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Coarse-to-Fine Minimization of Some Common Nonconvexities

  • Hossein Mobahi
  • John W. FisherIII
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8932)

Abstract

The continuation method is a popular heuristic in computer vision for nonconvex optimization. The idea is to start from a simplified problem and gradually deform it to the actual problem while tracking the solution. There are many choices for how to map the nonconvex objective to some convex task. One popular principle for such construction is Gaussian smoothing of the objective function. This involves an integration which may be expensive to compute numerically. We argue that often simple tricks at the problem formulation plus some mild approximations can make the resulted task amenable to closed form integral.

Keywords

Continuation Method Diffusion Equation Nonconvex Optimization Graduated Nonconvexity 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Hossein Mobahi
    • 1
  • John W. FisherIII
    • 1
  1. 1.Computer Science and Artificial Intelligence Lab. (CSAIL)Massachusetts Institute of Technology (MIT)USA

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