Band-Limited Stokes LDDMM

The class of registration methods proposed in the framework of Stokes Large Deformation
Diffeomorphic Metric Mapping is a particularly interesting family of physically
meaningful diffeomorphic registration methods.
Stokes-LDDMM methods are formulated as a conditioned variational problem,
where the different physical models are imposed using the associated partial differential equations
as hard constraints.
The most significant limitation of Stokes-LDDMM framework is its huge computational complexity.
The objective of this work is to promote the use of Stokes-LDDMM in Computational Anatomy applications
with an efficient approximation of the original variational problem.
Thus, we propose a novel method for efficient Stokes-LDDMM diffeomorphic registration.
Our method poses the conditioned variational problem in the space of band-limited vector fields and
it is implemented in the GPU.
The performance of band-limited Stokes-LDDMM has been compared and evaluated with original Stokes-LDDMM,
EPDiff-LDDMM, and band-limited EPDiff-LDDMM.
The evaluation has been conducted in 3D with the Non-rigid image registration evaluation project database.  
Since the update equation in Stokes-LDDMM involves the action of low-pass filters,
the computational complexity has been greatly alleviated with a modest accuracy lose.
We have obtained a competitive performance for some method configurations.
Overall, our proposed method may make feasible the extensive use of novel physically meaningful
Stokes-LDDMM methods in different Computational Anatomy applications.
In addition, our results reinforce the usefulness of band-limited vector fields in diffeomorphic
registration methods involving the action of low-pass filters in the optimization, even in
algorithmically challenging environments such as Stokes-LDDMM.