Abstract
There are three main mathematical problems in digital terrain analysis: (1) interpolation of digital elevation models (DEMs); (2) DEM generalization and denoising; and (3) computation of morphometric variables through calculating partial derivatives of elevation. Traditionally, these three problems are solved separately by means of procedures implemented in different methods and algorithms. In this chapter, we present a universal analytical method based on high-order orthogonal expansions using the Chebyshev polynomials of the first kind with the subsequent Fejér summation. The method is intended for the processing of regularly spaced DEMs within a single framework including DEM global approximation, denoising, generalization, and calculating the partial derivatives of elevation. The method is exemplified by a portion of the Great Rift Valley and central Kenyan highlands. The test results demonstrate that the method is characterized by good performance (ie, a distinct monotonic convergence of the approximation) and a high speed of data processing. The method can become an effective alternative to common techniques of DEM processing.
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