Rochester Institute of Technology RIT Scholar Works Theses 5-1-2007 Optimization of a new digital image compression algorithm based on nonlinear dynamical systems Anurag R. Sinha Follow this and additional works at: https://scholarworks.rit.edu/theses Recommended Citation Sinha, Anurag R., "Optimization of a new digital image compression algorithm based on nonlinear dynamical systems" (2007). Thesis. Rochester Institute of Technology. Accessed from This Thesis is brought to you for free and open access by RIT Scholar Works. It has been accepted for inclusion in Theses by an authorized administrator of RIT Scholar Works. For more information, please contact [email protected]. Page | 1 OPTIMIZATION OF A NEW DIGITAL IMAGE COMPRESSION ALGORITHM BASED ON NONLINEAR DYNAMICAL SYSTEMS BY ANURAG R SINHA A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN ELECTRICAL ENGINEERING Approved by: Prof. THESIS ADVISOR – DR. CHANCE M. GLENN SR. Prof. THESIS COMMITTEE MEMBER – DR. SOHAIL A. DIANAT Prof. HEAD OF DEPARTMENT, ELECTRICAL ENGINEERING – DR. VINCENT AMUSO DEPARTMENT OF ELECTRICAL ENGINEERING, THE KATE GLEASON COLLEGE OF ENGINEERING ROCHESTER INSTITUTE OF TECHNOLOGY MAY 2007 Page | 2 LIBRARY RIGHTS STATEMENT In presenting the thesis “OPTIMZATION OF A NEW DIGITAL IMAGE COMPRESSION ALGORITHM BASED ON NONLINEAR DYNAMICAL SYSTEMS” in partial fulfillment of the requirements for an advance degree at the Rochester Institute of Technology, I agree that permission for copying as provided for by the Copyright Law of the U.S. (Title 17, U.S. code) of this thesis for scholarly purposes may be granted by the Librarian. It is understood that any copying or publication of this thesis for financial gain shall not be allowed without my written permission. I hereby grant permission to the RIT Library to copy my thesis for scholarly purposes. ___________________________________________ Anurag R Sinha _____________________________________ Date Page | 3 PREFACE Over the years the need for compression of Audio/Video/Image data has been increasing exponentially due to several technological advances in data communication and file storage base. Although our current communication standards and protocols support variegated types and formats of data with multiple bitrates and advanced data encryption technologies which facilitate transmission of data with acceptable attenuation losses, issues such as exhaustible data storage media, fixed bandwidth, transmission speed over a channel etc. has caused a quite a considerable retardation in technological growth. Uncompressed Data (graphics, audio and video) requires considerable storage capacity and transmission bandwidth. Although there has been rapid progress in storage capacity of storage media, processing/compilation time of processes/compilers, and digital communication system performance, demand for data compression and data‐transmission bandwidth continues to acts as a bane on technological growth. While compression/bandwidth conservation theories are going at a snail’s pace, the recent growth of data intensive multimedia‐based web applications has made it even more imminent to come up with efficient ways to encode signals and images The table I below [1]shows the qualitative transition from simple text to full‐motion video data and the disk space, transmission bandwidth, and transmission time needed to store and transmit such uncompressed data. Transmission Uncompressed Transmission Time (using Bits/Pixel or Multimedia Data Size/Duration Size Bandwidth a Bits/Sample (B for bytes) (b for bits) 28.8K Modem) Varying 32‐64 A page of text 11'' x 8.5'' 4‐8 KB 1.1 ‐ 2.2 sec resolution Kb/page Telephone 10 sec 8 bps 80 KB 64 Kb/sec 22.2 sec quality speech 2.1 Grayscale Image 512 x 512 8 bpp 262 KB 1 min 13 sec Mb/image 6.29 Color Image 512 x 512 24 bpp 786 KB 3 min 39 sec Mb/image 41.3 23 min 54 Medical Image 2048 x 1680 12 bpp 5.16 MB Mb/image sec Page | 4 100 58 min 15 SHD Image 2048 x 2048 24 bpp 12.58 MB Mb/image sec 640 x 480, 1 Full‐motion min 24 bpp 1.66 GB 221 Mb/sec 5 days 8 hrs Video (30 frames/sec) Table 1 ‐ Qualitative Transition Data from simple text to full‐motion video The Example above gives several of our issues a subtle definition. Some of them are mentioned below: a. A Need for sufficient storage space. b. Large Transmission Bandwidth c. A very large transmission time for Data (especially video). So if we consider an option of successful compression of say for ratio of 32:1, the space, bandwidth, and transmission time requirements can be reduced by a factor of 32, provided the compressed data still exhibits acceptable quality. Page | 5 TABLE OF CONTENTS PREFACE ABSTRACT……………………………………………………………………………………………………………08 1. INTRODUCTION……………………………………………………………………………………………………09 1.1 Compression Theories…………………………………………………………………………09 1.2 What a New Compression Algorithm has to bring to the table………………10 2. CHAOS THEORY – AN INTRODUCTION……………………………………………………………………11 2.1 CHAOS DYNAMICS CONCEPTS……………………………………………………………… 11 2.1.1 Chaos Dynamics & Fractal Geometry………………………………11 2.1.2 Applications in Modern World………………………………………..14 2.2 OSCILLATOR INTRODUCTION………………………………………………………………….15 2.2.1 The Colpitts Oscillator……………………………………………………..15 2.3 CHAOS DYNAMAC THEORY…………………………………………………………………....18 2.3.1 Chaos and Waveform Dynamics – Audio Waveforms……….18 2.3.1.1 Background…………………………………………………….18 2.3.1.2 Chaotic Dynamics……………………………………………18 2.3.1.3 Example………………………………………………………….19 3. DYNAMAC COMPRESSION……………………………………………………………………………………..21 3.1 GENERATING WAVEFORMS USING OSCILLATORS…………………………………….21 3.2 FOURIER SERIES WAVEFORM CLASSIFICATION…………………………………………22 3.2.1 Fourier Series Classification – An Introduction………………….23 3.2.2 Waveform Classification …………………………………………………..24 3.2.3 CCO Waveform Types – Families & Sub‐Families……………….26 3.2.4 Advantages of FSWC………………………………………………………….26 3.3 COMPRESSION THEORY…………………………………………………………………………….27 3.3.1 Algorithm Description………………………………………………………..27 3.3.2 Waveform Type match using a New Classification Algorithm (To be discussed in detail in the next chapter)……………………29 3.3.3 The DYI File………………………………………………………………………..30 3.4 THE ADAPTIVE HUFFMAN ALGORITHM……………………………………………………..30 3.4.1 The Huffman Algorithm – An Introduction & Application……30 3.4.2 Design of A DYNAMAC compatible Adaptive Huffman Algorithm…………………………………………………………………………..31 4. OPTIMIZATION THEORY…………………………………………………………………………………………..32 4.1 DYNAMAC OPTIMIZATION……………………..…………………………………………………32 4.1.1 Shortcomings in the Current Compression Algorithm………..32 4.1.2 A Brief Description of Optimization Measures……………………33 4.2 THE ENTROPY APPROACH…………………………………………………………………………33 4.2.1 Entropy & Randomness of Data – An Introduction…………….33 4.2.2 Calculation of Entropy……………………………………………………….38 Page | 6 4.2.2.1 Probability Distribution Function (PDF) & Scott’s Rule………………………………………………………………….39 4.2.2.2 Entropy…………………………………………………………….43 4.2.3 Conclusion ………………………………………………………………………..44 4.3 THE PSNR ‐ A MEASURE OF QUALITY………………………………………………………..45 4.3.1 Peak Signal to Noise Ratio – An Introduction……………………..45 4.3.2 Calculation of PSNR – Parameters & Values……………………….45 4.3.3 Conclusions & Expectations from a Comparative Study………47 4.4 ENTROPY VS. PSNR…………………………………………………………………………………….47 4.4.1 ENTROPY & PSNR – A Comparative Study…………………………..47 4.4.2 Results & Inference…………………………………………………………….47 5. OPTIMIZATION THEORY II – THE CCO MATRIX………………………………………………………….50 5.1 THE ENTROPY OF CCO MATRIX…………………………………………………………………..50 5.1.1 The Impact of Entropy Study & Current Classification of Waveforms…………………………………………………………………………51 5.1.2 Conclusions………………………………………………………………………..51 5.2 UNDER/NON UTILIZED WAVEFORMS………………………………………………………..51 5.2.1 Histogram of a Compressed Image…………………………………….51 5.2.2 Under/Non Utilized Waveforms – Detection & Analysis…….54 5.2.3 Conclusions……………………………………………………………………….56 5.3 WAVEFORM EFFICIENCY – A THEORETICAL PERSPECTIVE………………………….56 5.3.1 What is Image‐Wise‐Waveform‐Efficiency?.........................56 5.3.2 The Square Wave – Introduction & Application…………………58 5.3.3 The CCO Matrix – New Waveform Inception & Results………61 6. THE CHANNEL ‐ A REAL WORLD PERSPECTIVE………………………………………………………….62 6.1 DYNAMAC Data Streaming……………………………………………………………………….62 6.1.1 The DYNAMAC Protocol…………………………………………………….62. 6.1.2 A Java Based Application for Streaming DYNAMAC data (Citations & Copyright Luis A Caceres Chong)…………………….65 6.2 De‐Compression Theory……………………………………………………………………………67 6.2.1 A Client Perspective…………………………………………………………..67 6.2.2 Advantages of DRM friendly data………………………………………67 7. THE DYNAMAC THEORY – APPLICATIONS………………………………………………………………..68 7.1 COMPRESSION APPLICATIONS………………………………………………………………….68 7.1.1 IPTV…………………………………………………………………………………..68 7.1.2 Online Media Sharing………………………………………………………..69 7.1.3 An alternative Approach to Data Security – DRM……………….69 7.2 BIO‐MEDICAL APPLICATIONS…………………………………………………………………….70 7.2.1 X‐RAY Pattern Recognition – An FSWC approach……………….70 8. EXAMPLES……………………………………………………………………………………………………………….71 9. REFERENCES…………………………………………………………………………………………………………….83 10. TABLES & FIGURES…………………………………………………………………………………………………..86 Page | 7 ABSTRACT In this paper we discuss the formulation, research and development of an Optimization process for a New compression algorithm known as DYNAMAC, which has its basis in the non‐linear systems theory. We establish that by increasing the measure of randomness of the signal, the peak signal to noise ratio and in turn the quality of compression