Registration

You can now take a scan as it comes off the instrument, remove its outliers (chapter 6), give every point an oriented normal (chapter 7) and reach its neighbours in microseconds through the indexes of chapter 4. All of that happens inside one scan, in the frame the instrument wrote it in, and that is exactly where it stops. Yet a site is never one scan.

So look at figure 8.3. Three terrestrial scans cover the same stand of mangrove prop roots on Babeldaob Island, each in its own scanner-centred frame. No transform, station coordinate or target position is published beside them. Until those frames share a common reference, the stand exists in the dataset as three separate descriptions of itself rather than as one object. You cannot compare a measurement in one scan with a measurement in another. Recovering the transform that brings them together is what registration means.

But recovering it accurately is the harder half. Every alignment is computed in the frame the previous one produced, so the residual errors compound. How badly? In figure 8.11, 794 chained links carry the estimated position 82 m from its own starting point over 7.94 km. The same links adjusted as one network close that gap to 33 mm. Eighty-two metres, and not one of those 794 links was bad. So you need two things from this chapter, a way to align one pair and a way to keep the errors of many pairs from accumulating.

The mangrove scans make that definition concrete. For one of them the recovered $\mathbf{R}$ is a turn of 45.04° about a near-vertical axis. Applying it with $\boldsymbol{t}$ puts that scan's prop roots on top of the prop roots of the scan you hold fixed.

Note where this occurs in your pipeline. Registration consumes the cleaned points of chapter 6 and the normals of chapter 7, which you will need for its most accurate variants. It issues its nearest-neighbour queries through the spatial indexes of chapter 4. Everything after it works on the single unified point cloud it delivers, the classification of chapter 12, the change detection of chapter 14 and the surface reconstruction of chapter 15 alike. And SLAM (section 8.9) is this same estimation run in real time, once per arriving sweep.

Four questions run through the chapter, and you will meet them in this order. How do you align a pair when you do not know which point corresponds to which? How close does the starting pose have to be before that works at all? How do you stop the errors of many pairs from accumulating around a site? And when the solver finally reports a millimetre, what is that number evidence of? Let's start with the six parameters themselves, and with what a scene has to contain before they are determined.