Two UD researchers are conducting innovative work to measure and develop accurate models of elusive three-dimensional fluid surfaces by using large arrays of specially modified digital cameras.

The camera arrays would have the advantage of collecting data about the fluid surfaces without having to touch the surfaces themselves, according to Jingyi Yu, an assistant professor in the Department of Computer and Information Sciences and principal investigator for the project. Besides being useful in scientific research on fluid surfaces, the system could allow for the integration of reconstructed fluid surfaces into animations and film footage to reproduce realistic phenomena, he says.

For example, the results of the research might be useful in rendering more lifelike images of such things as flowing water for use in movies and video games, Yu says.

The research, being conducted with co-principal investigator Philippe Guyenne, assistant professor of mathematical sciences, has been awarded a $499,430 National Science Foundation grant. Yu and Guyenne are designing an experimental system using a light field camera array that can simultaneously capture different views of a fluid surface.

Yu, who conducts research in computer graphics, computer vision and computational photography, says the modeling and reconstruction of fluid surfaces poses a number of challenges.

“Traditionally, this has been a very tough problem,” he says. “It is difficult to get accurate information on fluid surfaces without the use of intrusive devices, which can in turn change the dynamics of the fluid surface upon insertion.”

Another challenge is that fluid surfaces are governed by complex physical mechanisms that need to be incorporated in the reconstruction methods.
Guyenne, whose research involves applied and computational mathematics, has a particular focus on the modeling and numerical simulation of surface water waves, with applications to oceanography and coastal engineering.

He has developed models of fluid surfaces but has had limited ways to verify the models. He says that a goal of the new research is to capture the fluid surfaces and thereby validate both the model and the method.

The light field camera array features a number of digital cameras, from 16 to 128, with specially modified flashes, lenses and apertures. Instead of one flash, each camera is equipped with four.

Yu says the system works by placing a known pattern beneath the surface, with each camera in the array observing a distinct time-varying distortion pattern. A sampled fluid surface can then be measured by analyzing the distortions. For surface reconstruction, the researchers plan to develop an algorithm to minimize the error relative to the sampled data.

“The use of the camera array provides for dynamic depths of view,” Yu says. A single photograph from a single camera enables only one point to be in focus, whereas the array enables researchers to track from foreground to background, with all points in the image in focus.

In addition to the current research project, Yu is interested in high-end three-dimensional imaging. He has a particular focus on developing autostereoscopic 3-D displays using arrays of lenses to improve medical imaging and virtual three-dimensional surgery.

He also has an interest in developing the office and classroom of the future, using camera projection systems to create a new work environment. His own office features a dual desktop system, in which he can work at his desk on one task while projecting information onto a virtual whiteboard on a nearby wall to work on other problems. The system makes use of an ultrasonic pen and Bluetooth technology to emulate writing on the wall, which in reality remains unmarked.

Yu joined the UD faculty in 2005 after receiving his doctorate from the Massachusetts Institute of Technology. Computational photography is a relatively new area, he says, and UD is one of a handful of schools offering the program.

“This is a way to make algorithms and mathematics make sense, to make them useful in real life,” he says.

Guyenne came to UD in 2006. He earned his doctorate in 2000 from the University of Nice in Sophia Antipolis, France, and then worked as a postdoctoral fellow in the Department of Mathematics and Statistics at McMaster University in Ontario, Canada. He also held visiting positions at the Center for Mathematics and Its Applications at the École Normale Superieure de Cachan, in France, and at the Fields Institute for Research in Mathematical Science, in Toronto.
Guyenne’s research interests are in applied and computational mathematics, with emphasis on free-boundary problems and nonlinear waves.

—Neil Thomas, AS ’76