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


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.

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Correspondence to Richard Herrmann.

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Herrmann, R. Covariant fractional extension of the modified Laplace-operator used in 3D-shape recovery. fcaa 15, 332–343 (2012).

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MSC 2010

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

Key Words and Phrases

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