Compression of multifractal object boundaries: a comparison of two approaches

Abstract

This paper presents a comparative study of two approaches that address the problem of compression of arbitrary object boundaries resulting from image segmentation. The first approach uses multiresolution based techniques, in which the boundary is represented compactly by two sets of descriptors and control points which are obtained by applying wavelet and fractal analysis. The midpoint displacement algorithm is then applied to the two sets of control points in order to reconstruct the boundaries with the required fractal dimension. The second approach is based on the iterated function system (IFS). In this approach, the object boundary is regarded as an attractor of an IFS having the same Renyi fractal dimension spectrum as the original boundary. The experimental results show that the multifractal object boundaries can be modelled compactly using both approaches. The compression ratio achieved for the wavelet-based approach was 285:1, while for the IFS-based approach it was 52:1. These results can be compared with state of the art image compression techniques such as JPEG2000