Advances in elastic matching theory and its implementation

Computational anatomy via the deformable modeling or elastic matching paradigm is gaining increased prominence in medical imaging research. Our work in atlas-based localization of neuroanatomy has progressed toward statistical approaches that subsume the original elastic matching while retaining its practical flavor. In view of the complex geometries involved and the sparsity of image features in the localization problem, elastic matching is reformulated using variational principles to facilitate its numerical solution by the finite element method. The variational formulation in addition exposes the means by which Gibbs modeling and, thus, Bayesian analysis can be applied to the problem. In this paper, we review these developments and demonstrate the methods on MRI data, including the computation of interval estimates.