Improving a Constraint Programming Approach for Parameter Estimation

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. Calibration or geolocation can be viewed as specific parameter estimation problems. In this paper we address the problem of finding all the instances of a parametric model that can explain at least q observations within a given tolerance. 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. proposes a complete and combinatorial algorithm that exhaustively traverses the whole space of parameter vectors to extract the valid model instances. This algorithm is based on interval constraint programming methods and on a so called q-intersection operator, a relaxed intersection operator that assumes that at least q observed data are inliers. This paper proposes several improvements to Jaulin et al.' s algorithm. Most of them are generic and some others are dedicated to the shape detection problem used to validate our approach. Compared to Jaulin et al.' s algorithm, our algorithm can guarantee a number of fitted observations in the produced model instances. Also, first experiments in plane and circle recognition highlight speedups of two orders of magnitude.