Fractal Image compression, properties of fractals, Introduction to Fractals,

1. Fractal Image
Compression Using
Quadtree Decomposition
Course:- Co-450
(Multimedia technology)
Submitted By:-
Harshit Varshney
(S.No.- 04)
Submitted To:-
Md. Asraful Haque
Mohd. Imran

2. Introduction
 Need of Image compression
 Introduction to Fractals
 What are Fractals ?
 How to program Fractals
 Fractal Image Compression (FIC)
 Properties of Fractals
 Quadtree Decomposition Partitioning (QD)
 Why Quadtree Decomposition ?
 Results

3. Need of Image Compression
 Ease and flexibility in handling the digital
image or compressed image
 Increase in demand for images in video
sequences and computer animations
 Doing operation is easy on a compressed
image
 The rate of digital image data transfer or data
rate is more in compressed image

4. Introduction to Fractals
 Proposed by Mandelbrot in 1975
 Infinite structure
 Self similar

5. Introduction to Fractals
 Mandelbrat set ( z2
+ c = 0 )

6. What are Fractals ?
 Mathematical expressions
 Approach infinity in organized way
 Utilizes recursion on computers
 Dimensional:
 Line is one-dimensional
 Plane is two-dimensional
 Defined in terms of self-similarity

7. HOW TO PROGRAM FRACTALS
 Let us start by scanning every point in the rectangular plane
 Each point represents a Complex number (x + iY). Iterate that
complex number:-
[new value] = [old-value]^2 + [original-value]
While keep tracking of two things:
1). The number of iterations
2). The distance of [new-value] from Origin.
If you reach the max. number of iterations, then you are done with
iterations.

8. Fractal Image Compression (FIC)
 FIC is an image coding technology based in
the local similarity of the image structure.
 Lossy compression method for digital images
 This method is best suited for texture and
natural images.

9. Fractal Image Compression (FIC)
 Fractal image compression can be obtained
by dividing the original grey level image into
un-overlapped blocks.
 Depending on a threshold value and the well
known techniques of Quadtree
decomposition.

10. Properties of Fractals
 Iterations:-
 Iteration is defined as the process of repeating a method to
achieve a certain result.
 Self- Similarity:-
 Level of detail remains the same as we zoom in
 Connectivity:-
 Agents in the system connect to each other to form a pattern
 Self Organising:-
 system is continually self organising through the process of
emergence and feedback.

11. Fractal Image Compression
Input Image Quadtree
Decomposition
Huffman
Coding
Compressed
Image
Huffman
Decoding
Decompressed
Image

12. The Proposed Algorithm
 Divides the original image using Quadtree
decomposition of threshold is 0.2, minimum
Dimension and maximum dimension is 2 and 64
respectively.
 Record the values of x and y coordinates, mean
value and block size from Quadtree Decomposition.
 Record the fractal coding information to complete
encoding the image using Huffman coding and
calculating the compression ratio.
 For the encoding image applying Huffman decoding
to reconstruct the image.

13. Quadtree Decomposition
Partitioning (QD)
1. Partition the image into a set of large range
blocks
2. If a range is fail to find a match, the process
is repeated after partitioning that particular
range block into four quadrants
c
c
c
c
c c
c
cc
c c
c
cover
cover
Top-down
c

14. Why Quadtree Decomposition ?
 The main problem is that the fractal encoding
is taking too much time.
 Many approaches to reduce the encoding
time has bad affection on the image quality
after iteration, therefore the hybrid encoding
method of combining fractal coding and other
coding methods becomes an important
direction of fractal methods.

15. Results:-
Resolution:- 650 x 366
Size:- 82.6 KB
Resolution:- 256 x 256
Size:- 9.84 KB
Time taken for compression :- 15.96 sec
Compression ratio:- 2.45
Time taken for Decompression :- 189.9sec
PSNR:- 25.02

16. Results:-
Resolution:- 250 x 250
Size:- 9.0 KB
Resolution:- 256 x 256
Size:- 5.86 KB
Time taken for compression :- 8.35 sec
Compression ratio:- 5.28
Time taken for Decompression :- 72.5sec
PSNR:-27.35

17. Result:-
Resolution:- 256 x 256
Size:- 16.7 KB
Resolution:- 256 x 256
Size:- 2.99 KB
Time taken for compression :- 3.6 sec
Compression ratio:- 12.79
Time taken for Decompression :- 24.8sec
PSNR:- 22.24

18. Any Questions ?