Abstract : The parameter estimation problem is a widespread and challenging problem in engineering sciences consisting in computing the parameters of a parametric model that fit observed data. The computer vision community has proposed the RANSAC algorithm to deal with outliers in the observed data. This randomized algorithm is efficient but non-deterministic and therefore incomplete. Jaulin et al. propose a branch-and-contract algorithm that returns all the model instances fitting at least q observations. Assuming that at least q observed data are inliers, this algorithm achieves on the observations a relaxed intersection operator called q-intersection. First, this paper presents several improvements to Jaulin et al.'s algorithm. Second, an interval branch and bound algorithm is designed to produce a model that can explain the maximum number of observations within a given tolerance. Experiments are carried out on computer vision and image processing problems. They highlight a significant speedup w.r.t. Jaulin et al.'s interval method in 2D and 3D shape recognition problems. We have also investigated how the approach scales up in dimensions up to 7 for stereovision (estimation of essential and fundamental matrices).
https://hal-enpc.archives-ouvertes.fr/hal-01376601
Contributeur : Bertrand Neveu
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Soumis le : mercredi 5 octobre 2016 - 12:22:58
Dernière modification le : mercredi 30 mai 2018 - 17:22:02
Document(s) archivé(s) le : vendredi 6 janvier 2017 - 13:22:43
Bertrand Neveu, Martin De La Gorce, Gilles Trombettoni. An Interval Branch and Bound Algorithm for Parameter Estimation. GOW'16 XIII Globla Optimization Workshop, Sep 2016, Braga, Portugal. 〈hal-01376601〉
