Detection of intensity and motion edges within optical flow via multidimensional control

Christoph Brune, Helmut Maurer, Marcus Wagner*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

14 Citations (Scopus)
12 Downloads (Pure)


In this paper, we propose a new optimization approach for the simultaneous computation of optical flow and edge detection therein. Instead of using an Ambrosio-Tortorelli type energy functional, we reformulate the optical flow problem as a multidimensional control problem. The optimal control problem is solved by discretization methods and large-scale optimization techniques. The edge detector can be immediately built from the control variables. We provide three series of numerical examples. The first shows that the mere presence of a gradient restriction has a regularizing effect, while the second demonstrates how to balance the regularizing effects of a term within the objective and the control restriction. The third series of numerical results is concerned with the direct evaluation of a TV-regularization term by introduction of control variables with sign restrictions.

Original languageEnglish
Pages (from-to)1190-1210
Number of pages21
JournalSIAM journal on imaging sciences
Issue number4
Publication statusPublished - 1 Jan 2009
Externally publishedYes


  • Direct methods
  • Edge detection
  • Optical flow
  • Optimal control problem
  • Partial differential equation constrained optimization


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