Multifractal modelling of arbitrary object boundaries in image segmentation

This paper addresses the problem of approximation of arbitrary boundaries and edges resulting from image segmentation. Using MPEG-7 terminology, this problem can be considered as the search for a descriptor for a boundary feature of an object. The shape of an object is usually described by its boundaries, to differentiate it from the other regions of the image. Traditionally, Bezier curve fitting has been employed to model the boundaries of objects consisting of smooth and crisp curves. However, natural images contain complex shapes that are difficult to describe by such smooth-boundary modelling techniques. Consequently, we focus on fractals and multifractals to model arbitrary boundaries based on the singularity measure property of fractals. We use wavelets to identify boundary control points and reconstruct the self-similar boundaries with any fractal or multifractal dimension, using the midpoint displacement algorithm.