Measuring Fractal Dimension: Morphological Estimates And Iterative Optimization

Petros Maragos; Fang-Kuo Sun

doi:10.1117/12.970052

1 November 1989 Measuring Fractal Dimension: Morphological Estimates And Iterative Optimization

Petros Maragos, Fang-Kuo Sun

Proceedings Volume 1199, Visual Communications and Image Processing IV; (1989) https://doi.org/10.1117/12.970052
Event: 1989 Symposium on Visual Communications, Image Processing, and Intelligent Robotics Systems, 1989, Philadelphia, PA, United States

Abstract

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.

Citation Download Citation

Petros Maragos and Fang-Kuo Sun "Measuring Fractal Dimension: Morphological Estimates And Iterative Optimization", Proc. SPIE 1199, Visual Communications and Image Processing IV, (1 November 1989); https://doi.org/10.1117/12.970052

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