Algebra and Geometry of Camera Resectioning
This work addresses foundational algebraic geometry problems in computer vision, but it appears incremental as it builds on and clarifies existing theories without introducing new methods or data.
The paper tackles the camera resectioning problem by characterizing algebraic varieties associated with it using Gröbner basis techniques, resulting in the derivation and reinterpretation of known results in geometric computer vision and the proposal of a conjectural formula for the Euclidean distance degree.
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.