# densityVoronoi.lpp: Intensity Estimate of Point Pattern on Linear Network Using... In spatstat.linnet: Linear Networks Functionality of the 'spatstat' Family

## Description

Computes an adaptive estimate of the intensity function of a point pattern on a linear network, using the Dirichlet-Voronoi tessellation on the network.

## Usage

 ```1 2``` ```## S3 method for class 'lpp' densityVoronoi(X, f = 1, ..., nrep = 1, verbose = TRUE) ```

## Arguments

 `X` Point pattern on a linear network (object of class `"lpp"`). `f` Fraction (between 0 and 1 inclusive) of the data points that will be used to build a tessellation for the intensity estimate. `...` Arguments passed to `linim` determining the pixel resolution of the result. `nrep` Number of independent repetitions of the randomised procedure. `verbose` Logical value indicating whether to print progress reports.

## Details

This function is an alternative to `density.lpp`. It computes an estimate of the intensity function of a point pattern dataset on a linear network. The result is a pixel image on the network, giving the estimated intensity.

This function is a method for the generic `densityVoronoi` for the class `"lpp"` of point patterns on a linear network.

If `f=1` (the default), the Voronoi estimate (Barr and Schoenberg, 2010) is computed: the point pattern `X` is used to construct a Voronoi/Dirichlet tessellation on the network (see `lineardirichlet`); the lengths of the Dirichlet tiles are computed; the estimated intensity in each tile is the reciprocal of the tile length. The result is a pixel image of intensity estimates which are constant on each tile of the tessellation.

If `f=0`, the intensity estimate at every location is equal to the average intensity (number of points divided by network length). The result is a pixel image of intensity estimates which are constant.

If `f` is strictly between 0 and 1, the smoothed Voronoi estimate (Moradi et al, 2019) is computed. The dataset `X` is randomly thinned by deleting or retaining each point independently, with probability `f` of retaining a point. The thinned pattern is used to construct a Dirichlet tessellation and form the Voronoi estimate, which is then adjusted by a factor `1/f`. This procedure is repeated `nrep` times and the results are averaged to obtain the smoothed Voronoi estimate.

The value `f` can be chosen automatically by bandwidth selection using `bw.voronoi`.

## Value

Pixel image on a linear network (object of class `"linim"`).

\spatstatAuthors

## References

Moradi, M., Cronie, 0., Rubak, E., Lachieze-Rey, R., Mateu, J. and Baddeley, A. (2019) Resample-smoothing of Voronoi intensity estimators. Statistics and Computing, in press.

`densityVoronoi` is the generic, with a method for class `"ppp"`.

`lineardirichlet` computes the Dirichlet-Voronoi tessellation on a network.

`bw.voronoi` performs bandwidth selection of the fraction `f`.

See also `density.lpp`.

## Examples

 ```1 2``` ``` nr <- if(interactive()) 100 else 3 plot(densityVoronoi(spiders, 0.1, nrep=nr)) ```

spatstat.linnet documentation built on July 17, 2021, 9:07 a.m.