Mathematical Digest

Short Summaries of Articles about Mathematics
in the Popular Press

"Tracking Interfaces with Level Sets," by James Sethian. American Scientist, May/June 1997, pages 254-263

This subject of this article is boundaries of physical objects. Some boundaries, like the surface of the ocean, are fluid and changing, while some are static but hard to discern, like the edge of a tumor in a CAT scan. Progress has been made in the development of mathematical and computational tools used to analyze evolving boundaries of objects. The main tool described in this article is the "level set method," in which an extra dimension is added to the problem. Although the extra dimension might seem to add complexity, it actually simplifies the problem by allowing one to work with a fixed, rather than a moving, reference frame. The article also describes the application of this method to such areas as robot motion, medicine, and electronics.

--- Allyn Jackson

American Mathematical Society