Variable DEM generalization using local entropy for terrain representation through scale

ABSTRACT An automated method of variable digital elevation model (DEM) smoothing is presented. Using variably sized kernels to perform filtering, the method is driven by the entropy of local z-values in the DEM, i.e. the amount of information necessary to convey the elevation variety in the neighborhood of each pixel. This paper presents the method in service of low-pass filtering in order to smooth the raster, though other neighborhood-based filters could be implemented as well. When used in smoothing, the method successfully retains detail in areas of higher relief variation and suppresses it in areas of lower variation, thereby retaining more salient features like ridges, peaks, or incised valleys, while diminishing flatter ones. Varying the neighborhood size with which entropy calculations are made allows for filtering through continuous map scale, enabling multi-scale representation. The method also includes a simple correction for smoothed pixels such that their z-value range reflects that of the input DEM, thereby ensuring that subsequent products such as generated contour lines remain within correct ranges. Several illustrations are given of the method's results.