# sgt.irls.cylinder: Stem segmentation algorithm: Iterated Reweighted Least... In TreeLS: Terrestrial Point Cloud Processing of Forest Data

## Description

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.

## Usage

 1 sgt.irls.cylinder(tol = 0.1, n = 100) 

## Arguments

 tol numeric - tolerance offset between absolute radii estimates and hough transform estimates. n numeric - maximum number of points to sample for fitting stem segments.

## Iterative Reweighted Least Squares (IRLS) Algorithm

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.

## Least Squares Cylinder Fit

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

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

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)

## References

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.

TreeLS documentation built on Aug. 26, 2020, 5:14 p.m.