In this paper, we propose a generative statistical model to learn the spatiotemporal variability in longitudinal shape data sets, which contain repeated observations of a set of objects or individuals over time. From all the short-term sequences of individual data, the method estimates a long-term normative scenario of shape changes and a tubular coordinate system around this trajectory. Each individual data sequence is therefore (i) mapped onto a specific portion of the trajectory accounting for differences in pace of progression across individuals, and (ii) shifted in the shape space to account for intrinsic shape differences across individuals that are independent of the progression of the observed process. The parameters of the model are estimated using a stochastic approximation of the expectation–maximization algorithm. The proposed approach is validated on a simulated data set, illustrated on the analysis of facial expression in video sequences, and applied to the modeling of the progressive atrophy of the hippocampus in Alzheimer’s disease patients. These experiments show that one can use the method to reconstruct data at the precision of the noise, to highlight significant factors that may modulate the progression, and to simulate entirely synthetic longitudinal data sets reproducing the variability of the observed process.

中文翻译：

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学习纵向形状数据集中的时空变异性

在本文中，我们提出了一个生成统计模型来学习纵向形状数据集的时空变异性，其中包含随着时间的推移对一组对象或个人的重复观察。从单个数据的所有短期序列中，该方法估计形状变化的长期规范场景和围绕该轨迹的管状坐标系。因此，每个个体数据序列都被 (i) 映射到轨迹的特定部分，说明个体之间进展速度的差异，以及 (ii) 在形状空间中移动以说明与进展无关的个体之间的内在形状差异观察到的过程。使用期望最大化算法的随机近似估计模型的参数。所提出的方法在模拟数据集上得到验证，在视频序列中的面部表情分析中得到了说明，并应用于阿尔茨海默病患者海马体进行性萎缩的建模。这些实验表明，人们可以使用该方法以噪声的精度重建数据，突出可能调节进程的重要因素，并模拟完全合成的纵向数据集，再现观察到的过程的可变性。