C. Frigaard, J. Gade, T. Hemmingsen, T. Sand. Image compression based on fractal theory. Manuscript, Institute for Electronic Systems, Aalborg University, 1994.
Data compression has become an important issue in relation to storage and transmission of information. Specifically digital image compression is important due to the high storage and transmission requirements. Various compression methods have been proposed in recent years using different techniques to achieve high compression ratios. All these methods share the same characteristic of being approximate, i.e. the compressed images will be approximations of the originals. A relatively new approach is to construct compression algorithms by exploiting the theoretical foundation given by fractal theory. The basic principle is that an image can be reconstructed by using the self similarities in the image itself. When encoding an image, the algorithm partitions the image into a number of square blocks (domain blocks). After this a new partition into smaller blocks (range blocks) takes place. For every range block the best matching domain block is searched among all domain blocks by performing a set of transformations on the blocks. The compression is obtained by storing only the descriptions of these transformations. A crucial point in the encoding procedure is to be able to select only the "best matching" domain blocks in advance, by an efficient classification and only compute the transformations on these blocks. This is done exclusively to reduce the encoding time which would be unacceptable high otherwise. When decoding the image by continual iteration, the original image will be reconstructed with some approximation. In this paper we examine and describe an implementation of a fractal compression method proposed by [1], and state our improvements of the compression scheme. The results obtained will be compared with the original proposal and standard compression techniques. Finally, suggestions of further improvements and use of the method in other areas will be presented.
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@Misc{FGHS94,
Author = {Frigaard, C. and Gade, J. and Hemmingsen, T. and Sand, T.},
Title = {Image compression based on fractal theory},
Howpublished = {Manuscript, Institute for Electronic Systems, Aalborg University},
Year = {1994}
}