Second, the surfaces must be constrained to not self-intersect and to maintain their topology. Eulerian methods that elegantly handle the first problem that existed at the time did not have an easy way to impose topological constraints (a feature that was usually an asset to these techniques, but not in this problem domain),2 and also suffered from an inability to accurately model two interfaces that pass through the same voxel, something that occurs frequently when adjacent banks of a sulcus are almost touching. Finally, surface deformations were typically constrained to generate smooth surfaces either by a so-called “spring” term or curvature minimization. Unfortunately the cortex contains many locations of high curvature in which these terms underestimate the extent of for example small fingers of white matter.
