Missing data

If a form is distorted, parts have been broken off, or its surface details have been obscured, we have to deal with "missing data" from a statistical point of view.

In statistics, there are two main strategies to deal with this problem: (1) either cases or variables with missing values are deleted from the dataset, or (2) missing values are substituted by estimations based on complete cases.

During reconstruction, the researcher seeks to establish the most likely representation of a defective form. Because the form of any organism has been subject to various developmental, functional and biomechanical constraints, we know much more about the missing data than the mere fact that it is not present. The researcher uses a-priori knowledge of the biological and mechanical factors that govern form in the reconstruction process:

Symmetry: If landmarks are present on one side and missing on the other, the form can be completed by simple mirror imaging.

Allometry: Static or ontogenetic allometries are regressions of Procrustes shape coordinates on centroid size.
Morphological Integration: Using the method of partial least squares on the covariance matrix of the Procrustes coordinates allows to quantify the covariation of subsets of anatomical landmarks.
Curvature smoothness: The smoothness of a transformation can be quantified by the bending energy, the scalar measure of deformation associated with the thin plate spline interpolation.