Automatic Detection and Uncertainty Quantification of Landmarks on Elastic Curves

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.

统计形状分析（statistical shape analysis）中一类核心关注的总体量化指标为标志点（landmarks）的位置——这类点可辅助重建并表征物体的形状。本文提出一种基于模型的自动化推断方法，可在给定形状数据样本的前提下实现标志点的推断。该模型基于穿过指定点的形状线性重建框架构建，同时阐述了用于估计未知标志点位置的贝叶斯推断方法（Bayesian inferential approach）。针对“标志点选取数量”这一问题，本文通过两种不同路径予以解决：(1) 构建基于准则的选取范式；(2) 对标志点数量及其位置进行联合估计。本文同时探讨了后验采样（posterior sampling）的高效实现策略。本文通过多个仿真示例，以及计算机视觉、生物学与医学成像领域的实际应用数据，阐释了本方法的应用场景与合理性。本文的补充材料（含可复现研究所需材料的标准化说明）可通过在线补充资源获取。