Modeling and understanding the degree of correlations between brain structures is a challenging problem in neuroscience. Correlated anatomic measures may arise from common genetic and trophic influences across brain regions, and may be overlooked if structures are modeled independently. Here, we propose a new method to analyze structural brain correlations based on a large set of cortical sulcal landmarks (72 per brain) delineated in 98 healthy subjects (age: 51.8 +/-6.2 years). First, we evaluate the correlation between any pair of sulcal positions via the total covariance matrix, a 6x6 symmetric positive-definite matrix. We use Log-Euclidean metrics to extrapolate this sparse field of total covariance matrices to obtain a dense representation. Second, we perform canonical correlation analysis to measure the degree of correlations between any two positions, and derive from it a p-value map for significance testing. We present maps of both local and long-range correlations, including maps of covariation between corresponding structures in opposite hemispheres, which show different degrees of hemispheric specialization. Results show that the central and inferior temporal sulci are highly correlated with their symmetric counterparts in the opposite brain hemisphere. Moreover, several functionally unrelated cortical landmarks show a high correlation as well. This structural dependence is likely attributable to common genetic programs, experience-driven plasticity, and coordinated brain growth or presence of anatomical links (neural fibers).