# filters.covariancefeatures¶

This filter implements various local feature descriptors that are based on the covariance matrix of a point’s neighborhood.

The user can pick a set of feature descriptors by setting the feature_set option. The dimensionality set of feature descriptors introduced below is the default. The user can also provide a comma-separated list of features to explicitly itemize those covariance features they wish to be computed. This can be combined with any suppported presets like “Dimensionality”. Specifying “all” will compute all available features.

Supported features include:

• Anisotropy

• DemantkeVerticality

• Density

• Eigenentropy

• Linearity

• Omnivariance

• Planarity

• Scattering

• EigenvalueSum

• SurfaceVariation

• Verticality

Note

Density requires both OptimalKNN and OptimalRadius which can be computed by running filters.optimalneighborhood prior to filters.covariancefeatures.

## Example #1¶

[
"input.las",
{
"type":"filters.covariancefeatures",
"knn":8,
"feature_set": "Dimensionality"
},
{
"type":"writers.bpf",
"filename":"output.bpf",
"output_dims":"X,Y,Z,Linearity,Planarity,Scattering,Verticality"
}
]


## Example #2¶

[
"input.las",
{
"type":"filters.optimalneighborhood"
},
{
"type":"filters.covariancefeatures",
"knn":8,
"optimized":true,
"feature_set": "Linearity,Omnivariance,Density"
},
{
"type":"writers.las",
"minor_version":4,
"extra_dims":"all",
"forward":"all",
"filename":"output.las"
}
]


## Options¶

knn

The number of k nearest neighbors used for calculating the covariance matrix. [Default: 10]

The number of threads used for computing the feature descriptors. [Default: 1]

feature_set

A comma-separated list of individual features or feature presets (e.g., “Dimensionality”) to be computed. To compute all available features, specify “all”. [Default: “Dimensionality”]

stride

When finding k nearest neighbors, stride determines the sampling rate. A stride of 1 retains each neighbor in order. A stride of two selects every other neighbor and so on. [Default: 1]

min_k

If radius is specified, neighbors will be obtained by radius search rather than k nearest neighbors, subject to meeting the minimum number of neighbors (min_k).

mode

By default, features are computed using the standard deviation along each eigenvector, i.e., using the square root of the computed eigenvalues (mode="SQRT"). mode also accepts “Normalized” which normalizes eigenvalue such that they sum to one, or “Raw” such that the eigenvalues are used directly. [Default: “SQRT”]

optimized

optimized can be set to true to enable computation of features using precomputed optimal neighborhoods (found in the OptimalKNN dimension). Requires filters.optimalneighborhood be run prior to this stage. [Default: false]

where

An expression that limits points passed to a filter. Points that don’t pass the expression skip the stage but are available to subsequent stages in a pipeline. [Default: no filtering]

where_merge

A strategy for merging points skipped by a ‘where’ option when running in standard mode. If true, the skipped points are added to the first point view returned by the skipped filter. If false, skipped points are placed in their own point view. If auto, skipped points are merged into the returned point view provided that only one point view is returned and it has the same point count as it did when the filter was run. [Default: auto]

### Dimensionality feature set¶

The features introduced in [Demantke2011] describe the shape of the neighborhood, indicating whether the local geometry is more linear (1D), planar (2D) or volumetric (3D) while the one introduced in [Guinard2017] adds the idea of a structure being vertical.

The dimensionality filter introduces the following four descriptors that are computed from the covariance matrix of a point’s neighbors (as defined by knn or radius):

• linearity - higher for long thin strips

• planarity - higher for planar surfaces

• scattering - higher for complex 3d neighbourhoods

• verticality - higher for vertical structures, highest for thin vertical strips

It introduces four new dimensions that hold each one of these values: Linearity, Planarity, Scattering and Verticality.