Solving the Two-dimensional Inverse Fractal Problem with the Wavelet Transfrom

The methodology of the solution to the inverse fractal problem with wavelet transform is extended to two-dimensional self-affine functions. Similar to the one-dimensional case, the two-dimensional wavelet maxima bifurcation representation used is derived from the continuous wavelet decomposition. It possesses translational and scale invariance necessary to reveal the invariance of the self-affine fractal. As many fractals are naturally defined on two-dimensions this extension constitutes an important step towards solving the related inverse fractal problem for a variety of fractal types.