Automatic Detection and Uncertainty Quantification of Landmarks on Elastic Curves

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.

Keywords:

• Elastic metric
• Landmarks
• Linear reconstruction
• Markov chain Monte Carlo
• Shape analysis

Acknowledgments

We thank the reviewers and associate editor for their comments, which greatly improved the content and delivery of this manuscript.

Additional information

Funding

This work was partially supported by NSF DMS 1613054, NSF CCF 1740761, and NIH funding: NIH R37 CA214955 (SK).