R: Set Covariance of a Window

setcov {spatstat.geom} | R Documentation

## Set Covariance of a Window

### Description

Computes the set covariance function of a window.

### Usage

     setcov(W, V=W, ...)

### Arguments

`W` | A window (object of class `"owin"`.
`V` | Optional. Another window.
`...` | Optional arguments passed to `as.mask` to control the pixel resolution.

### Details

The set covariance function of a region W in the plane is the function C(v) defined for each vector v as the area of the intersection between W and W+v, where W+v is the set obtained by shifting (translating) W by v.

We may interpret C(v) as the area of the set of all points x in W such that x+v also lies in W.

This command computes a discretised approximation to the set covariance function of any plane region W represented as a window object (of class `"owin"`, see `owin.object`). The return value is a pixel image (object of class `"im"`) whose greyscale values are values of the set covariance function.

The set covariance is computed using the Fast Fourier Transform, unless `W` is a rectangle, when an exact formula is used.

If the argument `V` is present, then `setcov(W,V)` computes the set cross-covariance function C(x) defined for each vector x as the area of the intersection between W and V+x.

### Value

A pixel image (an object of class `"im"`) representing the set covariance function of `W`, or the cross-covariance of `W` and `V`.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

and Rolf Turner r.turner@auckland.ac.nz

### See Also

`imcov`, `owin`, `as.owin`, `erosion`

### Examples

      w <- owin(c(0,1),c(0,1))
      v <- setcov(w)
      plot(v)

[Package spatstat.geom version 2.3-2 Index]