Change Detection

You can now bring two surveys into one frame with the registration of chapter 8. You can put an oriented normal on every point with chapter 7 and separate the bare earth from what stands on it with chapter 9. In this chapter we use all three. The registration is the prerequisite, since any misalignment it leaves enters the distance map as a bias no later step removes. The normals supply the direction along which a patch comparison measures. The extracted ground supplies the surfaces that are differenced when a volume is wanted. What none of the three shows you is how the site changed between two visits, and that is what a repeat survey is paid to answer.

Here is the difficulty you are walking into. Two point clouds of the same scene, acquired three years apart and registered into one frame, differ almost everywhere. Part of that difference is the change you came to measure, the rest is the measurement itself, and nothing in the difference map separates the two. On the pair of airborne epochs of figure 14.7, a courtyard roofed over between April 2020 and March 2023 differs by a median of 18.2 m. The roofs and streets around it differ by a median of -0.01 m. That metre-scale event is legible on any colour map. The decimetre-scale question is not, since the same window carries a level of detection whose median is 0.11 m. So a roof reading that much lower at the second epoch may have settled or may simply have been measured twice.

Which part of that noise are you most likely to mistake for change? That would be the registration residual, and it is the one most often reported as change. A residual tilt of a few millimetres between the campaigns grows steadily across the scene and produces the same coherent gradient that differential settlement produces (figure 14.2). So what is it worth to model the noise explicitly rather than to read the colours off a map? Read the answer off one survey. Lague et al. (2013) report a detection threshold of 6 mm at 95 per cent confidence on smooth surfaces at 50 m range, rising to about 6 cm on rough natural terrain in the same campaign. So a colour map with no stated uncertainty is a field check rather than a result, and that is how I use one.

Now read the three questions of that definition straight off the courtyard of figure 14.7. Where the surface differs is the set of core points whose difference clears its own noise threshold, which is what marks the courtyard out from the roofs around it. By how much is the 18.2 m median rise over the 923 square metres those points cover. Whether it is significant is settled by that threshold. What the rise means, a new roof, is a statement the geometry does not supply on its own. This is why the chapter ends with reporting rules rather than with a distance.