Abstract:
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In this work, the estimation of fractal dimension is considered for one and two-dimensional cases. For one-dimensional case, we use the Bayesian approach to estimate the fractal dimension of a fractional Brownian motion. For two-dimensional case, we propose using the Euler characteristic of the excursion set of a Gaussian random field to estimate the fractal dimension of a three-dimensional object.The Euler characteristic is used to estimate the smoothness of a polished metal surface. The Bayesian approach is applied to estimate the Hurst index of 2011 daily Taiwan Stock Index.
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