cppicka | R Documentation |
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.
cppicka(xi, obswin = NULL, setcov_boundarythresh = NULL)
xi |
An observation of a RACS of interest as a full binary map (as an |
obswin |
If |
setcov_boundarythresh |
To avoid instabilities caused by dividing by very small quantities, if the set covariance of the observation window
is smaller than |
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.
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.
Kassel Liam Hingee
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.
xi <- heather$coarse
obswindow <- Frame(heather$coarse)
cp <- coverageprob(xi, obswindow)
cpp1 <- cppicka(xi, obswindow)
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.