R: Spatial Covariance of a Pixel Image

imcov {spatstat.geom} | R Documentation

## Spatial Covariance of a Pixel Image

### Description

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) = integral of X(u) * X(u-v) du

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) = integral of X(u) * Y(u-v) du.

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`.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

and Rolf Turner r.turner@auckland.ac.nz

### See Also

`setcov`, `convolve.im`, `owin`, `as.owin`, `erosion`

### Examples

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

[Package spatstat.geom version 2.3-2 Index]