setcov: Set Covariance of a Window

Description Usage Arguments Details Value Author(s) See Also Examples


Computes the set covariance function of a window.


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



A window (object of class "owin".


Optional. Another window.


Optional arguments passed to as.mask to control the pixel resolution.


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.


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



and \rolf

See Also

imcov, owin, as.owin, erosion


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

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