Pose and Focal Length Estimation Using Two Vanishing Points with Known Camera Position

Abstract

This paper proposes a new pose and focal length estimation method using two vanishing points and a known camera position. A vanishing point can determine the unit direction vector of the corresponding parallel lines in the camera frame, and as input, the unit direction vector of the corresponding parallel lines in the world frame is also known. Hence, the two units of direction vectors in camera and world frames, respectively, can be transformed into each other only through the rotation matrix that contains all the information of the camera pose. Then, two transformations can be obtained because there are two vanishing points. The two transformations of the unit direction vectors can be regarded as transformations of 3D points whose coordinates are the values of the corresponding unit direction vectors. The key point in this paper is that our problem with vanishing points is converted to rigid body transformation with 3D–3D point correspondences, which is the usual form in the PnP (perspective-n-point) problem. Additionally, this point simplifies our problem of pose estimation. In addition, in the camera frame, the camera position and two vanishing points can form two lines, respectively, and the angle between the two lines is equal to the angle between the corresponding two sets of parallel lines in the world frame. When using this geometric constraint, the focal length can be estimated quickly. The solutions of pose and focal length are both unique. The experiments show that our proposed method has good performances in numerical stability, noise sensitivity and computational speed with synthetic data and real scenarios and also has strong robustness to camera position noise.