Speeding Up Fractal Image Compression by Genetic Algorithms

Abstract

The main problem with all fractal compression implementation is execution time. Algorithms can spend hours to compress a single image. Most of the major variants of the standard algorithm for speeding up computation time have led to a bad-quality or a lower compression ratio. For example, the Fisher’s [7] proposed classification pattern greatly accelerated the algorithm, but image quality was poor due to the search-space reduction imposed by the classification, which eleminates a lot of good solutions.

By using genetic algorithms to address the problem, we optimize the domain blocks search. We explore all domain blocks present in the image but not in exhaustive way (like a standard algorithm) and without omitting any possible block (solution) as a classification pattern does. A genetic algorithm is the unique method for satisfying these constraints. And it is a way to do be a random search because the genetic one is directed by fitness selection, which produces optimal solutions.

Our goal in this work is to use a genetic algorithm to solve the IFS inverse problem and to build a fractal compression algorithm based on the genetic optimization of a domain blocks search. we have also implemented standard Barnsley algorithm, the Y. Fisher based on classification, and the genetic compression algorithm with quadtree partitioning. A population of transformations was evolved for each range block, and the result is compared with the standard Barnsely algorithm and the Fisher algorithm = based classification.

We deduced an optimal set of values for the best parameters combination, and we can also specify the best combination for each desired criteria: best compression ratio, best image quality, or quick compression process. By running many test images, we experimentally found the following set of optimal values of all the algorithm parameters that ensure compromise between execution time and solutions optimality: Population size = 100, Maximum generations = 20, Crossover rate = 0.7, Mutation rate = 0.1, RMS limit = 5, Decomposition error limit = 10, Flips and isometrics count = 8.

In our proposed algorithm, results were much better than those obtained both vences and Rudomin [5] and Lankhorst [4] approaches.