Computes the unnormalised spatial covariance function of a pixel image.
imcov(X, Y=X)
A pixel image (an object of class "im"
) representing the
spatial covariance function of X
,
or the cross-covariance of X
and Y
.
A pixel image (object of class "im"
.
Optional. Another pixel image.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au
and Rolf Turner rolfturner@posteo.net
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)
.
setcov
,
convolve.im
,
owin
,
as.owin
,
erosion
X <- as.im(square(1))
v <- imcov(X)
plot(v)
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