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)
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
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:\mjdeqn
D_p = |(p - q) \times a| - rDp = abs((p - q) x a) - r
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.661–670.
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.
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