Scan quality from stems

Between 1 and 3 m a tree stem is the one surface in a forest scan whose shape is known well enough to measure the scanner against. sylva.quality.stem_noise cuts every stem into thin slices, fits a circle to each slice from all scans together, and reads every point's radial residual per scan position:

from sylva import quality

scan = quality.scan_ids_from_origins(shots.origin[shots.shot_of_echo()])
q = quality.stem_noise(cloud, scan_id=scan)      # stems detected if not given
q.summary()
# sigma_total, sigma_corrected, sigma_within, sigma_local, tail_fraction,
# registration_rms, registration_max, worst_scan
q.scans["tx"], q.scans["ty"]                     # horizontal offset of each scan (m)
q.residual                                       # per point, for mapping

figure	what it contains
sigma_total	all points about the shared circle, as the cloud stands: range noise, bark, stem shape and misregistration
sigma_corrected	the same after moving each scan back by its offset
sigma_within	one scan's points about their own median in the slice: range noise, bark and stem shape over the arc it saw
sigma_local	after removing a smooth curve along that arc (constant, first and second harmonics of the angle): range noise and bark only
tx, ty	a scan's horizontal offset from sum (r - t . n)^2 over its points on every stem, n the outward normal, Huber-weighted (Huber 1964); refined by moving the scans back and refitting; relative to the mean of the scans
tail_fraction	stem points more than 4 σ off: mixed pixels at edges, ghosts

A whole-stem circle has a floor: stems are not perfect cylinders. On synthetic trees (exact meshes, a known range noise added along each beam) the whole-circle spread does not drop below about 7 mm however clean the points. sigma_local takes out the shape along each scan's arc and follows the added noise, over a floor of 5–9 mm from the synthetic trunks' bark and HELIOS's own noise:

added range noise	total (tree 015)	local (tree 015)
0 mm	8.8 mm	6.0 mm
3 mm	9.3 mm	6.5 mm
6 mm	10.1 mm	7.5 mm
10 mm	11.6 mm	9.9 mm

Registration comes from the offsets. On one stem a scan's offset is mixed up with the trunk's own shape where that scan sees it: a 20 × 10 mm shift of one of four scans came back as 20 × 12 mm on a straight stem (the other scans within 2.4 mm), but up to 10 mm off on irregular trunks. Over a plot of many stems at different bearings the shapes average out. A misregistered vertical component does not show on vertical stems.

On a real plot, CUP_2022 (Cumberland Plain, TERN; 51 VZ-2000i scans read from the raw RXPs with the curated registrations; every 4th pulse, 1 cm thinned, 0.5–3.5 m above ground):

stems / slices used	2,053 / 8,123
sigma_total / sigma_corrected	9.1 / 8.8 mm
sigma_within / sigma_local	8.5 / 6.7 mm
tail_fraction	2.3 %
per-scan offsets	median 4.0 mm, RMS 4.7 mm, worst 13 mm (one scan)
split-half agreement of the offsets	1.1 mm (median; two disjoint halves of the stems)

The offsets agree to about 1 mm between two independent sets of stems, so the 4–5 mm is the registration itself, not the method's noise. That puts the curated registration at about 5 mm, with one scan position to look at.