The investigator proposes to explore the foundations for a new, full-fledged theory of stochastic estimation for tracking boundaries of phenomena or objects that are described as level sets. Stochastic estimation for contours has shown its power in the literature of active contours, and level set methods have been shown to be very effective for describing boundaries that change topology frequently, and shape very rapidly.
Part of the proposed activities are theoretical in nature: the theory must be formalized from scratch, and several mathematical and computational challenges are to be overcome, including the formulation of methods for perturbing boundaries in a stochastically controlled way; the interleaving of boundary shape estimation with contour motion analysis; the invention of new methods for resampling, Maximum Likelihood, and Maximum A Posteriori estimation in the context of level sets; and the development of numerically efficient methods for the update and propagation of boundary estimates. Another important component of this proposal is work on applications ranging from the tracking of oil spills or clouds of pollutants by a swarm of robots; the identification and interpretation of hand gestures in image sequences; and the analysis of growth of skin lesions for dermatological diagnosis.
The proposed applications are important in their own right: tracking the spread of oil spills, pollutants, forest fires and similar phenomena is of clear and immediate usefulness to society. Tracking techniques for video analysis are of urgent importance for surveillance of public sites, monitoring of activities, and aiding of the speech or hearing impaired. In addition, the marriage of stochastic estimation and level sets is fundamental enough to make possible advances also in fields beyond computer vision.
