Fractal Dimension
Generating a pixel- by pixel fractal dimension image using box counting algorithm
Author: Omar Al-Kadi

Thank you Mohammad for your kind comment. Yes there are many ways to compute the FD other than the Box Counting method, such as the fractal Brownian motion by estimating the Hurst index, or via the signals' power spectrum, or using the autocorrelation function. All of these FD estimation approaches attempt to quantify the roughness of the 2D signal surface.

Thanks Martin, and I'm happy you found the script useful.
Yes as you guessed, the standard deviation mainly depends on the type of image you anslyse. That is, the more homogeneous the texture in the image is, the more homogeneous the Fractal dimension becomes, and thus the lower the standard deviation; and vice versa. To check, try to apply the script to images with different textures (e.g. rough and fine) and compare your results.

@Rajkumar Why to use this for signal processing? There are algorithms based on kNN, Higuchi's method and Multi-resolution box count that can perform much better for time series data.

27 Jan 2014

Fractal Dimension
Generating a pixel- by pixel fractal dimension image using box counting algorithm
Author: Omar Al-Kadi

Thank you Mohammad for your kind comment. Yes there are many ways to compute the FD other than the Box Counting method, such as the fractal Brownian motion by estimating the Hurst index, or via the signals' power spectrum, or using the autocorrelation function. All of these FD estimation approaches attempt to quantify the roughness of the 2D signal surface.

16 Jan 2014

Fractal Dimension
Generating a pixel- by pixel fractal dimension image using box counting algorithm
Author: Omar Al-Kadi

@Rajkumar Why to use this for signal processing? There are algorithms based on kNN, Higuchi's method and Multi-resolution box count that can perform much better for time series data.

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27 Mar 2012

Fractal dimension
Generating a fractal dimension image using box counting algorithm

Thanks Martin, and I'm happy you found the script useful.
Yes as you guessed, the standard deviation mainly depends on the type of image you anslyse. That is, the more homogeneous the texture in the image is, the more homogeneous the Fractal dimension becomes, and thus the lower the standard deviation; and vice versa. To check, try to apply the script to images with different textures (e.g. rough and fine) and compare your results.
Kind regards,
Omar

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18 Mar 2011

Fractal dimension
Generating a fractal dimension image using box counting algorithm

Thanks for useful script.
But the estimate of fractal dimension has large standard deviation in many case when I used this script. Is it a proprerty of box-method or it depends on source image?
Thank for respond.

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