title: Simultaneous optical flow and source estimation: Space-time discretization and preconditioning.
abstract: We consider the simultaneous estimation of an optical flow field and an illumination source term in a movie sequence. The particular optical flow equation is obtained by assuming that the image intensity is a conserved quantity up to possible sources and sinks which represent varying illumination. We formulate this problem as an energy minimization problem and propose a space-time simultaneous discretization for the optimality system in saddle-point form. We investigate a preconditioning strategy that renders the discrete system well-conditioned uniformly in the discretization resolution. Numerical experiments complement the theory.
authors.affiliation: RICAM, Austrian Academy of Sciences, Altenberger Str. 69, 4040 Linz, Austria.
authors.forename: R
authors.initials: R
authors.lastname: Andreev
authors.affiliation: RICAM, Austrian Academy of Sciences, Altenberger Str. 69, 4040 Linz, Austria ; Computational Science Center, University of Vienna, Oskar-Morgenstern Platz 1, 1090 Wien, Austria.
authors.forename: O
authors.initials: O
authors.lastname: Scherzer
authors.affiliation: Institute of Computational Mathematics, Johannes Kepler University, Altenberger Str. 69, 4040 Linz, Austria.
authors.forename: W
authors.initials: W
authors.lastname: Zulehner
keywords: Discretization; Linear-quadratic control; Optical flow; Preconditioning; Saddle-point; Space–time