We give two new, efficient solutions to the two-view, relative pose problem from three image point correspondences and one common reference direction. This three-plus-one problem can be used either as a substitute for the classic five-point algorithm using a vanishing point for the reference direction, or to make use of an inertial measurement unit (IMU) commonly available on robots and mobile devices, where the gravity vector becomes the reference direction. We provide a simple closed-form solution and a solution based on algebraic geometry (the action matrix method) and investigate numerical and computational advantages of each approach.

In practice, this algorithm can be used for outdoor, monocular visual odometry with 4-point hypothesis instead of usual 5 and without explicit vanishing point computation. Please see the paper for details.

This algorithm can be used in a purely visual odometry and vision-aided navigation settings.