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We present USLR, a computational framework for longitudinal registration ofbrain MRI scans to estimate nonlinear image trajectories that are smooth acrosstime, unbiased to any timepoint, and robust to imaging artefacts. It operateson the Lie algebra parameterisation of spatial transforms (which is compatiblewith rigid transforms and stationary velocity fields for nonlinear deformation)and takes advantage of log-domain properties to solve the problem usingBayesian inference. USRL estimates rigid and nonlinear registrations that: (i)bring all timepoints to an unbiased subject-specific space; and (i) compute asmooth trajectory across the imaging time-series. We capitalise onlearning-based registration algorithms and closed-form expressions for fastinference. A use-case Alzheimer's disease study is used to showcase thebenefits of the pipeline in multiple fronts, such as time-consistent imagesegmentation to reduce intra-subject variability, subject-specific predictionor population analysis using tensor-based morphometry. We demonstrate that suchapproach improves upon cross-sectional methods in identifying groupdifferences, which can be helpful in detecting more subtle atrophy levels or inreducing sample sizes in clinical trials. The code is publicly available inhttps://github.com/acasamitjana/uslr

USLR: an open-source tool for unbiased and smooth longitudinal registration of brain MR