gblcc | R Documentation |
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")
boxes |
Either a list of side lengths for square boxes or a list of |
cencovar |
A |
p |
The coverage probability. Typically estimated by the fraction of the observation window covered by the set of interest. |
xiim |
An observation of a stationary RACS as an |
estimator |
If an observation |
integrationMethod |
The integration method used by |
If we denote the estimated centred covariance by
\hat{\kappa}(v)
and coverage probability \hat{p}
then
the estimate of GBL is
1 + \frac{1}{\hat{p}^2 |B|^2}\int \gamma_B(v)\hat{\kappa}(v)dv,
where B
is each of the sets (often called a box) specified by boxes
,
\gamma_B
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.
If boxes
is a list of numerical values then GBL is estimated for square boxes with side length given by boxes
.
The returned object is then an fv
object containing estimates of GBL, box mass variance and box mass mean.
If 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.
Note if NA
or NaN
values in the covariance
object are used then gblc
will return NA
or 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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