  One-dimensional detrended fluctuation analysis (1D DFA) and multifractal
detrended fluctuation analysis (1D MF-DFA) are widely used in the scaling
analysis of fractal and multifractal time series because of being accurate and
easy to implement. In this paper we generalize the one-dimensional DFA and
MF-DFA to higher-dimensional versions. The generalization works well when
tested with synthetic surfaces including fractional Brownian surfaces and
multifractal surfaces. The two-dimensional MF-DFA is also adopted to analyze
two images from nature and experiment and nice scaling laws are unraveled.
