Feature Descriptors

Two scans of the same building from different stations share no points in common. They share only a surface, sampled at different places each time. Without something that summarises the local geometry around a point compactly enough to compare it across that gap, there is no feature-based registration, no place recognition for SLAM, no instance retrieval across datasets. The descriptor is that something. The coarse alignment of a multi-station TLS campaign rests on a few thousand FPFH descriptors per scan, 33 floating-point numbers each, matched in 33-dimensional space and filtered through RANSAC before ICP ever touches the data. This chapter moves from where to compute (the ISS and Harris 3D keypoint detectors) to how to compute (the Darboux frame, then PFH, FPFH, SHOT, spin images, and 3D Shape Context), continues with the learned descriptors that have displaced the hand-crafted family on the standard indoor benchmarks but not yet in production heritage and surveying work, and closes with the matching pipeline that turns descriptors into verified correspondences.

This chapter consumes the normals of Chapter 7, on which every angular feature below is built, and leans on the kd-trees of Chapter 4 for the neighbourhood queries during construction and the nearest-neighbour searches during matching. It extends the scalar geometric features of Chapter 10, which measure the magnitude of local shape but cannot tell two planar patches apart, into vectors discriminative enough to be matched across scans, and it supplies the correspondences that the feature-based coarse registration of Chapter 8 took as given.

From scalar features to rotation-invariant descriptors

The scalar geometric features of Chapter 10 (eigenvalue dimensionality features, curvature, roughness, density, verticality, height variance) summarise the local shape of a neighbourhood as a small handful of numbers. For segmentation and per-point classification this is sufficient. A Random Forest only needs to know that this neighbourhood is highly planar and roughly horizontal to label its points as ground. For feature matching, however, this is not enough. To match a point in scan A to its corresponding point in scan B, the descriptor must encode not just the magnitude of the local shape but its full geometric configuration, in a way that survives the unknown rigid transformation between the two scans. Two planar patches at the same physical location but observed from different viewpoints have identical eigenvalue features yet should match each other, and two planar patches at different physical locations also have identical eigenvalue features yet should not match. The eigenvalue family cannot tell these cases apart.