An Interval Branch and Bound Algorithm for Parameter Estimation

Bertrand Neveu (1, 2, 3) , Martin de La Gorce (2, 1, 3) , Gilles Trombettoni (4)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge
2 ENPC - École des Ponts ParisTech
3 imagine [Marne-la-Vallée]
4 COCONUT - Agents, Apprentissage, Contraintes

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).

Mots clés: Interval branch and bound; Shape detection; Parameter estimation

Domaines: Recherche opérationnelle [math.OC]

Bertrand Neveu, Martin de La Gorce, Gilles Trombettoni. An Interval Branch and Bound Algorithm for Parameter Estimation. GOW: Globla Optimization Workshop, Sep 2016, Braga, Portugal. ⟨hal-01376601⟩