Fractal Image Compression Using

Quadtree Decomposition

Course:- Co-450(Multimedia technology)

Submitted By:-Harshit Varshney (S.No.- 04)

Submitted To:-Md. Asraful HaqueMohd. Imran

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

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

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

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

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

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 iterations2). The distance of [new-value] from Origin.If you reach the max. number of iterations, then you are done with iterations.

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.

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.

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.

Fractal Image Compression

Input Image Quadtree Decomposition

Huffman Coding

Compressed Image

Huffman Decoding

Decompressed Image

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.

Quadtree Decomposition Partitioning (QD)1. Partition the image into a set of large range

blocks2. If a range is fail to find a match, the process

is repeated after partitioning that particular range block into four quadrants

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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.

Results:-

Resolution:- 650 x 366Size:- 82.6 KB

Resolution:- 256 x 256Size:- 9.84 KBTime taken for compression :- 15.96 secCompression ratio:- 2.45Time taken for Decompression :- 189.9secPSNR:- 25.02

Results:-

Resolution:- 250 x 250Size:- 9.0 KB

Resolution:- 256 x 256Size:- 5.86 KBTime taken for compression :- 8.35 secCompression ratio:- 5.28Time taken for Decompression :- 72.5secPSNR:-27.35

Result:-

Resolution:- 256 x 256Size:- 16.7 KB

Resolution:- 256 x 256Size:- 2.99 KBTime taken for compression :- 3.6 secCompression ratio:- 12.79Time taken for Decompression :- 24.8secPSNR:- 22.24

Any Questions ?