existing

work with minimum loss in image quality. The paper

suggested that affine parameter of FIC methods vary with

image quality estimation like SSIM and MSE. There is a

positive correlation between affine parameters and image

contrast i.e. by expanding parameter image upgrades and

by diminishing parameter smoothing of image occurs. The new system becomes more faster and has better

compression ratio with acceptable loss in image quality.

Other feature extraction techniques like skewness; neighbor

contrast etc. may also be used to obtain the outcomes in

near future.

John Kominek in his paper titled Advances in Fractal

Compression for Multimedia Applicationssuggested that

fast encoding is the need of fractal image compression in

the modern age. latest methods of fractal image

compression are five times faster than the older ones.the

paper begin with basic problems and then move it towards speed factor.the Fast Fractal Image Compression algorithm

is a critical progress in this direction. Some aspects are

deserving of further examinations. Alternative partitioning

structures, especially HV partitioning, should be contrasted with the full quad tree deterioration utilized as a part of this

work. Second, the domain pool filters might be refined, or

in view of some other amount than block. Third, there

might be justify in planning a hybrid algorithm by

combining FFIC with a local spiral search. Also, fourth, the

augmentation to bilinear fractal transforms surely appears

to be beneficial.All these considerations include uncertain

trade-offs between quality and speed with complexity

factor associate with used algorithm.

Mr.Pratyush Tripathi and Ravindra Pratap Singh in his paper entitled Fractal Image Compression with Spiht

Algorithmdiscussed some fractal-wavelet image

compression methods. the worth of developing adaptive

fractal image compression methods include performing

content-dependent image compression at pre-determined

bit rates. Generating rate distortion curves for these fractal-

based schemes provided a comparison of their performance

to each other as well to other image compression methods,

such as the SPIHT method. Application of these various

fractal and fractal-wavelet based image coding schemes for

the purpose of image restoration and enhancement be investigated.

Veenadevi.S.V. and A.G.Ananth in his paper titled ”

Fractal Image Compression Using Quadtree

Decomposition And Huffman Coding” says that Fractal

image compression can be gotten by isolating the first gray

level image into overlapped pieces relying upon an

threshold value and the outstanding systems of Quadtree

deterioration. By utilizing limitestimation of 0.2 and

Huffman coding for encoding and disentangling of the

image, these systems have been connected for the pressure

of satellite symbolisms. The compression ratio (CR) and Peak Signal to noise Ratio (PSNR) values are resolved for

three sorts of images to be specific standard Lena picture,

Satellite Rustic images and Satellite Urban images. The

Matlab reproduction comes about demonstrate that for the

Quad tree deterioration approach demonstrates

exceptionally huge change in the compression ratios and

PSNR value may be calculated from the fractal

compression with range blocks and iteration techniques.

The Quadtree decomposition and Huffman techniques can

be applied for achieving high compression ratios and better

PSNR values for satellite Images.

Jean Michel Marie-Julie, Hassane Essafi in his paper

titled “Image Database Indexing and Retrieval Using the

Fractal Transform” suggested a method for pattern

matching using fractal transform. It‟s mathematical

representation is related to the images of database.this

representation consists of a set of function parameters

estimated using a standard fractal compression.it works for

image and pattern fractal space of an image. The proposed

method may be upgraded by adding some features like

texture, text, shape etc. in it to perform primary selection of

used images. the task remains in optimizing the search process time.




Sonali V. Kolekar and Prof.Prachi Sorte. In her paper entitled “An Efficient and Secure Fractal Image and Video

Compression” proposed a fractal compression scheme

which shows the effectiveness in compressing the color

images whose experimental results reflect the effective

performance of system to compress the images in terms of

PSNR, SSIM and UIQI measurements. This method gives

better results than DCT and JPEG. There are some

blocking parameters in the decompressed image of the

proposed system but it affects only when the threshold

value increases. Overall it‟s a progressive approach of

image compression with high efficiency and high

compression ratio.

Shrimal Das and Dr. Dibyendu Ghoshalin his paper

entitled “A Proposed Method for Contour Detection of an

Image Based On Dynamic Parameterisation by Fractal

Coding” proposed a fractal compression approach in which

call fractal code is used for image segmentation and

Contour detection instead of image reconstruction. The

object contours in the image are identified by the inverse

mapping from the image block to the domain block.it

shows a vast mapping system produced a segmented image

and the limit set in the inverse system forms the contours.Contour detection can be useful for image editing,

recognition and other image processing operations.

Cordova Irving and Teng-Sheng Moh in his paper

entitled “DBSCAN on Resilient Distributed Datasets”

proposed an algorithm based on DBSCAN concept using

resilient distributed datasets approach named as RDD-

DBSCAN to overcome the problems associated with

measurement as it promotes distributed approach of data

resources. It also provides an insight of Apache Spark. In

this paper we described the assumptions for designing the

algorithm. RDD-DBSCAN algorithm works for the optimization of performance.but the limitation of this

algorithm is to ensure about occupying the data into

partitioned memory blocks. Another term of improvement

is to select an appropriate partition scheme.

M Salariana, E Nadernejad and H M Naim in his paper

entitled “A new modified fast fractal image compression

algorithm” proposed a new fractal compression method in

which the time consumed in encoding process get reduced.

The algorithm uses a domain pool reduction approach

along with the use of innovative contrast scaling factor S instead of searching it across .only those domain blocks are

allowed whose entropy is higher than a threshold value to

be considered. We analyze the performance of algorithm

with certain parameters like compression ratio, PSNR and

SSIM.

Wang Xing-Yuan, Wang Yuan-Xing and Yun Jiao-Jiao in his paper entitled “An improved fast fractal image

compression using spatial texture correlation” proposed a

procedure with intelligent classification algorithm (ICA)

and spatial texture correlation to reduce the encoding

process time and increase compression ratio of fractal image compression. Using this method we may search the

nearest range block and domain block with similar

textures. proposed scheme uses much less encoding time

while the compression ratio and the quality of the reconstructed image is almost the same.

3. RESULTS

S

N

O

Paper

Name

Authors Finding

s

Resear

ch Gap

1 A New

Approach

to Fractal

Image

Compressi

on Using

DBSCAN

Jaseela CC and

Ajay James

DBSCA

N can

pack the

shading

pictures

and

interpret them

rapidly

by

consider

ing their

RGB

values

indepen

dently.

It

require

an

efficien

t

algorith

m to separat

e

R,G,B

Values

2 “Intelligent

fuzzy

approach for fractal

image

compressio

n

Ali

Nodehi,GhazaliS

ulong,Mznaah al rodhaan,Abdulla

h-Al-

dheelan,AmjadRe

hmaan and

Tanjila Saba

A two–

phase

algorithm to

perform

fractal

image

compres

sion

which

decreas

es the

MSE

comput

ations using

DCT

and

ICA

algorith

m

A

proced

ure for optimal

ity of

ICA is

require

d

3. Image

compressio

n and

encryption

scheme

using fractal

dictionary

and Julia

set

Yuanyuan Sun,

Rudan Xu1, Lina

Chen and

Xiaopeng Hu

It

Suggest

ed a

novel

compres

sion-encrypti

onplan

utilizing

a fractal

word

referenc

e and

Julia

set.

A

determi

nistic

proced

ure for

Julia set is

require

d

4. Improved SarabjeetKaur The A




Fractal

Based Image

Compressi

on for

Grayscale

Using

Combined

Shear and

Skew

Transforma

tions

and Er. Anand

Kumar Mittal

force of

fractal encodin

g is

appeare

d by its

capacity

to

outflank

utilizing

the

DCT,

which

shapes the

premise

of

picture

compres

sion

having

skewnes

s .

mechan

ism for Identifi

cation

of

skewne

ss level

is

require

d

5. Using

fractal

compression scheme to

embed a

digital

signature

into an

image

Joan Puate and

Fred Jordan

The

paper

depict an

approac

h to

utilize

this

relation

ship as

a

method

for

insertin

g a Waterm

ark.

A

Proced

ure for waterm

ark

authent

ication

is

require

d

6. Iteration

Free

Fractal

Image

Compressi

on For

Color

Images

Using Vector

Quantizatio

n, Genetic

Algorithm

And

Simulated

Annealing

A.R .NadiraBanu

Kamal

It

suggest

ed that

vector

quantiza

tion,

genetic

algorith

m and simulate

d

annealin

g can be

utilized

for FIC.

Proper

Criterio

n for

simulat

ing

algorith

ms is

require

d

7. A Study on

Fractal

Image

Compressi

on using

D.SophinSeeli,

Dr.M.K.Jeyakum

ar

It

suggest

ed a

near

investig

Proced

ure for

Identifi

cation

of

Soft

Computing Techniques

ation of

existing Fractal

Image

Compre

ssion

techniq

ues to

look at

the

exhibiti

ons of

such

existing strategie

s as far

as their

compres

sion

proporti

on

maintai

ned

nearest

neighbours is

require

d

8. Fractal

Image

Compression-A

Review

Hitashi,Gaganpr

eetKaur and

Sugandha Sharma

Illustrat

es the

basic methods

of

fractal

compres

sion on

geometr

ical

images

There

should

be specific

standar

ds for

fractal

compre

ssion

method

s

9 A Survey of

Parallel

Algorithms

for Fractal

Image Compressi

on

Dan Liu, Peter K

Jimack

Analyze

the

perform

ance of

various algorith

ms

working

on

parallel

approac

h of

fractal

Image

Compre

ssion.

A

proced

ure to

reduce

the encodin

g cost

of

Fractal

compre

ssion is

require

d.

10 D.Sophin Seeli1, Dr.

M. K.

Jeyakumar

A Study on Fractal Image

Compression

using Soft

Computing

Techniques

Analyze the

differen

t fractal

compres

sion

techniq

ues

based

on their

compres

sion

An algorith

m or

mechan

ism is

require

d to

gain

high

compre

ssion

ratio




ratio,

encoding time

and

PSNR(P

eak

Signal-

to Noise

Ratio)

11 Gaurish

Joshi

Fractal Image

Compression and

its Application in

Image

Processing

Propose

d two

methods

RDPS

and

ERB to make

changes

in the

encodin

g time

of

fractal

image

compres

sion.

A

proced

ure

associat

ed with

other features

like

skewne

ss,

feature

contrast

should

be

suggest

ed.

12 John

Kominek

Advances in

Fractal Compression for

Multimedia

Applications

Fast

Encoding

method

of

fractal

image

compres

sion are

suggest

ed.

Concep

ts related

to HV

partitio

ning,

augmen

tation

to

bilinear

fractal

transfor

m

should be

implem

ented.

13 Mr.Pratyus

hTripathi

,RavindraP

ratap Singh

Fractal Image

Compression

with Spiht

Algorithm

Propose

d a

fractal-

wavelet

based

approac

h to

promote

higher bit rate

and

high

compres

sion

ratio

Some

constrai

nts

must be

followe

d on

the

proced

ure to maintai

n the

features

of

image

restorat

ion and

enhanc

ement.

14 Veenadevi.

S.V. and

Fractal Image

Compression

Suggest

ed a

Comple

xity of

A.G.Ananth Using Quadtree

Decomposition And Huffman

Coding

fractal

image compres

sion

approac

h using

quad-

tree and

Huffma

n

coding

to get

high

compression

ratio

and

high

PSNR

value.

quadtre

e-huffma

n

combin

ation

must be

analyze

d and

interpre

ted.

15 Jean

Michel

Marie-

Julie,

HassaneEs

safi

Image Database

Indexing and

Retrieval Using

the Fractal

Transform

Suggest

ed a

method

for

pattern

matching using

fractal

image

compres

sion

method

and

evaluate

the

paramet

ric

values to

define

the

results.

The

same

proced

ure

using

other features

like

texture,

shape

etc.

should

be

illustrat

ed.

16 Sonali V.

Kolekar

and Prof.

PrachiSort

e.

An Efficient and

Secure Fractal

Image and Video

Compression

Propose

d a

fractal

compres

sion

scheme

for

color images

to

produce

better

PSNR,

UIQI

and

SSIM

measure

ments.

Blockin

g

Parame

ters and

the

causes

of it‟s

effects of an

image

must be

clearly

illustrat

ed.

17 Shrimal

Das and

A Proposed

Method for

Propose

d a

Proced

ure to




Dr.

DibyenduGhoshal

Contour

Detection of an Image Based On

Dynamic

Parameterisation

by Fractal

Coding

method

for contour

detectio

n using

fractal

compres

sion

method

to

perform

image

editing

and it‟s recognit

ion.

identify

fractal compo

nents of

a

contour

should

be

given.

18 Codrova

Irving and

Teng-

Sheng Moh

DBSCAN on

Resilient

Distributed

Datasets

propose

d an

algorith

m based

on

DBSCA

N

concept

using

resilient distribut

ed

datasets

approac

h

named

as

RDD-

DBSCA

N to

overco

me the problem

s

associat

ed with

measure

ment as

it

promote

s

distribut

ed approac

h of

data

resource

s.

Mecha

nism

for

Occupy

ing the

data

into

partitio

ned

memory

blocks

and

make

patition

s

should

be

defined

.

19 M

Salariana,

E

Nadernejad

and H M

Naim

A new modified

fast fractal image

compression

algorithm

An

algorith

m

followin

g

domain

pool

reductio

Consid

eration

of

thresho

ld value

associat

ed with

domain

n

approach for

fractal

compres

sion is

propose

d to

reduce

encodin

g

process

time.

pool

block must be

clarifie

d.

20 Wang

Xing-Yuan, Wang

Yuan-Xing

and Yun

Jiao-Jiao

An improved fast

fractal image compression

using spatial

texture

correlation

Propose

d a procedu

re for

fractal

image

compres

sion

with

ICA

and

spatial

texture correlati

on to

search

the

nearest

range

block

with

similar

textures

in

domain block

toreduc

e

encodin

g

process

time

and to

increase

compres

sion ratio.

spatial

parameters and

their

constrai

nts are

require

d to

match

the

similari

ty

between

differen

t image

blocks.

4. CONCLUSION

After being studied about various fractal compression

algorithms, we have find merits and demerits of these

techniques under critical circumstances. So we find that

ICA and DBSCAN can give more optimal results than

other algorithms. we conclude that The main idea of

DBSCAN is that, for each object of a cluster the

neighborhood of a given radius; Eps must contain at least a




minimum number of points, minpts to compress the fractal

of an imagewhereas ICA works in two phases. In first

phase, it partition the image based on DCT coefficients and

in second phase, it perform imperialistic operations on

DCT blocks to reduce the fractal size. So the proposed

work is to make the hybrid framework using these two

algorithms, applying modification on the same and to

create a new approach that will increase the compression

ratio, decrease the error rate and eventually improve the

fractal image compression ratio results on an image.

5. REFERENCES

1. [Yuanyuan Sun, RudanXu, Lina Chen,

Xiaopeng Hu] Yuanyuan Sun, RudanXu, Lina

Chen, Xiaopeng Hu; Image compression and

encryption scheme using fractal dictionary and Julia set; IET Image Process., 2015, Vol. 9, Iss. 3, pp.

173–183

2. [KaurSarabjeet, Er. Mittal Anand Kumar]KaurSarabjeet,Er. Mittal Anand Kumar;

Improved Fractal Based Image Compression for Grayscale Using Combined Shear And Skew

Transformations; GJRA - Global Journal For Research Analysis 2015,156-160

3. [Nadira A. R., Banu Kamal]A. R. Nadira, Banu

Kamal; Iteration Free Fractal Image Compression For Color Images Using Vector Quantization,

Genetic Algorithm And Simulated Annealing; TOJSAT-The Online Journal of Science and

Technology - January 2015 Volume 5, Issue 1,39-48

4. [Ali Nodehi, GhazaliSulong, Mznaah al rodhaan,

Abdullah-Al-dheelan, AmjadRehmaan and Tanjila Saba]Ali Nodehi,Ghazali Sulong,Mznaah al

rodhaan,Abdullah-Al-dheelan,Amjad Rehmaan and Tanjila Saba; Intelligent fuzzy approach for fractal

image compression; EURASIP-Springer journal on advances in signal processing,2014,1-9

5. [Jaseela C C ,Ajay James]Jaseela C C ,Ajay

James; A New Approach to Fractal Image

Compression Using DBSCAN, International Journal of Electrical Energy, Vol. 2, No. 1, March

2014,18-22

6. [A.R.NadiraBanuKamal,P.Priyanga

2014]A.R.NadiraBanuKamal,P.Priyanga;ICTACT Journal On Image And Video Processing, February

2014, Volume: 04, Issue: 03,785-790

7. [S.MichaelVanitha,K.Kuppusamy]S.MichaelVani

tha,K.Kuppusamy; Survey on Fractal Image Compression;International Journal of Computer

Trends and Technology (IJCTT) - volume4 Issue5–May 2013,1462-1464

8. [D.Sophin Seeli1, Dr.M.K.Jeyakumar2] D.Sophin Seeli1,Dr.M.K.Jeyakumar2;A Study on Fractal

Image Compression using Soft Computing Techniques; IJCSI International Journal of

Computer Science Issues, Vol. 9, Issue 6, No 2, November 2012,ISSN (Online): 1694-0814,420-

430

9. [Hitashi, kaurGanganpreet, Sungandha Sharma] Hitashi, kaurGanganpreet, Sungandha Sharma:

Fractal Image Compression – a review. International Journal of Advanced Research in Computer Science

and Software Engineering(Feb 2012).

10. [Negi. A., Chauhan. Y.S, Rana ]Negi. A.,

Chauhan. Y.S, Rana. R: Complex Dynamics of Ishikawa Iterates for Non Integer Values,

International Journal of Computer Applications (0975 – 8887) Volume 9– No.2, November 2010

11. [Negi, A.; Rani, M. and Mahanti, P. K. 2008]Negi,

A.; Rani, M. and Mahanti, P. K.: Computer simulation of the behavior of Julia sets using

switching processes, Chaos, Solitons& Fractals 37 (2008), 1187-1192.

12. [Negi A. 2006]Negi A.: Fractal Generations and Applications, Ph.D. Thesis, Department of

Mathematics, GurukulaKangriVishwavidyalaya, Hardwar, 2006.

13. [Berinde, Vasile ] Berinde, Vasile: Iterative

approximation of fixed points, EdituraEfemeride, Baia Mare, 2002.

14. [Jun Kigami] Jun Kigami. Analysis on fractals. Cambridge: Cambridge University Press; 2001.

15. [Barnsley, Michael] Barnsley, Michael.: Fractals

everywhere. Academic Press, Inc., Boston, MA, 1988. xii+396 pp. ISBN: 0-12-079062-9

MR0977274(90e:58080)

16. [Barnsley, Michael, Devaney, R. L.; Mandelbrot,

Benoit B.; Peitgen, Heinz-Otto; Saupe, Dietmar;

Voss, Richard F]Barnsley, Michael F.; Devaney, R.

L.; Mandelbrot, Benoit B.; Peitgen, Heinz-Otto; Saupe, Dietmar; Voss, Richard F.: The science of

fractal images. With contributions by Yuval Fisher and Michael McGuire. Springer-Verlag, New York,

1988. xiv+312 pp. ISBN: 0-387-96608-0 MR0952853(92a:68145)

17. [H.-O. Peitgen and P. H. Richter] H.-O. Peitgen

and P. H. Richter, The Beauty of Fractals, Springer Verlag, Berlin (1986).

18. [Huang, Z.]Huang, Z.: Mann and Ishikawa iterations with errors for asymptotically non

expansive mappings. Comput. Math. Appl.37

(1999), no. 3, 1-7. MR1674407(2000a:47118)

http://www.ams.org/mathscinet-getitem?mr=977274






19. [ J. E. Hutchinson] J. E. Hutchinson, Fractals and self-similarity, Indiana Univ. J. Math. 30,713-743

(1981).

20. [K. J. Falconer] K. J. Falconer, Fractal Geometry: Mathematical Foumiations and Applications. J.

Wiley, Chichester (1990)

21. [ M. F. Bamsley and L. P. Hurd] M. F. Bamsley and L. P. Hurd, Fractal Image Compression. AK

Peters Ltd, Wellesley, MA (1993).

22. [Mandelbrot, B. B.; Cannon, J. W] Mandelbrot, B. B.; Cannon, J. W.: Reviews: The Fractal Geometry

of Nature. Amer. Math. Monthly91 (1984), no. 9, 594-598. MR1540536.

23. [Gonzalez, R. and Eugene, R.]Gonzalez, R. and

Eugene, R. Digital image processing, 466, . 2008.

24. [Thyagarajan, S.K.] Thyagarajan, S.K. Still image and video compression with matlab, 97100, 2007.

25. [Kaouri, A. H.]Kaouri, A. H. Fractal coding of still

images. Queen‟s university of Belfast, UK. 2002.

26. [Hu, L., Chen, Q. and qing, Z.] Hu, L., Chen, Q. and qing, Z An image compression method based on fractal theory. The 8th international conference on computer supported cooperative work in design proceedings, 546–550. 2003.

27. [Clarke r. J.],Clarke r. J. “digital compression of

still images and video”, London, academic press, 2nd printing, 1996.

28. [Jacquina. E.]Jacquina. E, “image coding based on

a fractal theory of iteratedcontractive image transformations”,ieee trans. Image processing, 1(1),18-30, 1992.

29. [M. F. Barnsley],M. F. Barnsley fractals everywhere. San Diego, ca: academic, 1988.

30. [E. Jacquin],E. Jacquin “image coding based on a

fractal theory of processing, vol. 1, pp. 18–30, jan. 1992.

31. [Y. Fischer],Y. Fischer “a discussion of fractal

image compression,” in chaos and fractals, h. O. Peitgen, h. Jurgens, and d. Saupe, eds. New York: springer-verlag, 1992.

32. [G. E. Oien],G. E. Oien “l2-optimal attractor

image coding with fast decoderconvergence,”PhD. Dissertation, institute for teleteknikk, universities iTrondheim, Trondheim, Norway, 1993.

33. [M. F. Barnsley and a. D. Sloan],M. F. Barnsley

and a. D. Sloan “a better way to compress images,” byte, vol. 13, no. 1, pp. 215– 233, 1988.

34. [M. Ghazel, g. H. Freeman, and e. R. Vrscay],M.

Ghazel,g. H. Freeman, and e. R. Vrscay “fractal image denoising,”ieee trans. Image process., vol.

12, no. 12, pp. 1560–1578, dec.2003.

35. [ Liu Dan and K Jimack Peter],Liu Dan and K Jimack Peter ” A Survey of Parallel Algorithms for Fractal Image Compression” LJ, p.No.1-15

36. [Seeli1 D.Sophin, Jeyakumar, M. K Seeli1

D.Sophin, Jeyakumar, M. K,” A Study on Fractal Image Compression using Soft Computing Techniques” IJCSI International Journal of Computer Science Issues, Vol. 9, Issue 6, No 2, November 2012,P.No. 420-430

37. [Joshi, Gaurish] Joshi Gaurish,” Fractal Image Compression and its Application in Image Processing”, International Journal of Science and Research (IJSR) ISSN (Online): 2319-7064 Index Copernicus Value (2013): 6.14 | Impact Factor (2015): 6.391,P.No.1-7

38. [Kominek John] Kominek John “Advances in Fractal Compression for Multimedia Applications” Journal of University of waterloo,P.No.-1-32

39. [Tripathi, Pratyush and Ravindra Pratap Singh] Tripathi, Pratyush and Ravindra Pratap Singh ” Fractal Image Compression with Spiht Algorithm” International Refereed Journal of Engineering and Science (IRJES) ISSN (Online) 2319-183X, (Print) 2319-1821 Volume 1, Issue 4(December 2012), PP.07-15

40. [Veenadevi.S.V. and A.G.Ananth] Veenadevi.S.V. and A.G.Ananth” Fractal Image Compression Using Quadtree Decomposition And Huffman Coding Signal & Image Processing : An International Journal (SIPIJ) Vol.3, No.2, April 2012 P.No. 1-6

41. [Jean Michel Marie-Julie, Hassane Essafi] Jean Michel Marie-Julie, Hassane Essafi” Image Database Indexing and Retrieval Using the Fractal Transform LETI(CEA-Technologies Avanc6es) P.No.1-14

42. [Kolekar Sonali V. and Sorte Prachi.]Kolekar Sonali V. and Sorte Prachi” An Efficient and Secure Fractal Image and Video Compression International Journal of Innovative Research in Computerand Communication Engineering, Vol. 4, Issue 12, December 2016 P.No. 1-6

43. [Das, Shrimal and Ghoshal, Dibyendu] Das, Shrimal and Ghoshal, Dibyendu “A Proposed Method for Contour Detection of an Image Based On Dynamic Parameterisation by Fractal Coding” Volume 2, No. 6, Nov-Dec 2011 International Journal of Advanced Research in Computer Science P.No. 1-5

44. [Irving Codrova and MohTeng-Sheng]Irving Codrova and MohTeng-Sheng “DBSCAN on





Resilient Distributed Datasets” IEEE Explorer, P.No. 531-540

45. [Salariana, M ;Nadernejad,E and Naim H M]Salariana, M ;Nadernejad,E and Naim H M “modified fast fractal image compression algorithm” The Imaging Science Journal Volume 61, 2013 - Issue 2 P.No.219-232

46. [Xing-Yuan, Wang; Yuan-Xing, Wang and Jiao-Jiao, Yun] Xing-Yuan, Wang; Yuan-Xing, Wang and Jiao-Jiao, Yun “An improved fast fractal image compression using spatial texture correlation”Chin. Phys. B Vol. 20, No. 10 (2011) 104202 P.No. 1-11

47. [R. Pan and s. J. Reeves],R. Pan and s. J. Reeves “efficient huber-markov edge-preserving imagerestoration,” ieee trans. Image process., vol. 15, no. 12, pp. 3728–3735,dec. 2006.

48. [Z. Wang, d. Zhang, and y. L. Yu],Z. Wang, d.

Zhang, and y. L. Yu“hybrid image coding based onpartial fractal mapping,” signalprocess. imagecommun., vol. 15,pp.767–779, 2000.

49. R. Distasi, m. Nappi, and d. Riccio],R. Distasi, m. Nappi, and d. Riccio“a range/domain approximationerror-based approach for fractal image compression,” ieee trans. Imageprocess. vol. 15, no. 1, pp. 89–97, jan. 2006.

50. [T. K. Truong, j. H. Jeng, i. S. Reed, p. C. Lee, and a. Q. Li],T. K. Truong, j. H. Jeng, i. S. Reed, p. C. Lee, and a. Q. Li “a fastencoding algorithm for fractal image compression using the dct inner product,” ieee trans. Image process., vol. 9, no. 4, pp. 529–535, apr.2000.

51. https://www.google.co.in/search?q=images+on+fractal+image+compression&source=lnms&tbm=isch&sa=X&ved=0ahUKEwj41sKM27_VAhVGp48KHcIEC3YQ_AUICigB&biw=1366&bih=659

52. https://www.google.co.in/search?q=images+of+koch+curve,contour+set+and+pascal+triangle&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjhu4jy27_VAhWKv48KHbmVA_QQ_AUICigB

http://www.tandfonline.com/toc/yims20/current

http://www.tandfonline.com/toc/yims20/61/2

https://www.google.co.in/search?q=images+on+fractal+image+compression&source=lnms&tbm=isch&sa=X&ved=0ahUKEwj41sKM27_VAhVGp48KHcIEC3YQ_AUICigB&biw=1366&bih=659




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