P. Gunz1, P. Mitteroecker1, FL. Bookstein1,2, GW. Weber1
1 Inst. Anthropology, Univ. Vienna, Austria
2 Dept. Biostatistics, Michigan, USA

We present statistical and geometrical techniques to reconstruct incomplete human crania using techniques that formalize the biologist's prior understanding of the considerations that govern form: continuity, symmetry or integration. The modern morphometrics of landmarks and curves makes it possible to blend statistical and biological reasoning in this domain. Factors such as size allometry or sex and also directional asymmetry whether zero or nonzero can be explicitly incorporated into the data estimation by way of the corresponding covariance structures.
For tasks of estimation based on very small samples we show a variant based on the continuity assumption of the thin-plate spline. When complete specimens are adequate in number our estimation can be regression-driven instead. All the missing points can be estimated at once by maximizing the likelihood of the resulting configuration in a reduced-rank model of a multivariate Gaussian distribution. Whatever integration the form possesses is automatically exploited in the course of these regressions.
We demonstrate the accuracy of these approaches using a dataset of 388 anatomical landmarks and semilandmarks on 52 complete H. sapiens crania. After deliberately deleting regions of landmarks we estimate the missing data and compare the estimated specimen to the original. Our results indicate that the accuracy of estimation is sufficiently close to the precision of measurement.
Research supported by the Austrian Science Foundation Project P14738.
Key words: Reconstruction, Geometric Morphometrics, Thin-plate spline, Regression