point_metrics: Point-based metrics

In lidR: Airborne LiDAR Data Manipulation and Visualization for Forestry Applications

Point-based metrics

Description

Computes a series of user-defined descriptive statistics for a LiDAR dataset for each point based on its k-nearest neighbours or its sphere neighbourhood.

Usage

point_metrics(las, func, k, r, xyz = FALSE, filter = NULL, ...)

point_eigenvalues(las, k, r, xyz = FALSE, metrics = FALSE, filter = NULL)

Arguments

las	An object of class LAS
func	formula. An expression to be applied to each point neighbourhood (see also template_metrics).
k, r	integer and numeric respectively for k-nearest neighbours and radius of the neighborhood sphere. If k is given and r is missing, computes with the knn, if r is given and k is missing computes with a sphere neighborhood, if k and r are given computes with the knn and a limit on the search distance.
xyz	logical. Coordinates of each point are returned in addition to each metric. Otherwise an ID refering to each point.
filter	formula of logical predicates. Enables the function to run only on points of interest in an optimized way. See examples.
...	unused.
metrics	logical. Compute metrics or not

Details

When the neighbourhood is knn the user-defined function is fed with the current processed point and its k-1 neighbours. The current point being considered as the 1-neighbour with a distance 0 to the reference point. The points are ordered by distance to the central point. When the neighbourhood is a sphere the processed point is also included in the query but points are coming in a random order. point_eigenmetrics computes the eigenvalues of the covariance matrix and computes associated metrics following Lucas et al, 2019 (see references). It is equivalent to point_metrics(las, .stdshapemetrics) but much faster because it is optimized and parallelized internally.

Performances

It is important to bear in mind that this function is very fast for the feature it provides i.e. mapping a user-defined function at the point level using optimized memory management. However, it is still computationally demanding.

To help users to get an idea of how computationally demanding this function is, let's compare it to pixel_metrics. Assuming we want to apply mean(Z) on a 1 km² tile with 1 point/m² with a resolution of 20 m (400 m² cells), then the function ⁠mean is called roughly 2500 times (once per cell). On the contrary, with ⁠point_metrics⁠, ⁠mean' is called 1000000 times (once per point). So the function is expected to be more than 400 times slower in this specific case (but it does not provide the same feature).

This is why the user-defined function is expected to be well-optimized, otherwise it might drastically slow down this already heavy computation. See examples.

Examples

## Not run: 
LASfile <- system.file("extdata", "Topography.laz", package="lidR")

# Read only 0.5 points/m^2 for the purposes of this example
las = readLAS(LASfile, filter = "-thin_with_grid 2")

# Computes the eigenvalues of the covariance matrix of the neighbouring
# points and applies a test on these values. This function simulates the
# 'shp_plane()' algorithm from 'segment_shape()'
plane_metrics1 = function(x,y,z, th1 = 25, th2 = 6) {
  xyz <- cbind(x,y,z)
  cov_m <- cov(xyz)
  eigen_m <- eigen(cov_m)$value
  is_planar <- eigen_m[2] > (th1*eigen_m[3]) && (th2*eigen_m[2]) > eigen_m[1]
  return(list(planar = is_planar))
}

# Apply a user-defined function
M <- point_metrics(las, ~plane_metrics1(X,Y,Z), k = 25)
#> Computed in 6.3 seconds

# We can verify that it returns the same as 'shp_plane'
las <- segment_shapes(las, shp_plane(k = 25), "planar")
#> Computed in 0.1 seconds

all.equal(M$planar, las$planar)

# At this stage we can be clever and find that the bottleneck is
# the eigenvalue computation. Let's write a C++ version of it with
# Rcpp and RcppArmadillo
Rcpp::sourceCpp(code = "
#include <RcppArmadillo.h>
// [[Rcpp::depends(RcppArmadillo)]]

// [[Rcpp::export]]
SEXP eigen_values(arma::mat A) {
arma::mat coeff;
arma::mat score;
arma::vec latent;
arma::princomp(coeff, score, latent, A);
return(Rcpp::wrap(latent));
}")

plane_metrics2 = function(x,y,z, th1 = 25, th2 = 6) {
  xyz <- cbind(x,y,z)
  eigen_m <- eigen_values(xyz)
  is_planar <- eigen_m[2] > (th1*eigen_m[3]) && (th2*eigen_m[2]) > eigen_m[1]
  return(list(planar = is_planar))
}

M <- point_metrics(las, ~plane_metrics2(X,Y,Z), k = 25)
#> Computed in 0.5 seconds

all.equal(M$planar, las$planar)
# Here we can see that the optimized version is way better but is still 5-times slower
# because of the overhead of calling R functions and switching back and forth from R to C++.

M <- point_eigenvalues(las, k = 25)
is_planar = M$eigen_medium > (25*M$eigen_smallest) & (6*M$eigen_medium) > M$eigen_largest

# Use the filter argument to process only first returns
M1 <- point_metrics(las, ~plane_metrics2(X,Y,Z), k = 25, filter = ~ReturnNumber == 1)
dim(M1) # 13894 instead of 17182 previously.

## End(Not run)

lidR documentation built on Sept. 8, 2023, 5:10 p.m.