Ostensibly, Sethian's research is quite esoteric. He studies "interfaces" that change position and shape. To help understand their behavior, he and his colleagues have developed numerical techniques that can be used to track the motion and evolution of these interfaces, techniques that go by the names of Fast Marching Methods and Level Set Methods. Sethian's website provides both technical and intuitive descriptions of these methods. However, it also tries to answer a question that might be on the mind of most nonmathematicians:  "Why care?"

Sethian responds to this perfectly legitimate question by describing commonplace examples of moving interfaces.  Ubiquitous in nature, they include breaking waves in an ocean, the combustion of gasoline inside an internal combustion engine, the animation of images, and even the manufacture of computer chips. In each case, tracking the movement of these interfaces is extremely difficult.

This helps answers the question of why someone might be interested in understanding and anticipating the behavior of evolving interfaces.  But what can you actually do with the Fast Marching Methods and Level Set Methods techniques?  How do they work?

Sethian's website makes it possible for you to see for youself.  The website allows you to try out and experiment with the following derivative applications:

• Build your own obstacle course and robot able to navigate the shortest path through the course
• Automatically extract shapes from a medical image scan
• Create curves that evolve under your own speed laws
• Design a "noisy" image and automatically clean it up

Sethian says his website serves as a technical resource, as an intuitive introduction to the field, but, above all, as simply an interesting place to play with some mathematics.

Additional Information:

• James Sethian website
• Understanding Fast Marching Methods and Level Set Methods