- Fractal Dimension: Wikipedia
- A course on Fractals in Yale U
- A course on Fractal dimension from images: Munich U
- Fractal Dimension explained
So, once you know about fractal dimensions, come to read the stuff on the right (Conti, 2001)
One can treat the image 3-D object. Compute the total number of occupied boxes in X-Y-I dimension box, as a function of size of the box. D = ln(number)/ ln(radius).
It is a little bit more complicated. Check the paper by Conci, a PPT talk can also be found.