Abstract To estimate the 6-DoF extrinsic pose of a pinhole camera with partially unknown intrinsic parameters is a critical sub-problem in structure-from-motion and camera localization. In most of existing camera pose estimation solvers, the principal point is assumed to be in the image center. Unfortunately, this assumption is not always true, especially for asymmetrically cropped images. In this paper, we develop the fifirst exactly minimal solver for the case of unknown principal point and focal length by using four and a half point correspondences (P4.5Pfuv). We also present an extremely fast solver for the case of unknown aspect ratio (P5Pfuva). The new solvers outperform the previous stateof-the-art in terms of stability and speed. Finally, we explore the extremely challenging case of both unknown principal point and radial distortion, and develop the fifirst practical non-minimal solver by using seven point correspondences (P7Pfruv). Experimental results on both simulated data and real Internet images demonstrate the usefulness of our new solvers.