相机重投影的代数与几何
Algebra and Geometry of Camera Resectioning
AI总结：
本文研究相机重投影问题的代数簇，利用Gröbner基技术刻画其多重分次消没理想，并重新解释了相机-点对偶性，探讨了最优重投影与三角测量的关系及欧氏距离度量猜想。
摘要：
我们研究与相机重投影问题相关的代数簇。我们使用Gröbner基技术刻画了这些重投影簇的多重分次消没理想。作为应用，我们推导并重新解释了与相机-点对偶相关的几何计算机视觉中的著名结果。我们还阐明了最优重投影与三角测量经典问题之间的某些关系，陈述了重投影簇的欧氏距离度量的猜想公式，并讨论了该猜想如何与最近解决的多视图猜想相关联。
英文摘要：
We study algebraic varieties associated with the camera resectioning problem. We characterize these resectioning varieties' multigraded vanishing ideals using Gröbner 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
