The Center for Applied Mathematics Presents a Special Lecture


              Creases as Local Features of Deformation Grids


                                  by

                          Fred L. Bookstein

 
   Professor Bookstein is a Distinguished Senior Research Scientist at the
Institute of Gerontology, University of Michigan, Ann Arbor.  He is an expert in
the field of medical image analysis, particularly of MRI brain images.

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Time:  Thursday February 18, 1999 at 10:40 (4th Period)

Place:  339 Little Hall (The Atrium)

Abstract:

   To help identify underlying developmental or pathological processes,
biological shape differences often are represented as diffeomorphisms of a 
Cartesian coordinate grid.  The problem addressed here is the extraction of spatially
discrete, localized, organized features of such transformation grids.
Some features can be identified with variants of the singularity F(x,y) = (x,x^2y + y^3)
that are visually evident as "creases" in suitably enhanced grid diagrams.  The crease 
is a nongeneric singularity at which a pair of cusps appears as a function of a 
parameter for extrapolation.  The examples here show how these representations extract
statistically informative and scientifically helpful features from deformations that 
help characterize two brain diseases, schizophrenia and Fetal Alcohol Syndrome,
in two dimensions.  Under relaxation of bending energy against Euclidean distance, one 
analogue to multiscale analysis for discrete punctate data, creases are robust in 
location and orientation.