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Titel: On the application of projection methods for computing optical flow fields
Verfasser: Schuster, Thomas
Weickert, Joachim
Sprache: Englisch
Erscheinungsjahr: 2007
Freie Schlagwörter: optical flow
variational methods
projection methods
tensor product B-spline
DDC-Sachgruppe: 510 Mathematik
Dokumentart : Preprint (Vorabdruck)
Kurzfassung: Detecting optical flow means to find the apparent displacement field in a sequence of images. As starting point for many optical flow methods serves the so called optical flow constraint (OFC), that is the assumption that the gray value of a moving point does not change over time. Variational methods are amongst the most popular tools to compute the optical flow field. They compute the flow field as minimizer of an energy functional that consists of a data term to comply with the OFC and a smoothness term to obtain uniqueness of this underdetermined problem. In this article we replace the smoothness term by projecting the solution to a finite dimensional, affine subspace in the spatial variables which leads to a smoothing and gives a unique solution as well. We explain the mathematical details for the quadratic and nonquadratic minimization framework, and show how alternative model assumptions such as constancy of the brightness gradient can be incorporated. As basis functions we consider tensor products of B-splines. Under certain smoothness assumptions for the global minimizer in Sobolev scales, we prove optimal convergence rates in terms of the energy functional. Experiments are presented that demonstrate the feasibility of our approach.
Link zu diesem Datensatz: urn:nbn:de:bsz:291-scidok-47246
hdl:20.500.11880/26412
http://dx.doi.org/10.22028/D291-26356
Schriftenreihe: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Band: 194
SciDok-Publikation: 15-Mär-2012
Fakultät: Fakultät 6 - Naturwissenschaftlich-Technische Fakultät I
Fachrichtung: MI - Mathematik
Fakultät / Institution:MI - Fakultät für Mathematik und Informatik

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