Invariant surface alignment in the presence of affine and some nonlinear transformations

Introduces a non-iterative geometric-based method to align 3D brain surfaces into standard coordinate system (SCS), which is based on a novel set of surface landmarks (e.g., inflection and/or zero torsion points residing on the parabolic contours), which are intrinsic and are computed from the differential geometry of the surface. This is in contrast to existing methods that depend on anatomical landmarks that require expert intervention to locate-a very hard task. The landmarks are local and are preserved under affine transformations. To reduce the sensitivity of the landmarks to noise, the authors use a B-Spline surface representation that smooths out the surface prior to the computation of the landmarks. The alignment is achieved by establishing correspondences between the landmarks after a conformal sorting based on derived absolute invariants (volumes confined between parallel-pipeds spanned by sets of the landmark point quadruplets). The method is tested for intra- and inter-brain alignments while entertaining cubic nonlinear transformations