# 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

```
X <- as.im(square(1))
v <- imcov(X)
plot(v)
```

*Documentation reproduced from package spatstat, version 1.29-0, License: GPL (>= 2)*