The statistical dependencies between the anatomical properties of brain structures, both in health and disease, is typically inferred in the severe undersampled regime. MRI scans are often segmented into hundreds of measures of localized brain areas, while the number of scanned volunteers often remains woefully below. Since naive estimation methods tend to overestimate the correlations between the measured properties, a drastic reduction in dimensionality is required. To that end, we developed a Bayesian inference method based on a probabilistic graphical model that detects collections of measures that co-vary tightly, and therefore, need not be described independently. We applied the method to T1 images segmented into 300 anatomical measures by the freely available software FreeSurfer, obtained from 207 subjects aged 18-60 of both sexes, with no known neurological disorders, from Buenos Aires and Bariloche. The inferred correlation matrix was structured into almost independent blocks. Some blocks contained only the thicknesses of the analyzed cortical areas, while others mixed cortical surfaces and volumes. Hence, thicknesses tend to vary independently from volumes and surfaces. Many of the blocks contained bilateral structures, yet, a few asymmetric cases were found, as for example, around the Broca area. The segmentation for Bariloche was almost identical to the one for Buenos Aires. Regional differences, hence, are not significant when defining the quasi-independent sets.