geometry features clarification

[wiesehahn]

Just for my understanding, the pointwise geometry features implemented in lasR are a different thing than metrics via segment_shapes in lidR, correct? While we get a value between 0 and 1 for the likeliyhood of being e.g. part of a linear feature here (lasR), the method in lidR uses thesholds to output if a point is e.g. part of a linear feature yes or no.

I am curious, can it be that all points for the MixedConifer testdata are 0 for linearity, planarity and sphericity? I tested with different number of neighbours and they are always 0. While e.g. Megaplot gives some plausible results.

library(lasR)
f <- system.file("extdata", "MixedConifer.las", package="lasR")
pipeline <- geometry_features(k = 10 , features = "lps") + write_las()
ans <- exec(pipeline, on = f)

library(lidR)
las <- readLAS(ans)
summary(las$linearity)
summary(las$planarity)
summary(las$sphericity)

[Jean-Romain]

I am curious, can it be that all points for the MixedConifer testdata are 0

zeros are definitively a bug. Everything is zero. It is now fixed. It was because the file already contains 1 extrabytes attribute (treeID) and this was incorrectly handled

Just for my understanding, the pointwise geometry features implemented in lasR are a different thing than metrics via segment_shapes in lidR, correct?

Yes and no. They are closely related. The same code is driving lasR::geometry_features, lidR::segment_shapes and lidR::point_eigenvalues. All functions compute the covariance matrix of a point’s neighborhood to get the principal components and the eigen values $\lambda_i$.

• lasR::geometry_features returns the principal components coefficients and the eigen values and computes metrics that can be derived from these values such as the planarity, curvature, linearity according to the well accepted definitions in table 1
• lidR::segment_shape() does the principal component stuff but does not return the coefficients or the eigen values. It uses the eigen values and computes if $\lambda_2 > th_1 \times \lambda_1$ and $th_2 \times \lambda_2 > \lambda_3$ to assert if the neighborhood of the point is planar (or other equations for other shapes). Thus, you can reproduce segment_shape with geometry_feature

library(lasR)
f <- system.file("extdata", "Megaplot.las", package="lasR") 
pipeline <- geometry_features(k = 10 , features = "E") + write_las()
ans <- exec(pipeline, on = f)

library(lidR)
las <- readLAS(ans)
planar = las$lambda2 > th1*las$lambda1 & th2*las$lambda2 > las$lambda3

• lidR::point_eigenvalues is similar to geometry_feature and is supposed to return the same values.

library(lasR)
f <- system.file("extdata", "Megaplot.las", package="lasR")
pipeline <- geometry_features(k = 4 , features = "Elcpsa") + write_las()
ans <- exec(pipeline, on = f)

library(lidR)
las = readLAS(ans)
head(las@data[,-(1:16)])
#>      lambda1   lambda2     lambda3 anisotropy  planarity  sphericity linearity curvature
#>        <num>     <num>       <num>      <num>      <num>       <num>     <num> <num>
#> 1: 1.2794592 0.2380226 0.005268082  0.9958826 0.18191633 0.004117429 0.8139662 0.003459584
#> 2: 0.8219272 0.6144714 0.016984632  0.9793356 0.72693396 0.020664399 0.2524016 0.011686272
#> 3: 0.8219272 0.6144714 0.016984632  0.9793356 0.72693396 0.020664399 0.2524016 0.011686272
#> 4: 6.1178975 1.2201468 0.986347556  0.8387767 0.03821562 0.161223292 0.8005611 0.118488848
#> 5: 1.7888292 1.0966250 0.063370854  0.9645741 0.57761472 0.035425883 0.3869594 0.021490205
#> 6: 1.9836067 0.3613420 0.012276238  0.9938111 0.17597531 0.006188847 0.8178359 0.005207920

las = readLAS(f)
M <- point_eigenvalues(las, k = 4, metrics = TRUE)[,-1]
head(M)
#>    eigen_largest eigen_medium eigen_smallest   curvature linearity  planarity  sphericity anisotropy
#>            <num>        <num>          <num>       <num>     <num>      <num> <num>      <num>
#> 1:     1.2794593    0.2380226    0.005268082 0.003459585 0.8139662 0.18191633 0.004117429  0.9958826
#> 2:     0.8219272    0.6144715    0.016984633 0.011686272 0.2524016 0.72693396 0.020664400  0.9793356
#> 3:     0.8219272    0.6144715    0.016984633 0.011686272 0.2524016 0.72693396 0.020664400  0.9793356
#> 4:     6.1178973    1.2201468    0.986347568 0.118488847 0.8005611 0.03821562 0.161223296  0.8387767
#> 5:     1.7888292    1.0966249    0.063370857 0.021490206 0.3869594 0.57761470 0.035425884  0.9645741
#> 6:     1.9836067    0.3613420    0.012276238 0.005207919 0.8178358 0.17597531 0.006188847  0.9938112

[Jean-Romain]

Side note :

• planarity in geometry_features and point_eigenvalues is $(\lambda_2 − \lambda_3)/\lambda_1$
• The planarity estimation in segment shape is based on a different equation $\lambda_2 > th_1 \times \lambda_1$ and $th_2 \times \lambda_2 > \lambda_3$

Thus, they are based on different definitions. References are given in the manual as usual.