In STBrinkmann/spatLac: R package for computing Lacunarity for Spatial Raster

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spatLac: Spatial Lacunarity

The spatLac R package helps researchers compute Lacunarity for binary and continuous Spatial Raster objects. spatLac uses fast C++ code, allowing for low memory usage and multithreading.

• Installation

• Lacunarity

• Examples

• Citation

Installation

You can install the development version from GitHub with:

# install.packages("devtools")
devtools::install_github("STBrinkmann/spatLac")

Lacunarity

"Lacunarity" literally refers to the gappiness or heterogeneity of a fractal or non-fractal image. As a scale dependent measure of heterogeneity, Dong (2000) introduced lacunarity for spatial heterogeneity measurements in GIS. Based on the research of Plotnick et al. (1993) he implemented a Lacunarity algorithm for raster images. Hoechstetter et al. (2011) further improved Lacunarity measurements for continuous images. In a recent paper Labib et al. (2020) applied Lacunarity on binary (Land Use) and continuous (NDVI and LAI) raster images, to derive scale sensitive weights used in a buffer analysis to build multiple-exposure metrics.

To compute Lacunarity we use a sliding box algorithm, the box can be either square or round as demonstrated in the animation below.

Lacunarity calculation algorithms

Lacunarity for binary raster images is calculated using Eq. 1-5, for continuous images only function 1 and 6 are being used.

Lacunarity $\Lambda(r)$ ("lambda") for box diameter $r$ of an image with width $W$ and length $L$ is beeing calculated as follows:

First the total number of boxes $N[r]$ can be described as (Eq. 1): $$ \begin{align} N[r] = (W - r + 1)(L - r + 1) && \text{(1)} \end{align} $$ Next, the box mass $S$ for each box of size $r$ is beeing calculated by taking the box sum, or the range of all box-values, for binary or continuous raster, respectively.

For binary images, the number of boxes of size $r$ containing box mass $S$ are counted as $n[S,r]$, and converted into a probability distribution $Q(S,r)$ by dividing by $N[r]$ (Eq. 2): $$ \begin{align} Q(S,r) = \cfrac{n[S,r]}{N[r]} && \text{(2)} \end{align} $$ Next, the first and second moments of this probability distribution are estimated using Eq. (3), (4) respectively: $$ \begin{align} Z(1) = \sum{S(r)\times Q(S,r)} && \text{ (3)} \end{align} $$ $$ \begin{align} Z(2) = \sum{S^2(r)\times Q(S,r)} && \text{(4)} \end{align} $$ Lacunarity $\Lambda(r)$ can now be computed as (Eq. 5): $$ \begin{align} \Lambda(r) = \cfrac{Z(2)}{Z^2(1)} && \text{(5)} \end{align} $$

If the raster is continuous the first and second moment can be expressed as the mean $E[S(r)]$ and variance $Var[S(r)]$ of the box mass values, respectively. Lacunarity can now be derived as (Eg. 6): $$ \begin{align} \Lambda(r) = 1 + \cfrac{Var[S(r)]}{E^2[S(r)]} && \text{(6)} \end{align} $$

$r$ should not be greater than half of the shorter dimension of the input raster. If $r$ is not provided by the user, it will be automatically generated as the function $r_p = 2^p + 1$, where $p$ is a whole number commencing at 1 until $r_p$ reaches half of the shorter dimension.

Examples

For demonstration purposes I replicated the examples provided by Hoechstetter et al. (2011).

library(spatLac)
library(terra)

sample_rast <- rast("data_raw/hoechstetter.tif")

plot(sample_rast, axes=FALSE, nr = 1)

sample_lac <- lacunarity(x = sample_rast, r_vec = 3:50, plot = TRUE)

To compute Lacunarity for a larger study, it can be computed for all raster objects (ending with .tif) in a folder. Furthermore, individual and summary plots can be automatically created, too.

lacunarity(x = "folder_path_with_TIF_files",
           save_plot = "folder_path_to_save_plots")

About

Citation

Run this command to get info on how to cite this package.

citation("spatLac")

Package contributors

Brinkmann, Sebastian (Creator and author) e-mail: sebastian.brinkmann\@fau.de

Dr. S.M. Labib (Contributor) e-mail: sml80\@medschl.cam.ac.uk

Bibliography

Dong P. (2000): Lacunarity for Spatial Heterogeneity Measurement in GIS. Geographic Information Sciences 6:1, pages 20-26. DOI: 10.1080/10824000009480530.

Hoechstetter S., Walz U. and Thinh N.X. (2011): Adapting lacunarity techniques for gradient-based analyses of landscape surfaces. Ecological Complexity 8:3, pages 229-238. DOI: 10.1016/j.ecocom.2011.01.001.

Labib S.M., Lindley S. and Huck J.J. (2020): Scale effects in remotely sensed greenspace metrics and how to mitigate them for environmental health exposure assessment. Computers, Environment and Urban Systems 82. DOI: 10.1016/j.compenvurbsys.2020.101501.

Plotnick R.E., Gardner R.H. and O'Neill R.V. (1993): Lacunarity indices as measures of landscape texture. Landscape Ecology 8, pages 201–211. DOI: 10.1007/BF00125351

STBrinkmann/spatLac documentation built on Feb. 13, 2022, 8:21 a.m.