Interpolations with elasticae in Euclidean spaces
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In this paper, the authors develop an algorithm to simulate curve straightening flows under which curves in Rra 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.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 Rra of fixed length and prescribed boundary conditions to first order evolve to elasticae, i.e., to (stable) 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 Einv, or the free elastic energy E\\. Einv is given by the product of L and the elastic energy E, and Ex is the energy functional obtained by adding a term A-proportional to the length of the curve to E. Details of the implementations, experimental results, and applications to edge completion problems are also discussed.read more
Citations
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References
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Journal ArticleDOI
Nonlinear dimensionality reduction by locally linear embedding.
Sam T. Roweis,Lawrence K. Saul +1 more
TL;DR: Locally linear embedding (LLE) is introduced, an unsupervised learning algorithm that computes low-dimensional, neighborhood-preserving embeddings of high-dimensional inputs that learns the global structure of nonlinear manifolds.
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Elastica and Computer Vision
TL;DR: In this article, the authors discuss the problem from differential geometry of describing those plane curves C which minimize the integral integral integral (α k^2 + β + β )d.