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
$$
C(v) = \int X(u)X(u-v)\, {\rm d}u
$$
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
$$
C(v) = \int X(u)Y(u-v)\, {\rm d}u.
$$
Note that imcov(X,Y) is equivalent to
convolve.im(X,Y,reflectY=TRUE).