Plastic surgery to the'nines'

ptual tools of the surgeon are experience and intuitive aesthetics. If you read the technical papers of the very best plastic surgeons it's like reading about art appreciation; there is a great emphasis on balance and perspective.

"But the face is a geometric surface and can be analyzed as such . Roughly speaking, that's what we're trying to do."

This software could have many applications outside the field of reconstructive surgery. For example, Krantz and his collaborators have taken a group of adults and a child, scanned in the faces, and matched the child to his parents.

"We hope to be able to predict the attributes of a child of two given parents, to match identical twins, and perform other 'facial recognition' functions," he said.

The capability of the system will be useful in security applications, in anthropology, in aesthetics, and in other as yet unforeseen areas.

Krantz discussed the research in a keynote address given at the Discrete Geometry Conference, held May 16-19, 2002, in Tallahassee, Fla. The conference was sponsored by the National Science Foundation. One of the main themes of the conference was brain mapping, but there were contributors who were interested in all aspects of physiological scanning and modeling.

The mathematics of beauty

Here's the mathematics behind beauty. A patient comes to a plastic surgeon's office for surgery to make him look like a young Paul Newman. His face is scanned with safe white light from the 3-D scanner ; instantaneously it turns the face into a very fine grid that looks like multiple triangles pieced together, representing the shape of the face with all its curves and creases. The grid is compared to a library of idealized faces and one is chosen. Upon this grid, the wavelet mathematics and differential geometric calculations go to work in measuring the nose, cheeks, eye sockets and calculating the difficulty in making changes as wel

Contact: Tony Fitzpatrick
Washington University in St. Louis

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