Band-Limited Stokes Large Deformation Diffeomorphic Metric Mapping

The class of registration methods proposed in the framework of Stokes large deformation diffeomorphic metric mapping (LDDMM) is a particularly interesting family of physically meaningful diffeomorphic registration methods. Stokes-LDDMM methods are formulated as constrained variational problems, 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 paper 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 constrained 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 3-D with the nonrigid 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.