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

TL;DR

This paper introduces a covariant fractional extension of the modified Laplace operator, significantly improving 3D shape recovery accuracy from 2D slide sequences by leveraging nonlocal fractional derivatives on Riemannian spaces.

Contribution

It proposes a novel nonlocal covariant fractional Laplace operator for 3D shape recovery, enhancing accuracy over traditional local methods.

Findings

Order of magnitude improvement in accuracy with nonlocal algorithm

Additional factor of 2 accuracy using fractional approach

Effective application to aperture-affected 2D slide sequences

Abstract

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.