User menu

Fast Method to Fit a C1 Piecewise-Bézier Function to Manifold-Valued Data Points: How Suboptimal is the Curve Obtained on the Sphere S2?

Bibliographic reference Gousenbourger, Pierre-Yves ; Jacques, Laurent ; Absil, Pierre-Antoine. Fast Method to Fit a C1 Piecewise-Bézier Function to Manifold-Valued Data Points: How Suboptimal is the Curve Obtained on the Sphere S2?.Geometric Science of Information (Paris, du 07/11/2017 au 09/11/2017). In: Nielsen F., Barbaresco F., Geometric Science of Information. GSI 2017. Lecture Notes in Computer Science, Springer International2017
Permanent URL
  1. Absil P.-A., Gousenbourger Pierre-Yves, Striewski Paul, Wirth Benedikt, Differentiable Piecewise-Bézier Surfaces on Riemannian Manifolds, 10.1137/16m1057978
  2. Arnould Antoine, Gousenbourger Pierre-Yves, Samir Chafik, Absil Pierre-Antoine, Canis Michel, Fitting Smooth Paths on Riemannian Manifolds: Endometrial Surface Reconstruction and Preoperative MRI-Based Navigation, Lecture Notes in Computer Science (2015) ISBN:9783319250397 p.491-498, 10.1007/978-3-319-25040-3_53
  3. Bergmann Ronny, Laus Friederike, Steidl Gabriele, Weinmann Andreas, Second Order Differences of Cyclic Data and Applications in Variational Denoising, 10.1137/140969993
  4. Boumal Nicolas, Interpolation and Regression of Rotation Matrices, Lecture Notes in Computer Science (2013) ISBN:9783642400193 p.345-352, 10.1007/978-3-642-40020-9_37
  5. Boumal, N., Mishra, B., Absil, P.A., Sepulchre, R.: Manopt, a matlab toolbox for optimization on manifolds. J. Mach. Learn. Res. 15, 1455–1459 (2014).
  6. Farin, G.: Curves and Surfaces for CAGD, 5th edn. Academic Press, New York (2002)
  7. Gousenbourger, P.Y., Massart, E., Musolas, A., Absil, P.A., Jacques, L., Hendrickx, J.M., Marzouk, Y.: Piecewise-Bézier $$C^1$$ smoothing on manifolds with application to wind field estimation. In: ESANN2017, to appear (2017)
  8. Machado L., Monteiro M. Teresa T., A numerical optimization approach to generate smoothing spherical splines, 10.1016/j.geomphys.2016.10.007
  9. Popiel Tomasz, Noakes Lyle, Bézier curves and C2 interpolation in Riemannian manifolds, 10.1016/j.jat.2007.03.002
  10. Pyta Lorenz, Abel Dirk, Interpolatory Galerkin Models for the Navier-Stokes-Equations, 10.1016/j.ifacol.2016.07.442
  11. Samir Chafik, Absil P.-A., Srivastava Anuj, Klassen Eric, A Gradient-Descent Method for Curve Fitting on Riemannian Manifolds, 10.1007/s10208-011-9091-7
  12. Sanguinetti Gonzalo, Bekkers Erik, Duits Remco, Janssen Michiel H. J., Mashtakov Alexey, Mirebeau Jean-Marie, Sub-Riemannian Fast Marching in SE(2), Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications (2015) ISBN:9783319257501 p.366-374, 10.1007/978-3-319-25751-8_44
  13. Su J., Dryden I.L., Klassen E., Le H., Srivastava A., Fitting smoothing splines to time-indexed, noisy points on nonlinear manifolds, 10.1016/j.imavis.2011.09.006