# contagpixelgrid: Pixel Adjacency Contagion In lacunaritycovariance: Gliding Box Lacunarity and Other Metrics for 2D Random Closed Sets

 contagpixelgrid R Documentation

### Description

Function for calculating the classic pixel-adjacency contagion landscape metric from a binary map (O'Neill, 1988).

### Usage

```contagpixelgrid(xi, obswin, normalise = FALSE)

```

### Arguments

 `xi` A raster binary map (as an `im` object) or as a foreground set (as an `owin` object). In the latter case the observation window, `obswin`, must be supplied. See `lacunaritycovariance-package` for details. If `xi` is an `owin` object it must be of `mask` type. `obswin` If `xi` is an `owin` object then `obswin` is an `owin` object that specifies the observation window. `normalise` If `TRUE` will divide result by 2 ln(2) and add 1 to make contagion between 0 and 1 for all binary maps.

### Details

The unnormalised contagion landscape metric of categorical map is defined as

∑_i ∑_j Qij ln(Qij),

where Qij is the probability of randomly selected adjacent pixels being in class i and class j respectively, and m is the number of classes.

Here m = 2 as `xi` is a binary map and we have defined 'adjacent' pixels using the 4-neighbourhood regime.

Contagion is calculated from an adjacency matrix created using the function `adjacency`. The adjacency matrix is a 2 by 2 table containing the number of pairs of neighbouring pixels (where order matters) such that:

 Second pixel in `xi` Second pixel not in `xi` First pixel in `xi` - - First pixel not in `xi` - -

### Value

The computed pixel-adjacency contagion value. If `normalise` is `TRUE` then the value will be between 0 and 1. Otherwise the value will be negative.

### Functions

• `contagpixelgrid`: Pixel-adjacency contagion landscape metric of a binary map.

• `adjacency`: Calculates the adjacency matrix used in the pixel contagion

### Warning

Will fail if map is either all foreground or all background.

### References

O'Neill, R.V., Krummel, J.R., Gardner, R.H., Sugihara, G., Jackson, B., DeAngelis, D.L., et al. (1988) Indices of landscape pattern. Landscape Ecology, 1, 153-162.

### Examples

```xi <- heather\$coarse
obswin <- owin(xrange = c(0,7),yrange=c(0,16))