We study algebraic varieties associated with the camera resectioning problem. We characterize these resectioning varieties' multigraded vanishing ideals using Gr\"obner basis techniques. As an application, we derive and re-interpret celebrated results in geometric computer vision related to camera-point duality. We also clarify some relationships between the classical problems of optimal resectioning and triangulation, state a conjectural formula for the Euclidean distance degree of the resectioning variety, and discuss how this conjecture relates to the recently-resolved multiview conjecture.

翻译：我们研究了与相机位姿恢复问题相关的代数簇。利用Gröbner基方法，我们刻画了这些位姿恢复簇的多重分次消去理想。作为应用，我们推导并重新阐释了几何计算机视觉中与相机-点对偶性相关的经典结果。我们还澄清了最优位姿恢复与三角测量这两个经典问题之间的某些关系，提出了位姿恢复簇欧氏距离度数的猜想公式，并讨论了该猜想与近期解决的多视图猜想之间的关联。