In this work, we use points, lines, and the linear extremal contours of cylinders to estimate the position and orientation of the camera in the world coordinate system. Other line-based pose estimation methods use the correspondences between 3D lines in space and 2D image lines, although the model and its observation are nite line segments. We present a noise model describing the probabilistic relationship between 3D lines and cylinders and their noisy observations. The noise model takes the nite nature of the observation into account. Position and orientation of cameras are estimated using a maximum-likelihood approach. Covariance matrices, con dence limits, and standard translation and rotation errors are estimated by singular value decomposition of the Jacobian matrix. The method provides clear indications on the reliability of each of the estimated parameters, and enables the user to add appropriate information, in terms of feature correspondence, to improve the accuracy if necess...