Global minimization of Markov random fields with applications to optical flow

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

8 Scopus Citations
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Author(s)

  • Tom Goldstein
  • Xavier Bresson
  • Stan Osher

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)623-644
Journal / PublicationInverse Problems and Imaging
Volume6
Issue number4
Publication statusPublished - Nov 2012

Abstract

Many problems in image processing can be posed as non-convex minimization problems. For certain classes of non-convex problems involving scalar-valued functions, it is possible to recast the problem in a convex form using a "functional lifting" technique. In this paper, we present a variational functional lifting technique that can be viewed as a generalization of previous works by Pock et. al and Ishikawa. We then generalize this technique to the case of minimization over vector-valued problems, and discuss a condition which allows us to determine when the solution to the convex problem corresponds to a global minimizer. This generalization allows functional lifting to be applied to a wider range of problems then previously considered. Finally, we present a numerical method for solving the convexified problems, and apply the technique to find global minimizers for optical flow image registration. © 2012 American Institute of Mathematical Sciences.

Research Area(s)

  • Functional lifting, Nonconvex optimization, Optical flow

Citation Format(s)

Global minimization of Markov random fields with applications to optical flow. / Goldstein, Tom; Bresson, Xavier; Osher, Stan.

In: Inverse Problems and Imaging, Vol. 6, No. 4, 11.2012, p. 623-644.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal