Fundamental Constraints on Camera Centers Arising from 3D-2D Matches of Points and Lines
Jaired Collins, Taci Kucukpinar, Timothy Duff, Joshua Fraser, Guna S. Seetharaman, Kannappan Palaniappan · International Journal of Computer Vision · 2026
We investigate combinations of 3D-2D matches of points and lines for a single calibrated camera that imply a nontrivial constraint on the camera’s position. Specifically, we address the minimal cases for which n point matches and m line matches constrain the camera center to lie on an algebraic surface in $$\mathbb {R}^3$$ . For two points $$(m,n) = (0,2)$$ , the constraint is well-known to be a self-intersecting torus. We complete the classification problem by deriving explicit, general equations for the cases $$(m,n) \in \{ (2,0), (1, 1) \}$$ for two lines and one point, one line, respectively. We also report preliminary experiments investigating the suitability of these constraints for pose estimation tasks.