# setcov

0th

Percentile

##### Set Covariance of a Window

Computes the set covariance function of a window.

Keywords
spatial, math
##### 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.

imcov, owin, as.owin, erosion

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

Documentation reproduced from package spatstat, version 1.62-2, License: GPL (>= 2)

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