Data-Driven Model Order Reduction for Diffeomorphic Image Registration

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This paper presents a data-driven model reduction algorithm to reduce the computational complexity of diffeomorphic image registration in the context of large deformation diffeomorphic metric mapping (LDDMM). In contrast to previous methods that repeatedly evaluate a full-scale regularization term governed by partial differential equations (PDEs) in the parameterized space of deformation fields, we introduce a reduced order model (ROM) to substantially lower the overall computational cost while maintaining accurate alignment. Specifically, we carefully construct the registration regularizer with a compact set of data-driven basis functions learned by proper orthogonal decomposition (POD), based on a key fact that the eigen spectrum decays extremely fast. This projected regularization in a low-dimensional subspace naturally leads to effective model order reduction with the underlying coherent structures well preserved. The iterative optimization involving computationally expensive PDE solvers is now carried out efficiently in a low-dimensional subspace. We demonstrate the proposed method in neuroimaging applications of pairwise image registration and template estimation for population studies.