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Maximum Consensus Parameter Estimation by Reweighted \(\ell _1\) Methods

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Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR 2017)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10746))

Abstract

Robust parameter estimation in computer vision is frequently accomplished by solving the maximum consensus (MaxCon) problem. Widely used randomized methods for MaxCon, however, can only produce random approximate solutions, while global methods are too slow to exercise on realistic problem sizes. Here we analyse MaxCon as iterative reweighted algorithms on the data residuals. We propose a smooth surrogate function, the minimization of which leads to an extremely simple iteratively reweighted algorithm for MaxCon. We show that our algorithm is very efficient and in many cases, yields the global solution. This makes it an attractive alternative for randomized methods and global optimizers. The convergence analysis of our method and its fundamental differences from the other iteratively reweighted methods are also presented.

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Notes

  1. 1.

    Since \(\mathbf {s}^{(l)}\) is only used to compute the weights \(\mathbf {w}^{(l+1)}\) in the next iteration, an approximate solution, which still minimizes the objective, is sufficient to initialize \(\mathbf {s}^{(l+1)}\).

  2. 2.

    http://pulakpurkait.com/Data/astar_cvpr15_code.zip.

  3. 3.

    http://statweb.stanford.edu/~candes/l1magic/.

  4. 4.

    http://cvxr.com/cvx/.

  5. 5.

    http://www.robots.ox.ac.uk/~vgg/data/.

  6. 6.

    http://www.vlfeat.org.

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Authors and Affiliations

  1. Toshiba Research Europe, Cambridge, UK

    Pulak Purkait & Christopher Zach

  2. Queensland University of Technology, Brisbane, Australia

    Anders Eriksson

Authors
  1. Pulak Purkait
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  2. Christopher Zach
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  3. Anders Eriksson
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Corresponding author

Correspondence to Pulak Purkait .

Editor information

Editors and Affiliations

  1. Ca’ Foscari University of Venice, Venice, Italy

    Marcello Pelillo

  2. University of York, York, United Kingdom

    Edwin Hancock

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Purkait, P., Zach, C., Eriksson, A. (2018). Maximum Consensus Parameter Estimation by Reweighted \(\ell _1\) Methods. In: Pelillo, M., Hancock, E. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 2017. Lecture Notes in Computer Science(), vol 10746. Springer, Cham. https://doi.org/10.1007/978-3-319-78199-0_21

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  • DOI: https://doi.org/10.1007/978-3-319-78199-0_21

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