Where the Inaccuracy in Cranial Shape Measurement Comes From: Measurement Convention, Point Placement, and a 20-Point Alternative

Cranial asymmetry indices are defined inconsistently, and protocol differences can change severity classification. I asked which element matters, by how much relative to the difference between infants, and whether the same points would serve better placed otherwise. On synthetic instances from a published statistical shape model of craniosynostosis and control infants, I computed 2 asymmetry indices and the cephalic index by a published protocol, perturbing each element in turn and comparing the result against an area-weighted normalized Gram matrix invariant under translation, scaling, and rotation. No element of the protocol moved any index by a full between-subject SD, and the midline dominated: 1 mm of lateral displacement moved the anterior symmetry rate by 0.90 SD, whereas 3 mm of center displacement moved the diagonal index by 0.07. The reference frame was larger: a 1 mm landmark error moved that rate by 0.52 SD and left only 43% to 58% of a 20-point configuration in place; it alone reaches a full SD. Midline error biases the symmetry rates toward greater asymmetry, but only in heads symmetric enough for the error to cross the point where the half areas are equal. The indices accounted for 29% of the true asymmetry of the control vault. Eight points in one plane correlated 0.66 with the full-surface distance, and 20 over 3 levels 0.81. Among 15,000 configurations, a rank on one sample predicted another with a Spearman of 0.05 over the leading 200, and none could be shown better than the anatomic placement.