idw {spatstat}R Documentation

Inverse-distance weighted smoothing of observations at irregular points

Description

Performs spatial smoothing of numeric values observed at a set of irregular locations using inverse-distance weighting.

Usage

idw(X, power=2, at="pixels", ...)

Arguments

X

A marked point pattern (object of class "ppp").

power

Numeric. Power of distance used in the weighting.

at

String specifying whether to compute the intensity values at a grid of pixel locations (at="pixels") or only at the points of X (at="points").

...

Arguments passed to as.mask to control the pixel resolution of the result.

Details

This function performs spatial smoothing of numeric values observed at a set of irregular locations.

Smoothing is performed by inverse distance weighting. If the observed values are v[1],...,v[n] at locations x[1],...,x[n] respectively, then the smoothed value at a location u is

g(u) = (sum of w[i] * v[i])/(sum of w[i])

where the weights are the inverse p-th powers of distance,

w[i] = 1/d(u,x[i])^p

where d(u,x[i]) is the Euclidean distance from u to x[i].

The argument X must be a marked point pattern (object of class "ppp", see ppp.object). The points of the pattern are taken to be the observation locations x[i], and the marks of the pattern are taken to be the numeric values v[i] observed at these locations.

The marks are allowed to be a data frame. Then the smoothing procedure is applied to each column of marks.

If at="pixels" (the default), the smoothed mark value is calculated at a grid of pixels, and the result is a pixel image. The arguments ... control the pixel resolution. See as.mask.

If at="points", the smoothed mark values are calculated at the data points only, using a leave-one-out rule (the mark value at a data point is excluded when calculating the smoothed value for that point).

An alternative to inverse-distance weighting is kernel smoothing, which is performed by smooth.ppp.

Value

If X has a single column of marks:

If X has a data frame of marks:

Author(s)

Adrian Baddeley Adrian.Baddeley@csiro.au http://www.maths.uwa.edu.au/~adrian/ and Rolf Turner r.turner@auckland.ac.nz

See Also

density.ppp, ppp.object, im.object.

See smooth.ppp for kernel smoothing.

To perform interpolation, see also the akima package.

Examples

   # data frame of marks: trees marked by diameter and height
   data(finpines)
   plot(idw(finpines))
   idw(finpines, at="points")[1:5,]

[Package spatstat version 1.25-3 Index]