Camera Relative Pose Estimation With Gravity Prior

Camera relative pose estimation,which is also called camera motion estimation,is one of the fundamental problems in computer vision and robotics.Existing methods mainly have two drawbacks: the large number of samples lead to large number of iterations,and finding the globally optimal relative pose is extremely difficult.A key observation is that,smartphones,tablets and camera systems used,e.g.,in cars and UAVs,are typically equipped with IMUs(inertial measurement units)that can measure the gravity vector accurately.Using this additional information,the y-axes of the cameras can be aligned,reducing their relative orientation to a single degree-of-freedom.With this assumption,we propose new efficient solutions,which achieve the state-of-the-art performance in terms of speed and accuracy,to relative pose estimation.The main contributions of this paper are:(1)We propose homography-based minimal solutions to relative pose estimation.In indoor and outdoor environments,planar parts of the scene are often dominant,such as floor,walls,doors,street or other general structures.However,recovering the focal length and camera motion from two views of a planar surface is a degenerate case for the standard methods.In this paper,we assume that the scene contains at least one plane,and propose new homography-based minimal solvers to calibrated and semi-calibrated relative pose estimation with known gravity direction.Our semi-calibrated solvers are the first ones which recover focal length from plane structure based on two views.(2)We propose minimal solutions to relative pose estimation with epipolar constraint.For general scenes with more application scenarios,relative pose estimation is more challenging.When the focal length is unknown,standard methods have some de-generate configurations,such as pure translation,arbitrary planar motions when the optical axes lie in the plane and so on.In this paper,we propose three new efficient solutions to relative pose estimation with epipolar constraint.We focus on three practical camera configurations,calibrated case,the focal length is unknown and fixed,the focal lengths are different and unknown.Compared with standard methods,our methods significantly improve the speed and accuracy.(3)We propose the first globally optimal relative pose estimation with known gravity direction.Due to the non-linearity of the rotation matrix,finding the globally opti-mal solution to relative pose estimation is still an open problem.Existing methods either rely on the non-linear refinement or some mathematical optimization toolbox.Such methods mainly have two drawbacks: first,the non-linear refinement relies on good initial values and could not give certifiably global optimization;second,there are time consuming and could not achieve real-time applications.To deal with these drawbacks,we propose globally optimal relative pose estimation with gravity prior,which only needs to solve a system of two polynomials with two unknowns.Fur-ther,we propose a simple using the first-order Taylor approximation of the rotation matrix.Both the two methods achieve the state-of-the-art performance.(4)Relative pose estimation problems can be converted into solving a system of poly-nomial equations.we propose a simple and general technique to find complete algebraic constraints so that we can derive efficient algorithms.We show that using the quaternion to formulate the rotation matrix we can eliminate any unknowns from the original equations and obtain constraints on the rest of the unknowns based on Gr(?)bner basis.Based on these constraints,we propose transposed polynomial eigenvalue solution which achieves the state-of-the-art performance.