Computation of scale-independent surface roughness via the generation of multiscale digital elevation models

The quantitative computation of surface roughness has received increasing attention due to its importance in numerical surface study. A number of algorithms have been employed to compute surface roughness. These algorithms, which operate at singular scales of measurement, provide scale-dependant roughness parameters. In this paper, the computation of a scale-independent roughness parameter is performed via the generation of multiscale digital elevation models (DEMs).The proposed procedure employs the lifting scheme to generate multiscale DEMs. Using the mask of pixels modified at each scale, granulometric analysis is employed to compute the average size of convex and concave regions in the DEM, and the scale-independent average roughness of the terrain of the DEM due the distribution of convex and concave regions in the terrain. The proposed procedure provides a surface roughness parameter that is realistic with respect to the amplitudes and frequencies of the terrain, invariant with respect to rotation and translation, and has intuitive meaning.