Previous work in cortical surface reconstruction had focused on topological accuracy by deforming a surface with a known topology to lie at the specified interface in the imaging data (e.g. either gray/white or pial) (MacDonald, 1998; MacDonald et al., 1994,2000). The issue with these models is the difficulty of generating surfaces that accurately follow the entire boundary of interest, as illustrated in Fig. 1. The left-hand image exhibits typical topological defects: a bridge across the banks of a sulcus and a hole in the wall of a gyrus. These are topologically equivalent, but any accurate topology correction procedure must resolve them differently—cutting the handle and filling the hole. The right-hand drawing demonstrates the difficulty of using a topologically-constrained deformable surface to accurately model the entire cortex. The deformable surface (shown in red) is typically driven by an energy functional designed to move it towards the true surface (a portion of which is shown in black). The cortex contains many deep folds with narrow openings, such as the one indicated by the blue arrow. It is exceedingly difficult to design an
