The Hierarchical approach is linked to the Biological problem itself, coming out of the various kinds of information which is provided by the anatomists. The algorithm is driven by these sub-manifolds. We follow the approach that the highest dimensional transformation is a result from the solution of a sequence of lower dimensional problems driven by successive refinements or partitions of the images into various Biologically meaningful sub-structures. The sulci are examples of 1 dimensional sub-manifolds in the Brain. The transformation was further refined by solving the the elasticity based PDE on the full volume using the procedure outlined in section 4.
Figure below demonstrates the hierarchical procedure.
The figure shows slices through the template volume 87A and the corresponding slices through the deformed template at the different levels of the hierarchy. Column two shows the result based on the sulcal map constraints. The target 93G is shown on the right. The flow of coarse to fine information is depicted in the Figure below. The left panel shows the large differences before any transformation has been applied.