In order to resolve these problems, we developed a surface deformation procedure that adaptively determined the MR intensity of the boundaries in question at each point in the cortex (Fischl and Dale, 2000). Instead of using curvature minimization or spring terms that seek a flat surface, we modeled the surface with local quadratic patches that constrained the surfaces to be well-modeled using a second order polynomial as opposed to a plane. This allowed us to prevent noise-induced oscillations in the surfaces while avoiding underestimation in regions of high curvature. Finally, we borrowed techniques from the computer graphics literature to implement fast triangle–triangle intersection (Möller, 1997) that provided a hard constraint and prevented the surface from developing self-intersections. The combination of these approaches yielded a procedure that generates models of the gray/white and pial surfaces that were topologically correct, handled acquisition artifacts and tissue variability, was robust to variations in sequence parameters and generated models that were accurate enough to reliably measure the thickness of the gray matter of the human cerebral cortex and detect pathology induced variations of less than ¼ mm.
