"Endophrenology": New morphometric techniques
applied to brain form
Fred L. Bookstein
Medical School, University of Michigan
For hundreds of years the arrangements and derangements of
extents and hollows, planes and bulges of the solid
brain in its environment of fluids and bone have
preoccupied physicians, psychologists, and biological
scientists in a great variety of disciplines. A method
combining statistics with this intuitive
geometry of form-change was earnestly sought through most
of this century. Recently, beginning in the 1980's, we
have made substantial progress toward that goal. Techniques
from mathematical statistics, multivariate biometrics,
non- Euclidean geometry, and computer graphics can now be
combined into a coherent new system of tools for the complete
analysis of pictures or whole solid brain images whenever they can
be labeled with reference to terms from an atlas.
Some key formalisms of the toolkit are
David Kendall's Riemannian geometry of shape, its linearization
by Procrustes fits to a Procrustes average shape, permutation
tests for reduced-rank problems in this domain, the
thin-plate spline visualization of any biometric effects that
are found, and extension of all these to data sets of curving form
that do not have landmarks. The new methods are illustrated, in various
combinations, using data sets recently accrued in the course
of the Human Brain Project: the form of the corpus callosum and
the cerebral ventricle in schizophrenia, and the form of the
callosum in Fetal Alcohol Syndrome.