gbl | R Documentation |
Estimates gliding box lacunarity (GBL) for square boxes using all estimators described in (Hingee et al., 2017).
It calls the functions gblc
, gblg
, gblcc
and gblemp
.
gbl( xi, boxwidths, estimators = c("GBLcc.pickaH"), obswin = NULL, includenormed = FALSE, setcov_boundarythresh = 1e-06 ) gbl.cvchat( boxwidths, estimators = c("GBLg.mattfeldt", "GBLg.pickaint", "GBLg.pickaH", "GBLcc.mattfeldt", "GBLcc.pickaint", "GBLc"), phat = NULL, cvchat = NULL, cpp1 = NULL )
xi |
An observation of a RACS of interest as a full binary map (as an |
boxwidths |
A list of box widths |
estimators |
A vector of estimator names - see details for possible names. |
obswin |
If |
includenormed |
A logical value. If TRUE then GBL estimates normalised by the GBL values at zero will be included in a returned list of |
setcov_boundarythresh |
To avoid instabilities caused by dividing by very small quantities, if the set covariance of the observation window
is smaller than |
phat |
The fraction of foreground area in the observation window, which is the usual estimator of coverage probability given by |
cvchat |
The plug-in moment covariance estimate (often from |
cpp1 |
Picka's estimate of coverage probability for subsets of the observation window. See |
As empirical GBL is one of the GBL estimators available through this function, non-square boxes are not allowed.
To estimate GBL for non-square boxes use gblcc
or gblg
directly.
If xi
is an owin
object then obswin
and xi
are converted
into an im
object using as.im
The estimators available are
"GBLc"
The unmodified (unbalanced) covariance estimator provided by gblc
"GBLemp"
Empirical gliding box lacunarity (Allain and Cloitre, 1991). Calls gblemp
"GBLg.mattfeldt"
See help for gblg
and paircorr
"GBLg.pickaint"
See help for gblg
and paircorr
"GBLg.pickaH"
See help for gblg
and paircorr
"GBLcc.mattfeldt"
See help for gblcc
"GBLcc.pickaint"
See help for gblcc
"GBLcc.pickaH"
See help for gblcc
The default, GBLcc.pickaH, is a method based on centred covariance. Centred covariance approaches zero for large vectors, and are thus easier to integrate with the set covariance of the boxes.
The set covariance of the boxes 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.
An fv
object.
gbl
: computes GBL estimates from a binary map.
gbl.cvchat
: computes covariance-based estimator of GBL from the plug-in moment estimate of covariance,
Picka's reduced window coverage probability estimates (see cppicka
) and the usual coverage probability estimate, phat
.
Allain, C. and Cloitre, M. (1991) Characterizing the lacunarity of random and deterministic fractal sets. Physical Review A, 44, 3552-3558.
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 <- as.im(heather$coarse, value = TRUE, na.replace = FALSE) boxwidths <- seq(1, 10, by = 0.5) # reduce resolution in setcov() for faster (less accurate) computation oldopt <- spatstat.options() spatstat.options("npixel" = 2^5) gblests <- gbl(xi, boxwidths, estimators = "GBLcc.pickaH") spatstat.options(oldopt)
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