Newton-Krylov PDE-constrained LDDMM in the space of band-limited vector fields

TL;DR

This paper introduces two PDE-constrained LDDMM methods using band-limited vector fields, significantly reducing computational complexity and improving accuracy in diffeomorphic registration tasks.

Contribution

The paper proposes novel PDE-constrained LDDMM algorithms parameterized in band-limited vector fields, enhancing efficiency and accuracy over existing methods.

Findings

Reduced computational burden by avoiding high-frequency velocity components

Improved registration accuracy compared to benchmark methods

Effective in large deformation diffeomorphic mapping

Abstract

PDE-constrained Large Deformation Diffeomorphic Metric Mapping is a particularly interesting framework of physically meaningful diffeomorphic registration methods. Newton-Krylov optimization has shown an excellent numerical accuracy and an extraordinarily fast convergence rate in this framework. However, the most significant limitation of PDE-constrained LDDMM is the huge computational complexity, that hinders the extensive use in Computational Anatomy applications. In this work, we propose two PDE-constrained LDDMM methods parameterized in the space of band-limited vector fields and we evaluate their performance with respect to the most related state of the art methods. The parameterization in the space of band-limited vector fields dramatically alleviates the computational burden avoiding the computation of the high-frequency components of the velocity fields that would be suppressed by the action of the low-pass filters involved in the computation of the gradient and the Hessian-vector products. Besides, the proposed methods have shown an improved accuracy with respect to the benchmark methods.