Hierarchical brain mapping via a generalized Dirichlet solution for mapping brain manifolds

In this paper we present a coarse-tone approach for the transformation of digital anatomical textbooks from the ideal to the individual that uni es the work on landmark deformations and volume based transformation. The Hierarchical approach is linked to the Biological problem itself, coming out of the various kinds of information which is provided by the anatomists. This information is in the form of points, lines, surfaces and sub-volumes corresponding to 0,1,2 and 3 dimensional sub-manifolds respectively. The algorithm is driven by these submanifolds. 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 re nements or partitions of the images into various Biologically meaningful sub-structures. This work was supported by NIH grants RR01380 and RO1-MH52158-01A1 and ARO DAAL-03-86-K-0110