idw {spatstat} | R Documentation |
Performs spatial smoothing of numeric values observed at a set of irregular locations using inverse-distance weighting.
idw(X, power=2, at="pixels", ...)
X |
A marked point pattern (object of class |
power |
Numeric. Power of distance used in the weighting. |
at |
String specifying whether to compute the intensity values
at a grid of pixel locations ( |
... |
Arguments passed to |
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
.
If X
has a single column of marks:
If at="pixels"
(the 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
.
If X
has a data frame of marks:
If at="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 class listof
, for which there is a plot method.
If at="points"
, the result is a data frame
with one row for each point of X
,
and one column for each column of marks.
Entries are values of the interpolated function at the points of X
.
Adrian Baddeley Adrian.Baddeley@csiro.au http://www.maths.uwa.edu.au/~adrian/ and Rolf Turner r.turner@auckland.ac.nz
density.ppp
,
ppp.object
,
im.object
.
See smooth.ppp
for kernel smoothing.
To perform interpolation, see also the akima
package.
# data frame of marks: trees marked by diameter and height data(finpines) plot(idw(finpines)) idw(finpines, at="points")[1:5,]