Fast Fractal Compression of Satellite and Medical Images Based on Domain-Range Entropy

Fractal image Compression is a lossy compression technique developed in the early 1990s. It makes use of the local self-similarity property existing in an image and finds a contractive mapping affine transformation (fractal transform)T, such that the fixed point of T is close to the given image in a suitable metric. It has generated much interest due to its promise of high compression ratios with good decompression quality. The other advantage is its multi resolution property, i.e. an image can be decoded at higher or lower resolutions than the original without much degradation in quality. However, the encoding time is computationally intensive. In this paper, a fast fractal image compression method based on the domain-range entropy is proposed to reduce the encoding time, while maintaining the fidelity and compression ratio of the decoded image. The method is a two-step process. First, domains that are similar i.e. domains having nearly equal variances are eliminated from the domain pool. Second, during the encoding phase, only domains and ranges having equal entropies (with an adaptive error threshold, λdepth for each quadtree depth) are compared for a match within the rms error tolerance. As a result, many unqualified domains are removed from comparison and a significant reduction in encoding time is expected. The method is applied for compression of satellite and medical images (512x512, 8-bit gray scale). Experimental results show that the proposed method yields superior performance over Fisher’s classified search and other methods.