An Adaptive Fractal Image Compression

Compression and decompression technology of digital image has become animportant aspect in the storing and transferring of digital image in informationsociety. Fractal Image Compression FIC is one of the most promising encodingtechnologies in the new generation of image compression for its novel idea, highcompression ratio, rapid decoding process and resolution independence.The problem with fractal coding is its high computational complexity in theencoding process. Most of the encoding time is spent on finding the best-matcheddomain block from a large domain pool to represent an input range block withrespect to contrast and intensity offset, as well as the isometric transformations.Therefore, improving the encoding speed is an interesting research topic for theFIC. Many encoding techniques were presented by the researchers to speed up thefractal encoder. These techniques include classification techniques, quad-treetechniques, spatial correlation, and evolutionary computation techniques.In this thesis, four methods have been proposed to: reduce the long time of theFIC，increase the compression ratio and keep the reconstructed image quality. Thefour methods are:1-The Range Exclusion (RE) method, which is responsible for reducing thenumber of the ranges blocks that needed in the matching process. RE used avariance factor as a criterion to indicate and exclude the homogenous ranges fromthe matching process which lead to increase the compression ratio and decreasethe encoding time.2-Reducing the Domain Image Size (RDIZ) method, which reduced thedomain pool by minimizing the Domain Image Size to only1/16thof the originalimage size. This in turn will affect the encoding time, compression ratio and theimage quality. The RE and RDIZ were coupled to work under one algorithmcalled the RD-RE. The experimental results show that RD-RE can achieve ahigher compression ratio and a significant reduction in the encoding time butwith some decay in the reconstructed image quality.3-The ZM-RDE method, which is the development of the RD-RE method. Thedevelopment comes from combining the RD-RE with the Zero Mean IntensityLevel (ZMIL) method. The ZMIL method introduces the transforms of the fullsearch problem using a more convenient form by adopting an unconventionalaffine parameter (i.e. The range mean r) which has better properties than theconventional offset parameter and a new search algorithm has been developed.Using ZMIL will lead to: Reducing the complexity of matching operations whichcan speed up the encoding operation; Increase both of the compression ratio andthe reconstructed image quality. The results showed that ZM-RDE can achieve abetter performance in terms of the CR, ET and the PSNR than the RD-RE.4-The Adaptive Fractal Image Compression AFIC method, which made ondeveloping the ZM-RDE method by adopting the Adaptive Quadtree PartitioningTechnique (AQPT) and the Domain Block Selection Technique (DBST). TheAQPT is an adaptive partitioning technique which depends on the uniformity ofthe blocks as a partitioning criterion. It is independent of the fractal mapping unlike the metric based quadtree method therefor the AQPT is very fast and canminimize the tradeoff of the performance results. The DBST technique isproposed to minimize the number of domain blocks required to be searched foreach not homogenous range block. For that, three processes were adopted in theDBST as the following:Select only the domain blocks that have a variance close to the rangevariance.Using a stopping condition for the search process.Adopting only the first four symmetry transform cases (T0, T1, T2and T3).By comparing the AFIC with some existing FIC methods, the results showthat AFIC is indeed has better performance results than the comparative methods.In addition, AFIC is compared with the JPEG2000compression method, thecomparisons show that the performance of the methods vary from one image toanother depending on the type of images. In general, in most images like the Lenaimage, JPEG2000has the superiority; it got a higher performance results than theAFIC while in some other images like the Rice Grains image, AFIC got a higherperformance results since the image has many self-similar objects that can becompressed perfectly using the FIC.