Spatial Covariance of a Pixel Image

Description

Computes the unnormalised spatial covariance function of a pixel image.

Usage

 imcov(X, Y=X)

Arguments

Details

The (uncentred, unnormalised) spatial covariance function of a pixel image X in the plane is the function C(v) defined for each vector v as the integral

C(u) = integral of X(u) * X(u+v) du

over all spatial locations u, where X(u) denotes the pixel value at location u.

This command computes a discretised approximation to the spatial covariance function, using the Fast Fourier Transform. The return value is another pixel image (object of class "im") whose greyscale values are values of the spatial covariance function.

If the argument Y is present, then imcov(X,Y) computes the set cross-covariance function C(u) defined as

C(u) = integral of X(u) * Y(u+v) du.

Value

A pixel image (an object of class "im") representing the spatial covariance function of X, or the cross-covariance of X and Y.

Author(s)

Adrian Baddeley Adrian.Baddeley@csiro.au http://www.maths.uwa.edu.au/~adrian/ and Rolf Turner r.turner@auckland.ac.nz

See Also

setcov, owin, as.owin, erosion

Examples

  w <- owin(c(0,1),c(0,1))
  X <- as.im(w)
  v <- imcov(X)
  plot(v)