Paper ID sheet UCL-INMA-2014.10


Piecewise-Bezier C1 interpolation on Riemannian manifolds with application to 2D shape morphing

Pierre-Yves Gousenbourger, Chafik Samir, P.-A. Absil
We present a new framework to fit a path to a given finite set of data points on a Riemannian manifold. The path takes the form of a continuously-differentiable concatenation of Riemannian Bezier segments. The selection of the control points that define the Bezier segments is partly guided by the differentiability requirement and by a minimal mean squared acceleration objective. We illustrate our approach on specific manifolds: the Euclidean plane (for sanity check), the sphere (as a first nonlinear illustration), the special orthogonal group (with rigid body motion applications), and the shape manifold (with 2D shape morphing applications).
Key words
shape modeling and encoding; motion, tracking and video analysis
Proceedings ICPR 2014