Optimization is a powerful paradigm for expressing and solving a variety of imaging problems. Modern optimization methods have had considerable success on problems that involve interactions between pairs of pixels. This has lead to important advances, but many imaging problems clearly require explicit modeling of higher-order interactions. This project is addressing this challenge through a close collaboration between researchers with expertise in graph algorithms and computer vision. The project is focused on two core applications: MRI image reconstruction and boundary detection in natural images. Besides their innate interest, these applications are closely related to other important imaging problems such as fMRI distortion correction, super-resolution, angiography and road detection.
Optimization problems with high-order interactions are inherently difficult from a computational point of view. The computational complexity can be reduced for problems with specific properties. By identifying common properties in many important imaging problems it is possible to design powerful optimization methods that are broadly applicable. The project is bringing together researchers in computer vision and algorithms. The collaboration is leading to new algorithms that are of broad interest to the computer vision and imaging communities. These algorithms have the potential to transform the way that several important classes of problems are solved. All of the algorithms being developed are being carefully evaluated, with their implementations made widely available on a web repository. Dissemination of the ideas is facilitated by workshops and mini-courses being organized at Brown, Cornell and Rutgers.
