Extracting topographic terrain features from elevation maps
CVGIP: Image Understanding
Skeletonizing a DEM into a drainage network
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IEEE Transactions on Pattern Analysis and Machine Intelligence
Topographical Properties of Generic Images
International Journal of Computer Vision
Evaluation of Methods for Ridge and Valley Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Algorithms for using a DEM for mapping catchment areas of stream sediment samples
Computers & Geosciences
Multiresolution Analysis of Ridges and Valleys in Grey-Scale Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Tracing Crease Curves by Solving a System of Differential Equations
ECCV '96 Proceedings of the 4th European Conference on Computer Vision-Volume I - Volume I
Creaseness from Level Set Extrinsic Curvature
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume II - Volume II
Environmental Modelling & Software
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Loci of extreme curvature of the topographic surface may be defined by the derivation function (T) depending on the first-, second-, and third-order partial derivatives of elevation. The loci may partially describe ridge and thalweg lines. The first-and second-order partial derivatives are commonly calculated from a digital elevation model (DEM) by fitting the second-order polynomial to a 3×3 window. This approach cannot be used to compute the third-order partial derivatives and T. We deduced formulae to estimate the first-, second-, and third-order partial derivatives from a DEM fitting the third-order polynomial to a 5×5 window. The polynomial is approximated to elevation values of the window. This leads to a local denoising that may enhance calculations. Under the same grid size of a DEM and root mean square error (RMSE) of elevation, calculation of the second-order partial derivatives by the method developed results in significantly lower RMSE of the derivatives than that using the second-order polynomial and the 3×3 window. An RMSE expression for the derivation function is deduced. The method proposed can be applied to derive any local topographic variable, such as slope gradient, aspect, curvatures, and T. Treatment of a DEM by the method developed demonstrated that T mapping may not substitute regional logistic algorithms to detect ridge/thalweg networks. However, the third-order partial derivatives of elevation can be used in digital terrain analysis, particularly, in landform classifications.