A comprehensive computational pipeline for foramen magnum shape analysis integrating elliptic Fourier transform, polygon approximation, and Procrustes heatmaps from CT images: application to forensic sex estimation

Background The foramen magnum (FM) exhibits well-documented size-based sexual dimorphism, yet whether its shape independently differs between sexes remains unresolved. Previous attempts to characterize FM shape have relied on subjective visual classification into categorical types, producing inconsistent and irreproducible results. This study aimed to apply a comprehensive suite of computational geometric methods to CT-derived FM contours in order to objectively quantify shape variation and evaluate its discriminative capacity for sex estimation. Methods FM boundaries were automatically extracted from axial CT images of 473 adults (234 males, 239 females) from an Eastern Turkish population. Seven complementary geometric analyses—classical morphometry, Fitzgibbon and genetic-algorithm-optimized ellipse fitting, systematic polygon approximation (3–13 sides), normalized elliptic Fourier transform (20 harmonics), radial distance profiling, and Procrustes-based point-density heatmap construction—yielded 231 quantitative features per specimen. Sex differences were assessed using Mann–Whitney U tests with Bonferroni correction and Cohen’s d effect sizes. Classification performance was evaluated with linear discriminant analysis, support vector machines, and random forest under stratified 10-fold cross-validation. Within-sex morphological subtypes were explored using Gaussian mixture model clustering. Results Of 234 morphometric features, 92 (39.3%) showed significant sex differences after Bonferroni correction. Dimorphism was overwhelmingly size-driven: all six size measurements showed large effect sizes (Cohen’s d = 1.13–1.28, perimeter strongest at d = 1.284), while only 17 of 146 pure shape features (11.6%) reached significance and the FM index showed no sex difference (d = 0.088). The highest classification accuracy was 80.9% ± 4.9% (sensitivity 76.4%, specificity 85.3%), achieved by forward-selected shape features with LDA, outperforming size-only classification (75.6%). A novel Procrustes heatmap-based method yielded near-chance accuracy (54.1%), confirming size dominance. Gaussian mixture model analysis revealed greater male morphological heterogeneity (25.2% atypical variants) compared to more homogeneous female FM morphology (71.5% single dominant subtype). Conclusions FM sexual dimorphism is predominantly size-mediated, but computationally derived shape features provide incremental discriminative value that exceeds what size alone can achieve. This study introduces a fully automated, reproducible geometric morphometric pipeline that replaces subjective shape categorization with objective, continuous measurements. The framework is openly available and readily transferable to other skeletal structures amenable to CT-based contour analysis.