Camera Pose Revisited -- New Linear Algorithms

Camera pose estimation is the problem of determining the position and orientation of an internally calibrated camera from known 3D reference points and their images. We briefly survey several existing methods for pose estimation, then introduce four new linear algorithms. The first three give a unique linear solution from four points by SVD null space estimation. They are based on resultant matrices: the 24×24 method is the raw resultant matrix, and the 12 × 12 and 9 × 9 methods are compressed versions of this obtained by Gaussian elimination with pivoting on constant entries. The final method returns the four intrinsic solutions to the pose from 3 points problem. It is based on eigendecomposition of a 5 × 5 matrix. One advantage of all these methods is that they are simple to implement. In particular, the matrix entries are simple functions of the input data. Numerical experiments are given comparing the performance of the new algorithms with several existing algebraic and linear methods.