spatstat (version 1.52-1)

# setcov: 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.

## Value

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

## 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 \(V+x\).

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

## Examples

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

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