# setcov

##### Set Covariance of a Window

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`

.

##### See Also

##### Examples

```
# NOT RUN {
w <- owin(c(0,1),c(0,1))
v <- setcov(w)
plot(v)
# }
```

*Documentation reproduced from package spatstat, version 1.56-1, License: GPL (>= 2)*