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Globally Optimal Least Squares Solutions for Quasiconvex 1D Vision Problems

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Author

Summary, in English

Solutions to non-linear least squares problems play an essential role in structure and motion problems in computer vision. The predominant approach for solving these problems is a Newton like scheme which uses the: hessian of the function to iteratively find a, local solution. Although fast, this strategy inevitably leeds to issues with poor local minima, and missed global minima. In this paper rather than trying to develop all algorithm that is guaranteed to always work, we show that it is often possible to verify that a local solution is in fact; also global. We present a simple test that verifies optimality of a solution using only a few linear programs. We show oil both synthetic and real data that for the vast majority of cases we are able to verify optimality. Further more we show even if the above test fails it is still often possible to verify that the local solution is global with high probability.

Publishing year

2009

Language

English

Pages

686-695

Publication/Series

Image Analysis, Proceedings

Volume

5575

Document type

Conference paper

Publisher

Springer

Topic

  • Mathematics

Conference name

16th Scandinavian Conference on Image Analysis

Conference date

2009-06-15 - 2009-06-18

Conference place

Oslo, Norway

Status

Published

ISBN/ISSN/Other

  • ISSN: 1611-3349
  • ISSN: 0302-9743