Integrative diffeomorphic metric mapping based on image and unlabeled points

This paper introduces a variational problem under the setting of large deformation diffeomorphic metric mapping (LDDMM) for whole brain mapping when images and unlabeled points on sulcal and gyral curves are simultaneously carried from one subject to the other through a flow of diffeomorphisms. Its Euler-Lagrange equation is described in terms of momentum, a linear transformation of the velocity vector field of the diffeomorphic flow. The numerical implementation for solving this variational problem, which involves kernel application in an irregular grid, is made feasible by the introduction of a class of computationally friendly kernels. This algorithm is applied to register 40 magnetic resonance (MR) brain images. Our results show the alignment improvement in the cortical regions when compared with the intensity-based LDDMM.