Algebraic Relations and Triangulation of Unlabeled Image Points
This addresses a common challenge in computer vision for applications like 3D reconstruction, but appears incremental as it builds on existing multiview geometry concepts.
The paper tackles the problem of triangulating 3D points from multiple camera views when correspondences between image points are unknown, by modeling unlabeled point configurations on the Chow variety and developing an algorithm for two unlabeled points.
In multiview geometry when correspondences among multiple views are unknown the image points can be understood as being unlabeled. This is a common problem in computer vision. We give a novel approach to handle such a situation by regarding unlabeled point configurations as points on the Chow variety $\text{Sym}_m(\mathbb{P}^2)$. For two unlabeled points we design an algorithm that solves the triangulation problem with unknown correspondences. Further the unlabeled multiview variety $\text{Sym}_m(V_A)$ is studied.