Reconstructing the geometry of the human cerebral cortex from MR images is an important step in both brain mapping and surgical path planning applications. Difficulties with imaging noise, partial volume averaging, image intensity inhomogeneities, convoluted cortical structures, and the requirement to preserve anatomical topology make the development of accurate automated algorithms particularly challenging. In this paper we address each of these problems and describe a systematic method for obtaining a surface representation of the geometric central layer of the human cerebral cortex. Using fuzzy segmentation, an isosurface algorithm, and a deformable surface model, the method reconstructs the entire cortex with the correct topology, including deep convoluted sulci and gyri. The method is largely automated and its results are robust to imaging noise, partial volume averaging, and image intensity inhomogeneities. The performance of this method is demonstrated, both qualitatively and quantitatively, and the results of its application to six subjects and one simulated MR brain volume are presented.