In this article, we address the pose estimation for planar motion under the framework of generalized camera models. We assume the knowledge of the coordinates of 3D straight lines in the world coordinate system. Pose is estimated using the images of the 3D lines. This approach does not require the determination of correspondences between pixels and 3D world points. Instead, and for each pixel, it is only required that we determine to which 3D line it is associated with. Instead of identifying individual pixels, it is only necessary to establish correspondences between the pixels that belong to the images of the 3D lines, and the 3D lines. Moreover and using the assumption that the motion is planar, this paper presents a novel method for the computation of the pose using general imaging devices and assuming the knowledge of the coordinates of 3D straight lines. The approach is evaluated and validated using both synthetic data and real images. The experiments are performed using a mobile robot equipped with a non-central camera.