Fractal characterization via morphological analysis

Abstract

In this paper, we provide an approach based on mathematical morphological operators to quantify the complexity of thematic information (map) or binary image object as a quantitative index that is scale invariant, but shape-dependant. We demonstrate the applicability of this approach on a binary Koch quadric fractal. We define an shape-size based fragmentation technique for both foreground and background of the considered deterministic fractal. Further, we utilize this technique to: a) quantify the roughness of binary fractal, b) explore possible relations between the results generated via this fragmentation technique and fractal dimension. This exercise was further extended to draw the results for a binary random Koch quadric fractal.