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Presentation on Seminar Topic

IMPROVEMENT OF FRACTAL IMAGE CODING USING

CUDA

By

SAMEER THIGALE

ROLL NO: T3171, DIV A

Guided ByPROF. HANUMANT PAWAR

MAEER’s MIT COLLEGE OF ENGINEERING, PUNE, INDIAApril 10, 2023

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A BRIEF OUTLINE

• CURRENT SCENARIO: INCREASE IN IMAGE SIZE RANGE TO ORDER OF TBs

• NEED FOR AN EFFECTIVE IMAGE COMPRESSION ALGORITHM

• THE FRACTAL CODING• IDEA OF PARALLELIZING THE ALGORITHM• A PROMISING ARCHITECTURE: CUDA

A Fractal that models the surface of a mountain

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AGENDA

• RECAP: FRACTALS• FRACTAL IMAGE CODING• THE PROBLEM STATEMENT• INTRODUCTION TO CUDA• PARALLEL FRACTAL IMAGE CODING• EXPERIMENTS AND ANALYSIS

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FRACTALS

• Fractal is a structure made up of similar forms and patterns that occur in many different sizes

• The Mandelbrot “SELF SIMILARITY” Property

A fractal that begins with an equilateral triangle and then replaces the middle third of every line segment with a pair of

line segments that form an equilateral "bump"

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FRACTAL IMAGE COMPRESSION• Relies on the fact that parts of an

image often resemble other parts of the same image

• Fractal compression stores only the self similar regions

• Algorithm:– Divide the image into blocks– Find the blocks that are almost similar– Store the similar blocks

Based on work by Jacquin

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FRACTAL CODES

• Describe the entire image in terms of it’s fractal properties

• The mathematical equations can then be used to recreate the entire image

• Similar to vectors where mathematical descriptions of objects are stored

30 ⁰

Why store all the pixels of this line??Store only the angle and the length of vector

This is Fractal code.

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AN EXAMPLE

• We store only the fractals that are similar• We store the fractal codes required for

generating the image

Bitmap image When stored using fractal coding algorithm:Fractal + code

For block [1][2], show fractal

For block [2][1], rotate fractal 90⁰ and display

For block [2][2], rotate fractal 180⁰ and display

+

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KEY POINTS OF THE ALGORITHM

• Compression is lossy• Size of the physical data used to store fractal

codes is much smaller than the original bitmap• Fractal images can be scaled up/down without

loss in details• Suited in applications where decompression is

required frequently than compression• Ex. Image databases and CD-ROM applications

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THE PROBLEM STATEMENT

• Encoding is extremely computationally intensive.

• Millions or billions of iterations are required to find the fractal patterns in the image

• Compression could take from a few seconds to even few hours!

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THE SOLUTION

• Why do sequential pattern search? When it can be done in parallel

• Do data dependency while compressing• Employ massive parallel computation using

GPUs

Block wise thread grouping

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Why GPU and NOT CPU?

• Lots of math units• GPUs are great for “data” parallelism

– CPUs are great for “task” parallelism• GPU optimized for higher arithmetic intensity

for parallel nature(floating Point)• APIs are available

– CUDA is one such!

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CUDA(SUPERCOMPUTING FOR THE MASSES)

• CUDA is a set of developing tools to create applications that will perform execution on GPU (Graphics Processing Unit).

• CUDA was developed by NVidia and as such can only run on NVidia GPUs of G8x series and up.

 

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WHY CUDA?

• CUDA provides ability to use high-level languages such as C

• GPUs contain much larger number of dedicated ALUs then CPUs.

• Full support for integer and bitwise operations.

• Compiled code will run directly on GPU.

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PARALLEL FRACTAL IMAGE CODING

• The fractal image coding algorithm consists of three two fold loops which include no data dependency

• So very easy to parallelize• By distributing loop

elements on multiple cores

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EXPERIMENTS AND OBSERVATIONS

NOTE: Charts prepared by the work of August Sodora on NVidia GeForce Tesla C1060 GPU

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CONTINUED..

NOTE: Charts prepared by the work of August Sodora on NVidia GeForce Tesla C1060 GPU

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CONCLUSION

• Our graphs show the performance gain for parallel fractal image coding.

• We achieve speedup of up to 171.98 using NVidia GeForce Tesla C1060 GPU

• Further Scope:– Parallel fractal coding can be applied to audio– Across Frequency Domain– Error simpler to compute using Fourier Analysis

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THANK YOU!