Finding Ridge Lines in Point Clouds
This project was executed for het Waterschapshuis over the course of two months. Het Waterschapshuis is the overseeing managing body for all 21 water boards in the Netherlands. It bundles the water boards' needs and realises products that are out of the individual waterboards' reach, but are still deemed vital. One of such products arises from the AHN program, which sees its fifth version fullfilled around 2025. The Actueel Hoogtebestand Nederland (AHN) program realizes aerial laser altimetry derived elevation models every few years, at an ever-increasing rate, and is a combined effort of het Waterschapshuis (and thus the waterboards), provincial governments and the ministry of infrastructure and waterways (Rijkswaterstaat). With AHN4 at the ready and AHN5 already partially public (at the time of writing March 26th, 2025) the potential of comparisons between the different AHN versions has grown sufficiently large. Comparisons between point clouds are however not straightforward.
The AHN4 point cloud contains about 10-14 height measurement points every square meter. This comes down to a data product with nearly 1 trillion (1012) points and these are scattered irregularly over the entirety of the Netherlands, with the exception of (nearly) all water bodies. In addition to the AHN products, point cloud datasets from a dense matching procedure added another 3 dense national point clouds. Although earlier AHN products contain less points, the incredibly vast number of measurement points require a specialized and tailored approach. Another challenge is posed by the irregularity of the measurement, i.e. which points to compare with which points across 6 national point clouds?
Thanks to earlier work by het Waterschapshuis as well as the University of Twente and 3DGI, it had been shown that a tractable and comprehensive comparison is however possible. From those studies, it was concluded that ridge lines are excellent entities for comparing point cloud positioning qualities. Ridge lines may be estimated from the virtual crossing of two slanted roof planes, each of which can conveniently be supported by many point measurements. As such, the problem reduces to estimating roofs and therefore ridge lines, whose position and orientation can be compared among the different national point clouds. After all, ridge lines are much more recognizable and suitable for a comparison exercise than the billions of individual point measurements.
This still means however that the detection and estimation of ridgelines must take place consistently, accurately and most importantly in great abundance. The latter is important because it is not assumed that the differences between the point clouds are spatially homogeneous.
To this end, with the support of Adriaan van Natijne, I have written a small software package (heavily paralllized with Numba) to extract the ridge lines from the AHN and dense matching products. A satisfying set of nearly 6 million ridgelines were detected in AHN4, increasing the number by roughly 1 million with respect to earlier efforts. The ridgelines were also validated for consistency through comparison against a few small datasets from other parties, with successful results. Comparison of ridgelines also turned out to be non-trivial, for which a new method was developed. After all, think about it, how would you compute the difference between two arbitrary lines in a 3D space?
The estimated ridgelines for each point cloud together encompass the national ridgeline database (nationaal noklijnenbestand), which could serve several purposes, such as:
- Local point clouds may be linked (and thus geocoded/co-registered) to the national point cloud if the ridgelines are estimated in the same way.
- Differences between point cloud can be inspected spatially, potentially identifying discrepancies originating from different flight lines.
- Automatic quality control for future point clouds based on their (new) ridgeline positions.
