May 31 – June 2, 2000. The 3rd Zumtobel Lectures. Organized by Horst Seidler and Katrin Schaefer.

Reviewed by Marcus and Reddy.

A well-received workshop for the Austrian physical anthropology community was held in Vienna under the sponsorship of the Institute of Anthropology, at the University of Vienna, Austria. The Institute of Anthropology is a world leader in stereolithographic reconstruction from CT scans of recent and fossil hominines. The title and main topic of this meeting was “Missing Data in Physical Anthropology”. Invited speakers were Fred Bookstein, University of Michigan; Leslie Marcus, City University of New York; Dennis Slice, State University of New York; and David Reddy, American Museum of Natural History. Faculty, staff and students of the Institute and colleagues attended and participated in the program

On the first day Fred Bookstein presented an overview of the general missing landmark problem including direct and indirect constraints. His main message was that all of the reasonable ways for dealing with missing data in physical anthropology were in fact versions of the classic EM algorithm. One version looks like multivariate regression specialized for shape coordinates, and another looks like bending energy minimization alternating with Procrustes averaging, possibly with a reflection. Algorithms were presented together with precomputed examples involving all of these versions. Dennis Slice discussed an unreleased version of Morpheus (still under development), which incorporates missing data imputation for several classes of missing landmarks using a variety of techniques.

On the second day Bookstein presented methods of estimating landmarks at the intersection of ridge curves, where the intersection and a portion of the connecting curves were missing, corresponding to a broken off process on a skull – also possibly representing a version of the EM algorithm. Examples of the inputs and outputs of the algorithm were presented using simulated data as inputs. David Reddy discussed missing semi-landmarks, where parts of ridge curves are missing, and suggested several extrapolation approaches for imputation of the missing data.

Leslie Marcus presented background information for a large data set (704
baboon skulls with 45 landmarks and 186 semi-landmarks), where every individual
landmark or ridge curve is missing on at least one specimen, with 454 specimens
complete. An earlier presentation of
this material is available at *http://research.amnh.org/nycep/manuscripts.html*. The missing-data-capable pre-release of
Morpheus was applied to this data to estimate points on or near the sagittal
plane, and missing points on one or the other side. The topic of reflection and maximum-likelihood estimation of
bilateral points aroused the most discussion.
A lively discussion of the predictive value of the mid-sagittal points
in estimating the bilateral points ensued.

On the third day the results for an estimation of inion for the Kabwe fossil were presented as an example of Bookstein’s intersecting ridge curves problem. The curves were digitized from mid-sagittal CT slices of the fossil, and landmarks were digitized on this and a mid-sagittal CT of Petralona for use in a maximum-likelihood estimation of inion. Both methods proved to be in reasonable agreement in this case. Estimation of this landmark for this fossil was an important result of the meeting.

Next, three undergraduate students, Phillipp Gunz, Philipp Mitterocker, and Gerald Takehisa, gave an impressive presentation of a 3D morphometric analysis of 1 to 11 year old human skulls. They discussed size and shape changes and allometry over age. This presentation was fascinating, as preliminary results indicate only minor pre-puberty shape changes. The students developed all of the Procrustes and 3D-spline software themselves using Mathematica. The graphics were remarkable, and Hermann Prossinger is to be applauded for guiding the students in this endeavor. Incidentally, this was their first exposure to both geometric morphometrics and computer programming.

Johann Kim of the Institute of Mathematics, a Computational Mathematics student studying under Prof. Arnold Neumaier, gave a stimulating talk titled “Comparison and reconstruction of recent and fossil skulls using mathematical reference models”. An important part of the presentation was the independence from input data modality (landmarks, surface and volume image data, craniometer data, etc.) achieved through the use of a “model construction program” to parameterize the inputs into coefficients of functions. Graphical examples of deformations of implicit (e.g. isosurface) and parametric surfaces to parameterized “reference models” were shown along with the underlying mathematical formalisms. This was another very strong and impressive graduate student presentation.

>Understandably, a major task in palaeoanthropology is the reconstruction of a skull from fragments. Gerhard Weber introduced the question to the mathematicians from a perspective of an anthropologist. An experimental data set was described based on a artificailly smashed modern skull, haveing been CT scanned before and after its deliberate destruction. Playing with the original fragments, all participants discussed possible parameters for the identification of the location of a fragment. Using the intended parameterized reference models, introduced by J. Kim before, CT-scanned fragments should be placed to their most likely position on the model. Bookstein suggested that this was not a statisical problem, and the topic was reserved for discussion at a future meeting.

Again, the University of Vienna Institute for Anthropology faculty, staff, students, and environs provided a stimulating atmosphere. Our discussions and presentations produced important advances in solving morphometric problems including missing data. This meeting format generates much more discussion and interaction than the largely pedagogical workshops or purely research presentations at symposia.