Jaap Eldering

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  A distance on curves using orthogonal transformations
  Jaap Eldering

  We construct a geometric method to directly quantify the difference between curves. That is, we construct a distance for parametrized curves in R^n modulo Euclidean transformations. This distance measures the local dissimilarity of k-jets (Taylor polynomials) of the curves. The distance is obtained from a variational principle, and can be constructed by solving a boundary value problem for a second-order ODE. As such it may prove to be computationally less expensive than EPdiff methods if one is only interested in a distance measure.