Motivated by interpolation problems arising in applications to image
analysis, computer vision, shape reconstruction and signal processing, we
develop an algorithm to simulate curve straightening flows under which
curves in R^n of fixed length and prescribed boundary conditions to first
order evolve to elasticae, i.e., to critical points of the elastic energy E
given by the integral of the square of the curvature function.
We also consider variations in which the length L is allowed to vary and the
flows seek to minimize the scale-invariant elastic energy, or the free
elastic energy. Details
of the implementations, experimental results, and applications to
contour interpolation problems are also discussed.