A Power Differentiation Method of Fractal Dimension Estimation for 2-D Signals
A Power Differentiation Method of Fractal Dimension Estimation for 2-D Signals
复制标题
DOI：
10.1006/jvci.1998.0394
复制
发表时间：
1998-12
期刊：
影响因子：
--
通讯作者：
P. Asvestas;G. Matsopoulos;K. Nikita
中科院分区：
文献类型：
--
作者：
P. Asvestas;G. Matsopoulos;K. Nikita
分形维数已用于纹理分析，因为它与人类对表面粗糙度的感知高度相关。已经提出了几种用于估计图像的分形维数的方法。最流行的方法之一是通过其功率谱密度，前提是它被建模为分数布朗函数。本文提出了一种称为功率微分法（PDM）的新方法，用于从功率谱密度估计二变量信号的分形维数。该方法首先应用于已知分形维数的无噪声数据。它还使用噪声损坏和量化数据进行了测试。特别是，在噪声损坏数据的情况下，开发了改进的功率微分法（MPDM），从而可以更准确地估计分形维数。将 PDM 和 MPDM 获得的结果直接与使用其他四种众所周知的分形维数方法获得的结果进行比较。最后，介绍了应用新方法获得的超声肝脏图像分类的初步结果。
Fractal dimension has been used for texture analysis as it is highly correlated with the human perception of surface roughness. Several methods have been proposed for the estimation of the fractal dimension of an image. One of the most popular is via its power spectrum density, provided that it is modeled as a fractional Brownian function. In this paper, a new method, called the power differentiation method (PDM), for estimating the fractal dimension of a two-variable signal from its power spectrum density is presented. The method is first applied to noise-free data of known fractal dimension. It is also tested with noise-corrupted and quantized data. Particularly, in the case of noise-corrupted data, the modified power differentiation method (MPDM) is developed, resulting in more accurate estimation of the fractal dimension. The results obtained by the PDM and the MPDM are compared directly to those obtained using four other well-known methods of fractal dimension. Finally, preliminary results for the classification of ultrasonic liver images, obtained by applying the new method, are presented.