| Nonlinear elasticity has been widely used in image registration for large deformation in engineering and medical fields. We investigate several hyper-elastic models in a variational framework, where we solve unconstrained optimization problem by minimizing energy functional consisting of dissimilarity measure, elasticity regularization, and constraint-based penalty term. Optimization techniques, such as the operator-splitting, the augmented-Lagrangian and logarithmic barrier, are utilized to improve the performance of the models in rendering smoother Jacobian field. The Sobolev H¹ gradient descent method is adopted to improve the convergence rate and the Bregman iterative algorithm is added to achieve better feature matching and geometric alignment. All models are put through a ground truth test for the validity of registration and are applied to registration of mouse brain from gene expression data to standard atlas. The two dimensional Mooney-Rivlin elasticity model with the Sobolev H¹ gradient descent and the Bregman iteration proves to be substantially efficient and accurate. |
