Robust Parametric Estimation of Avian Cranial Morphology

Understanding the growth and form of complex morphological structures is one of the most fundamental problems in biology. While many prior works have analyzed the beak morphology 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.