Lagrangian frame diffeomorphic image registration: Morphometric comparison of human and chimpanzee cortex

We develop a novel Lagrangian reference frame diffeomorphic image and landmark registration method. The algorithm uses the fixed Langrangian reference frame to define the map between coordinate systems, but also generates and stores the inverse map from the Eulerian to the Lagrangian frame. Computing both maps allows facile computation of both Eulerian and Langrangian quantities. We apply this algorithm to estimating a putative evolutionary change of coordinates between a population of chimpanzee and human cortices. Inter-species functional homologues fix the map explicitly, where they are known, while image similarities guide the alignment elsewhere. This map allows detailed study of the volumetric change between chimp and human cortex. Instead of basing the inter-species study on a single species atlas, we diffeomorphically connect the mean shape and intensity templates for each group. The human statistics then map diffeomorphically into the space of the chimpanzee cortex providing a comparison between species. The population statistics show a significant doubling of the relative prefrontal lobe size in humans, as compared to chimpanzees.