Methods for representing curves in \mathbb{R}^2 and \mathbb{R}^3 using fractal interpolation techniques are presented. We show that such representations are both effective and convenient for irregular or complicated data. Experiments in various datasets, including geographical and medical data, verify the practical usefulness of these methods.

The Hutchinson metric is a natural measure of the discrepancy between two images for use in fractal image processing. An efficient solution to the problem of computing the Hutchinson metric between two arbitrary digitized images is considered. The technique proposed here, based on the shape of the objects as projected on the digitized screen, can be used as an effective way to establish the error between the original and the, possibly compressed, decoded image. To test the performance of our method, we apply it to compare pairs of fractal objects, as well as to compare real-world images with the corresponding reconstructed ones.