Addressing scale dependence in roughness and morphometric statistics derived from point cloud data.
Abstract:The heights of natural surfaces can be measured with such spatial density that almost the entire spectrum of physical roughness scales can be characterized, down to the morphological form and grain scales. With an ability to measure ‘microtopography’ comes a demand for analytical/computational tools for spatially explicit statistical characterization of surface roughness. Detrended standard deviation of surface heights is a popular means to create continuous maps of roughness from point cloud data, using moving windows and reporting window-centered statistics of variations from a trend surface.
If 'roughness' is the statistical variation in the distribution of relief of a surface, then 'texture' is the frequency of change and spatial arrangement of roughness. The variance in surface height as a function of frequency obeys a power law. In consequence, roughness is dependent on the window size through which it is examined, which has a number of potential disadvantages: 1) the choice of window size becomes crucial, and obstructs comparisons between data; 2) if windows are large relative to multiple roughness scales, it is harder to discriminate between those scales; 3) if roughness is not scaled by the texture length scale, information on the spacing and clustering of roughness `elements’ can be lost; and 4) such practice is not amenable to models describing the scattering of light and sound from rough natural surfaces.
We discuss the relationship between roughness and texture. Some useful parameters which scale vertical roughness to characteristic horizontal length scales are suggested, with examples of bathymetric point clouds obtained using multibeam from two contrasting riverbeds, namely those of the Colorado River in Grand Canyon, and the Snake River in Hells Canyon. Such work, aside from automated texture characterization and texture segmentation, roughness and grain size calculation, might also be useful for feature detection and classification from point clouds.