NETWORK%20SECURITY

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Fractal image compression
Presented by Sushruta Pradhan Roll
CS200118309 Under the Guidance of Dr. S.K.Meher
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OVERVIEW

• Introduction
• What is fractal image compression?
• How much Compression can Fractal achieve?
• Theorem realated to fractal image compression
• Procedure for Fractal Compression
• Encoding Algorithm

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INTRODUCTION

• First promoted by M. Barnsley
• Barnsleys, A. Jacquin, was the first to publish
  a similar fractal image compression scheme

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FRACTAL BASICS

• A fractal is a structure that is made up of
  similar forms and patterns that occur in many
  different sizes.
• These patterns appeared nearly identical in form
  at any size and occurred naturally in all things.
• If we make a copy of a small part of the floor's
  surface and compare it to every other part of the
  floor, we would find several areas that are
  nearly identical in appearance to our copy.
  
  CONT..

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• If we change the copy slightly by scaling,
  rotating, or mirroring it, we can make it match
  even more parts of the floor. Once a match is
  found, we can then create a mathematical
  description of our copy.
• If we repeat this process for the entire floor,
  we will end up with a set of mathematical
  equations called fractal codes that describe the
  entire surface of the floor in terms of its
  fractal properties
• Fractal encoding is largely used to convert
  bitmap images to fractal codes

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What is fractal image compression ?

• All the copies seem to converge to the same final
  image of small size.
• 
  

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How much Compression can Fractal achieve?

• The compression ratio for the fractal scheme is
  hard to measure since the image can be decoded at
  any scale.
• It is decoded at 4 times its original size.
• so the full decoded image contains 16 times as
  many pixels and hence this compression ratio
  is 91.2 to 1.

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ITERATED FUNCTION SYSTEM

• We have seen that IFS can be used Simulate very
  realistic, natural looking
• pictures
• If such an IFS can be found, then we can achieve
  very high compression since IFS only involve
  storing a few numbers to define the affine
  transformations
• 
  CONT..

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• Decoding is carried out by iterating the function
  on any arbitrary function.
• In order to ensure that the decoding scheme
  actually converges, we restrict our choice of
  F to be a contractive map with contractivity clt1,
  i.e.

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ENCODING ALGORITHM

• i) Image name, image size, minimum partition
  exponent, maximum partition exponent (both of
  which determine the size of domains and
  ranges), tolerance for fidelity, e.g. xxx.img,
  256x256,4(corresponding to 16x16 blocks),
  (corresponding to 4x4 blocks), 0 (corresponding
  to tolerance as zero).
• 1) Determine the parameters for compressing
• 2) Read the image to be compressed.
• 
  CONT..
• 
  

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• 3) Process domains
• (a).Scale the image by calculating the average
  values of each four-pixel group,
• then save the calculated values into an
  array domain
• (b).Divide the image (in domain) into
  overlapping domains (16x16 or 8x8)
• (c).Divide each domain block into 4 quadrants and
  calculate the varianc
• of each quadrant.
• 
  CONT..

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• (d).Classify the domains into 24 classes
  according to the order of
• the variances of the quadrants of the domain
  blocks. Record the position, the
• size and the class of the domain blocks in the
  corresponding class chain.
• (e).After processing the 16x16 domains, the
  procedure is repeated until you each
• the smallest domains (4 x 4) as specified
  by the maximum partition exponent.
• 
  CONT..

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• 6) Calculate the compression rate the number
  of bytes of the original image divided by the
  number of bytes in the output compressed file.

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CONCLUSION

• So called because of the similarities between the
  form of image representation and a mechanism
  widely used in generating deterministic fractal
  images, fractal compression represents an image
  by the parameters of a set of affine transforms
  on image blocks under which the image is
  approximately invariant.

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Thank You...