Statistical Interpolation of Missing Parts in Human Crania Using Regularized Multivariate Linear Regression Analysis

Abstract

Anatomically-accurate interpolation of missing parts in fossil crania is important for correct estimation of brain morphology based on cranial shape information. In the present study, we attempted to establish a method to mathematically interpolate missing coordinates of crania based on a reference database of cranial morphology. Specifically, a total of 151 landmarks were acquired for each specimen using anatomical and sliding landmarks, and a reference database of human cranial shape was constructed. Based on the sample of complete specimens as reference data, multivariate regressions were calculated with the missing coordinates as dependent variables, and other remaining coordinates as independent variables. We used a Moore-Penrose pseudo-inverse matrix to solve for the under-constrained linear algebraic regression equations. In order to examine the efficacy of the proposed interpolation method, we virtually created crania with missing portions, and the missing landmarks in the crania were then re-estimated for comparisons with their true values. The computed positions of the missing landmarks are located reasonably close to the corresponding landmarks on the original cranium, indicating that the present interpolation method may be effective for subjective estimation of missing parts in fossil crania. However, this estimation method seems not to be applicable to the estimation of missing landmarks in the basicranial region, possibly because of the low correlation between the shape of the basicranium and the rest of the cranium.