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Hausdorff Dimension by the box counting method

version (1.36 MB) by Paul French
uses box counting method to calculate the degree of roughness of an input image


Updated 13 Aug 2007

No License

A quantitative analysis of perimeter roughness is carried out to illustrate the degree of roughness of input images. Commonly known as the Hausdorff Dimension (H.D.), the algorithm shown in figure 1.1 gives the aggregate perimeter roughness as a fractal dimension. The fractal dimension describes the complexity of an object; in the case of devices presented here, this algorithm gives perimeter roughness which implies parasitic emission sites for extremely rough perimeters [1]. On Hausdorff Dimension scale, a dimension of 1 equates to a smooth line, while 2 implies fractal complexity like that of a Julia set, and because the devices presented here are considered truncated fractals, the fractal dimension calculated is bound by the above limits, i.e. 1 < H.D. < 2.

Comments and Ratings (4)

José Araujo

I need to measure the fractal dimension over a surface

The program really works, but I need to measure the fractal dimension over a surface. Is there a way to measure the area instead of the perimeter?

noureddine benhmed

take me an exemple for a heat equation with the difference methode

F Moisy

1) This script erases all. Make it a function, with the image file as an input argument.
2) The spaces ' ' have to be removed from the main filename, otherwise it does not work.
3) See submission 13063

MATLAB Release Compatibility
Created with R13
Compatible with any release
Platform Compatibility
Windows macOS Linux

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