基于傅里叶变换的闭合轮廓分形维数估计
Closed Contour Fractal Dimension Estimation by the Fourier Transform
摘要：
这项工作提出了一种新的技术，可以表示为一个封闭的轮廓的分形对象的分形维数的数值演算。该方法将分形轮廓映射到一个复杂的信号，并使用傅里叶变换计算其分形维数。通过傅立叶功率谱分析，验证了功率与频率之间的指数关系。由关系式的参数（指数）求出分形维数。并与文献中的其他经典分维估计方法进行了比较.例如，在一个实施例中，Bouligand-Minkowski，盒子计算和经典傅立叶。比较是通过微积分的分形轮廓的维数是众所周知的分析。结果表明，该方法具有较高的精度和鲁棒性。
英文摘要：
This work proposes a novel technique for the numerical calculus of the fractal dimension of fractal objects which can be represented as a closed contour. The proposed method maps the fractal contour onto a complex signal and calculates its fractal dimension using the Fourier transform. The Fourier power spectrum is obtained and an exponential relation is verified between the power and the frequency. From the parameter (exponent) of the relation, it is obtained the fractal dimension. The method is compared to other classical fractal dimension estimation methods in the literature, e. g., Bouligand-Minkowski, box-couting and classical Fourier. The comparison is achieved by the calculus of the fractal dimension of fractal contours whose dimensions are well-known analytically. The results showed the high precision and robustness of the proposed technique.
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