Cet article présente un nouvel algorithme EM (Expectation-Maximization) pour le recalage robuste de nuages de points 2D–3D issus d’une caméra et d’une carte de référence. Nous nous intéressons à l’estimation conjointe des paramètres d’intérêt (i.e., orientation et position de la caméra), de la proportion d’observations aberrantes et de la variance du bruit de mesure. L’approche proposée repose sur un modèle statistique intégrant des variables latentes permettant de gérer les associations inconnues entre points 2D, points 3D et observations aberrantes, via un modèle de mélange. Des résultats obtenus à partir de données synthétiques montrent l’intérêt de cette démarche en termes de rapidité de convergence de l’algorithme proposé et de robustesse face aux mesures aberrantes.

This work studies a new Expectation-Maximization (EM) algorithm for solving the 2D-3D registration problem, which consists of estimating the position and orientation of a camera using a 3D map and a 2D image of the same scene. This algorithm associates each image feature coordinate to one vector of the 3D map using the pinhole camera model or to a class of outliers, making the registration robust to the presence of abnormal image features. It iteratively improves the camera pose by estimating the associations between the image features and the 3D map coordinates (using a robust mixture model) and minimizing the reprojection errors between the image and map points. Experimental results demonstrate that the proposed EM algorithm achieves competitive results in both absolute position and orientation compared to the Iterative Closest Point (ICP) approach.

This paper studies a robust algorithm allowing the estimation of the center and the radius of a hypersphere in the presence of outliers. To that extend, the Student-t distribution is assigned to the noise samples to mitigate the impact of the outliers. A von Mises-Fisher prior distribution is also assigned to latent variables in order to exploit the fact that the observed samples are located in a part of the hypersphere. A robust Bayesian algorithm based on a Gibbs sampler is then proposed to solve the hypersphere fitting problem. This algorithm generates samples asymptotically distributed according to the joint distribution of the unknown parameters of the hypersphere (radius and center), as well as the other model parameters such as the noise variance. Simulations conducted on synthetic data with controlled ground truth allow the performance of this algorithm to be appreciated.