  Two-view relative pose estimation and structure reconstruction is a classical
problem in computer vision. The typical methods usually employ the singular
value decomposition of the essential matrix to get multiple solutions of the
relative pose, from which the right solution is picked out by reconstructing
the three-dimension (3D) feature points and imposing the constraint of positive
depth. This paper revisits the two-view geometry problem and discovers that the
two-view imaging geometry is equivalently governed by a Pair of new Pose-Only
(PPO) constraints: the same-side constraint and the intersection constraint.
From the perspective of solving equation, the complete pose solutions of the
essential matrix are explicitly derived and we rigorously prove that the
orientation part of the pose can still be recovered in the case of pure
rotation. The PPO constraints are simplified and formulated in the form of
inequalities to directly identify the right pose solution with no need of 3D
reconstruction and the 3D reconstruction can be analytically achieved from the
identified right pose. Furthermore, the intersection inequality also enables a
robust criterion for pure rotation identification. Experiment results validate
the correctness of analyses and the robustness of the derived pose
solution/pure rotation identification and analytical 3D reconstruction.
