Bayesian Inference of Elevation to Reduce Large Interpolation Errors in 2-d Road Features Draped Over Digital Elevation Models

The usual approach for adding elevation data to two dimensional (2-d) vector features in a Geographic Information System (GIS) is to infer heights from a Digital Elevation Model (DEM), either through traditional (naïve) interpolation, Kriging, or deep learning. Where the terrain contains steep slopes, however, any of these approaches can generate large errors due to the limited resolution of the DEM, and model error in the DEM concept itself. In the case of road networks, these errors have a severe and nonlinear effect on cycling route planners and transport models, especially those based on open elevation data. This paper introduces a Bayesian maximum likelihood approach to correcting interpolated heights, by combining a DEM with prior expectations of feature gradient. The topological network defined by feature shapes is used as auxiliary information. Correcting the output of naïve interpolation shows reduction of mean errors, and reduced overprediction of elevation change outliers, compared to both naïve interpolation and Kriging.