高维分形和多重分形的去趋势涨落分析
Detrended fluctuation analysis for fractals and multifractals in higher dimensions
摘要：
一维去趋势波动分析（1D DFA）和多重分形去趋势波动分析（1D MF-DFA）因其精度高、易于实现而被广泛应用于分形和多重分形时间序列的标度分析。在本文中，我们推广一维DFA和MF-DFA到高维版本。当测试与合成表面，包括分数布朗表面和多重分形表面的推广工作。采用二维MF-DFA对两幅自然图像和实验图像进行了分析，得到了较好的标度律。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
