Robust Parametric Estimation of Avian Cranial Morphology

TL;DR

This paper introduces a fully unsupervised geometric and statistical framework for analyzing avian skull morphology, enabling scalable, high-throughput phenotyping and revealing strong correlations between skull features.

Contribution

It develops novel computational geometry and statistical methods for skull analysis, surpassing traditional landmark-based approaches in efficiency and scalability.

Findings

Strong correlation between skull size and orbit curvature.

Predictive model explains 85.48% of curvature variance.

Average prediction error of 6.35%.

Abstract

Understanding the growth and form of shapes is one of the most fundamental problems in biology. While many prior works have analyzed the beak shapes of Darwin's finches, other cranial features are relatively less explored. In this work, we develop geometric and statistical methods for analyzing the skull morphology of Darwin's finches and their relatives, focusing on the relationship between their skull dimensions, orbit curvature, and neurocranial geometries. Unlike traditional landmark-based approaches that scale linearly with human labor, our framework is fully unsupervised. Specifically, by utilizing tools in computational geometry, differential geometry, and numerical optimization, we develop efficient algorithms for quantifying various key geometric features of the skull. We then perform a statistical analysis and discover a strong correlation between skull size and orbit curvature. Based on our findings, we further establish a predictive model that can estimate the orbit curvature using easily obtainable linear skull measurements. Our results show that the predictive model is highly effective and capable of explaining 85.48\% of the variance in curvature with an average prediction error of only 6.35\%. Altogether, our work establishes a rigorous foundation for the digital estimation and high-throughput phenotyping of large-scale museum collections, overcoming the scalability bottlenecks of manual methods.