Modelling multifractal object boundaries using iterated function system

This paper addresses the problem of approximation of arbitrary object boundaries that result from image segmentation. We present a new technique to reconstruct the self-similar boundaries with any fractal or multifractal dimension, using the iterated function system (IFS). The boundaries are assumed to be rough (non-smooth) but crisp (one-pixel wide) and are fractal or multifractal in nature. We show that such boundaries can be regarded as an attractor of a linear IFS having the same multifractal spectrum as the boundaries. We also discuss the hidden variable IFS in order to reconstruct multifractal boundary curvatures, while preserving the original multifractal spectrum of the boundary. Experimental results show that such arbitrary boundaries can be reconstructed more accurately using the IFS as compared to other standard techniques like the midpoint displacement algorithm.