Journal of Mathematical Imaging and Vision

, Volume 30, Issue 1, pp 105–123 | Cite as

Sampling and Reconstruction of Surfaces and Higher Dimensional Manifolds

Article

Abstract

We present new sampling theorems for surfaces and higher dimensional manifolds. The core of the proofs resides in triangulation results for manifolds with boundary, not necessarily bounded. The method is based upon geometric considerations that are further augmented for 2-dimensional manifolds (i.e surfaces). In addition, we show how to apply the main results to obtain a new, geometric proof of the classical Shannon sampling theorem, and also to image analysis.

Keywords

Image sampling Image reconstruction Geometric approach Fat triangulation Image manifolds 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Emil Saucan
    • 1
  • Eli Appleboim
    • 1
  • Yehoshua Y. Zeevi
    • 1
  1. 1.Department of Electrical EngineeringTechnionHaifaIsrael

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