Software that carries out most of these computations is publicly available. Those of you with a modern workstation might FTP to my web site,, go to the directory pub/edgewarp or pub/ edgewarp3.1, and there grab a program and a manual to browse through. The Edgewarp software family, constructed by my colleague William D. K. Green, includes a variety of programs for digitizing two-dimensional and three-dimensional medical images, averaging the shape information they bear, and averaging the images after unwarping to those average shapes. There are versions for many modern Unix workstations and also for Linux, the Unixlike operating system for PCs. I would also gladly share the source files in Splus (a commercial statistical package) that produced all the statistical analyses and diagrammatic figures here.

acknowledgments Preparation of this contribution was supported by NIH grants DA09009 and GM37251 to Fred L. Bookstein. I thank John DeQuardo, the University of Michigan, for the subjects and the selection of image planes underlying the schizophrenia data set here (example 1), Christos Davatzikos of Johns Hopkins University for the gerontological data set (example 2), and Ann Streissguth, grant AA10836, and the Fetal Alcohol and Drug Unit at the University of Washington for the fetal alcohol structural and behavioral data (example 3).

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