spatstat.linnet (version 3.4-0)

densityVoronoi.lpp: Intensity Estimate of Point Pattern on Linear Network Using Voronoi-Dirichlet Tessellation

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

# S3 method for lpp
densityVoronoi(X, f = 1, ...,
              metric=c("shortestpath", "Euclidean"),
              nrep = 1, verbose = TRUE)

Value

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

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.

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 29 (5) 995--1010.

See Also

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

   if(interactive()) {
     X <- spiders
     nr <- 100
   } else {
     X <- runiflpp(10, simplenet)
     nr <- 3
   }
   plot(densityVoronoi(X))
   plot(densityVoronoi(X, 0.1, nrep=nr))
   plot(densityVoronoi(X, metric="E"))
   plot(dirichlet(as.ppp(X)), add=TRUE, lty=2)