Use of diffusion techniques for edge preservation for fractal coders

Abstract

Based on the correlation of self-similarity, fractal coders compress digital images by relating image blocks pairs at different scales in the images. The pairing of large to small block sizes dictates the compression ratio and the quality of the reconstructed image. Inaccurate fractal mappings at large image block sizes increase losses of edge information, discontinuities at boundaries and blocking effects. Partitioning the large block into smaller blocks overcomes these problems but significantly lowers the compression ratios. In addition, partitioning does not insure the retention of significant edges. We show how diffusion techniques can be used to overcome some of these problems while preserving significant edge information at a lower bit rate cost. By expanding the basic diffusion equation to contain a scalar function based on the edges of the original image, we can use the diffusion process to smooth along the direction of significant edges and sharpen in the direction of the edges. In this manner, we can restore edge information and smooth discontinuities and blocking effects.