2011/11/05 by Richard Herrmann · 1 citation
Computer Science · Mathematics · #Covariant derivative #Covariant transformation #Extension (predicate logic) #Fractional calculus #Generalization #Medical Image Segmentation Techniques #Numerical methods in inverse problems #Optical measurement and interference techniques #Order (exchange) #cs.CV
paper · pdf · doi:10.2478/s13540-012-0024-1
published in Fractional Calculus and Applied Analysis 15(2), 332-343 (Springer Science+Business Media) · 5 pages, 3 figures, draft for proceedings IFAC FDA12 in Nanjing, China
arxiv created 2011/11/05 · openalex publication_date 2012/03/17 · arxiv updated 2012/03/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.