lacunaritycovariance-package | R Documentation |

Functions for estimating the gliding box lacunarity (GBL), covariance, and pair-correlation of a random closed set (RACS) in 2D from a binary coverage map (e.g. presence-absence land cover maps). Contains a number of newly-developed covariance-based estimators of GBL (Hingee et al., 2019) <doi:10.1007/s13253-019-00351-9> and balanced estimators, proposed by Picka (2000) <http://www.jstor.org/stable/1428408>, for covariance, centred covariance, and pair-correlation. Also contains methods for estimating contagion-like properties of RACS and simulating 2D Boolean models. Binary coverage maps are usually represented as raster images with pixel values of TRUE, FALSE or NA, with NA representing unobserved pixels. A demo for extracting such a binary map from a geospatial data format is provided. Binary maps may also be represented using polygonal sets as the foreground, however for most computations such maps are converted into raster images. The package is based on research conducted during the author's PhD studies.

Random closed sets (RACS) (Chiu et al., 2013; Molchanov, 2005) are a well known tool for modelling binary coverage maps. The package author recently developed new, improved estimators of gliding box lacunarity (GBL) for RACS (Hingee et al., 2017) and described contagion-like properties for RACS (Hingee, 2016). A forthcoming PhD thesis (Hingee, 2019) will provide additional background for GBL, and for RACS in landscape metrics (which includes contagion).

This package expects RACS observations to be in the form of binary maps either in raster format, or as a set representing foreground with a second set giving the observation window.
If in raster format, the binary map is expected to be a spatstat `im`

object with pixel values that are only 1 and 0, or are logically valued (i.e. TRUE or FALSE). In both cases the observation window is taken to be the set of pixels with values that are not `NA`

(i.e. `NA`

values are considered outside the observation window).
The foreground of the binary map, corresponding to locations within the realisation of the RACS, is taken to be pixels that have value 1 or TRUE.
If the binary map is in set format then a spatstat `owin`

object is used to represent foreground and a second `owin`

object is used to represent the observation window.

We will usually denote a RACS as *Ξ* ('Xi') and a realisation of *Ξ* observed as a binary map as *xi*. We will usually denote the observation window as `obswin`

.

A demonstration converting remotely sensed data into a binary map in `im`

format can be accessed by typing `demo("import_remote_sense_data", package = "lacunaritycovariance")`

.
A short example of estimating RACS properties can be found in the vignette `estimate_RACS_properties`

, which can be accessed with `vignette("estimate_RACS_properties")`

.

The key functions within this package for estimating properties of RACS are:

`coverageprob`

estimates the coverage probability of a stationary RACS`racscovariance`

estimates the covariance of a stationary RACS`gbl`

estimates the GBL of a stationary RACS`cencovariance`

estimates the centred covariance of a stationary RACS`paircorr`

estimates the pair-correlation of a stationary RACS`secondorderprops`

estimates GBL, covariance and other second order properties of stationary RACS`contagdiscstate`

estimates the disc-state contagion of a stationary RACS

Key functions for simulating RACS are:

`rbdd`

simulates a Boolean model with grains that are discs with fixed radius (deterministic discs).`rbdr`

simulates a Boolean model with grains that are rectangles of fixed size and orientation.`rbpto`

simulates a Boolean model with grains that of fixed shape and random scale distributed according to a truncated Pareto distribution.`placegrainsfromlib`

randomly places grains on a set of points (used to simulate Boolean models and other germ-grain models).

Kassel Liam Hingee

Maintainer: Kassel Liam Hingee <kassel.hingee@gmail.com>

Chiu, S.N., Stoyan, D., Kendall, W.S. and Mecke, J. (2013) *Stochastic Geometry and Its Applications*, 3rd ed. Chichester, United Kingdom: John Wiley & Sons.

Hingee, K.L. (2016) Statistics for patch observations. *International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences* pp. 235-242. Prague: ISPRS.

Hingee, K.L. (2019) *Spatial Statistics of Random Closed Sets for Earth Observations*. PhD: Perth, Western Australia: University of Western Australia. Submitted.

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.

Molchanov, I.S. (2005) *Theory of Random Sets*. USA: Springer.

# Estimates from the heather data in spatstat xi_owin <- heather$coarse xi_owin_obswin <- Frame(heather$coarse) # Convert binary map to an im object (optional) xi <- as.im(xi_owin, value = TRUE, na.replace = FALSE) # Estimate coverage probability, covariance, GBL, and disc-state contagion cphat <- coverageprob(xi) cvchat <- racscovariance(xi, estimator = "pickaH") gblhat <- gbl(xi, seq(0.1, 5, by = 1), estimators = "GBLcc.pickaH") contagds <- contagdiscstate(Hest(xi), Hest(!xi), p = cphat) # Simulate a Boolean model with grains that are discs of fixed radius: xi_sim <- rbdd(10, 0.1, owin())

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