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Euler's elastica energy (the mean squared acceleration) of parameterized curves may serve as a regularization for fitting or approximating temporal data. We study the case of data in a Riemannian manifold, as is relevant for various applications such as keyframe interpolation in computer graphics or interpolation in the space of images, equipped with an appropriate Riemannian metric. The analysis of the energy and its discretization hold some surprises fundamentally different from the Euclidean setting.
This presentation is part of Minisymposium “MS31 - Variational Approaches for Regularizing Nonlinear Geometric Data (3 parts)”
organized by: Martin Storath (Universität Heidelberg) , Martin Holler (École Polytechnique, Université Paris Saclay) , Andreas Weinmann (Hochschule Darmstadt) .