R: Translation Edge Correction

edge.Trans {spatstat.core} | R Documentation

## Translation Edge Correction

### Description

Computes Ohser and Stoyan's translation edge correction weights for a point pattern.

### Usage

    edge.Trans(X, Y = X, W = Window(X),
          exact = FALSE, paired = FALSE,
          ...,
          trim = spatstat.options("maxedgewt"),
          dx=NULL, dy=NULL,
          give.rmax=FALSE, gW=NULL)

    rmax.Trans(W, g=setcov(W))

### Arguments

`X,Y` | Point patterns (objects of class `"ppp"`).
`W` | Window for which the edge correction is required.
`exact` | Logical. If `TRUE`, a slow algorithm will be used to compute the exact value. If `FALSE`, a fast algorithm will be used to compute the approximate value.
`paired` | Logical value indicating whether `X` and `Y` are paired. If `TRUE`, compute the edge correction for corresponding points `X[i], Y[i]` for all `i`. If `FALSE`, compute the edge correction for each possible pair of points `X[i], Y[j]` for all `i` and `j`.
`...` | Ignored.
`trim` | Maximum permitted value of the edge correction weight.
`dx,dy` | Alternative data giving the x and y coordinates of the vector differences between the points. Incompatible with `X` and `Y`. See Details.
`give.rmax` | Logical. If `TRUE`, also compute the value of `rmax.Trans(W)` and return it as an attribute of the result.
`g, gW` | Optional. Set covariance of `W`, if it has already been computed. Not required if `W` is a rectangle.

### Details

The function `edge.Trans` computes Ohser and Stoyan's translation edge correction weight, which is used in estimating the K function and in many other contexts.

The function `rmax.Trans` computes the maximum value of distance r for which the translation edge correction estimate of K(r) is valid.

For a pair of points x and y in a window W, the translation edge correction weight is

e(u, r) = area(W) / area(intersect(W, W + y - x))

where W + y - x is the result of shifting the window W by the vector y - x. The denominator is the area of the overlap between this shifted window and the original window.

The function `edge.Trans` computes this edge correction weight. If `paired=TRUE`, then `X` and `Y` should contain the same number of points. The result is a vector containing the edge correction weights `e(X[i], Y[i])` for each `i`.

If `paired=FALSE`, then the result is a matrix whose `i,j` entry gives the edge correction weight `e(X[i], Y[j])`.

Computation is exact if the window is a rectangle. Otherwise,

- if `exact=TRUE`, the edge correction weights are computed exactly using `overlap.owin`, which can be quite slow.

- if `exact=FALSE` (the default), the weights are computed rapidly by evaluating the set covariance function `setcov` using the Fast Fourier Transform.

If any value of the edge correction weight exceeds `trim`, it is set to `trim`.

The arguments `dx` and `dy` can be provided as an alternative to `X` and `Y`. If `paired=TRUE` then `dx,dy` should be vectors of equal length such that the vector difference of the ith pair is `c(dx[i], dy[i])`. If `paired=FALSE` then `dx,dy` should be matrices of the same dimensions, such that the vector difference between `X[i]` and `Y[j]` is `c(dx[i,j], dy[i,j])`. The argument `W` is needed.

The value of `rmax.Trans` is the shortest distance from the origin (0,0) to the boundary of the support of the set covariance function of `W`. It is computed by pixel approximation using `setcov`, unless `W` is a rectangle, when `rmax.Trans(W)` is the length of the shortest side of the rectangle.

### Value

Numeric vector or matrix.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au and Rolf Turner r.turner@auckland.ac.nz.

### References

Ohser, J. (1983) On estimators for the reduced second moment measure of point processes. Mathematische Operationsforschung und Statistik, series Statistics, 14, 63 – 71.

### See Also

`rmax.Trans`, `edge.Ripley`, `setcov`, `Kest`

### Examples

      v <- edge.Trans(cells)
      rmax.Trans(Window(cells))

[Package spatstat.core version 2.3-1 Index]