English

On Ullman's theorem in computer vision

Computer Vision and Pattern Recognition 2007-08-21 v1 Artificial Intelligence

Abstract

Both in the plane and in space, we invert the nonlinear Ullman transformation for 3 points and 3 orthographic cameras. While Ullman's theorem assures a unique reconstruction modulo a reflection for 3 cameras and 4 points, we find a locally unique reconstruction for 3 cameras and 3 points. Explicit reconstruction formulas allow to decide whether picture data of three cameras seeing three points can be realized as a point-camera configuration.

Cite

@article{arxiv.0708.2438,
  title  = {On Ullman's theorem in computer vision},
  author = {Oliver Knill and Jose Ramirez-Herran},
  journal= {arXiv preprint arXiv:0708.2438},
  year   = {2007}
}

Comments

16 pages, 13 figures

R2 v1 2026-06-21T09:08:28.852Z