Abstract A population quantity of interest in statistical shape analysis is the location of landmarks, which are points that aid in reconstructing and representing shapes of objects. We provide an automated, model-based approach to inferring landmarks given a sample of shape data. The model is formulated based on a linear reconstruction of the shape, passing through the specified points, and a Bayesian inferential approach is described for estimating unknown landmark locations. The question of how many landmarks to select is addressed in two different ways: (1) by defining a criterion-based approach and (2) joint estimation of the number of landmarks along with their locations. Efficient methods for posterior sampling are also discussed. We motivate our approach using several simulated examples, as well as data obtained from applications in computer vision, biology, and medical imaging. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

中文翻译：

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弹性曲线上地标的自动检测和不确定性量化

摘要：统计形状分析中感兴趣的人口数量是地标的位置，这些点有助于重建和表示对象的形状。我们提供了一种基于模型的自动化方法来推断给定形状数据样本的地标。该模型是基于形状的线性重建，通过指定的点来制定的，并且描述了用于估计未知地标位置的贝叶斯推理方法。选择多少地标的问题以两种不同的方式解决：（1）通过定义基于标准的方法和（2）联合估计地标的数量及其位置。还讨论了后验采样的有效方法。我们使用几个模拟示例来激发我们的方法，以及从计算机视觉、生物学和医学成像应用中获得的数据。本文的补充材料，包括可用于复制作品的材料的标准化描述，可作为在线补充获得。