Combining the Band-Limited Parameterization and Semi-Lagrangian Runge–Kutta Integration for Efficient PDE-Constrained LDDMM

The family of PDE-constrained Large Deformation Diffeomorphic Metric Mapping (LDDMM) methods is emerging as a particularly interesting approach for physically meaningful diffeomorphic transformations. original combination Gauss–Newton–Krylov optimization and Runge–Kutta integration shows excellent numerical accuracy fast convergence rate. However, its most significant limitation the huge computational complexity, hindering extensive use in Computational Anatomy applied studies. This has been treated independently by problem formulation space band-limited vector fields semi-Lagrangian integration. purpose this work to combine both three variants LDDMM further increasing their efficiency. resulting evaluated extensively. For all variants, proposed combined increment In addition, variant based on deformation state equation positioned consistently best performing method across evaluation frameworks terms