The emerging discipline of Computational Functional Anatomy.

Computational Functional Anatomy (CFA) is the study of functional and physiological response variables in anatomical coordinates. For this we focus on two things: (i) the construction of bijections (via diffeomorphisms) between the coordinatized manifolds of human anatomy, and (ii) the transfer (group action and parallel transport) of functional information into anatomical atlases via these bijections. We review advances in the unification of the bijective comparison of anatomical submanifolds via point-sets including points, curves and surface triangulations as well as dense imagery. We examine the transfer via these bijections of functional response variables into anatomical coordinates via group action on scalars and matrices in DTI as well as parallel transport of metric information across multiple templates which preserves the inner product.