A fractal image compression algorithm based on improved imperialist competitive algorithm

Fractal image compression (FIC) is a lossy compression method that has the potential to improve the performance of image transmission and image storage and provide security against illicit monitoring. The important features of FIC are high compression ratio and high resolution of decompressed images but the main problem of FIC is the computational complexity of the algorithm. Besides that, the FIC also suffers from a high number of Mean Square Error (MSE) computations for the best matching search between range blocks and domain blocks, which limits the algorithm. In this thesis, two approaches are proposed. Firstly, a new algorithm based on Imperialist competitive algorithm (ICA) is introduced. This is followed by a two-tier algorithm as the second approach to improve further the performance of the algorithm and reduce the MSE computation of FIC. In the first tier, based on edge property, all the range and domain blocks are classified using Discrete Cosine Transform. In the second tier, ICA is used according to the classified blocks. In the ICA, the solution is divided into two groups known as developed and undeveloped countries to maintain the quality of the retrieved image and accelerate the algorithm operation. The MSE value is only calculated for the developed countries. Experimental results show that the proposed algorithm performed better than Genetic algorithms (GAs) and Full-search algorithm in terms of MSE computation. Moreover, in terms of Peak Signal-to-Noise Ratio, the approaches produced high quality decompressed image which is better than that of the GAs

Three dimensional DCT based video compression.

by Chan Kwong Wing Raymond.Thesis (M.Phil.)--Chinese University of Hong Kong, 1997.Includes bibliographical references (leaves 115-123).Acknowledgments --- p.iTable of Contents --- p.ii-vList of Tables --- p.viList of Figures --- p.viiAbstract --- p.1Chapter Chapter 1 : --- IntroductionChapter 1.1 --- An Introduction to Video Compression --- p.3Chapter 1.2 --- Overview of Problems --- p.4Chapter 1.2.1 --- Analog Video and Digital Problems --- p.4Chapter 1.2.2 --- Low Bit Rate Application Problems --- p.4Chapter 1.2.3 --- Real Time Video Compression Problems --- p.5Chapter 1.2.4 --- Source Coding and Channel Coding Problems --- p.6Chapter 1.2.5 --- Bit-rate and Quality Problems --- p.7Chapter 1.3 --- Organization of the Thesis --- p.7Chapter Chapter 2 : --- Background and Related WorkChapter 2.1 --- Introduction --- p.9Chapter 2.1.1 --- Analog Video --- p.9Chapter 2.1.2 --- Digital Video --- p.10Chapter 2.1.3 --- Color Theory --- p.10Chapter 2.2 --- Video Coding --- p.12Chapter 2.2.1 --- Predictive Coding --- p.12Chapter 2.2.2 --- Vector Quantization --- p.12Chapter 2.2.3 --- Subband Coding --- p.13Chapter 2.2.4 --- Transform Coding --- p.14Chapter 2.2.5 --- Hybrid Coding --- p.14Chapter 2.3 --- Transform Coding --- p.15Chapter 2.3.1 --- Discrete Cosine Transform --- p.16Chapter 2.3.1.1 --- 1-D Fast Algorithms --- p.16Chapter 2.3.1.2 --- 2-D Fast Algorithms --- p.17Chapter 2.3.1.3 --- Multidimensional DCT Algorithms --- p.17Chapter 2.3.2 --- Quantization --- p.18Chapter 2.3.3 --- Entropy Coding --- p.18Chapter 2.3.3.1 --- Huffman Coding --- p.19Chapter 2.3.3.2 --- Arithmetic Coding --- p.19Chapter Chapter 3 : --- Existing Compression SchemeChapter 3.1 --- Introduction --- p.20Chapter 3.2 --- Motion JPEG --- p.20Chapter 3.3 --- MPEG --- p.20Chapter 3.4 --- H.261 --- p.22Chapter 3.5 --- Other Techniques --- p.23Chapter 3.5.1 --- Fractals --- p.23Chapter 3.5.2 --- Wavelets --- p.23Chapter 3.6 --- Proposed Solution --- p.24Chapter 3.7 --- Summary --- p.25Chapter Chapter 4 : --- Fast 3D-DCT AlgorithmsChapter 4.1 --- Introduction --- p.27Chapter 4.1.1 --- Motivation --- p.27Chapter 4.1.2 --- Potentials of 3D DCT --- p.28Chapter 4.2 --- Three Dimensional Discrete Cosine Transform (3D-DCT) --- p.29Chapter 4.2.1 --- Inverse 3D-DCT --- p.29Chapter 4.2.2 --- Forward 3D-DCT --- p.30Chapter 4.3 --- 3-D FCT (3-D Fast Cosine Transform Algorithm --- p.30Chapter 4.3.1 --- Partitioning and Rearrangement of Data Cube --- p.30Chapter 4.3.1.1 --- Spatio-temporal Data Cube --- p.30Chapter 4.3.1.2 --- Spatio-temporal Transform Domain Cube --- p.31Chapter 4.3.1.3 --- Coefficient Matrices --- p.31Chapter 4.3.2 --- 3-D Inverse Fast Cosine Transform (3-D IFCT) --- p.32Chapter 4.3.2.1 --- Matrix Representations --- p.32Chapter 4.3.2.2 --- Simplification of the calculation steps --- p.33Chapter 4.3.3 --- 3-D Forward Fast Cosine Transform (3-D FCT) --- p.35Chapter 4.3.3.1 --- Decomposition --- p.35Chapter 4.3.3.2 --- Reconstruction --- p.36Chapter 4.4 --- The Fast Algorithm --- p.36Chapter 4.5 --- Example using 4x4x4 IFCT --- p.38Chapter 4.6 --- Complexity Comparison --- p.43Chapter 4.6.1 --- Complexity of Multiplications --- p.43Chapter 4.6.2 --- Complexity of Additions --- p.43Chapter 4.7 --- Implementation Issues --- p.44Chapter 4.8 --- Summary --- p.46Chapter Chapter 5 : --- QuantizationChapter 5.1 --- Introduction --- p.49Chapter 5.2 --- Dynamic Ranges of 3D-DCT Coefficients --- p.49Chapter 5.3 --- Distribution of 3D-DCT AC Coefficients --- p.54Chapter 5.4 --- Quantization Volume --- p.55Chapter 5.4.1 --- Shifted Complement Hyperboloid --- p.55Chapter 5.4.2 --- Quantization Volume --- p.58Chapter 5.5 --- Scan Order for Quantized 3D-DCT Coefficients --- p.59Chapter 5.6 --- Finding Parameter Values --- p.60Chapter 5.7 --- Experimental Results from Using the Proposed Quantization Values --- p.65Chapter 5.8 --- Summary --- p.66Chapter Chapter 6 : --- Entropy CodingChapter 6.1 --- Introduction --- p.69Chapter 6.1.1 --- Huffman Coding --- p.69Chapter 6.1.2 --- Arithmetic Coding --- p.71Chapter 6.2 --- Zero Run-Length Encoding --- p.73Chapter 6.2.1 --- Variable Length Coding in JPEG --- p.74Chapter 6.2.1.1 --- Coding of the DC Coefficients --- p.74Chapter 6.2.1.2 --- Coding of the DC Coefficients --- p.75Chapter 6.2.2 --- Run-Level Encoding of the Quantized 3D-DCT Coefficients --- p.76Chapter 6.3 --- Frequency Analysis of the Run-Length Patterns --- p.76Chapter 6.3.1 --- The Frequency Distributions of the DC Coefficients --- p.77Chapter 6.3.2 --- The Frequency Distributions of the DC Coefficients --- p.77Chapter 6.4 --- Huffman Table Design --- p.84Chapter 6.4.1 --- DC Huffman Table --- p.84Chapter 6.4.2 --- AC Huffman Table --- p.85Chapter 6.5 --- Implementation Issue --- p.85Chapter 6.5.1 --- Get Category --- p.85Chapter 6.5.2 --- Huffman Encode --- p.86Chapter 6.5.3 --- Huffman Decode --- p.86Chapter 6.5.4 --- PutBits --- p.88Chapter 6.5.5 --- GetBits --- p.90Chapter Chapter 7 : --- "Contributions, Concluding Remarks and Future Work"Chapter 7.1 --- Contributions --- p.92Chapter 7.2 --- Concluding Remarks --- p.93Chapter 7.2.1 --- The Advantages of 3D DCT codec --- p.94Chapter 7.2.2 --- Experimental Results --- p.95Chapter 7.1 --- Future Work --- p.95Chapter 7.2.1 --- Integer Discrete Cosine Transform Algorithms --- p.95Chapter 7.2.2 --- Adaptive Quantization Volume --- p.96Chapter 7.2.3 --- Adaptive Huffman Tables --- p.96Appendices:Appendix A : The detailed steps in the simplification of Equation 4.29 --- p.98Appendix B : The program Listing of the Fast DCT Algorithms --- p.101Appendix C : Tables to Illustrate the Reording of the Quantized Coefficients --- p.110Appendix D : Sample Values of the Quantization Volume --- p.111Appendix E : A 16-bit VLC table for AC Run-Level Pairs --- p.113References --- p.11

Principal Component Classification for Fractal Volume Compression

Fractal volume compression is an extension of fractal image compression to volumetric data. The technique partitions the volume into range blocks which are replaced in the output dataset by transformations that map larger portions of the volume into blocks that resemble the original range partitions. Principal component analysis provides a classification system which directs the search for these self-similar maps to likely candidates. Classification also allows for simpler maps to represent less complex range blocks thus providing a higher compression rate

Principal Component Classification for Fractal Volume Compression

Fractal volume compression is an extension of fractal image compression to volumetric data. The technique partitions the volume into range blocks which are replaced in the output dataset by transformations that map larger portions of the volume into blocks that resemble the original range partitions. Principal component analysis provides a classification system which directs the search for these self-similar maps to likely candidates. Classification also allows for simpler maps to represent less complex range blocks thus providing a higher compression rate. Keywords: Compression, fractal, iterated function system, volume visualization, principal component analysis. 1 Introduction The problem of managing enormous data sets often arises in applications employing volumetric data. This has prompted research in new techniques for economizing both storage space and processing time. Data compression techniques reduce the size of volumetric data, converting the array into a representation w..