Measuring Fractal Dimension: Morphological Estimates And Iterative Optimization
Petros A. Maragos, Fang-Kuo Sun · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1989
An important characteristic of fractal signals is their fractal dimension. For arbitrary fractals, an efficient approach to evaluate their fractal dimension is the covering method. In this paper we unify many of the current implementations of covering methods by using morphological operations with varying structuring elements. Further, in the case of parametric fractals depending on a parameter that is in one-to-one correspondence with their fractal dimension, we develop an optimization method, which starts from an initial estimate and by iteratively minimizing a distance between the original function and the class of all such functions, spanning the quantized parameter space, converges to the true fractal dimension.