This function is meant to be used inside stemSegmentation. It applies a reweighted least squares cylinder fit algorithm using M-estimators and Nelder-Mead optimization in order to remove outlier effects.
sgt.irls.cylinder(tol = 0.1, n = 100)numeric - tolerance offset between absolute radii estimates and hough transform estimates.
numeric - maximum number of points to sample for fitting stem segments.
irls circle or cylinder estimation methods
perform automatic outlier assigning through iterative reweighting
with M-estimators, followed by a Nelder-Mead optimization of squared distance sums
to determine the best circle/cylinder parameters for a given point
cloud. The reweighting strategy used in TreeLS is based on
Liang et al. (2012). The Nelder-Mead algorithm implemented in Rcpp was provided by
kthohr/optim.
The cylinder fit methods implemented in TreeLS estimate a 3D cylinder`s axis direction and radius. The algorithm used internally to optimize the cylinder parameters is the Nelder-Mead simplex, which takes as objective function the model describing the distance from any point to a modelled cylinder`s surface on a regular 3D cylinder point cloud:
D_p = |(p - q) a| - rDp = abs((p - q) x a) - r
where:
Dp: distance from a point to the model cylinder`s surface
p: a point on the cylinder`s surface
q: a point on the cylinder`s axis
a: unit vector of cylinder`s direction
r: cylinder`s radius
The Nelder-Mead algorithm minimizes the sum of squared Dp from a set of points belonging to a stem segment - in the context of TreeLS.
The parameters returned by the cylinder fit methods are:
rho,theta,phi,alpha: 3D cylinder estimated axis parameters (Liang et al. 2012)
Radius: 3D cylinder radius, in point cloud units
Error: model cylinder error from the least squares fit
AvgHeight: average height of the stem segment's points
N: number of points belonging to the stem segment
PX,PY,PZ: absolute center positions of the stem segment points, in point cloud units (used for plotting)
Liang, X. et al., 2012. Automatic stem mapping using single-scan terrestrial laser scanning. IEEE Transactions on Geoscience and Remote Sensing, 50(2), pp.661<U+2013>670.
Conto, T. et al., 2017. Performance of stem denoising and stem modelling algorithms on single tree point clouds from terrestrial laser scanning. Computers and Electronics in Agriculture, v. 143, p. 165-176.