This paper investigates the use of fractal coding for image compression and reconstruction. The encoder exploits self-similarity of the image at different resolutions, mapping larger blocks of the image to similar smaller blocks through a series of contractive transformations. The decoder can apply these transformations iteratively to any image, and recover the original. We show that varying th...

Optimal fractal coding consists of finding in a finite set of contractive affine mappings one whose unique fixed point is closest to the original image. Optimal fractal coding is an NP-hard combinatorial optimization problem. Conventional coding is based on a greedy suboptimal algorithm known as collage coding. In a previous study, we proposed a local search algorithm that significantly improve...

A fractal coder partitions an image into blocks that are coded via self-references to other parts of the image itself. In this paper we present a fractal coder that derives highly image-adaptive partitions and corresponding fractal codes in a time-eecient manner using a region-merging approach. The proposed merging strategy leads to improved rate-distortion performance compared to previously re...

A video coding method is proposed which is based upon fractal block coding. The method utilizes a novel three-dimensional partitioning of input frames for which a number of efficient block-matching search methods can be used, and permits spatio-temporal splitting of the input blocks to improve overall-encoding quality. After describing the basic fractal block coding algorithm, the details of th...

A fractal coder partitions an image into blocks that are coded via self-references to other parts of the image itself. We present a fractal coder that derives highly image-adaptive partitions and corresponding fractal codes in a time-efficient manner using a region-merging approach. The proposed merging strategy leads to improved rate-distortion performance compared to previously reported pure ...

This paper presents a method for fast encoding and decoding of image sequences based on fractal coding theory and the hybrid coding concept. The DPCM-loop accounts for statistical dependencies of natural image sequences in temporal direction. Those regions of the original image where the prediction, i.e. motion estimation and compensatio, fails are encoded using an advanced fractal coding schem...

Fractal coding and classi ed transform coding exhibit strong structural similarity, but they use di erent types of redundancy in image data: piecewise self-similarity in one case and local correlation in the other. Comparing performance of the two techniques leads to a quantitative, compression-oriented de nition of piecewise self-similarity. The amount of piecewise self-similarity is evaluated...

-Fractal compression is the lossy compression technique in the field of gray/color image and video compression. It gives high compression ratio, better image quality with fast decoding time but improvement in encoding time is a challenge. This review paper/article presents the analysis of most significant existing approaches in the field of fractal based gray/color images and video compression,...

We undertake a study of the performance difference of different transform coding techniques i.e. Block truncating coding, wavelet and fractal image compression. This paper focuses important features of transform coding in compression of still images, including the extent to which the quality of image is degraded by the process of compression and decompression. The above techniques have been suc...

Smooth regions and edges are very self similar and can be coded efficiently by fractal coders. One problem of fractal image coding is to achieve a high quality or a lossless representation of an image. This can be overcome by a hybrid coding approach as proposed by the authors in [3]. An extension to 3-D fractal video coding is described in [4]. Due to the block based algorithm, however, blocki...