Tree-based adaptive finite element methods for deformable image registration

In this work we propose an adaptive Finite Element Method (FEM) formulation for the Deformable Image Registration problem (DIR) together with a residual-based a posteriori error estimator, whose efficiency and reliability are theoretically established. This estimator is used to guide Adaptive Mesh Refinement and coarsening (AMR). The nonlinear Euler–Lagrange equations associated with the minimisation of the relevant functional are solved with a pseudo time-stepping fixed-point scheme which is further accelerated using Anderson Acceleration (AA). The efficient implementation of these solvers relies on an efficient adaptive mesh data structure based on forests-of-octrees endowed with space-filling-curves. Several numerical results illustrate the performance of the proposed methods applied to adaptive DIR in application-oriented problems.