Gaussian Process Landmarking for Three-Dimensional Geometric Morphometrics

TL;DR

This paper applies a Gaussian process-based landmarking algorithm to 3D geometric morphometrics, demonstrating its effectiveness in automatically identifying landmarks comparable to expert manual annotations for evolutionary biological shape analysis.

Contribution

It extends Gaussian process landmarking to geometric morphometrics, providing detailed procedures and showing it performs as well or better than manual landmarking.

Findings

Automated landmarks match or outperform manual ones in coverage and analysis.

The method produces meaningful diffeomorphisms between anatomical surfaces.

Numerical procedures enhance the quality of shape correspondence.

Abstract

We demonstrate applications of the Gaussian process-based landmarking algorithm proposed in [T. Gao, S.Z. Kovalsky, and I. Daubechies, SIAM Journal on Mathematics of Data Science (2019)] to geometric morphometrics, a branch of evolutionary biology centered at the analysis and comparisons of anatomical shapes, and compares the automatically sampled landmarks with the "ground truth" landmarks manually placed by evolutionary anthropologists; the results suggest that Gaussian process landmarks perform equally well or better, in terms of both spatial coverage and downstream statistical analysis. We provide a detailed exposition of numerical procedures and feature filtering algorithms for computing high-quality and semantically meaningful diffeomorphisms between disk-type anatomical surfaces.