Improving a Constraint Programming Approach for Parameter Estimation

The parameter estimation problem is awidespread and challenging problem in engineering sciencesconsisting in computing the parameters of a parametricmodel that fit observed data. Calibration or geolocation canbe viewed as specific parameter estimation problems. In thispaper we address the problem of finding all the instances ofa parametric model that can explain at least q observationswithin a given tolerance. The computer vision communityhas proposed the RANSAC algorithm to deal with outliersin the observed data. This randomized algorithm is efficientbut non-deterministic and therefore incomplete. Jaulin etal. proposes a complete and combinatorial algorithm thatexhaustively traverses the whole space of parameter vectors toextract the valid model instances. This algorithm is based oninterval constraint programming methods and on a so calledq-intersection operator, a relaxed intersection operator thatassumes that at least q observed data are inliers. This paperproposes several improvements to Jaulin et al.'s algorithm.Most of them are generic and some others are dedicated tothe shape detection problem used to validate our approach.Compared to Jaulin et al.'s algorithm, our algorithm canguarantee a number of fitted observations in the producedmodel instances. Also, first experiments in plane and circlerecognition highlight speedups of two orders of magnitude.