Fractal Surface Investigations Using Iterated Functional Systems

Within the field of fractal image compression and modeling, Iterated Functional Systems (IFS) have been used with ever increasing success over the past few years. In this paper, we analyze the set of affine transformations (the fractal code) that defines the IFS to see what useful information it conveys when applied to fractal surfaces.

How this set can be interpreted to supplement or evaluate the simple fractal dimension has not been reported. We perform an exhaustive search analysis on range images of a classic set of fractal surfaces in order to cover fractal properties like isotropy, weak and strong anisotropy, and study how these are represented in the fractal code.

The main characteristics of this approach are (i) it relies on the assumption that the image redundancy can be efficiently exploited through self-transformability on a block-wise basis, and (ii) it approximates an original image by a fractal image.