Algebra and Geometry of Camera Resectioning

Author:

Erin Connelly, Timothy Duff, Jessie Loucks-Tavitas

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Computer Vision and Pattern Recognition (cs.CV), Commutative Algebra (math.AC)

journal:

date:

2023-09-06 16:00:00

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.

PDF: Algebra and Geometry of Camera Resectioning.pdf