# plugincvc: Plug-in moment covariance estimator In lacunaritycovariance: Gliding Box Lacunarity and Other Metrics for 2D Random Closed Sets

 plugincvc R Documentation

## Plug-in moment covariance estimator

### Description

This function computes the plug-in moment covariance estimate of a stationary RACS from a binary map. For a stationary RACS, Ξ, the covariance for a vector v is the probability of two points separated by a vector v are covered by Ξ

C(v) = P({x, x+ v} in Xi).

### Usage

```plugincvc(xi, obswin = NULL, setcov_boundarythresh = NULL)
```

### Arguments

 `xi` An observation of a RACS of interest as a full binary map (as an `im` object) or as the foreground set (as an `owin` object). In the latter case the observation window, `obswin`, must be supplied. `obswin` If `xi` is an `owin` object then `obswin` is an `owin` object that specifies the observation window. `setcov_boundarythresh` To avoid instabilities caused by dividing by very small quantities, if the set covariance of the observation window is smaller than `setcov_boundarythresh`, then the covariance is given a value of NA.

### Details

The plug-in moment covariance estimator is (Serra, 1982)

C(v) = gammaWX(v) / gammaW(v)

where gammaW(v) is the set covariance of the observation window W and gammaWX(v) is the set covariance of the foreground within W. `plugincvc` uses Fourier transforms to calculate the set covariance (using the `setcov` of the foreground and observation window. Vectors with small gammaW(v) are eliminated using `setcov_boundarythresh` as division by small values is numerically unstable.

### Value

A SpatStat `im` object containing the estimated covariance.

### Author(s)

Kassel Liam Hingee

### References

Serra, J.P. (1982) Image Analysis and Mathematical Morphology. London; New York: Academic Press.

### Examples

```xi <- as.im(heather\$coarse, na.replace = 0)
covar <- plugincvc(xi)
```

lacunaritycovariance documentation built on March 18, 2022, 5:20 p.m.