Novel imaging technologies provide a detailed look at structure and function of the tremendously complex and variable human brain. Optimal exploitation of the information stored in the rapidly growing collection of acquired and segmented MRI data calls for robust and reliable descriptions of the individual geometry of the cerebral cortex. A mathematical description and representation of 3-D shape, capable of dealing with form of variable appearance, is at the focus of this paper. We base our development on the Medial Axis Transformation (MAT) customarily defined in 2-D although the concept generalizes to any number of dimensions. Our implementation of the 3-D MAT combines full 3-D Voronoitesselation generated by the set of all border points with regularization procedures to obtain geometrically and topologically correct medial manifolds. The proposed algorithm was tested on synthetic objects and has been applied to 3-D MRI data of 1 mm isotropic resolution to obtain a description of the sulci in the cerebral cortex. Description and representation of the cortical anatomy is significant in clinical applications, medical research, and instrumentation developments.