gblemp: Empirical Gliding Box Lacunarity

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

Empirical Gliding Box Lacunarity

Description

Calculates empirical gliding box lacunarity of a binary map, which was proposed by Allain and Cloitre (1991).

Usage

gblemp(boxwidths, xiim, obswin = Frame(xiim))

gbltrad(boxwidths, xiim, obswin = Frame(xiim))

Arguments

boxwidths	A list of suggested box widths in the same units as xiim. Note the actual box widths used by gblemp will be the closest multiple of an odd number of pixel widths.
xiim	An image of pixels valued either 0, 1 or NA. NA valued pixels are assumed to be outside the observation window.
obswin	Optional observation window. The observation window used for the estimator will be the intersection of obswin and the pixels that are not NA in xiim.

Details

Calculates empirical gliding box lacunarity (Allain and Cloitre, 1991) for a given range of square box sizes,

1 + Var(area(B . xi)) / E[area(B . xi)]^2,

where B is a box that has a random location in the observation window and area(B . xi) is the (random) area of the foreground in B. This is an estimate of the gliding box lacunarity of a RACS (Hingee et al., 2017).

The algorithm uses the pixel locations in xiim as an array of box centre locations to compute the mean and variance of the area in a random box of a given size. Locations where the box is not completely within the observation window are ignored.

Value

An fv object containing empirical GBL, variance of the area in the box and mean of the area in the box. The box widths (labelled s) are always odd multiples of the pixel width.

Functions

• gbltrad(): An alias of gblemp used in past versions of this package. This alias may be removed in future versions.

WARNING

The box side lengths are rounded such that they are an odd number of pixels across. gblemp uses the roll_sum function in RcppRoll to operate, so RcppRoll must be installed to run gblemp.

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

xiim <- as.im(heather$coarse, na.replace = 0)
boxwidths <- seq(0.2, 14, by = 0.2) #in units of xiim
gblest <- gblemp(boxwidths, xiim)

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