cppicka {lacunaritycovariance}

Picka's Reduced Window Estimator of Coverage Probability

Description

This function provides estimates of coverage probability from subsets of the observation window, which are a key component of balanced estimators of covariance, centred covariance, pair-correlation and gliding box lacunarity.

Usage

cppicka(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 returned pixel value is NA.

Details

The plug-in moment covariance estimator (plugincvc) uses less of the observation window than the usual coverage probability estimators. Picka (1997, 2000) created new 'balanced' estimators of centred covariance and pair-correlation that accounted for this difference. A key component of Picka's estimators is an estimate of the coverage probability from the subregion of the binary map that is the intersection between W and W shifted by vector v, where W is the observation window (p.~687, Picka, 2000). If we treat X and W as indicator functions representing the foreground and observation window respectively, this coverage probability estimator used by Picka is

\frac{\int X(u) W(u) W(u - v) du} {\int W(u) W(u - v) du}.

cppicka produces these estimates for an array of vectors v using fast Fourier transforms.

Value

An im object. Pixel values correspond to estimates of the coverage probability from the subregion of the observation window, W, that is the intersection of W and W shifted by vector v, where v is the pixel location.

Author(s)

Kassel Liam Hingee

References

Picka, J.D. (1997) Variance-Reducing Modifications for Estimators of Dependence in Random Sets. Ph.D.: Illinois, USA: The University of Chicago.

Picka, J.D. (2000) Variance reducing modifications for estimators of standardized moments of random sets. Advances in Applied Probability, 32, 682-700.

Examples

xi <- heather$coarse
obswindow <- Frame(heather$coarse)
cp <- coverageprob(xi, obswindow)
cpp1 <- cppicka(xi, obswindow)