Algebra and Geometry of Camera Resectioning

Abstract

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.