Urban textural analysis from remote sensor data: Lacunarity measurements based on the differential box counting method

Lacunarity is related to the spatial distribution of gap or hole sizes. For low lacunarity, all gap sizes are the same and geometric objects are deemed homogeneous; conversely, for high lacunarity, gap sizes are variable and objects are therefore heterogeneous. Textures that are homogeneous at small scales can be quite heterogeneous at large scales and vice versa, and hence, lacunarity can be considered a scale-dependent measure of heterogeneity or texture. In this article, we use a lacunarity method based on a differential box counting approach to identify urban land-use and land-cover classes from satellite sensor data. Our methodology focuses on two different gliding box methods to compute lacunarity values and demonstrate a mirror extension approach for a local moving window. The extension approach overcomes, or at least minimizes, the boundary problem. The results from our study suggest that the overlapping box approach is more effective than the skipping box approach, but that there is no significant difference between window sizes. Our work represents a contribution to not only advances in textural and spatial metrics as used in remote-sensing pattern interpretation but also for broadening understanding of the computational geometry of nonlinear shape models of which lacunarity is the reciprocal of fractal theory.