Estimating fractal dimension from range images of natural terrain

Abstract: "We investigate two published approaches to the problem of estimating fractal dimension: the box-counting approach, and the fractal Brownian function approach. In experiments with synthetic images, we find the fractal Brownian function methods proposed by Pentland and Yokoya to be superior to the box-counting approaches described by Voss, because the former do not require data sampled at equal intervals, and are more robust to Gaussian noise. For experiments with real images, we extend the fractal Brownian function methods to accomodate irregularly sampled data supplied by a scanning laser rangefinder.Applying the extended methods to noisy range imagery of natural terrain (sand and rocks), we find (1) that the resulting estimates of fractal dimension correlate closely to the human perception of the roughness of the terrain, (2) that it is appropriate to model the natural terrain studied as a fractal Brownian function, and (3) that the fractal dimension of the sensed point set is a practical and effective measure of the roughness of natural terrain."