fractal image compression using quadtree decomposition
TRANSCRIPT
![Page 1: Fractal Image Compression Using Quadtree Decomposition](https://reader036.vdocuments.net/reader036/viewer/2022062306/58ed19901a28ab260c8b4703/html5/thumbnails/1.jpg)
Fractal Image Compression Using
Quadtree Decomposition
Course:- Co-450(Multimedia technology)
Submitted By:-Harshit Varshney (S.No.- 04)
Submitted To:-Md. Asraful HaqueMohd. Imran
![Page 2: Fractal Image Compression Using Quadtree Decomposition](https://reader036.vdocuments.net/reader036/viewer/2022062306/58ed19901a28ab260c8b4703/html5/thumbnails/2.jpg)
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
![Page 3: Fractal Image Compression Using Quadtree Decomposition](https://reader036.vdocuments.net/reader036/viewer/2022062306/58ed19901a28ab260c8b4703/html5/thumbnails/3.jpg)
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
![Page 4: Fractal Image Compression Using Quadtree Decomposition](https://reader036.vdocuments.net/reader036/viewer/2022062306/58ed19901a28ab260c8b4703/html5/thumbnails/4.jpg)
Introduction to Fractals Proposed by Mandelbrot in 1975 Infinite structure Self similar
![Page 5: Fractal Image Compression Using Quadtree Decomposition](https://reader036.vdocuments.net/reader036/viewer/2022062306/58ed19901a28ab260c8b4703/html5/thumbnails/5.jpg)
Introduction to Fractals Mandelbrat set ( z2 + c = 0 )
![Page 6: Fractal Image Compression Using Quadtree Decomposition](https://reader036.vdocuments.net/reader036/viewer/2022062306/58ed19901a28ab260c8b4703/html5/thumbnails/6.jpg)
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
![Page 7: Fractal Image Compression Using Quadtree Decomposition](https://reader036.vdocuments.net/reader036/viewer/2022062306/58ed19901a28ab260c8b4703/html5/thumbnails/7.jpg)
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.
![Page 8: Fractal Image Compression Using Quadtree Decomposition](https://reader036.vdocuments.net/reader036/viewer/2022062306/58ed19901a28ab260c8b4703/html5/thumbnails/8.jpg)
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.
![Page 9: Fractal Image Compression Using Quadtree Decomposition](https://reader036.vdocuments.net/reader036/viewer/2022062306/58ed19901a28ab260c8b4703/html5/thumbnails/9.jpg)
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.
![Page 10: Fractal Image Compression Using Quadtree Decomposition](https://reader036.vdocuments.net/reader036/viewer/2022062306/58ed19901a28ab260c8b4703/html5/thumbnails/10.jpg)
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.
![Page 11: Fractal Image Compression Using Quadtree Decomposition](https://reader036.vdocuments.net/reader036/viewer/2022062306/58ed19901a28ab260c8b4703/html5/thumbnails/11.jpg)
Fractal Image Compression
Input Image Quadtree Decomposition
Huffman Coding
Compressed Image
Huffman Decoding
Decompressed Image
![Page 12: Fractal Image Compression Using Quadtree Decomposition](https://reader036.vdocuments.net/reader036/viewer/2022062306/58ed19901a28ab260c8b4703/html5/thumbnails/12.jpg)
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.
![Page 13: Fractal Image Compression Using Quadtree Decomposition](https://reader036.vdocuments.net/reader036/viewer/2022062306/58ed19901a28ab260c8b4703/html5/thumbnails/13.jpg)
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
ccc
c
c c
c
cc
c c
c
cover
cover
Top-down
c
![Page 14: Fractal Image Compression Using Quadtree Decomposition](https://reader036.vdocuments.net/reader036/viewer/2022062306/58ed19901a28ab260c8b4703/html5/thumbnails/14.jpg)
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.
![Page 15: Fractal Image Compression Using Quadtree Decomposition](https://reader036.vdocuments.net/reader036/viewer/2022062306/58ed19901a28ab260c8b4703/html5/thumbnails/15.jpg)
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
![Page 16: Fractal Image Compression Using Quadtree Decomposition](https://reader036.vdocuments.net/reader036/viewer/2022062306/58ed19901a28ab260c8b4703/html5/thumbnails/16.jpg)
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
![Page 17: Fractal Image Compression Using Quadtree Decomposition](https://reader036.vdocuments.net/reader036/viewer/2022062306/58ed19901a28ab260c8b4703/html5/thumbnails/17.jpg)
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
![Page 18: Fractal Image Compression Using Quadtree Decomposition](https://reader036.vdocuments.net/reader036/viewer/2022062306/58ed19901a28ab260c8b4703/html5/thumbnails/18.jpg)
Any Questions ?