Robust Estimation for an Inverse Problem Arising in Multiview Geometry

Arnak S. Dalalyan (1, 2) , Renaud Keriven (1, 2)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge
2 imagine [Marne-la-Vallée]

We propose a new approach to the problem of robust estimation for an inverse problem 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 L1-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.

Mots clés: Structure from motion; Sparse recovery; Robust estimation; L1-relaxation

Domaines: Statistiques [math.ST]; Théorie [stat.TH]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Arnak S. Dalalyan, Renaud Keriven. Robust Estimation for an Inverse Problem Arising in Multiview Geometry. Journal of Mathematical Imaging and Vision, 2012, 43 (1), pp.10-23. ⟨10.1007/s10851-011-0281-3⟩. ⟨hal-00415603v2⟩