Computes the unnormalised spatial covariance function of a pixel image.
Usage
imcov(X, Y=X)
Arguments
X
A pixel image (object of class "im".
Y
Optional. Another pixel image.
Value
A pixel image (an object of class "im") representing the
spatial covariance function of X,
or the cross-covariance of X and Y.
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
$$C(u) = \int X(u)X(u+v)\, {\rm d}u$$
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
$$C(u) = \int X(u)Y(u+v)\, {\rm d}u.$$