Automatic Detection and Uncertainty Quantification of Landmarks on Elastic Curves

Area of Science:

• Statistical Shape Analysis
• Computational Geometry
• Bayesian Inference

Background:

• Landmarks are crucial for shape representation and reconstruction in various scientific fields.
• Automated methods for landmark identification are needed to handle complex shape data.

Purpose of the Study:

• To develop an automated, model-based approach for inferring landmark locations from shape data.
• To address the challenge of determining the optimal number of landmarks for accurate shape analysis.

Main Methods:

• Formulation of a linear shape reconstruction model.
• Application of Bayesian inference for estimating unknown landmark locations.
• Development of criterion-based and joint estimation approaches for landmark number selection.

Main Results:

• An automated method for landmark inference in statistical shape analysis.
• Efficient posterior sampling techniques for estimating landmark parameters.
• Demonstration of the approach's efficacy across simulated data and real-world applications.

Conclusions:

• The proposed Bayesian approach provides an effective solution for automated landmark inference.
• The methods developed can accurately determine both landmark locations and their optimal number.
• This work has significant implications for computer vision, biology, and medical imaging applications.