Modelling of multifractal object boundaries

Abstract

This paper presents a new technique that combines fractal and wavelet analyses to model rough (nonsmooth) but crisp (one-pixel wide) object boundaries that have fractal or multifractal characteristics. The boundary is represented compactly by two sets of descriptors and control points. The first set contains information about complexities present on the boundary and is calculated using a fractal dimension analysis. The second set contains information about the shape of the boundary and is calculated by using wavelet analysis. We apply the midpoint displacement algorithm on the two sets of control points in order to reconstruct boundaries with the required fractal or multifractal dimension. The quality of reconstruction is measured using the Renyi fractal dimension singularity measure. Experimental results produced compression ratios in the range of 300:1 to 450:1, while preserving the complexities of the original boundary, as measured by the above multifractal metrics.