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 model was tested previously on natural images [J. Vernon-Carter et al., Physica A 388, 4305 (2009)]. Here, the computational aspects of multilacunarity are validated using synthetic binary images that consist of random maps, spatial stochastic patterns, patterns with circular or polygonal elements, and a plane fractal. Furthermore, monolacunarity and detrended fluctuation analysis were employed to quantify the mesostructural changes in the intercellular air spaces of frozen-thawed parenchymatous tissue of pome fruit [N. A. Valous et al., J. Appl. Phys. 115, 064901 (2014)]. Here, the aim is to further examine the coherence of the multilacunarity model for quantifying the mesostructural changes in the intercellular air spaces of parenchymatous tissue of pome and stone fruit, acquired with X-ray microcomputed tomography, after storage and ripening, respectively. The multilacunarity morphometric is a multiscale multi-mass fingerprint of spatial pattern composition, assisting the exploration of the effects of metabolic and physiological activity on the pore space of plant parenchyma tissue.