Topological–Multifractal Characterization of Adaxial–Abaxial Leaf Surface Asymmetry in Theobroma grandiflorum via Minkowski Functionals and Confocal Profilometry

This study presents a unified topological and multifractal framework for the characterization of leaf surface complexity in Theobroma grandiflorum. By combining laser scanning confocal microscopy (LSCM)-derived three-dimensional profilometry with Minkowski functionals and multifractal analysis, we quantitatively distinguished the structural organization of adaxial and abaxial surfaces beyond conventional morphological descriptions. The analysis of the Minkowski functionals revealed distinct connectivity regimes and threshold-dependent transitions, indicating differences in surface topology and percolation behavior. These findings were further supported by multifractal spectra, which exhibited a broader distribution of singularities for the abaxial surface, reflecting increased heterogeneity and structural complexity. The introduction of the normalized differential parameter ΔP proved to be an effective strategy for directly quantifying morphological asymmetry, while radar plots enabled an integrated visualization of multivariate descriptors. From a physical perspective, the observed differences are consistent with the functional specialization of leaf surfaces, where the abaxial side exhibits greater structural complexity associated with gas exchange and environmental interaction, while the adaxial surface remains more compact and protective. Overall, the proposed approach advances the application of fractal and topological methods to biological systems, offering a scalable and transferable framework for the analysis of complex natural surfaces. This methodology opens new perspectives for studies in plant morphology, taxonomy, and environmental adaptation, aligning with the broader scope of fractal and fractional analysis in complex systems.