Lacunarity Indices as a Measure of Texture Images

Lacunarity is a counterpart to the fractal dimension that describes the texture of a fractal. Lacunarity is a measure of how the fractal fills space, if the fractal is dense, the Lacunarity is small, and the Lacunarity increases with coarseness. The Lacunarity of a data set can be calculated by using a gliding box method. In this paper, we consider two dimensional maps and texture images for calculating the number of pixels in each r-sized box in a grid that was placed on a map or image is counted during standard non-overlapping or overlapping box counting. Lacunarity analysis is broadly applicable to many data sets used in the natural sciences. We illustrate its application to geological data.