New Applications of Geometry to Analysis of Brain Imagery
Wednesday, October 11, 2000 - 2:45pm - 3:30pm
Fred Bookstein (University of Washington)
Recently a new methodological discipline, morphometrics, has emerged as a combination of geometry, computer science, statistics, and mathematical biology. The new techniques bridge two domains of mathematics usually applied separately in medical imaging: one, the domain of image acquisition, emphasizing physical noi se models and the associated signal-processing task, and the other, the domain of biometrical pattern analysis, emphasizing the ties of image information to the larger world of covariance structures, group averages, and scientific hypotheses . This talk will sketch the flavor of the new discipline in two applications to empirical investigations into endophrenology, the correlation of brain form w ith behavior in disease. One application is an algorithm for usefully parametrizin g stable localized shape difference in the presence of substantial biological variation. The other demonstrates a powerful modeling protocol for identifying the midline of the corpus callosum, an approximately symmetric structure the shape of which turns out to be strongly informative about embryological conditi ons associated with the diagnosis of Fetal Alcohol Syndrome. In sketching these applications my talk will touch on a range of classical topics including Riemann ian geometry, analytic geometry of planes, interpolation theory, and singularity theory.