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

翻译：摘要：我们提出了USLR，一种用于脑部MRI扫描纵向配准的计算框架，旨在估计随时间平滑、对任何时间点无偏且对成像伪影鲁棒的非线性图像轨迹。该框架基于空间变换的李代数参数化（兼容刚性变换和非线性形变的平稳速度场），并利用对数域特性通过贝叶斯推断求解问题。USLR估计的刚性和非线性配准能够：(i) 将所有时间点映射至无偏的受试者特定空间；(ii) 计算成像时间序列中的平滑轨迹。我们基于学习型配准算法和闭式表达式实现快速推断，并通过阿尔茨海默病研究案例展示了该流程在多方面的优势，例如：通过时相一致图像分割减少受试者内变异性、受试者特定预测或基于张量形态计量学的群体分析。我们证明，该方法在识别组间差异方面优于横截面方法，有助于检测更细微的萎缩水平或减少临床试验样本量。代码已开源发布于 https://github.com/acasamitjana/uslr