Tree-based adaptive finite element methods for deformable image registration

TL;DR

This paper introduces a novel adaptive finite element method with error estimation and mesh refinement strategies for deformable image registration, improving accuracy and efficiency in medical imaging applications.

Contribution

It presents a new FEM formulation with residual-based error estimation and adaptive mesh refinement for DIR, combined with an accelerated fixed-point solver using Anderson Acceleration.

Findings

The method achieves reliable error control in DIR tasks.

Numerical results demonstrate improved registration accuracy.

The adaptive approach reduces computational cost.

Abstract

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.