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

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 Sushruta Pradhan

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

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.. Sushruta Pradhan

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

What is fractal image compression ? All the copies seem to converge to the same final image of small size.

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 it’s original size. so the full decoded image contains 16 times as many pixels and hence this compression ratio is 91.2 to 1.

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..

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 c<1, i.e.

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..

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..

(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..

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

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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