Spatial smoothing of observations at irregular points

Performs spatial smoothing of numeric values observed at a set of irregular locations.

methods, smooth, spatial
smooth.ppp(X, ..., weights = rep(1, X$n), at="pixels")
markmean(X, ...)
markvar(X, ...)
A marked point pattern (object of class "ppp").
Arguments passed to density.ppp to control the kernel smoothing and the pixel resolution of the result.
Optional weights attached to the observations.
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").

The function smooth.ppp performs spatial smoothing of numeric values observed at a set of irregular locations. The functions markmean and markvar are wrappers for smooth.ppp which compute the spatially-varying mean and variance of the marks of a point pattern.

Smoothing is performed by Gaussian kernel 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 (ignoring edge corrections) $$g(u) = \frac{\sum_i k(u-x_i) v_i}{\sum_i k(u-x_i)}$$ where $k$ is a Gaussian kernel. 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 numerator and denominator are computed by density.ppp. The arguments ... control the smoothing kernel parameters and determine whether edge correction is applied. See density.ppp.

The optional argument weights allows numerical weights to be applied to the data. If a weight $w_i$ is associated with location $x_i$, then the smoothed function is (ignoring edge corrections) $$g(u) = \frac{\sum_i k(u-x_i) v_i w_i}{\sum_i k(u-x_i) w_i}$$


  • By default, the result is a pixel image (object of class "im"). Pixel values are values of the interpolated function.

    If at="points", the result is a numeric vector of length equal to the number of points in x. Entries are values of the interpolated function at the points of x. In either case, the return value has attributes "sigma" and "varcov" which report the smoothing bandwidth that was used.

See Also

density.ppp, ppp.object, im.object. To perform interpolation, see the akima package.

  • smooth.ppp
  • markmean
  • markvar
# Longleaf data - tree locations, marked by tree diameter
   # Local smoothing of tree diameter
   Z <- smooth.ppp(longleaf)
   # Kernel bandwidth sigma=5
   plot(smooth.ppp(longleaf, 5))
   # mark variance
Documentation reproduced from package spatstat, version 1.19-2, License: GPL (>= 2)

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