Classification

You arrive here holding a tile that has been measured, cleaned and taken apart. The segmentation of chapter 11 grouped the points that belong together. The terrain models of chapter 9 gave you the height of each point above the ground. The features of chapter 10 describe the shape of every neighbourhood. Yet not one of those steps put a name on anything. You open the file and find coordinates, sensor attributes and, at best, unnamed groups, and nothing in it separates a roof from the ground beneath it. In this chapter we supply the missing name, one label to every point. Everything downstream is then built from your labels rather than from the coordinates. You have to pull the vegetation away before a digital terrain model (DTM) is interpolated. You have to isolate the building footprints before extraction and tag the power line catenary before a utility inventory can measure its clearance.

The errors you make here do not stay here. If you label a steep ridge as building, a phantom structure appears downstream. If you leave canopy in the ground class, the error enters the DTM and travels into every contour drawn from it. How large is that exposure? Here the airborne window of figure 12.11 puts a number on it. Of its 42 190 test points, 2 236 are labelled wrongly, and 228 of the 328 low-vegetation points are handed to the terrain model as ground.

Now, the methods that make the assignment span thirty years, and I develop them here in the order of what each one requires rather than of what it scores. At one end is the hand-crafted-features-plus-Random-Forest pipeline, which still ships in operational software and stays competitive on mobile-mapping benchmarks when you train it on 1 000 labelled examples per class (Weinmann et al., 2014). At the other are the deep architectures now run on national airborne surveys. There, a RandLA-Net baseline reaches 77.5 per cent mean intersection over union (mIoU) and 96.1 per cent overall accuracy on the seven classes of FRACTAL. FRACTAL contains 9.3 billion labelled points sampled from the French LiDAR HD programme (Hu et al., 2020; Gaydon et al., 2024). 1 000 labelled examples against 9.3 billion: that span is the practical content of the choice you face, and it is the model-driven versus data-driven axis on which every method of this chapter lies.

Notice that $\mathcal{L}$ is fixed before any classifier is trained, and that fixing it is the first real decision of the work. You might expect a small vocabulary to be a safe one. The five-class scheme of figure 12.3, ground with low, medium and high vegetation and building, is about as small as a useful scheme gets. Even there the forest recovers only 18 per cent of the low-vegetation points. So a class belongs in $\mathcal{L}$ only if something in the feature vector separates it from its neighbours. This means you choose the vocabulary and the features against each other rather than one after the other.