Brain warping with implicit representations

In this paper, a new framework for brain warping via landmark matching is proposed using implicit representations or the level set method. We demonstrate this powerful technique by matching landmark curves identified on brain surfaces. Each landmark curve to be matched is represented by the intersection of the zero level sets of two level set functions. A diffeomorphic mapping from the template to the target image is then generated by solving a non-linear Euler transport equation with a semi-Lagrangian formulation for the corresponding level set functions. This representation technique has applications in mapping growth processes, recovering intra-operative brain deformation, and integrating and comparing brain imaging data across subjects and groups.