Improve topographic LiDAR point cloud interpolation accuracy with geodesic distance

Abstract

High-precision topographic LiDAR point clouds provide a concrete elevation basis for many environmental and ecological applications, but they suffer from distinctly uneven density with voids of varying sizes. Interpolation tools most commonly serve to resample the density and fill the voids under the designated scale of the application. However, the target spaces in which the topographic point clouds reside are essentially non-Euclidean surfaces; the true distances between sample points are curved geodesic distances, which differ significantly from the conventionally used Euclidean distances, so classical interpolation models should be investigated for potential systematic biases.

First, we introduce geodesic distance to topographic point clouds as a dimensionality reduction constraint to project the point cloud. This ensures the positive definiteness of the autocorrelation matrix and the revision of conventional interpolation algorithms. Then, we carried out a benchmark interpolation with deterministic and geostatistical models on a relatively “regular” topographic point cloud. Product point cloud resampling was subsequently examined with the optimal method. In response to the computational challenge, we devise a feature-points embedded domain decomposition calculation and propose a cross-validation-based point-to-point distance for better evaluation of the interpolation accuracy.

The experimental results with different scenarios show substantial improvement in interpolation accuracy with the introduction of geodesic distance, which is of universal significance in prompting the precise utilization of topographic models.

The related data and code will be open-sourced in the community.