Fingerprints and fractal terrain

Scale space fingerprints provide a natural formalism for modeling terrains because they describe a hierarchy of edges over a broad range of physical scales. The simplest fingerprint descriptor is the feature density function N (σ)-the number of terrain edges remaining after smoothing a terrain profile with a Gaussian of standard deviation σ. Feature density functions computed from Digital Elevation Model data are not only clearly different for landforms, such as shales and granite, but also for landform expressions, such as arid and humid shale. Feature density also provides a description of fractal behavior that agrees with conventional fractal computations, such as area and trail length scaling; shales exhibit fractal behavior over scales up to about 200 meters, while granites are not fractal over any meaningful range. The feature density evaluation of fractal behavior, however, is superior to the conventional methods: it is more sensitive to the expression of fractal scaling and does not exhibit a dependence on measuring units that can mask fractal behavior in the conventional methods.