Parcellation and labeling of cortical features are important, often manually intensive processes in visualization and interpretation of neuroimaging data. Labeling cortical structures is critical for cartography and conveying pertinent information to compare individual subjects or different populations. As the number of subjects in studies increases and larger data sets are acquired, it is critical to have automated tools. Large sample sizes mandate the use of automated procedures that are sensitive to relevant anatomical features. Additionally, such automated procedures can be used as valuable tools in teaching and training medical students. Due to the variability in folding patterns of each individual cortex, it is often a challenging task for the novice (and sometimes expert!) to identify and label cortical features.
Mathematically, properties of the shape of curves and surfaces in 3D space can be described by features such as their velocity fields, writhe, extremal length, principal curvatures, and Gaussian curvatures. For parcellation, additional information such as the location of cortical features is also of interest; these can be described by simpler features such as position and mathematical moments. We present a variety of geometric invariants to quantify properties of the shape of the cortical surface on a global as well as local level.
In our preliminary studies, topologically correct cortical surfaces representing the white matter and gray matter have been reconstructed using freeware software that is available to the neuroscience community (for example, FreeSurfer (Fischl et al., 1999) and BrainVisa (Mangin et al., 2001)). Curves of maximal and minimal principal curvature have been traced on 15 cortical surfaces. A user identifies a start and end point of a sulcus or gyrus and dynamic programming methods are used to automatically compute the path of principal curvature between these two points, thus tracking the ridge of a gyrus of the fundus of a sulcus. Five curves on each hemisphere, resulting in 150 curves from 15 subjects have been traced. Kernel Optimal Component Analysis was applied to moments, writhe invariants and their higher order analogues to extract features for parcellation and labeling. We were able to classify sulcal and gyral curves into left and right hemispheres, as well as distinguish the type of curve (i.e. central sulcus, occipital sulcus). These results indicate that the selected features vectures represent promising characteristics for automatically parcellating sulcal curves.