Hello Everyone,

I am currently working on a project where I need to do extract the fractal dimension from greyscale images. I have some MATLAB code for running the mass radius method to computing the same.

the code basically starts from a fixed point(centre of image) and considers concentric circles with increasing radii (R).For each circle, the number of pixels which are "set" and which lie inside the circle are counted (N) and then finally the dimension if extracted from a log-log plot of N v.s R. However, I read in a paper that the number of pixels which are not set should also be counted but i am unsure as to how this data can be used.

If anyone has some good links on the mass-radius method or even some code/pseudocode and can pass it on, it would be a great help.

Thanks in advance.

Greetings and welcome to this Forum!!   

It looks like Thomas Ludwig (lycium) has got you off to a good start with those links.  If you need some more references, let us know.

definitely count 1 as mass and 0 as not!

regarding the inside/outside counting, i think you can considerably improve the accuracy of this estimate, especially for small circles, if you consider sub-pixel converage. that is, if you have a set pixel which overlaps the circle boundary, consider the fractional area of the overlap instead of just 0 or 1. i worked out and simplified the equations for this some years ago using stokes' theorem, for drawing anti-aliased (or "blurred" as it is known on these forums ) circles, and it was quite fast as you only need to compute it on the boundary.

of course, you can approximate this analytical answer to any degree of accuracy desired by simply increasing the resolution of your source image, which has the added benefit of giving a truer estimate of the actual "mass of the fractal". beyond this you can actually plot the fractal in a sub-pixel-correct manner and consider that weight in addition to the area-weighting above...


edit: sorry, i meant green's theorem; stokes' theorem is the next one up.