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.

@Article{BMW09a,
  author       = {Brune, C. and Maurer, H. and Wagner, M.},
  title        = {Detection of Intensity and Motion Edges within Optical Flow via Multidimensional Control},
  journal      = {SIAM J. Imag. Sci.},
  number       = {4},
  volume       = {2},
  pages        = {1190-1210},
  month        = {november},
  year         = {2009},
  publisher    = {SIAM},
  doi          = {10.1137/080725064},
  url          = \{/2009/BMW09a},
}