Robust Parametric Estimation of Avian Cranial Morphology

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.

Figures (12)

• Figure 1: An overview of the proposed skull shape quantification pipeline. (a) An example of Darwin's finches (Pinaroloxias inornata). Image credit: Howard Laidlaw (Macaulay Library at the Cornell Lab of Ornithology, Ithaca, NY) image. (b) A raw skull mesh of a Pinaroloxias inornata specimen in the dataset we considered. (c) The preprocessed skull mesh with enhanced smoothness. (d)--(f) Based on the preprocessed skull mesh, we can perform (d) bounding box calculation for quantifying the skull dimensions, (e) sphere fitting for quantifying the curvature of the orbits, and (f) ellipsoid fitting for quantifying the geometry of the neurocranium (braincase).
• Figure 2: Comparison between bounding box calculation methods for quantifying the skull dimensions of a Geospiza septentrionalis skull. (a) The Oriented Bounding Box (OBB) result with two different views. (b) The Axis-Aligned Bounding Box (AABB) result with two different views.
• Figure 3: An illustration of the robust and iterative sphere fitting method. (a) A 3D skull mesh of Pinaroloxias inornata. (b) A seed point (green) is found to locate the orbital socket. (c) Selected points (red) are then identified via connected component identification and distance-based thresholding. (d) An optimal sphere (blue) is finally obtained via an optimization problem for approximating the curvature of the orbital socket.
• Figure 4: Four examples of the sphere fitting results for orbit curvature quantification. In each example, the seed point is highlighted in green, and the identified points for the fitting are highlighted in red. The optimal sphere is displayed in blue. Note that the figures are not displayed to scale.
• Figure 5: An illustration of the ellipsoid fitting algorithm for a Pinaroloxias inornata skull. (a) The input skull mesh with the seed point (green dot), selected points (red dots), and the computed axis $a$ (red line), $b$ (green line), and $c$ (blue line). (b) The best-fit ellipsoid obtained by the proposed algorithm.