Dual-tree wavelets for estimation of locally varying and anisotropic fractal dimension

The dual-tree wavelet transform is here applied to the problem of fractal dimension estimation. The Hurst parameter of fractional Brownian surfaces is estimated using various wavelet bases. Results are given for global, local, anisotropic, and both local and anisotropic Hurst parameters. It is shown that the directional selectivity of the dual-tree wavelets can be exploited effectively to compute and distinguish Hurst parameters that vary non-trivially with direction and space.