Interpolations with Elasticae in Euclidean Spaces   (W. Mio, A. Srivastava and E. Klassen)

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.