Spatial Covariance of a Pixel Image
Computes the unnormalised spatial covariance function of a pixel image.
imcov(X, Y=X)
X |
A pixel image (object of class |
Y |
Optional. Another pixel image. |
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
C(v) = integral of X(u) * X(u-v) du
where the integral is over all spatial locations u, and 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(v) = integral of X(u) * Y(u-v) du.
Note that imcov(X,Y) is equivalent to
convolve.im(X,Y,reflectY=TRUE).
A pixel image (an object of class "im") representing the
spatial covariance function of X,
or the cross-covariance of X and Y.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au
and Rolf Turner r.turner@auckland.ac.nz
X <- as.im(square(1)) v <- imcov(X) plot(v)
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