Energy minimization of contours using boundary conditions

Reconstruction of objects from a scene may be viewed as a data fitting problem using energy minimizing splines as the basic shape. The process of obtaining the minimum to construct the "best" shape can sometimes be important. Some of the potential problems in the Euler-Lagrangian variational solution proposed by Kass et al. (1988), were brought to light by Amini et al. (1990), and a dynamic programming (DP) method was also suggested. In this paper we further develop the DP solution. We show that in certain cases, the discrete form of the solution presented by Amini et al., and adopted subsequently by others may also produce local minima, and develop a strategy to avoid this. We provide a stronger form of the conditions necessary to derive a solution when the energy depends on the second derivative, as in the case of "active contours".