Lacunarity analysis of raster datasets and 1D, 2D, and 3D point patterns

Spatial scale plays an important role in many fields. As a scale-dependent measure for spatial heterogeneity, lacunarity describes the distribution of gaps within a set at multiple scales. In Earth science, environmental science, and ecology, lacunarity has been increasingly used for multiscale modeling of spatial patterns. This paper presents the development and implementation of a geographic information system (GIS) software extension for lacunarity analysis of raster datasets and 1D, 2D, and 3D point patterns. Depending on the application requirement, lacunarity analysis can be performed in two modes: global mode or local mode. The extension works for: (1) binary (1-bit) and grey-scale datasets in any raster format supported by ArcGIS and (2) 1D, 2D, and 3D point datasets as shapefiles or geodatabase feature classes. For more effective measurement of lacunarity for different patterns or processes in raster datasets, the extension allows users to define an area of interest (AOI) in four different ways, including using a polygon in an existing feature layer. Additionally, directionality can be taken into account when grey-scale datasets are used for local lacunarity analysis. The methodology and graphical user interface (GUI) are described. The application of the extension is demonstrated using both simulated and real datasets, including Brodatz texture images, a Spaceborne Imaging Radar (SIR-C) image, simulated 1D points on a drainage network, and 3D random and clustered point patterns. The options of lacunarity analysis and the effects of polyline arrangement on lacunarity of 1D points are also discussed. Results from sample data suggest that the lacunarity analysis extension can be used for efficient modeling of spatial patterns at multiple scales.