R: Point-based metrics

point_metrics {lidR} | R Documentation

## Point-based metrics

### Description

Computes a series of user-defined descriptive statistics for a LiDAR dataset for each point. This function is very similar to grid_metrics but computes metrics for each point based on its k-nearest neighbours or its sphere neighbourhood.

### Usage

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

### Arguments

`las` | An object of class LAS
`func` | formula. An expression to be applied to each point neighbourhood (see section "Parameter func").
`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. If `filter = NULL` coordinates are references to the original coordinates and do not occupy additional memory. If `filter != NULL` it obviously takes memory.
`filter` | formula of logical predicates. Enables the function to run only on points of interest in an optimized way. See examples.
`...` | unused.

### 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.

### 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 grid_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.
Last but not least, `grid_metrics()` relies on the `data.table` package to compute a user-defined function in each pixel. `point_metrics()` relies on a similar method but with a major difference: it does not rely on `data.table` and thus has not been tested over many years by thousands of people. Please report bugs, if any.

### Parameter `func`

The function to be applied to each cell is a classical function (see examples) that returns a labeled list of metrics. For example, the following function `f` is correctly formed.

    f = function(x) {list(mean = mean(x), max = max(x))}

And could be applied either on the `Z` coordinates or on the intensities. These two statements are valid:

    point_metrics(las, ~f(Z), k = 8)
    point_metrics(las, ~f(Intensity), k = 5)

Everything that works in grid_metrics should also work in `point_metrics` but sometimes might be meaningless. For example, computing the quantile of elevation does not really makes sense here.

### See Also

Other metrics: `cloud_metrics()`, `grid_metrics()`, `plot_metrics()`, `tree_metrics()`, `voxel_metrics()`

### 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_shape(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++.

    # 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.

    # is a memory-optimized equivalent to:
    first = filter_first(las)
    M2 <- point_metrics(first, ~plane_metrics2(X,Y,Z), k = 25)
    all.equal(M1, M2)

    ## End(Not run)

[Package lidR version 3.2.2 Index]