Active contours (deformable curves that evolve within an image in order to capture an object of interest) rank among the most widely used tools in image processing and computer vision. This investigation focuses on the mathematical reformulation of many existing active contour models to improve their robustness and performance as well as the formulation of brand new active contour models that are not possible under the more traditional formulation. The impact of the this investigation is therefore expected to be quite broad given the prominence of active contour applications in many fields ranging from medical imaging, manufacturing, survelliance, target tracking, visual inspection, and video compression.
For over twenty years, gradient flow schemes for active contours have been mathematically founded upon a common, though often overlooked, geometric L2 norm. The investigator will study the benefits of changing this fundamental unifying mathematical foundation by proposing alternative classes of norms to greatly improve the behavior of gradient flow schemes for active contours. A tremendous amount of effort has gone into designing more and more sophisticated energy functionals yet not into considering the mathematical foundations behind the ""standard recipe"" gradient flow calculations. By changing the underlying norm behind gradient descent caluclations for active contours, the investigator will introduce in a mathematically rigorous and principled manner new active contour flows whose behaviors can be improved and tailored regardless of the corresponding energy functional.
