Interpolations with elasticae in Euclidean spaces

Authors:
W. Mio, A. Srivastava and E. Klassen

Journal:
Quart. Appl. Math. **62** (2004), 359-378

MSC:
Primary 41A05; Secondary 58E10, 65D05, 68U10, 94A08

DOI:
https://doi.org/10.1090/qam/2054604

MathSciNet review:
MR2054604

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Abstract: Motivated by interpolation problems arising in image analysis, computer vision, shape reconstruction, and signal processing, we develop an algorithm to simulate curve straightening flows under which curves in of fixed length and prescribed boundary conditions to first order evolve to *elasticae*, i.e., to (stable) critical points of the elastic energy given by the integral of the square of the curvature function. We also consider variations in which the length is allowed to vary and the flows seek to minimize the scale-invariant elastic energy , or the free elastic energy . is given by the product of and the elastic energy , and is the energy functional obtained by adding a term -proportional to the length of the curve to . Details of the implementations, experimental results, and applications to edge completion problems are also discussed.

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DOI:
https://doi.org/10.1090/qam/2054604

Article copyright:
© Copyright 2004
American Mathematical Society