Active Contouring of Images with Physical A-splines

A-splines are implicit real algebraic curves in Bernstein-B ezier (BB) form that are smooth. We use these in an algorithm for active contouring of images. One advantage of A-splines is that any change to the controlling weights only a ects the curve locally, which results in fast convergence. Our active A-splines are also level sets of a time-dependent function with the added exibility of a dynamic unstructured mesh. Other advantages include the ability to use lower degree polynomials than traditional polynomial parametric B-splines. A-splines also avoid the necessity of dealing with poles that can arise from rational parametric B-splines (NURBS), and they also allow an easy speci cation of orientation, so that they may be driven to converge to an interior or exterior contour. Our algorithm nds image contours by using a level-set method to obtain an initial close tting polygon, constructing a physical A-spline contour by minimizing the image energy, and then minimizing the total energy by considering the energy in each spline segment individually.