We are concerned with the problem of computing the pose of a (so-called query) camera, from the sole contour of a circular marker in a single view, assuming that we have at one's disposal a set of reference views seeing circular markers, from which the full camera pose and calibration have been precisely estimated. In the calibrated case, regarding the query image alone, there is also a twofold ambiguity in the pose as well as an unknown rotation in the supporting plane of the marker that cannot be fixed. The key idea of this paper is to show that with the additional information of one pair of matched points in both query and reference views, an exact solution for the query pose can be obtained. In order to answer the question whether a given reference view corresponds to the query view, another pair of matched points in both views is then necessary. With multiple matched point pairs, it is possible to deploy a RANSAC-based scheme to assess accurately the best configuration while maintaining robustness to mismatched point pairs. This method shows some promising results especially when the set of point correspondences contains a lot of outliers (erroneous matches).