Fast method to fit a C1 piecewise-Bézier function to manifold-valued data points: how suboptimal is the curve obtained on the sphere S2?

07/11/2017
Publication GSI2017
OAI : oai:www.see.asso.fr:17410:22522
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We propose an analysis of the quality of the tting method proposed in [7]. This method ts smooth paths to manifold-valued data points using C1 piecewise-Bezier functions. This method is based on the principle of minimizing an objective function composed of a data-attachment term and a regularization term chosen as the mean squared acceleration of the path. However, the method strikes a tradeo between speed and accuracy by following a strategy that is guaranteed to yield the optimal curve only when the manifold is linear. In this paper, we focus on the sphere S2. We compare the quality of the path returned by the algorithms from [7] with the path obtained by minimizing, over the same search space of C1 piecewise-Bezier curves, a nite-di erence approximation of the objective function by means of a derivative-free manifold-based optimization method.

Fast method to fit a C1 piecewise-Bézier function to manifold-valued data points: how suboptimal is the curve obtained on the sphere S2?

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application/pdf Fast method to fit a C1 piecewise-Bézier function to manifold-valued data points: how suboptimal is the curve obtained on the sphere S2? Pierre-Yves Gousenbourger, Laurent Jacques, Pierre-Antoine Absil
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contenu protégé  Document accessible sous conditions - vous devez vous connecter ou vous enregistrer pour accéder à ou acquérir ce document.
- Accès libre pour les ayants-droit

We propose an analysis of the quality of the tting method proposed in [7]. This method ts smooth paths to manifold-valued data points using C1 piecewise-Bezier functions. This method is based on the principle of minimizing an objective function composed of a data-attachment term and a regularization term chosen as the mean squared acceleration of the path. However, the method strikes a tradeo between speed and accuracy by following a strategy that is guaranteed to yield the optimal curve only when the manifold is linear. In this paper, we focus on the sphere S2. We compare the quality of the path returned by the algorithms from [7] with the path obtained by minimizing, over the same search space of C1 piecewise-Bezier curves, a nite-di erence approximation of the objective function by means of a derivative-free manifold-based optimization method.
Fast method to fit a C1 piecewise-Bézier function to manifold-valued data points: how suboptimal is the curve obtained on the sphere S2?
application/pdf Fast method to fit a C1 piecewise-Bézier function to manifold-valued data points: how suboptimal is the curve obtained on the sphere S2? (slides)

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            <title>Fast method to fit a C1 piecewise-Bézier function to manifold-valued data points: how suboptimal is the curve obtained on the sphere S2?</title></titles>
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        <publicationYear>2018</publicationYear>
        <resourceType resourceTypeGeneral="Text">Text</resourceType><subjects><subject>Optimization on manifolds</subject><subject>Bézier functions</subject><subject>Path fitting on Riemannian manifolds</subject></subjects><dates>
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