SIAM Journal on Imaging Sciences, Volume 14, Issue 1, Page 349-388, January 2021.
This paper provides a coherent framework for studying longitudinal manifold-valued data for which the dynamic changes over time. We introduce a Bayesian mixed-effects model that allows estimating both a group-representative piecewise-geodesic trajectory in the Riemannian space of shape and interindividual variability. We prove the existence of the maximum a posteriori estimate and its asymptotic consistency under reasonable assumptions. Due to the nonlinearity of the proposed model, we use a stochastic version of the expectation-maximization algorithm to estimate the model parameters. Our simulations show that our model is not noise-sensitive and succeeds in explaining various paths of progression.

中文翻译：

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一个从纵向流形值数据中学习时空分段大地轨迹的相干框架

SIAM影像科学杂志，第14卷，第1期，第349-388页，2021年1月。
本文为研究纵向流形值数据提供了一个连贯的框架，这些数据随时间动态变化。我们引入了贝叶斯混合效应模型，该模型允许估计形状和黎曼空间中的群体代表分段分段大地轨迹以及个体间的可变性。我们在合理的假设下证明了最大后验估计的存在性及其渐近一致性。由于所提出模型的非线性，我们使用期望最大化算法的随机版本来估计模型参数。我们的仿真表明，我们的模型对噪声不敏感，并且成功地解释了各种进展路径。