Digital elevation modeling via curvature interpolation for LiDAR data

Digital elevation model (DEM) is a three-dimensional (3D) representation of a terrain's surface - for a planet (including Earth), moon, or asteroid - created from point cloud data which measure terrain elevation. Its modeling requires surface reconstruction for the scattered data, which is an ill-posed problem and most computational algorithms become overly expensive as the number of sample points increases. This article studies an effective partial differential equation (PDE)-based algorithm, called the curvature interpolation method (CIM). The new method iteratively utilizes curvature information, estimated from an intermediate surface, to construct a reliable image surface that contains all of the data points. The CIM is applied for DEM for point cloud data acquired by light detection and ranging (LiDAR) technology. It converges to a piecewise smooth image, requiring O(N) operations independently of the number of sample points, where $N$ is the number of grid points.