A method for computation of surface roughness of digital elevation model terrains via multiscale analysis

In this paper, an algorithm to compute surface roughness of digital elevation model (DEM) terrains via multiscale analysis is proposed. The algorithm employs the lifting scheme to generate multiscale DEMs. At each scale, the areas of pixels that are modified are computed. Granulometric analysis is employed to compute the average area of curvature regions in the terrain, and the average roughness of the terrain due the distribution of curvature regions. The selected case studies of the algorithm implementation demonstrated that the proposed algorithm 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. The algorithm allows for a good quantification of a region's convexity/concavity over varying scales, distinguishing between shallow and deep incisions of valleys and ridges of the terrain, and hence, provides an accurate surface roughness parameter.