UCLA's Picture-Perfect Math Awareness WeekJune 15, 1998
Rev Lebaredian from Dream Quest Images/Walt Disney speaks about digital hair in movies like George of the Jungle during UCLA's celebration of Mathematics Awareness Week. (Photograph by Lynn Nishimura/Daily Bruin.)
It wasn't quite the Academy Awards, but UCLA's celebration of Mathematics Awareness Week had all the hallmarks of a Hollywood spectacular. Mathematics department chair Tony Chan and his doctoral student Peter Blomgren were co-producers of the April 27–May 1 event, lining up an array of speakers from movies, mathematics, medicine, and engineering to highlight the week's theme, Mathematics and Imaging.
The event was a natural for UCLA---surrounded by a movie industry whose biggest hits are powered by digital special effects, the university's mathematics faculty also includes many leaders in image processing. "We're in the middle of LA," Chan explains, "so we had to get Hollywood!"
His week-long production included three speakers from the movie industry. Doug Roble of Digital Domain elicited many questions from students with his enthusiastic display of special effects from Titanic, True Lies, Apollo 13, and several television commercials. "What do I have to learn in order to do what you do?" the students wanted to know. "Learn some math!" Roble answered.
Roble identified computational fluid dynamics, free surface flows, differential equation solvers, and computational linear algebra as among the specific mathematical ideas underlying his digital special effects. That list provoked some animated technical exchanges during the reception following his talk. Roble and Stan Osher of the UCLA mathematics department, for example, discussed the use of level set methods to simulate free surface flows.
Rev Lebaredian of Dream Quest Images/Walt Disney and Dave Wasson of Arete Associates described the difficulties of creating images of the natural world. In a talk titled "Digital Hair," Lebaredian discussed the problem of simulating the motion of individual hairs on the digital gorilla that stars in the remake of Mighty Joe Young. Newton's law governs the movement of individual hairs, he explained, and numerical simulation is used to track their positions. Aliasing is eliminated before the image is motion-blurred to produce natural-looking, moving hair.
Wasson and his colleagues at Arete were responsible for the software used to create most of the panoramic ocean scenes in Titanic. They simulated the motion of the ocean--primarily by solving the wave equation--using code that their research consulting firm had originally developed for the Department of Defense. The move from DoD to the movies was pure serendipity: A Hollywood friend of one of Arete's researchers happened to mention a movie that required a simulation of wave motion!
Stan Osher presented a special colloquium on partial differential equations and geometry-based image restoration, work that is included in the 1998 Mathematics Awareness Week theme essay. "Osher's talk," reports Chan, "was one of the best-attended applied mathematics colloquia we have had in some years--standing room only, with pure mathematicians, statisticians, and many people from outside the department."
Providing an engineering view of mathematics for image compression was Michelle Effros of the electrical engineering department at Caltech. In a colloquium talk she described the information and coding theory that underlies data and image compression.
The week of celebration ended with an invited address on mathematics in medical imaging by Henry Huang of UCLA's Medical School. Using comparisons with 40-year-old x-ray technology, he demonstrated the dramatic improvements in medical imaging made possible by the Radon transform and related mathematical ideas.
Mathematics Awareness Week is sponsored by the American Mathematical Society, the Mathematical Association of America, and SIAM. SIAM was primarily responsible for this year's event.
Paul Davis is a professor of mathematical sciences at Worcester Polytechnic Institute.