Automatic Detection and Uncertainty Quantification of Landmarks on Elastic Curves

TL;DR

This paper introduces a Bayesian, model-based method for automatically detecting landmarks on elastic curves, including uncertainty quantification and joint estimation of the number of landmarks, demonstrated through simulations and real data applications.

Contribution

It presents a novel Bayesian approach for automated landmark detection on elastic curves, incorporating uncertainty quantification and methods for selecting the number of landmarks.

Findings

Effective landmark detection demonstrated on simulated data

Successful application to computer vision and biological shape data

Quantified uncertainty in landmark placement

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 and biology; additionally, we explore placements and associated uncertainty in landmarks for various substructures extracted from magnetic resonance image slices.