FWF - Glatth v nl Unterteilung - Smoothness of nonlinear subdivision algorithms

  • Nava Yazdani, Esfandiar, (Co-Investigator (CoI))
  • Wallner, Johannes (Principal Investigator (PI))

Project: Research project

Project Details

Description

This project has been funded by the Austrian Science Fund (FWF) under grant No. P-18575, supporting the work of Philipp Grohs and Esfandiar Nava Yazdani at both TU Wien and TU Graz in the years 2006-2007. A successor of this research project is Multivariate Subdivision Processes.
Curve subdivision schemes on manifolds and in Lie groups are constructed from linear subdivision schemes by first representing the rules of affinely invariant linear schemes in terms of repeated affine averages, and then replacing the operation of affine average either by a geodesic average (in the Riemannian sense or in a certain Lie group sense), or by projection of the affine averages onto a surface. Other ways of defining subdivision for manifold-valued data is via D. Donoho's log/exp analogy. The analysis of these schemes is based on their proximity to the linear schemes which they are derived from.

Apart from the nonlinearities entailed by the underlaying geometry, subdivision schemes are perturbed by discretization and incomplete computing. Even with such errors present we can stay within the realm of smooth limits.
StatusFinished
Effective start/end date1/01/0631/12/08