gbl: Gliding box lacunarity estimation using all estimators In lacunaritycovariance: Gliding Box Lacunarity and Other Metrics for 2D Random Closed Sets

 gbl R Documentation

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 March 18, 2022, 5:20 p.m.