Authors: Charles K. Toth, Zoltan Koppanyi, Dorota A. Grejner-Brzezinska, and Grzegorz Jóźków
Digital elevation models (DEM) are baseline geospatial products widely used in mapping and other applications. Generally obtained from airborne sensor data, DEMs can be made available at various spatial resolutions and accuracy levels. As DEM production costs vary significantly depending on the detail level of these two parameters, plans for data acquisition must be carefully balanced so as to satisfy spacing and accuracy requirements at the lowest possible cost. While most standard mapping techniques provide methods for determining the required resolution, they are usually based on qualitative surface definitions such as open, built-up and/or urban terrain, or by land cover such as weeds, crops, scrub, wooded, etc. These categories, however, are not necessarily correlated to the complexity of the surface, which ultimately defines the spatial sampling distance for any given surface representation requirements. This paper investigates a method for surface characterization that uses the spatial spectrum. Mathematically, DEMs can be modeled as real, single-valued functions of two variables. Using a 2D Fourier transform, surfaces can be represented in the spatial frequency domain, where each frequency can be interpreted as a different sampling rate of the measurements (i.e., spacing). In a simple interpretation: low-frequency components characterize slow changes of the surface, such as average slope, while high-frequency components describe the microstructure, or local, details. Evaluating representative DEMs, the most typical spatial spectra can be determined which, subsequently, can help practitioners define the optimal sampling distances and/or error requirements to determine DEM resolution and data acquisition for major surface categories.
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