Fractional Calculus and Applied Analysis

, Volume 15, Issue 2, pp 332–343 | Cite as

Covariant fractional extension of the modified Laplace-operator used in 3D-shape recovery

  • Richard Herrmann
Survey Paper


Extending the Liouville-Caputo definition of a fractional derivative to a nonlocal covariant generalization of arbitrary bound operators acting on multidimensional Riemannian spaces an appropriate approach for the 3D shape recovery of aperture afflicted 2D slide sequences is proposed. We demonstrate, that the step from a local to a nonlocal algorithm yields an order of magnitude in accuracy and by using the specific fractional approach an additional factor 2 in accuracy of the derived results.

Key Words and Phrases

fractional calculus computer graphics image processing shape recovery confocal microscopy modified Laplacian 

MSC 2010

26A33 35R11 62H35 65D18 68U10 94A08 35J05 


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Copyright information

© © Versita Warsaw and Springer-Verlag Wien 2012

Authors and Affiliations

  1. 1.GigaHedronDreieichGermany

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