HARFA: SCREENSHOTS AND TUTORIALS: BOX COUNTING METHOD - TRADITIONAL APPROACH   Fractal Analysis Box Counting Method - Traditional Approach Traditionally, box counting method works by laying meshes of different sizes r and then counting number of boxes N needed to cover tested object COMPLETLY. Slope D of the linear portion of function log N(r) = D(log(1/r)) + log k is assumed to be the box (fractal) dimension and its k intercept is the fractal measure. For example, we have black&white image of a tree. We cover it by mesh of square size 10 pixels, and then we count number of squares needed to cover the tree completely (they are marked by blue colour, we need 520 such squares). We repeat this for the mesh size of 17 (201 squares needed), then for mesh size of 28 (80 squares needed) and so on. When we have sufficient number of data points (e.g. 9 values), we can perform linear regression of the dataset and determine Box - dimension and fractal measure. By this method we will find out, that the box dimension of black&white image of the tree is equal to 1.7826 with the coefficient of correlation R = 0.9994. You can download program that demonstrates Box-Counting method here (242 134 bytes). Previous Next