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Robust Estimation for an Inverse Problem Arising in Multiview Geometry

  • Arnak Dalalyan
  • Renaud Keriven
Article

Abstract

We propose a new approach to the problem of robust estimation for a class of inverse problems arising in multiview geometry. Inspired by recent advances in the statistical theory of recovering sparse vectors, we define our estimator as a Bayesian maximum a posteriori with multivariate Laplace prior on the vector describing the outliers. This leads to an estimator in which the fidelity to the data is measured by the L -norm while the regularization is done by the L 1-norm. The proposed procedure is fairly fast since the outlier removal is done by solving one linear program (LP). An important difference compared to existing algorithms is that for our estimator it is not necessary to specify neither the number nor the proportion of the outliers; only an upper bound on the maximal measurement error for the inliers should be specified. We present theoretical results assessing the accuracy of our procedure, as well as numerical examples illustrating its efficiency on synthetic and real data.

Keywords

Structure from motion Sparse recovery Robust estimation L1-relaxation 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Université Paris Est, IMAGINEEcole des Ponts ParisTechMarne-la-ValléeFrance

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