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.

中文翻译：

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双视图几何的等效约束：姿态解/纯旋转识别和 3D 重建

双视图相对姿态估计和结构重建是计算机视觉中的经典问题。典型的方法通常采用本质矩阵的奇异值分解来获得相对位姿的多个解，通过重构三维（3D）特征点并施加正深度约束从中选出正确的解。本文重新审视了双视图几何问题，发现双视图成像几何等效地由一对新的仅姿态 (PPO) 约束：同侧约束和相交约束。从求解方程的角度，显式导出了本质矩阵的完整位姿解，我们严格证明了在纯旋转的情况下，位姿的方向部分仍然可以恢复。PPO 约束被简化并以不等式的形式表达，以直接识别正确的姿势解决方案，无需 3D 重建，并且可以从识别的正确姿势解析实现 3D 重建。此外，相交不等式还为纯旋转识别提供了稳健的标准。实验结果验证了分析的正确性和导出的姿态解/纯旋转识别和解析 3D 重建的鲁棒性。相交不等式还为纯旋转识别提供了可靠的标准。实验结果验证了分析的正确性和导出的姿态解/纯旋转识别和解析 3D 重建的鲁棒性。相交不等式还为纯旋转识别提供了可靠的标准。实验结果验证了分析的正确性和导出的姿态解/纯旋转识别和解析 3D 重建的鲁棒性。