Hausdorff (Box-Counting) Fractal Dimension

Returns the Haussdorf fractal dimension D of an object represented by the binary image I. Nonzero pixels belong to an object and 0 pixels constitute the background.

Algorithm:

1 - Pad the image with background pixels so that its dimensions are a power of 2.
2 - Set the box size 'e' to the size of the image.
3 - Compute N(e), which corresponds to the number of boxes of size 'e' which contains at least one object pixel.
4 - If e > 1 then e = e / 2 and repeat step 3.
5 - Compute the points log(N(e)) x log(1/e) and use the least squares method to fit a line to the points.
6 - The returned Haussdorf fractal dimension D is the slope of the line.

In this blog post I show how this code can be used to compute the fractal dimension:

http://www.alceufc.com/2013/11/fractal-dimension-from-image.html