Estimates the gliding box lacunarity (GBL) of a stationary RACS using centred covariance estimates (Hingee et al., 2017). The centred covariance and coverage probability can be provided or estimated from binary map.
gblcc( boxes, cencovar = NULL, p = NULL, xiim = NULL, estimator = "pickaH", integrationMethod = "harmonisesum" ) gblcc.inputcovar(boxes, cencovar, p, integrationMethod = "harmonisesum")
Either a list of side lengths for square boxes or a list of
The coverage probability. Typically estimated by the fraction of the observation window covered by the set of interest.
An observation of a stationary RACS as an
If an observation
The integration method used by
If we denote the estimated centred covariance by k(v) and coverage probability p then the estimate of GBL is
1 + \int gammaB(v) k(v) dv / (p^2 |B|^2),
where B is each of the sets (often called a box) specified by
gammaB is the set covariance of B,
|B| is the area of B,
p is the coverage probability of a stationary RACS.
The set covariance of B is computed empirically using spatstat's
setcov function, which converts B into a binary pixel mask using
as.mask defaults. Computation speed can be increased by setting a small default number of pixels,
npixel, in spatstat's global options (accessed through
spatstat.options), however fewer pixels also decreases the accuracy of the GBL computation.
boxes is a list of numerical values then GBL is estimated for square boxes with side length given by
The returned object is then an
fv object containing estimates of GBL, box mass variance and box mass mean.
boxes is a list of
owin objects then
gblcc returns a dataframe of with columns corresponding to estimates of GBL, box mass variance and box mass mean.
NaN values in the
covariance object are used then
gblc will return
NaN instead of an GBL value.
gblcc.inputcovar: GBL estimates from already estimated centred covariance.
Hingee K, Baddeley A, Caccetta P, Nair G (2019). Computation of lacunarity from covariance of spatial binary maps. Journal of Agricultural, Biological and Environmental Statistics, 24, 264-288. DOI: 10.1007/s13253-019-00351-9.
xi <- heather$coarse cencovar <- cencovariance(xi, obswin = Frame(xi), estimators = c("pickaH"), drop = TRUE) p <- area(xi) / area(Frame(xi)) sidelengths <- seq(0.3, 14, by = 1) # reduce resolution in setcov() for faster (less accurate) computation oldopt <- spatstat.options() spatstat.options("npixel" = 2^5) # compute GBL estimate for square boxes from estimated centred covariance gblccest <- gblcc(sidelengths, cencovar, p) # compute GBL estimate for boxes that are discs discboxes <- lapply(sidelengths / 2, disc) discgbls <- gblcc(discboxes, cencovar, p) # compute GBL estimates from binary map xiim <- as.im(xi, na.replace = 0) gblccest <- gblcc(sidelengths, xiim = xiim, estimator = "pickaH") spatstat.options(oldopt)
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