Energy Minimization of Contours using Boundary Conditions
Abstract:
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 in the original formulation [1],
were brought to light in [2],
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 in [2],
and adopted subsequently [3,4,5,6]
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.''
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