Measuring the multiscale and multi-mass heterogeneity of complex spatial patterns in synthetic and real datasets

Spatial patterns may exhibit scale-dependent changes in structure and are often difficult to characterize. Lacunarity measures how data fill space enabling the parsimonious analyses of patterns. The lacunarity index (monolacunarity) averages the behavior of variable size structures in a binary image. The generalized lacunarity concept (multilacunarity) on the basis of generalized distribution moments is an appealing model that can account for differences in the mass content at different scales. The method was proposed in Physica A 388, 4305 (2009). Here, the aim is to provide validation on synthetic images (lacking in the original paper) and to quantify the mesostructural changes in the intercellular air spaces of pome and stone fruit parenchymatous tissue after storage and ripening, respectively. These generalized moments can yield an enhanced measure of the spatial organization of intercellular air spaces which is complementary to the monolacunarity model. Essentially, the multilacunarity morphometric is a multiscale multi-mass measure of spatial heterogeneity that offers insights regarding modifications upon the arrangement of cells and voids. This can further stimulate research interest in analyzing tissue (plant, human) under various metabolic and physiological changes.