gbl: Gliding box lacunarity estimation using all estimators

In lacunaritycovariance: Gliding Box Lacunarity and Other Metrics for 2D Random Closed Sets

Gliding box lacunarity estimation using all estimators

Description

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.

Usage

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
)

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.
boxwidths	A list of box widths
estimators	A vector of estimator names - see details for possible names. estimators = "all" will select all estimators.
obswin	If xi is an owin object then obswin is an owin object that specifies the observation window.
includenormed	A logical value. If TRUE then GBL estimates normalised by the GBL values at zero will be included in a returned list of fv objects
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 covariance is given a value of NA. If NULL is supplied (default) then setcov_boundarythresh is set to 1E-6.
phat	The fraction of foreground area in the observation window, which is the usual estimator of coverage probability given by coverageprob.
cvchat	The plug-in moment covariance estimate (often from plugincvc).
cpp1	Picka's estimate of coverage probability for subsets of the observation window. See cppicka.

Details

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.

Value

An fv object.

Functions

• 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.

References

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.

Examples

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)

lacunaritycovariance documentation built on Nov. 2, 2023, 6:08 p.m.