An Interval Branch and Bound Algorithm for Parameter Estimation and Application to Stereovision

Abstract : The parameter estimation problem is a challenging problem in engineering sciences consisting in computing the parameters of a parametric model that fit observed data. The system is defined by unknown parameters and sometimes internal constraints. The observed data provide constraints on the parameters. The parameter estimation problem is particularly difficult when some observation constraints correspond to outliers and/or the constraints are non convex. For dealing with outliers, the RANSAC ran-domized algorithm is efficient, but non deterministic, and must be specialized for every problem. In this work, we propose a generic interval branch and bound algorithm that produces a model maximizing the number of observation constraints satisfied within a given tolerance. This tool is inspired by the IbexOpt Branch and Bound algorithm for constrained global optimization (NLP) and is endowed with an improved version of a relaxed intersection operator applied to the observations. The latest version of our B&B follows the Feasible diving strategy to visit the nodes in the search tree. Experiments on a stereovision problem have validated the approach.