A Locally Linear Method for Enforcing Temporal Smoothness in Serial Image Registration

Deformation fields obtained from image registration are commonly used for deriving measurements of morphological changes between reference and follow-up images. As the underlying image matching problem is ill-posed, the exact shape of these deformation fields is often dependent on the regularization method. In longitudinal and cross-sectional studies this effect is amplified if time between acquisitions varies and smoothness between serial deformations is neglected. Existing solutions suffer from high computational costs, strong modeling assumptions and the bias towards a single reference image. In this paper, we propose a computationally efficient solution to this problem via a temporal smoothing formulation in the one-parameter subgroup of diffeomorphisms parametrized by stationary velocity fields. When applied to modeling fetal brain development, the proposed regularization results in smooth deformation fields over time and high data fidelity.