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

 gblemp R Documentation

## 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))

```

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