Fractal image compression is a technique based on the representation of an image by a contractive transform, on the space of images, for which the fixed point is close to the original image. This broad principle encompasses a very wide variety of coding schemes, many of which have been explored in the rapidly growing body of published research. While certain theoretical aspects of this representation are well established, relatively little attention has been given to the construction of a coherent underlying image model that would justify its use. Most purely fractal-based schemes are not competitive with the current state of the art, but hybrid schemes incorporating fractal compression and alternative techniques have achieved considerably greater success. This review represents a survey of the most significant advances, both practical and theoretical, since the publication of Jacquin's (1990) original fractal coding scheme.

A review of the fractal image coding literature

A new method for fractal image compression is proposed using genetic algorithm (GA) with an elitist model. The self transformation property of images is assumed and exploited in the fractal image compression technique. The technique described utilizes the GA, which greatly decreases the search space for finding the self similarities in the given image. This article presents theory, implementation, and an analytical study of the proposed method along with a simple classification scheme. A comparison with other fractal-based image compression methods is also reported.

Technique for fractal image compression using genetic algorithm

Contrast enhancement of images using Partitioned Iterated Function Systems

Fractal image compression is a new technique for encoding images compactly. It builds on local self-similarities within images. Image blocks are seen as rescaled and intensity transformed approximate copies of blocks found elsewhere in the image. This yields a self-referential description of image data, which --- when decoded --- shows a typical fractal structure. This paper provides an elementary introduction to this compression technique. We have chosen the similarity to a particular variant of vector quantization as the most direct approach to fractal image compression. We discuss the hierarchical quadtree scheme and vital complexity reduction methods. Furthermore, we survey some of the advanced concepts such as fast decoding, hybrid methods, and adaptive partitionings. We conclude with a list of relevant WEB resources including complete public domain C implementations of the method and a comprehensive list of up-to-date references.

Fractal Image Compression - An Introductory Overview

Region-based functionality offered by the MPEG-4 video compression standard is also appealing for still images, for example to permit object-based queries of a still-image database. A popular method for still-image compression is fractal coding. However, traditional fractal image coding uses rectangular range and domain blocks. Although new schemes have been proposed that merge small blocks into irregular shapes, the merging process does not, in general, produce semantically-meaningful regions. We propose a new approach to fractal image coding that permits region-based functionalities; images are coded region by region according to a previously-computed segmentation map. We use rectangular range and domain blocks, but divide boundary blocks into segments belonging to different regions. Since this prevents the use of standard dissimilarity measure, we propose a new measure adapted to segment shape. We propose two approaches: one in the spatial and one in the transform domain. While providing additional functionality, the proposed methods perform similarly to other tested methods in terms of PSNR but often result in images that are subjectively better. Due to the limited domain-block codebook size, the new methods are faster than other fractal coding methods tested. The results are very encouraging and show the potential of this approach for various internet and still-image database applications.

Fractal image compression with region-based functionality

Presents work carried out on fractal (or attractor) image compression. The approach relies on the assumption that image redundancy can be efficiently exploited through self-transformability. The algorithms described utilize a novel region-based partition of the image that greatly increases the compression ratios achieved over traditional block-based partitionings. Due to the large search spaces involved, heuristic algorithms are used to construct these region-based transformations. Results for three different heuristic algorithms are given. The results show that the region-based system achieves almost double the compression ratio of the simple block-based system at a similar decompressed image quality. For the Lena image, compression ratios of 41:1 can be achieved at a PSNR of 26.56 dB. >

L. Thomas

Papers

Region-based fractal image compression using heuristic search