Pose and Focal Length Estimation Using a Point and a Line With Known Camera Position

Abstract

2D-3D point or line correspondences are usually used to estimate the camera pose and intrinsic parameters, such as the focal length. There are many point-based methods and line-based methods, i.e., PnP solvers and PnL solvers. However, methods that use both point and line correspondences are not used widely. Hence, this paper proposed a new method to estimate the pose and focal length using a 2D-3D point correspondence and a 2D-3D line correspondence. In addition, the camera position is known as the prior knowledge to simplify the calculating process. In the world frame, the 3D point and camera position can determine a line, and the 2D projection of the 3D point and camera position can also determine a line in the camera frame. In fact, the two lines are the same line in space and their unit direction vectors can convert to each other using the rotation matrix from the world frame to the camera frame. In the world frame, the 3D line and camera position can determine a plane, and the 2D projection of the 3D line and camera position can also determine a plane in the camera frame. In fact, the two planes are the same plane in space and their unit normal vectors can also convert to each other using the rotation matrix from the world frame to the camera frame. Now there are two transformations of the direction vectors and the normal vectors. The transformations of vectors can be regarded as the transformations of 3D-3D point correspondences when the world frame and camera frame have the same origin. This is the key point in this paper and then the pose can be estimated efficiently. What’s more, the angle between the line passing through the 3D point and camera position, and the plane passing through the 3D line and camera position in the world frame, is equal to the angle between the line passing through the 2D projection of the 3D point and camera position, and the plane passing through the 2D projection of the 3D line and camera position in the camera frame. This is another key point to estimate the focal length. Experiments show our proposed method has good performance in numerical stability, noise sensitivity and computational speed with synthetic data and real scenarios. In addition, compared with other SOTA (state-of-the-art) methods, our method has a single solution and performs better.

Keywords

• Camera position
• direction vector
• focal length
• line correspondence
• normal vector
• point correspondence