Multi-view 3D circular target reconstruction with uncertainty analysis

Abstract. The paper presents an algorithm for reconstruction of 3D circle from its apparition in n images. It supposes that camera poses are known up to an uncertainty. They will be considered as observations and will be refined during the reconstruction process. First, circle apparitions will be estimated in every individual image from a set of 2D points using a constrained optimization. Uncertainty of 2D points are propagated in 2D ellipse estimation and leads to covariance matrix of ellipse parameters. In 3D reconstruction process ellipse and camera pose parameters are considered as observations with known covariances. A minimal parametrization of 3D circle enables to model the projection of circle in image without any constraint. The reconstruction is performed by minimizing the length of observation residuals vector in a non linear Gauss-Helmert model. The output consists in parameters of the corresponding circle in 3D and their covariances. The results are presented on simulated data.