A global approach to the refinement of manifold data

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Abstract

A refinement of manifold data is a computational process, which produces a denser set of discrete data from a given one. Such refinements are closely related to multiresolution representations of manifold data by pyramid transforms, and approximation of manifold-valued functions by repeated refinements schemes. Most refinement methods compute each refined element separately, independently of the computations of the other elements. Here we propose a global method which computes all the refined elements simultaneously, using geodesic averages. We analyse repeated refinements schemes based on this global approach, and derive conditions guaranteeing strong convergence.

Original languageEnglish
Pages (from-to)375-395
Number of pages21
JournalMathematics of Computation
Volume86
Issue number303
DOIs
StatePublished - Jan 2017

Keywords

  • Convergence analysis
  • Geodesic average
  • Manifold data

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