# idw

0th

Percentile

##### Inverse-distance weighted smoothing of observations at irregular points

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

Keywords
methods, smooth, spatial
##### 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 $v_1,\ldots,v_n$ at locations $x_1,\ldots,x_n$ respectively, then the smoothed value at a location $u$ is $$g(u) = \frac{\sum_i w_i v_i}{\sum_i w_i}$$ where the weights are the inverse $p$-th powers of distance, $$w_i = \frac 1 {d(u,x_i)^p}$$ where $d(u,x_i) = ||u - x_i||$ 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:
• Ifat="pixels"(the default), the result is a pixel image (object of class"im"). Pixel values are values of the interpolated function.
• Ifat="points", the result is a numeric vector of length equal to the number of points inX. Entries are values of the interpolated function at the points ofX.
If X has a data frame of marks:
• Ifat="pixels"(the default), the result is a named list of pixel images (object of class"im"). There is one image for each column of marks. This list also belongs to the classlistof, for which there is a plot method.
• Ifat="points", the result is a data frame with one row for each point ofX, and one column for each column of marks. Entries are values of the interpolated function at the points ofX.

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

See smooth.ppp for kernel smoothing. To perform interpolation, see also the akima package.

• idw
##### Examples
# data frame of marks: trees marked by diameter and height
data(finpines)
plot(idw(finpines))
idw(finpines, at="points")[1:5,]
Documentation reproduced from package spatstat, version 1.24-1, License: GPL (>= 2)

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