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Fractal Dimension

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Generating a pixel- by pixel fractal dimension image using box counting algorithm



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The fractal dimension (FD) image is generated by considering each pixel in the original CT image as a single fractal dimension estimated from its 7x7 neighbours. The FD generated image remarkably enhances the tissue texture, and the internal subtle structures become more obvious as compared to the original CT image. This could help the physician's eyes in better delineating the tumour from the surrounding normal tissue; furthermore, the mean Fractal Dimension value of the tumour region of interest can give an indication of tumour aggressiveness. See the following reference: O. S. Al-Kadi and D. Watson, “Texture Analysis of Aggressive and non-Aggressive Lung Tumor CE CT Images,” IEEE Transactions on Biomedical Engineering, vol. 55, pp. 1822-1830, 2008.

Comments and Ratings (5)

Can you tell me how to specifically calculate fractal surface dimension by 3D box counting method?


Only concern is that this runs slow. Can you recommend any optimization?


Faraz (view profile)

Thanks for posting it (y)

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 for sharing, you did a nice job.
I have a question. Is there any other way to generate the slope (FD image) than linear regression of Nd and r?

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