This project addresses the development of a comprehensive research and educational program in mathematical techniques applied to the areas of image processing and computer vision. In particular, Geometric Partial Differential Equations (GPDE's) are used. Using GPDE's is a relatively new approach to image analysis that brings numerous benefits and has already lead to several state-of-the-art results. This research focuses on the theoretical and practical study of ways to introduce advanced a-priori and learned knowledge and information into the GPDE's framework, moving beyond the simple edge information commonly used.
Key examples where knowledge can be incorporated include MRI and SAR, where the number of different objects present in the image is known a-priori; object tracking in video, for human-computer interaction for example, where information from previous frames can be used; and medical image analysis and visualization, where important biological information is available. This knowledge is incorporated combining Bayes rule, learning techniques, systems of coupled GPDE's, and special geometric forces driving the GPDE's. The theoretical study of these new equations is an integral part of the program. The educational component of this project focuses on improving multi-disciplinary training and creating a new image processing laboratory based on personal computers. New courses on GPDE's and on Geometric Visual Tracking are being introduced. These and the basic image processing courses are oriented to a diverse audience and are attended by students from many departments across the University. The collaboration with industry and other departments is also addressed defining joint projects. The whole research and educational program is oriented toward making advanced tools in image analysis more accessible to users that frequently interact with visual information in their personal computers.
