# rbpto: Simulate Boolean Model with Grains Scaled According to a... In lacunaritycovariance: Gliding Box Lacunarity and Other Metrics for 2D Random Closed Sets

 rbpto R Documentation

## Simulate Boolean Model with Grains Scaled According to a Truncated Pareto Distribution

### Description

Functions for simulation and computing theoretical values of a Boolean model with identically shaped grains with size given by a truncated Pareto distribution.

### Usage

```rbpto(lambda, grain, win, xm, alpha, lengthscales, seed = NULL, xy = NULL)

bpto.coverageprob(lambda, grain, xm, alpha, lengthscales = 1:500)

bpto.germintensity(coverp, grain, xm, alpha, lengthscales = 1:500)

bpto.covar(lambda, grain, xm, alpha, lengthscales = 1:500, xy)
```

### Arguments

 `lambda` Intensity of the germ process (which is a Poisson point process) `grain` A single `owin` object that gives the shape and size of the grain at scale 1 `win` The window to simulate in (an `owin` object) `xm` A parameter governing the shape of the Pareto distribution used - see details `alpha` A parameter governing the shape of the Pareto distribution used see details `lengthscales` A list of scales of the `grain` for which to approximate the Pareto distribution: The grain for a germ is chosen by selecting a scaled version of `grain` where `lengthscales` specifies the possible scales and the Pareto distribution is used to specify the probability of selection of each scale. `seed` Optional input (default in NULL). Is an integer passed to `set.seed`. Used to reproduce patterns exactly. `xy` A raster object that specifies pixel coordinates of the final simulated binary map. It is used the same way as `xy` is `as.mask` in spatstat. If non-null then the computations will be performed using rasters. Otherwise if `grain` and `win` are polygonal then computations may be all polygonal. `coverp` Coverage probability of the Boolean model.

### Details

The parameters `xm` and `alpha` are such that the CDF of the Pareto distribution is P(s <= x) = 1 - (xm / x)^{alpha}. The distribution of grains scales is a step-function approximation to the CDF with steps at `lengthscales`.

### Value

An `owin` object.

### Functions

• `rbpto`: Simulate Boolean model with grain size distributed according to a truncated Pareto distribution.

• `bpto.coverageprob`: The coverage probability of the Boolean model with grain size distributed according to a truncated Pareto distribution.

• `bpto.germintensity`: The germ intensity of the Boolean model with grain size distributed according to a truncated Pareto distribution.

• `bpto.covar`: The covariance of the Boolean model with grain size distributed according to a truncated Pareto distribution. `xy` is required to specify resolution and offset of pixel grid.

### Examples

```lambda <- 0.2
win <- square(r = 10)
grain <- disc(r = 0.2)
xm <- 0.01
alpha <- 2
lengthscales <- seq(1, 5, by = 0.1)
xi <- rbpto(lambda, grain, win, xm, alpha, lengthscales = lengthscales)

# Compute properties of the Boolean model from parameters
bpto.coverageprob(lambda, grain, xm, alpha, lengthscales = lengthscales)
covar <- bpto.covar(lambda, grain, xm, alpha, lengthscales = lengthscales,
xy = as.mask(win, eps = 2))
```

lacunaritycovariance documentation built on March 18, 2022, 5:20 p.m.