We present a novel approach to parcellate – delineate the anatomical feature (folds, gyri, sulci) boundaries – the brain cortex. Our approach is based on extracting the 3D brain cortical surface mesh from magnetic resonance (MR) images, computing the shape measures (area, mean curvature, geodesic, and travel depths) for this mesh, and delineating the anatomical feature boundaries using these measures. We use angle-area preserving mapping of the cortical surface mesh to a simpler topology (disk or rectangle) to aid in the visualization and delineation of these boundaries. Contrary to commonly used generic 2D brain image atlas-based approaches, we use 3D surface mesh data extracted from a given brain MR imaging data and its specific shape measures for the parcellation. Our method does not require any non-linear registration of a given brain dataset to a generic atlas and hence, does away with the structure similarity assumption critical to the atlas-based approaches. We evaluate our approach using Mindboggle manually labeled brain datasets and achieve the following accuracies: 72.4% for gyri, 78.5% for major sulci, and 98.4% for folds. These results warrant further investigation of this approach as an alternative or as an initialization to the atlas-based approaches.