Optimization of fractal image compression with genetic algorithms A. BEN JMAA, M. BEN JEMAA and Y. BEN JEMAA Abstract— Fractal image compression explores the self- similarity property of a natural image and utilizes the par- titioned iterated function system (PIFS) to encode it. The image compression method is time consuming in the encoding process. The time is essentially spent on the search of the similar domain block. In this paper, we present a method that uses Genetic algorithms to speed up computation time in fractal image compression with acceptable image quality and high compression rate. These improvements are obtained by encoding all regions in the image with different size blocks. I. INTRODUCTION Fractal image compression (FIC) was introduced by Bernesly [1] and Jacquin [2]. Since then, many researches have improved the original approach in various ways [3]. The image compression problem puts forward three major requirements : speeding up the compression algorithm, improving image quality after compression/decompression or increasing compression ratio. The method based on the theory of Local Iterated Function Systems (LIFS) [3] has received a lot of attention in the last ten years. To encode an image according to the self-similarity property, each block must find the most similar domain block in a large domain pool. In fractal image compression, the original image is parti- tioned into range blocks and for each range block, a suitable domain block D j is searched, so it exists a transformation T : Dom(I ) → Ranges(I ); T must guaranty ∀i, ∃j/T (D j ) ≃ R i A transformation is associated to each R i , it codes the D j coordinates and parameters of the transformation. The associated parameters for each R i are : the isometric flip Rotation π/2 ,π ,3π/2 , the horizontal flip, the vertical flip, the transposed of Dom(I), the rotation π of the transposed of Dom(I), the luminance and contrast. We use a Quadtree method [4] [5]to partition an image that must be compressed. This process is shown at Fig. 1. and can be summarized with the FIC algorithm. A. BEN JMAA is with National School of Engineering of Sfax, BP W, 3038 Sfax ahmed.benjmaa@gmail.com M. BEN JEMAA is with National School of Engineering of Sfax, BP W, 3038 Sfax maher.benjemaa@enis.rnu.tn Y. BEN JEMAA is with National School of Engineering of Sfax, BP W, 3038 Sfax and Research unit on signals and systems, ENIT, BP37, 1002 Tunis yousra.benjemaa@enis.rnu.tn Fig. 1. Regions decomposition FIC Algorithm: Decompose Image to 16x16 Regions size; While Exist (Regions not coded) If Regions size > 4 Try to Code all available Regions; Else Code all Regions; IEnd (Region size)=(Region size)/2 Wend The major problem of this method is time consuming compared with others methods of image compression. We present in this paper, a new Genetic Algorithm for image compression, that speed up this method when finding a LIFS [6] whose attractor is close to a given image. The next section is dedicated to the details of our algo- rithm: the representation of the fitness function, the Genetic operators and some others improvements to the simple Ge- netic Algorithms. With experimental results, we prove that our Genetic compression method is a good choice. II. GENETIC ALGORITHM FOR FRACTAL IMAGE COMPRESSION There are many algorithms of optimization used for differ- ent domains. We have chosen Genetic Algorithm [7] [8] [9] to accelerate our fractal image compression algorithm. We will give details of Genetic characteristics in this section. A. Chromosome attributes According to the Regions parameters coding, a chromo- some is constituted by N genes where N is the number of image Regions not yet coded.