# imcov

##### Spatial Covariance of a Pixel Image

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.

##### 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
$$
C(v) = \int X(u)X(u-v)\, {\rm d}u
$$
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)`

.

##### Value

A pixel image (an object of class `"im"`

) representing the
spatial covariance function of `X`

,
or the cross-covariance of `X`

and `Y`

.

##### See Also

##### Examples

```
# NOT RUN {
X <- as.im(square(1))
v <- imcov(X)
plot(v)
# }
```

*Documentation reproduced from package spatstat, version 1.63-0, License: GPL (>= 2)*