Change Detection

It is natural to assume that the difference between two point clouds of the same scene is the change in the scene. My first attempt to monitor stone settlement on a heritage façade produced a map of millimetre displacements that was statistically tight and read as a clean settlement signal. The displacement was real to four millimetres at most points, and almost none of it was change: it was the artefact of a 4 mm registration drift between the two campaigns. The lesson is that what a comparison measures is the change plus the noise of two acquisitions, two registrations, and two slightly different sensor calibrations, and the measured difference cannot be reported as physical change until that noise is accounted for. Detecting genuine change of 2-5 mm on stable surfaces and 1-2 cm on rough natural terrain has been routine since Lague and colleagues (2013), but only with methods that model the noise envelope explicitly and produce statistically defensible distances rather than colour maps that merely look quantitative.

Change detection sits near the end of the pipeline and inherits everything that precedes it. The registration of Chapter 8 is its silent prerequisite, since any residual misalignment enters the distance map as a systematic bias, and the methods draw on the normal estimation of Chapter 7, along which M3C2 measures its distances, and on the ground extraction of Chapter 9 when volumes are computed by DEM differencing. Its outputs, displacement maps and volume budgets with stated confidence, drive the monitoring workflows of Chapter 17, from landslide kinematics to structural compliance. The chapter builds from the simplest distance to the most defensible: cloud-to-cloud and cloud-to-mesh comparison, the M3C2 algorithm with its per-point level of detection, volumetric and deformation analysis, and finally the 4D analysis of time series spanning three or more epochs.

The change detection problem

Suppose we acquire two point clouds $\mathcal{P}_1$ and $\mathcal{P}_2$ of the same scene, each at a different epoch, a single acquisition campaign at a given time, separated by some interval. A comparison of exactly two epochs is a bitemporal analysis, the before-and-after case that most of this chapter treats, in contrast to the multitemporal time series treated towards the end of the chapter. Our goal is to answer three questions:

1. Where did the surface change?
2. How much did it change (magnitude and sign)?
3. Is the detected change real, or an artefact of measurement noise, registration error, or point density variation?

The third question is often the most challenging. Every measurement contains noise, and the two point clouds are rarely acquired from exactly the same position, so residual registration errors add a systematic component. A robust change detection method must distinguish genuine change from these confounding effects, as the figure below sketches.