HARFA: SCREENSHOTS AND TUTORIALS: BOX COUNTING METHOD - MODIFICATION USED IN HARFA   Fractal Analysis Box Counting Method - Modification used in HarFA As was mentioned earlier, the traditional Box Counting method consist of counting squares, which are needed to cover tested object COMPLETLY. In HarFA we use modification of traditional Box Counting. We count separately squares, which are completely black and separately squares, which cover border of black object, e.g. those squares which contain at least part of the tested black object and finally we count separately squares, which contain just white background, e.g. which are completely white. By this modification we obtain not one, but three fractal dimensions DB, DBW, DW, which characterise properties of black plane DB, black-white border of black object DBW (and this information seems to be the most interesting) and properties of white background DW. The practice for obtaining these dimensions is the same as by classical Box-Counting. Let's take e.g. a black-white picture of eye. Let's cover it by the mesh of square size 20 pixels. Then we can count squares, which are black completly (there are 39.00 these squares), then count we count squares, which are completely white (there are 199.85 such squares) and finally we count squares, which cover black-white border of the eye (there are 146.00 such squares). If we carry on such measurements for several sizes of square of overlaid mesh, we can etablish individual fractal dimensions as slopes of functions: NB(r) = DB(log(1/r)) + kB NBW(r) = DBW(log(1/r)) + kBW NW(r) = DW(log(1/r)) + kW You can download the program which demonstrates Box Counting method here (242 134 bytes). Previous Next